Teaching Math in The

 

TEACHING MATH IN  THE  PRIMARY GRADES 

 CARLO FLOR B.  

(BEED- 2B)

Table of Contents  

UNIT I: THE MATHEMATICS CURRICULUM IN THE PRIMARY GRADES

 

Lesson 1: Mathematics in the Primary Grades……………………………………………………………..1 Lesson 2: Mathematics Curriculum in the Primary Grades…………………………………………..1 Lesson 3: Constructivist Theory in Teaching Mathematics in the Primary Grades………..1 Grades………..1 UNIT II: INSTRUCTIONAL Lesson 4: ThePLANNING Teaching

Cycle………………………………………………………………………………………2-4 Lesson 5: Things to Consider Consider in Planning Instruction in Mathematics in the Primary Grades……………………………………………………………………………………5-7 Lesson 6: Instructional Planning Models…………………………………………………………………….8-9 UNIT III: INSTRUCTIONAL STRATEGIES FOR MATHEMATICS IN THE PRIMARY GRADES

Lesson 7: Problem Solving………………………………………………………………………………………10-12 Lesson 8: Inductive Learning……………………………………………………………………………………13-15 Lesson 9: Concept  Attainment………………………………  Attainment……… ……………………………………………… ……………………………………………… ……………………….16-17 .16-17 Lesson 10: Mathematical Investigation…………………………………………………………………..18-19 Lesson 11: Design Thinking…………………………………………………………………………………….20-21 Lesson 12: Game-based Learning……………………………………………………………………………22-23 Lesson 13: Use of Manipulative………………………………………………………………………………24-26 Lesson 14: Values Integration………………………… Integration… ……………………………………………… ……………………………….........................27-28 ……….........................27-28 Lesson 15: Collaboration……………… Collabor ation……………………………………… ……………………………………………… ………………………...........................29-31 ...........................29-31 Lesson 16: Teaching by  Asking………………………………  Asking……… ……………………………………………… ………………………...........................32-34 ...........................32-34 Lesson 17: Assessing Learning…………………………………………………………………………………35-37 Lesson 18: Traditional  Assessment……………………………  Assessment…… ……………………………………………… …………………………………………….38 …………………….38-39 -39 Lesson 19: Authentic  Assessment……………………………  Assessment…… ……………………………………………… ………………………........................40-42 ........................40-42 Lesson 20: Designing Learning Portfolios………………………………………………………………..43-44

 

 

 

 Acknowledgment   Acknowledgmen t  Would like to express my heartfelt gratitude to my mathematics teacher, Miss Anicil Disomimba, for her attention to teaching us.

  I'd therefore like to thank my classmate for sharing his or her thoughts with us during class. And I'd want to express my gratitude to my family for their constant financial and educational support.

Curriculum Vitae

 

 

CARLO BUSTAMANTE FLOR

 _________________  _______ ___________________ ___________________ ___________________ ___________________ ___________________ _________________  ________ 

PERSONAL DATA Birth

:

January 26, 1997

 Address

:

P-3 Barangay Barangay Obrero, Calbayog Calbayog City

Phone :

+639057039059

E-Mail :

[email protected]

 _________________  _______ ___________________ ___________________ ___________________ ___________________ ___________________ __________________  _________ 

EDUCATION

TERTIARY

:

Christ the King College Calbayog City 2020 – 2022

SECONDA SEC ONDARY RY :

San Policarpo National high School Calbayog City 2019 – 2020

ELEMENTARY

:

Obrero elementary s sc chool Calbayog city  

2013 – 2014

 _________________  _______ ___________________ ___________________ ___________________ ___________________ ___________________ _______________  ______  SKILLS

• 

Dancing Cooking

 

OPENING PRAYER We open the prayer by addressing God because he is the one we are praying to.  Start by saying "Father in Heaven" or "Heavenly Father." We address Him as our Heavenly Father, Because He is the father of our spirits. He is our creator and the one to whom we owe  Everything we have, including our live

Narrative report

Our teacher gave us lessons and explained everything everything to us. Because it is for our good, what we are taught t aught is good. During the reporting of my classmates, it became apparent who was capable of reporting. In terms of reporting, it is here that the children who will go on to become teachers will be discovered. This is one way for students to develop their reporting skills while avoiding shame in front of their t heir peers. This is one that students should be able to handle in order to be given more simple options. This method is really helpful to the pupil. Our math teacher was a pleasure being around. It has a good grasp when it comes to giving god because he is a wonderful instructor and an understanding teacher to his students. She corrects mistakes and emphasizes the importance of items. It emphasizes the significance of minor details and gives guidelines on how to continue in the future.

LESSON 1: Mathematics in the primary grades This lecture taught us the importance of mathematics in primary school. The preparation of kids for formal schooling is one of the most important aspects of mathematics in primary school. Primary school children are intuitive and have a basic understanding of shapes and numbers. As they develop, students must learn or have  have numbers numbers,, a good understanding of   shapes, and basic operations such as addition and subtraction. In particular, they were

 

 Anticipated to be be able to progress progress to mental operations. operations. Math also also contributes to the development developm ent of primary school students' cognitive ability by being taught at a young age. Teaching Mathematics Mathematics in Primary Grade School or at a young age, in my experience, experience, has helped children to fully understand Math, which prepares them as they grow and progress through the grades. Math also challenges the brain's cognitive abilities. Math will become a delight and a game for children if it is taught to them t hem on a regular basis.

LESSON 2: Mathematics curriculum in the primary grades I learned how to comprehend and enjoy elementary school mathematics in this lesson. Mathematics is both a scientific and a linguistic tool, with its own notations, symbols, and grammar rules. This concept is expressed in a number of ways, including numbers, measurement, measuremen t, geometry, patterns, mathematics, statistics, and probability. Numbers, its operations,, and their operations t heir symbols The number can be used to represent quantity, estimation, or applications.The applicati ons.The measures are used to define and compare real and mathematical concepts such as height, weight, distance, volume, and so on. Geometry is a term that refers to spatial visualization, visualizati on, reasoning, and geometric modelling. Patterns and Algebra is a part of mathematics that studies patterns, relationships, and transformations in shapes and values. Statistics and probabilities probabilities is a branch of mathematics concerned with the process of learning in data collection and organization through the use of charts, tables, t ables, and graphs. It helps in the measurement of an object's mass, in my experience. Measure the child's height and sketch a beautiful shape. Statistics aid the teacher in keeping track of the students' progress. Geometry encourages children to become familiar with and manipulate 2 dimensional dimensio nal and 3 dimensional dimensional objects. As a result, mathematics is essential in every stage of life, from childhood to adulthood.

LESSON 3: Constructivist Theory in Teaching Mathematics in the Primary Grades

In this lesson, I learnt how to understand and appreciate constructivist learning theory and how to apply it to teaching t eaching primary school mathematics. mathematics. Learning that occurs as a result of an active process of deriving meaning from a variety of experiences is referred to as constructivist learning. As a result, students learn by problem solving on their own with the help of a teacher. The term constructivism was developed by academic Jean Piaget.  According to Piaget, Piaget, children children learn by doing, doing, absorbing information information from tales tales rather than being lectured by adults about their surroundings. Constructivism, in my opinion, is the best method for teaching mathematics becaus Constructivism, because e it is a vertically based, comprehensive discipline. New math is learned by building on what has already been learned. Students' leadership, leadership, teamwork, information gathering, and presenting of ideas are all encouraged encouraged by constructivist constructivist teachers. Students are encouraged to ttest est their own ideas by constructivist educators. Through student interaction, constructivist educators develop cooperative coaching approaches. Constructivist instructors rent cooperative coaching approaches approaches through student interaction. interaction. Mutual respect simply represents the exchange of ideas and the final approval of responsibilities.

 

LESSON 4: The Teaching Cycle OBJECTIVES

•Demonstrate an understanding and appreciation of the instructional planning cycle. Introduction •The teaching process is not a linear activity that starts with planning and ends with testing. Instead it is a cycle of repeating stages until the students st udents acquire an understandin understanding g of the targeted concepts and skills. You may think of the teaching cycle as a spring you go through the same process over and over again, but each time with a more informed objective and a better understanding understanding of what it means to learn and teach mathematics. Think •There are many models of the t he teaching cycle that various education have developed over the years. However, all models boil down to six common stages (1) identify objectives (2) plan instruction, (3) implement plan, (4) check understanding, (5) reflect on teaching , and (6) assess learning and reflect on results. The cycle below that involves these stages is illustrated below.

 

1. Identify objectives •What knowledge and/or skills do the students need to lear? You must be guided by the content standards, performance standards, and the learning competenci competencies es that are found in the curriculum guide. 2. Plan instruction •What strategies must be implemented for the students to achieve the objectives targeted in the previous stage? In planning instruction, it is important that you have mastered the content of the lesson that you are about to teach. It is also beneficial to be familiar with your students- what they know, how they learn, etc. 3. Implement plan

 

•This is the stage where you conduct the learning activities that you have prepared during the planning stage. A word of advice– even though you have carefully and delicately planned for the  Lesson, you must be flexible with the possible changes that you need to accommodate. How will you know whether change is needed? 4. Check for Understanding. •Teaching is about teaching students learn. During the implementation of the lesson plan, you must every now and then check whether the students understood what you have covered so far. Facial reactions and verbal cues help in assessing whether or not the students can move on to another concepts or skill. If not, you might need to give more elaborate explanation, explanation, more examples, or whatever you think is needed based on the student’s reactions. 5. Reflect on teaching. •You must evaluate every teaching period that you have finished. Where the objectives achieved? Were the implemented strategies effective? How can instruction be improved? Your answers to the last two questions will give you an insight on how to improve instructions the next time you teach same lesson. However if your answer in the first question is no, i.e., the objectives are not met, then you need to plan again. What do you need to do differently in order to achieve the objectives? 6. Assess leaning and reflect on the results. •This stage gives you a concrete measure of what the students have learned. In math, this is usually through paper and pen examination. examination. However, some authentic assessments may also be implemented as you will learn in the later chapters of this book. Take note that this state does not end in assessing learning. You need to need to reflect on the results. What can you learn about students learning and teaching practice based on the t he results?

Experience •The Following is a narrative of how a teacher might experience the teaching cycle. 1. Identify objectives •Teacher Gina identified “multiplication “multiplication of whole numbers up to two digits” as the goal of her next lesson. 2. Plan instruction •Teacher Gina thought it is the best to apply a constructivist approach to help her students learn techniques in multiplying whole numbers. She planned a lesson which incorporates the problem-solving strategy.. problem-solving 3. Implement plan

 

•The class went on smoothly. The activities that teacher Gina prepared were successfully done by her students.  4. Check for understanding •To make sure that her students understood the lesson, Teacher Gina gave a three-item exercise as an exit pass. 5. Reflect on teaching •Based on the exit pass, Teacher Gina found out that many of the students have difficulty multiplying multiplyin g numbers that involve the digit 8, 50, she decided to do a find-your-er f ind-your-error ror activity the next days for the students to realize their mistakes. She also planned to give a short drill on skip counting by 8.  6. Assess learning and reflect on the results •Teacher Gina, later on, gave a multiplication quiz. Ninety percent of the students passed. She planned to give remedial exercises to those who failed. This teaching cycle taught Teacher Gina that students can discover concepts on their own. However they must still be guided by a teacher because misconceptions may arise. •Teaching involves a repetitive cycle of defining objectives, planning and implementing instruction, assessing learning, learning, and reflecting on teaching and learning. Each part of the cycle provides a better understanding of what it means to teach and learn mathematics and should result in better instruction in the next repetition of the cycle.

Reflection: I gained a better knowledge and appreciation appreciation for the t he instructional planning planning cycle in this lesson. In the instructional instructional planning process, there are six (6) stages: (1) establish the goal, (2) plan instruction, (3) implement the plan, (4) check understanding, understanding, (5) reflect on teaching, and (6) measure learning and report on the outcome. Determine the objectives, which are the content standards that must be reached in order for the competences to be

met. The instructional technique that is being executed for the learning competencies competencies to attain the objectives is called plan instruction. This is where you put your strategy into action and either do the activities you prepared or examine the learner.  As   As a result, the learner learner will either need to better or learn from it. In this t his stage, you must check for student knowledge by asking the learner if they understand the instruction. instruction. As a result, you can move on to the next lesson, and if they don't comprehend, the teacher must explain it again or provide more examples to help them recognize. Consider how you teach. After you've finished teaching, review your teaching methods to see if they're meeting the demands of the students. You will gain insight into how to strengthen your instructional strategy at this stage. Examine what you've learned and think about what you've learned. In this final stage, you will learn what the students have studied. This instructional cycle is connected to one another and must be followed in order.

 

 According to my experience, experience, a teacher teacher will have have a clear image image in his or her mind mind of the students' desired learning outcomes and will create appropria appropriate te and effective instructional activities to help them master those outcomes. 

LESSON 5: Things to Consider in Planning Instruction I nstruction in Mathematics in the Primary Grades Lesson Planning Teacher’s detailed description description of the course of instruction for an individual lesson with specific outcome objectives. Objective: > Demonstrate understanding understanding and appreciation of the things to consider in planning in mathematics in the primary grades Introduction: In education planning refers to the designing and preparation of learning activities for students. In lesson planning the teacher thoughtfully contemplates about the lesson objectives, the activities that will meet these objectives, the sequence of those activities, the materials needed, how long each activity might take, how the class would be managed during those activities, and the evaluation method to assist how far the objective where met. This lesson enumerates the things to consider planning instruction mathematics in the primary grades Think:

 

Here are the important elements in lesson planning that we need to consider: > Content > Objectives > Students > learning environment > Availability of resources Content:  Research to subject matter that you will be teaching. You should consult the curriculum and teaching guides publish publish by Dep Ed. Aside from books you can also visit website which will give you information relevant to your subject area. You should master the content of your

 

lesson before you teach it. Remember, you cannot give what you do not have moreover, you would not want to teach wrong content to the students. It is easier to learn than to unlearn. It is difficult to take back wrong content that have already been taught. Teachers have a big responsibility in mastering the content.  

Objectives: Before you begin planning, you need to know what specific knowledge and skills you want your students to develop during the lesson or unit. Teachers often focus to much on knowledge, knowled ge, forgetting about developing skills which in the long terms are more important the knowing mere facts. So, in planning your instruction always consider both knowledge and skills.   Students: • Get Get tto o kno know w you yourr stu stude dent nt’s ’s need needss-Wh Wher ere e tthe hey y cam came e ffro rom, m, th thei eirr int inter eres estt , wha whatt they they already know, their learning style, attention span, special needs etc. • You You nee need d tto o pre prepa pare re a lles esso son n wit with h all all your your st stud uden ents ts in mi mind nd and and ttha hatt y you ou main main goal goal should be to meet their needs and often then enabling environments to learn their preferred way. • Know Knowin ing g your your stud studen ents ts wil willl also also help help your your buil build d rapp rappor ortt w wit ith h them them whic which h is im impo port rtan antt if  you want your students to be freely sharing their ideas with you and their classmates. Student’s mind-set- considering important that needs serious attention in teaching mathematics. Things to consider: •

Lesson mastery

•

Focus objective

•

Comprehensive understanding of students. ts.

Fixed mindset- Children have come to believe that math is difficult and they can never be good. Growth mindset- students believed that they can be better at math. They know that their efforts are not wasted and that they can learn even in their failures. Learning environment • Asid Aside e the the phy physi sica call e env nvir iron onme ment nt whe where re the the lear learni ning ng tak takes es plac place e it is also also imp impor orta tant nt to to consider the social and emotional learning environment environment of the class. • You You nee need d to to mak make e sur sure e tha thatt you you prom promot ote e pos posit itiv ive e env envir iron onme ment nt wher where es stu tude dent nts s are are motivated and supportive of each other growth.

 

• The The s stu tude dent nt must must feel feel safe safe to expr expres ess s tthe heir ir thin thinki king ng wi with thou outt ffea earr of of bei being ng embarrassed because of mistakes or different views.  • It must must cr crea eate te an atmo atmosp sphe here re wh wher ere e stu stude dent nts s are are open open to lear learni ning ng th thro roug ugh h the the activities you prepared and interactions with their classmates.  Availability  Availabil ity of resources: Take into consideration the instructional materials materials that you will be needing before you write your lesson plan.

•

Is a bl blac ackb kbo oar ard d ava avaiilabl able, ifif not not can yo you u imp impro rovi vise se? ?

• ar are e tthe here re spec specif ific ic mani manipu pula lati tive ves s tha thatt y you ou need need? ? Whe Where re can can you you get get them them? ? Can Can you you make them instead? •

Do you need technology resources?

• Have Have you you che check cked ed wi with th your your devi device ces s are are comp compat atib ible le wi with th what what are are ava avail ilab able le in school?

Reflection: In this lesson, I gained a better understanding of and appreciation for the factors to consider while preparing math lessons for primary school students. The term "education planning"" refers to the process of creating and preparin planning preparing g academic resources. Students are familiarizing familiariz ing themselves with various activities. When creating lesson plans, tthe he teacher considers the lesson objectives, the activities that will help meet those objectives, the collection of these activities, the materials needed, how long each activity will take, how the learners will be controlled throughout those activities, and the assessment approach that will help determine how the goal will be met. You should know what precise knowledge and abilities you want your learners to achieve before you build lesson plans, and you should practice the material of your class before you start.

LESSON 6: Instructional Planning Models Objectives: Demonstrate understanding understanding and appreciation of the most commonly used instructional instructional planning models in the Philippines. Introduction: - Now that you have learned the things to consider when planning planning instruction, you are ready to create one yourself. Teachers usually plan lessons following a specific model. In this lesson, you will learn about the two most commonly used instructional planning model in the Philippines Philippi nes and their common features.

 

- In a traditional classroom, classroom, the input is where the teachers lectures. However, in a constructivist classroom, classroom, this is the part where the students would share the concepts that they learned based on the activity and the discussion. Nevertheless, no matter which learning theory applied in the lesson, this is the part where the concepts are clearly established.  Adidas 1. Activity - A motivating and engaging activity. 2. Discussion – Processing of information. 3. Input – Concept must clearly established. 4. Deepening- Critical and creative thinking. 5. Activity – Assessment process. 6. Synthesis - Reflection part. Synthesis: The last part of the ADIDAS model is the synthesis. Here the students are given the opportunity to express what they have learned by verbally giving a summary of what transpired in class and what they have learned. The students may also be given a short assessment to give the teacher feedback on what they have learned.  Another commonly commonly used in instructional instructional planning planning model in the country is the Five Es. The five E’s are, Engage, Explore, Explain, Elaborate, and Evaluate.

The Five E’s - Engage - Explore - Explain - Elaborate - Evaluate

Engage - This part activates the students’ prior knowledge and engages them into new concepts by doing short activities. The aim of this part is to arouse the students’ curiosity. Explore -In this part, the t he students are exposed to different experiences that will facilitate the discovery of new concepts. Explore may involve observation exercises, simulations, or manipulations manipula tions of instructional materials. The goal here is for the students to discover something new. Explain - Here the students explain what they have experienced in Explore. The role of the teacher is to facilitate the discussion that should lead to students seeing patterns that will help them to describe the new concept in their own words.

 

Elaborate – The Elaborate part of the lesson allows students to expand their understanding of the concept by applying the concept that they have learned in solving mathematica mathematicall problems. Evaluate - The last part of the Five Es model, Evaluate, lets the teacher and the students evaluate their learning. Though giving short exercises are usually the mode of evaluation, evaluation, the teacher can be creative by implementing implementing other evaluation activities. Reflection: In the Philippines, the most used instructional planning planning approaches are something I understand and like. There are two types of instructional planning in this lesson: ADIDAS and The Five E's. ADIDAS has an activity in which the students practice and assess the learning materials. materials. This section of the discussion is about learning information. Input is where the teacher will present themes and more information about the lesson. Synthesis is where the final result of the activities, discussion, input, and deepening must review and identify the goal of the learning competencies competencies before it ends. Deepening is the part where the learner hands on to deepen the skill that they have learned, and Synthesis is where the final result of the activities, discussion, discussion, input, and deepening must review and address the goal of the learning competencies before it ends.  The Engage phase activities are designed to help students integrate previous and present learning experiences, expose pre-existing beliefs, and organize their thoughts around the learning sequence's significant issues and learning goals. Students might investigate items, events, or situations as part of their exploration. exploratio n. As a result of their mental and physical involvement in these activities, students investigate occurrences, occurrences, see patterns, identify and test factors, and build causal relationships. relationsh ips. Students use these tools t ools and information, as well as inputs from other students, to construct or update their evidence-based evidence-based models and explanations. More experiences experienc es that apply, extend, or expand the concepts, procedures, or abilities they've gained are important. And Evaluation Encourages Encourages students to t o reflect on their understanding and talents, allowing teachers to measure individual student progress toward learning goals and outcomes.

Lesson 7: Problem Solving Introduction Not all word problems promote problem-solving skills. In this lesson, you will the characteristics characteristic s of a good word problem, problem, when it is best to give a word problem and how to process students' varied solutions. Think The problem-solving strategy involves students being challenged to collaboratively solve real-world math problems which they have not yet previously encountered is studentcentered and promotes critical and creative thinking skills, problem solving abilities, and communication communica tion skills. The integral part of this strategy is the time given to the students to struggle with the problem and its beauty is in the varied solution that the students would produce. There are three main elements of problem-solving that you should take note of (1)

 

the word problem, (2) the time given for the students to struggle with the problem and (3) the mathematicall discourse that happens during the struggle and during the processing of the mathematica student generated solutions. THE WORD PROBLEM  In many Filipino classrooms, word problems problems are given at the end of the lesson and students are expected to answer them by applying the concept or skills that had just been taught to them. In most cases, the teacher first demonstrates how to solve a problem and then the students would independently independently answer a similarly-structured problem. problem. IIn n this practice, the students are not doing problem-solving--they problem-solving--they already know how to solve the problem! They know that the just-taught lesson is the key to solve the problem and they pattern their solutions to what the teacher demonstrated. In using the problem-solvi problem-solving ng strategy, the problem serves as the starting point of the learning experience experience.. Therefore, it is given at the t he beginning beginnin g of the lesson. The challenge for you, the teacher, is to t o choose or create a problem, which can be solved using the target concept of the lesson at hand, but can also be answered using previously previously learned knowledge and skills. It is not always helpful to introduce the problem by posting it on the board doing this may intimidate some students, and reading and comprehension comprehension skills may intervene. intervene. Instead, it is suggested to narrate narrate the problem in a storytelling manner manner to engage the learners, encourage the students to imagine the scenario and allow them to clarify information if they find some details confusing. Showing drawings or real objects might help. THE TIME GIVEN TO STRUGGLE WITH THE PROBLEM The goal is for the students to collaborate, share their ideas with each other, to come up with a solution. Encourage the students to use their previously learned knowl knowledge edge and skills to solve the problem and to communicate communicate their ideas with their classmates through words, equations,, and or illustration. It is natural for the students to find this phase burdensome, equations especially especiall y when it's their first time to engage in such an activity; critical thinking and communicating communica ting ideas are not easy tasks, after all. So, it is the task of the teacher to encourage the students to think out of the box, tell the students that there is more than one way to solve the problem, so they do not need to worry about their t heir solution being being wrong, as long as every step they did is meaningful in solving the problem. THEN MATHEMATICAL DISCOURSE This is the most exciting element of the problem solving strategy. While the students are working in small groups to solve the problem, you got to move around and enjoy the

Mathematical talk that Mathematical t hat the students are engaging in. Of course, you may intervene in the student’s discussion discussion when corrections and clarifications are needed, but be careful not to give hints. It may be tempting to do so, especially when the studen students ts are struggling, but do not. As you encourage your students to think, believe that they actually can. Allow yourself to be amazed at how the t he students would defend their thinking, correct their ideas, and figure f igure things out on their own. Remember that all this student generated solutions. As long as correct can be directed to the concept or skill that is the objective of the lesson. The challenge is how you would process those various solutions make sense of each of them and use them to generalize, or come up with a solution that makes use of the knowledge or

 

skill that is the objective of the lesson. In this phase comes the importance of the teachers fluency of the subject matter. Experience Study the following lesson plan. Take note that the plan shows the development of the lesson, which involves the problem-solving strategy.  Apply properties properties of multiplication multiplication to mentally mentally multiply whole whole numbers, up to two digits. By the end of the lesson, the learners will be able to more mentally multiply whole numbers up to two digits. Mentally multiply 18 and 5. Present the problem, above in the narrative approach, which will engage the students. See an example below. Hannah is next in line to pay at the counter. She will buy 5 pieces of bread, which cost, 18 pesos each. She would like to show how much she needs to pay for all the bread. Her hands are full, so she couldn't write her solution, nor use her phone calculator. She needs to solve mentally. If you're in Hannah's shoes, how would you solve it? Students will work in pairs or triads. Encourage the students to think about the problem and share their thoughts with their classmates.  Assure them that that there is no one right right solution. They They may do calculations calculations or draw, any any solution is welcome as long as they can explain why they did such. The problem calls for mental calculations but for the t he sake of discussion and to facilitate mathematicall communication through writing instruct the students to write down their mathematica thoughts, as they explain to their group mates, or partner. Reflection: In this lesson, I learn about a problem-solving strategy in which students collaborate to solve real-world real-worl d arithmetic issues they have never seen before. It is student-centere student-centered d and promotes critical and creative thinking, as well as problem-solving and communication skills. The time allotted for students to experience the battle with the topic is a key component of this technique, and the beauty is in the variety of answers that the students come up with. We must understand three critical aspects of problem-solving. the term problem, as well as the length of time provided for students to work on the problem, and the mathematical discussion discussio n that happens throughout the struggle and competitive processing processing of the learners' responses

Lesson 8: Inductive Learning OBJECTIVE: Plan a lesson that allows students to t o inductively learn a concept. INTRODUCTION In our contemporary society, teachers are discouraged to spoon-feed information to learners. Instead teachers are to provide opportunities for students to discover concepts on their own. One way of doing this is through the inductive learning strategy.

 

THINK: •

The The in indu duct ctiv ive e lear learni ning ng stra strate tegy gy is base based d on the the prin princi cipl ple e of indu induct ctio ion. n.

• In Indu duct ctio ion n mea means ns to deri derive ve a con conce cept pt by show showin ing g that that if it is tr true ue to some some case cases, s, the then n it is true for all. This is in contrast to deduction where a concept is established by logicall logically y proving that it is true based on generally known facts. •

The The iind nduc ucti tive ve meth method od in teac teachi hing ng is comm common only ly desc descri ribe bed d as as ““sp spec ecif ific ic to gene genera ral, l,””

“concrete to abstract,” or examples to formula.” • In an an indu induct ctiv ive e lear learni ning ng les lesso son, n, ttea each cher ers s desi design gn and and fac facil ilit itat ate e acti activi viti ties es tha thatt guid guide e the the learners in discovering a rule. Activities may involve comparing and contrasting, grouping and labeling, or finding patterns. • In mat mathe hema mati tics cs cl clas asse ses, s, lea learn rner ers s eng engag age e iin n iind nduc ucti tive ve lear learni ning ng when when th they ey obse observ rve e examples and then, later on, generalize a rule or formula based on the examples.

There are four process that the students go through when given an inductive learning activity. •

Observe

•

Hypothesize

•

Collect evidence

•

Generalize

OBSERVE Children love looking looking for patterns. When given a lot of examples, it is natural for them to look for similarities and assume rules. So, the key is to give them examples to observe. These examples must be well-thought-of so that the students would eventually arrive at a complete rule. For instance, if you want your students to discover the rule in multiplying by powers of 10, it is better to use the examples in set B than those in set A.  A.

6X10= 60

18X10 X10= 180 321X10= 3,210

457X10= 4,570

B. 6X10= 60 18X10 X10= 180 10X327= 3,210

40X10= 400

Both sides will lead students to discover that the technique in multiplying by 10 is placing a 0 after the number being multiplied. However, the variety of examples in Set B allows students to establish that the rule works even when exchanging 10 and the other factor (18x10 = 180) and if the other factor ends with a zero, that zero is not neglected (40x10). Set B allows students to have a more comprehensive comprehensive understanding of the rule. HYPOTHESIS

 

The students form rules is in their minds as they observe. In this stage, encourage the students to share their thoughts. Assure them that there are no wrongs hypothesis.  Acknowledge  Acknowled ge the variety of the student’s student’s idea ideas s but also streamline streamline them to, later on, on, test only the unique hypothesis. COLLECT EVIDENCE Here the students would test their hypothesis. How? By applying their hypothesis to other examples. If there are more than one hypothesis generated by the class, intentionally give a counterexample counterexam ple for them to test. GENERALIZE Finally, the students would now formalize their hypothesis to a rule. Support the students so that they would use mathematical terms in stating their rule. Doing this would develop the students’ mathematical vocabulary and therefore their overall mathematical communication skills. EXPERIENCE Study the lesson plan on the next page. Take note that the plan only shows the development of the lesson, which involves the inductive learning learning strategy: other parts are not included. In this lesson, inductive learning was not used to discover a rule but rather to discover a relationship. TOPIC: MULTIPLICATION AND DIVISION AS INVERSE OPERATION OBSERVE

12 ÷ 2 =

15 ÷ 3 =

6x2=

5x3=

24 ÷ 6 =

36 ÷4 =

4x6=

9x4=

 Ask the students students to fill in the blanks blanks by dividing o orr multiplying. multiplying. Then lead them to observe observe each pair of division and multiplication number sentences. Give some time for the students to observe the examples. Fast learners may become too excited to share their hypothesis, but do not allow them to spill it. The goal is for all students to have the “Aha!” moment.

HYPOTHESIS Struggling students may not see the pattern right away. Help them by focusing their attention to the quotient and the first factor. Call some students to explain their hypothesis. After each explanation, explanation, ask who has the same hypothesis.

 

COLLECT EVIDENCE  Apply the hypothesis hypothesis to each example example to see if the they y always work.  GENERALIZE Based on the result of the “collect evidence” stage, ask the students which hypothesis is true for all? Then instruct the students to write, using their own words, the rule in their notebook. Have two three students read aloud what they t hey have written.

 Reflection: In this lesson, I learned how to plan a lesson for students to teach a subject experimentally. experimen tally. Students should be able to discover topics on their own with the help of their teachers. To learn an inductive learning technique based on the concept of induction, learners must observe, hypothesize, collect evidence, and generalize. generalize. Inductive language teaching, for example, starts with examples and encourages pupils to look for rules. It's akin to a deductive approach, in which rules are followed by instances and finally practice. It progresses from the concrete to the abstract, from the particular to the general, and from an illustration to a formula. Operation: Perform a large number of examples before generalizing generalizing the formula. Draw a couple sets of parallel lines and then measure the angle between them, for example. Despite the fact that inductive learning takes longer than deductive learning, Many educators believe believe it is a more effective method in the long run. One of the benefits is the ability to connect with and participate with other students.

LESSON 9: Concept attainment Objective Plan a lesson that applies concept attainment strategy Introduction

 

In mathematics, students do not only study rules, but they also need to remember and understand many definitions definitions of terms. For better retention, it is best for students to discover the meaning of the different mathematical terminologies that they encounter. The concept attainment strategy is useful for this purpose. THINK Concept attainment is another instructional strategy anchored to the constructivist learning theory. In this strategy, the concept is not directly taught to students. Instead, the students understand and learn concepts by identifying common attributes through comparison and contrast of examples and non- example. Since concept attainment is used understanding understanding meaning, it is often applied in English vocabulary in lessons. However, it is also useful in learning mathematics terminologies. terminologies. There are five simples’ steps in the concepts attainment strategy: (1) presentation of examples and non-examples, (2) listing of common attributes, (3) adding student-given examples, (4) defining the mathematical term, and (5) checking of understanding. understanding.  ADDITIONAL DEFINITION DEFINITION OF CONCEPT CONCEPT ATTAINMENT:  Additional definition definition of Concept Concept Attainment: Attainment:   By studying the features of of multiple examples and and non-examples non-examples of the word, concept, concept, or issue, the Concept Attainment technique engages students in constructing their own definition of a concept. The target concept or idea is not transmitted to the students using this technique. The teacher gives examples (verbal or visual) and the pupils try to figure out what the concept is by looking at the similar similar characteristics. You should select thoughts thoughts or ideas with distinct features. Here’s an example of how to use the concept attainment strategy with brain pop ell: 1. Use pictures, words, or actual objects to present both examples and non-examples of the concept. 2. Present the examples in two t wo columns on the board. Always start with a “yes” example. 3. Follow with a “no” example. The additional examples should be given in random order.  Avoid giving giving too many “no” examples examples at one ti time. me. They are given given to help clarify clarify what the “yes” examples have in common.

4. During the strategy, ask students for “yes” examples to verify that they are getting the concept. 5. Once most students seem to have the concepts, ask for attributes that describe it. 6. Come up with a rule or a name for the concept. 7. Have students discuss their thinking processes throughout the strategy.

 

Reflection: Here's what I've learned about getting a math strategy. Making a lesson plan should have a guide so that you can follow what you teach to students. To know what you are teaching, you must use your heart and one mind when instructing kids. The meanings of the words should be thoroughly taught to them so that they can help understand and widen their  mathematicall perspectives. mathematica

LESSON 10: Mathematical Investigation INTRODUCTION Contemporary leaders in mathematics education revolutionized Contemporary revolutionized the goal of mathematics teaching and learning from passive learning dictated by the curriculum to an active process where the students are developed developed to think like mathematicians. What is Mathematical Mathematical Investigation?  

Mathematicall tasks Mathematica Task A – Problem Solving the

There are 50 children at a playground and each child high-fives with each other of other children. Find the total number of high-fives.

Task B – Mathematical Investigation other

There are 50 children at a playground and each children high-fives with each of the children. Investigate.

Three main phases of a Mathematical Investigation

  Problem-posing

Conjecturing

Justifying Conjectures

 

Problem-posing The students explore the given situation and come up with a mathematical problem that they would want to engage in.

Conjecturing Involves collecting and organizing data, looking for patterns, inferencing, and generalizing Justifying Conjectures Conjectures Students are to justify and explain their inferences and generalizations. generalizations.

 Always remember remember that although although mathematical mathematical rules or theorems theorems may arise as results of the mathematicall investigation, they are not the objectives of an investigative lesson – the mathematica objective is the investigation itself; the exercise of creative thinking and problem-solving problem-solving that the students underwent as they investigated.

Summary Mathematical investigation is an open-ended teaching strategy that capitalizes Mathematical capitalizes on the student’s ability to identify a problem. Any word problem can be transformed into a mathematicall investigation by limiting the given information and omitting the specific mathematica question that it is asking.

Reflection: In this lesson, I discovered that a mathematical investigation investigation is an open-ended open-ended mathematicall teaching technique that capitalizes on a student's ability to recognize a mathematica problem, which entails not just problem solving but also problem posing. Investigate does not refer to the steps involved in solving a closed-ended closed-ended problem; rather, it encourages encourages independent indepen dent mathematical thinking. Students investigate the situation by working on a mathematical problem. It involves data collection and organization, pattern detection, mathematical

 

learning, and generalization. learning, generalization. In the problem, students must explain and justify their observations and generalization.

Lesson 11: Design Thinking Objective Execute the empathize, define, define, ideate, prototype, and test stages stages of the design thinking process. Introduction Students find learning mathematics most engaging when they are involved in a thinking process that results in an output that can be applied to a relevant context. The design thinking process engages the students in such a thought-provoking thought-provoking and purposeful activity. Think Design thinking is a progressive teaching strategy that allows students to look for real-world problems and findings creative solution. Student do this by focusing on the needs of others, collaborating collabora ting for possible solutions, and prototyping and testing their creations. This can be summarized in five stages: empathize, define, ideate, prototype, and test. These stages are adapted from the institute of design at Stanford University. Empathize The goal of design thinking is for students to respond to a particular need (a real-world problem), so it is fitting that the first stage is empathy. In this stage, the teacher needs to be explicit in guiding the students to put themselves in the shoes of others through activities like immersed observation observation and interviews. According to the developmental developmental stages, it is not natural for children in the primary grades to be empathetic toward others. It is a common observation by teachers that students at these levels often do not realize that their actions affect others. So, applying design thinking in the classroom gives the children the opportunity to cultivate empathy, and at the same time, develop their problem-solving skills. Define The next stage is for the students to define the specific problem or issue that they want to address. First, the students will identify an audienceaudience- the future users of the product they will develop. Their audience can be students, teachers, family members, or just anyone in

Their community. Then the students will use the t he information they gathered from the Empathize stage and focus on one aspect of the problem. It is important that the students be able to identify a true problem because it is impossible to successfully successfully complete the design thinking process without a meaningful meaningful problem to solve. Ideate

 

The third stage of design is the generation of ideas to solve the identified problem. This involves brainstorming brainstorming and research. The students are to be encouraged to think out of the box and produce radical ideas. What sets this stage apart from the usual brainstorming brainstorming is that all ideas must be written or illustrated. Ideas are usually written or drawn on sticky notes and students, later on, organize them into a mind map. It is at this stage that the students will be able to apply their mathematical knowle knowledge dge and skills. Aside from being able to operate their problem-solving problem-solving skills, they will also be able to apply specific content knowledge like measurement, proportion, geometry, and statistics. Prototype and Test Finally, the students go through a repetitive cycle of prototyping and testing. A prototype is anything that a user can interact with in order to, later on, provide feedback about it. It can be made of easily accessible materials like papers, cardboard, sticky tapes, recycled plastics and so on. Once a prototype is created, they test it or allow a users to test it and then make improvements, improvemen ts, or possibly overhaul the design, depending on their observations observations and the feedback of the user. In these stages. It is important to emphasize that is it totally fine to fall at the first attempt of prototyping. The trial-and-errors aspects of the design thinking process is glorified because it is believed that the students learn a lot through their failures. Even through a physical product is the expected output of design thinking, it should be emphasized that going through the process is what is more important because it is where the learning takes place.

Reflection: I learned how to connect, define, and generate ideas, prototype, and test steps of the design thinking process in this class. The first f irst stage of design tthinking hinking is empathy, which is necessary because the goal of design thinking is for students to respond to a specific need.  At this time, the teacher's teacher's involvement involvement is critical. Through Through exercise exercises s such as observation observation and interviews while immersed in the environment, clear encouragement encouragement is given to students to put themselves in others' shoes. Teachers frequently observe that students at this age are unaware of how their actions affect others. First, the students will choose who their supplier's target audience will be: the people who will utilize it in the t he future. Because the design thinking process cannot be completed without a major problem to solve, students must be able to spot a genuine problem. Students will be

able to answer issues using their math skills. In addition to ttheir heir problem-solving problem-solving talents, they will be able to apply specialist content knowledge knowledge such as measurement, proportion, geometry, and statistics. A prototype is something that allows a user to engage with and provide feedback later.

 

LESSON 12: GAME-BASED LEARNING OBJECTIVE •Develop a game to motivate students, cater mathematical mathematical investigation, or practice a mathematical skill. INTRODUCTION • Play iis s ch children’s wo work an and they llo ove itit! • Well Well-- des desig igne ned d lles esso sons ns usin using g gam gamee-ba base ses s lea learn rnin ing gs str trat ateg egy y ttak akes es adva advant ntag age e of of children’s natural love for play to lead them toward complex problem-solving. • Game Game –b –bas ased ed lear learni ning ng re refe fers rs to the the bor borro rowi wing ng of cert certai ain n gam gamin ing g pri princ ncip iple les s and and applying them to real-life settings to engage users. (Trybus 2015) • The The m mot otiv ivat atio iona nall psy psych chol olog ogy y inv invol olve ved d iin n gam gamee-ba base sed d llea earn rnin ing ga all llow ows s stud studen ents ts to to engage with educational materials in a playful and dynamic way. THINK • Chil Childr dren en fi find nd game games s bot both h mot motiv ivat atin ing g and and enjo enjoya yabl ble, e, so it is not not a surp surpri rise se th that at teachers harness games to cater to learning. learning. • Game Games s are are som somet etim imes es used used a as s les lesso son n sta start rter ers s to get get the the stu stude dent nts s enga engage ged. d. • In som some e lles esso sons ns,, g gam ames es are are use used d tto o exp explo lore re math mathem emat atic ical al conc concep epts ts and and proc proces esse ses s or cater mathematical investigation. investigation. But most of the time, games are used to practice mathematicall skills. mathematica • Not Not o onl nly y do do gam games es make make the the lles esso son n eng engag agin ing g for for you young ng lear learne ners rs but but tthe hey y als also o cre creat ate e a relaxed environment in a mathematics class. • Game Games s ass assoc ocia iate te mat mathe hema mati tics cs wit with h posi positi tive ve fee feeli ling ngs s like like exc excit item emen ent, t, vic victo tory ry,, and and fun fun competition.. So, students who might have developed mathematics anxiety, or those who competition simply “hate” math, might being open up and be more receptive. •

Game Games s tha thatt req requi uire re stud studen ents ts to work work in grou groups ps adva advanc nce e tthe heir ir soci social al skil skills ls as well well..

•

A goo good d mat mathe hema mati tica call gam game e iis s not not only only abou aboutt “hav “havin ing g fun” fun” but but a als lso o abo about ut “doi “doing ng math math””

in itself.  A teacher has three three important tasks in a lesson tha thatt implements a game-based game-based learning learning strategy: 1.

Lay down rules clearly

2.

Obse Observ rve, e, asse assess ss,, a and nd proc proces ess s stu stude dent nts su und nder erst stan andi ding ng

3.

Work Work with stud tudents ents who nee need d add addiitio tional he help.

 

SUMMARY Game-based learning learning is a strategy that takes advantage of children’s love for games.  Applying this this strategy is good in in reducing ma math th anxiety. Reflection: My experience in this lesson has taught me that when you become a teacher, you must play games in order for the kids to like what you are teaching. It will be more appealing and provide value to the duties. It is vital to offer life and pleasure to the minds of pupils, not only for the poor, but also for them to play a game. Even better is a strange game that captures the attention of the students. This will be incorporated in order to increase learning motivation.

LESSON 13: Manipulatives Objective Develop a manipulative to aid mathematics instruction. What is Manipulatives? Manipulatives physical tools of teaching, engaging students visually and physically with Manipulatives objects such as coins, block, puzzles markers etc. These physical objects are used as teaching aids to engage students in the hand-ons learning. learning. Guidelines in using Manipulative in the classroom 1. Orien Orientt the the stud student ents s on on how how to use the manip manipula ulativ tive. e. Give Give some some time time for the stude students nts to play with the manipulative. Allow them to explore the object and what they can do it. 2. Give Give clea clearr speci specific fic instru instructi ction. on. State State the goal goal of of the the acti activit vity y on how the manip manipula ulativ tive e can help them achieve the goal.  Advantage of Using Using Manipulatives: Manipulatives: •

Help ma make abstract id ideas c co oncrete.

•

Math Math mani anipula lati tive ve buil uild stud tudents ents’’ co conf nfiiden dence ce..

•

Useful tto ools ffo or so solving problems.

•

Make le learning m ma ath interesti tin ng an and en enjoyable.

 

Disadvantage of Using Manipulatives: •

Can be a source of disturbance

•

If not provide can be very costly to teacher

•

It Its s use use has has to to be be ca carefu refullly an and ca can be be ve very tim time co consu sumi min ng

•

May May no not lla ast long witho thout p pro rop per ca care and wear out o off a ag ge.

MANIPULATIVES MANIPULAT IVES AS A TEACHING METHODS Mathematical manipulatives play a key role in young children's mathematics understanding Mathematical understanding and development. These concrete objects facilitate children's understanding of important math concepts, then later help them link these ideas to representations and abstract ideas. Manipulatives Examples Base ten blocks Base Ten Blocks are a great way for students to learn about place value in a spatial way. The units represent ones, rods represent tens, flats represent hundreds, hundreds, and tthe he cube represents thousands.

Their relationship relationship in size makes them a valuable part of the exploration in number concepts. Students are able to physically represent place value in the operations of addition, subtraction, multiplication, multiplication, and division. Example:

Pattern blocks  Are a set of mathematical mathematical manip manipulatives ulatives developed developed in the 1960s. 1960s. The six shapes shapes are both a play resource and a tool for learning in mathematics, which serve to develop spatial reasoning skills that are fundamental to the learning of mathematics. Among other things,

 

they allow children to see how shapes can be composed and decomposed into other shapes, and introduce children to ideas of tilings. Example:

Symmetry Dodecagon Dodecagon Polygon Jessica's

Pattern Block Templates from

Edge Geomertry – Pattern blocks

Corner of Cyberspace

Unifix cubes Unifix cubes are the basic block for any classroom. They are made of plastic and connect to each other on two opposing sides. They can be used to t o teach almost all math concept areas, ranging from one-to-one correspondence, correspond ence, patterns and basic number operations to fractions, multi-base projects and beginning algebra.

Tangrams Tangrams are ancient Chinese puzzles made of seven three- and four-sided shapes. Each set of tangrams contains four tangram puzzles in four different colors. Each puzzle consists of five triangles (two small, one medium, and two large), a square, and a parallelogram. parallelogram. Tangrams can be used to solve puzzles in which all seven pieces must be put together to create a specified shape. Tangram puzzles teach many geometric concepts, including symmetry, congruency, transformations, and problem solving.

Reflection: This is where the student is first introduced to maths in this session. To go into their minds and come up with a concept. This is a source that encourages students to use more examples in their work. I've discovered that it should be utilized as an example to illustrate what's being talked to the student. It is important for the student to have a concept.

 

LESSON 14: Values Integration Objective:  Tobplan a lesson in which Values education can be incorporated into existence mathematics curricula Introduction:   You do not teach math, you teach students-with students-with young and impressionable impressionable brains. Primary teachers play an important role in developing young learner’s hearts and minds. What students learn in primary years can mold the person’s they will become. Instilling good values in children early will help them grow into successful and responsible citizens of the nation. Mathematics can be used as a tool for values integration. Values such as honesty, patience and resilience in facing failures are some of the t he many values that can be developed through mathematics. In this lesson, you will learn how to deliberately integrate positive values into your mathematics topic. Integrating Math into other Subject Areas:   Integrating mathematics into the curriculum can be quite challenging challenging and rigorous. However, math is connected to a lot of discipline and should not be isolated from other subjects. Our complex brain looks for patterns and interconnec interconnections tions as it’s way of making sense of things. Our learners developed developed an appreciation for mathematics and a deeper understanding understand ing of concepts when they make connections connections with prior experiences or with different areas of learning. Tapping Into the Affective Domain:   Dr. Benjamin Bloom classified three domains of educational learning: cognitive, affective, and psychomotor. In the formal classroom set –up, the bulk of the teachers lesson planning focuses on the cognitive and psychomotor aspect of the teaching learning process. The third domain, which is the affective domain, is often overlooked. The affective domain includes the manner in which we deal with things emotionaly, such as feelings, values, appreciation, appreciati on, motivations, and attitudes (Kratwohl, 1964). This curricular domain, when tapped during the learning process, can really make students reflect on the connection between mathematical mathematical concepts and values or standards st andards of behavior that will help them deal with the pressures and difficulties difficulties in life. As further teacher, you want to form not only competent students but students with moral caurage, clear values, and excellent character. Values Integration and Retention of Information:  Associating values or standards  Associating standards of behavior behavior with mathematical mathematical concepts can serve as a source of motivation for students. Values integration will help students get life lessons through math. If students find a learning material engaging and meaningfu meaningful, l, then they will ask for more (since curiosity will start to kick in). Curiosity is the force behind lifelong learning.

 

Reflection:

This lesson has taught me that the environment contributes to our well-being. Our surroundings encourage us in gaining information and being productive in our daily lives. When the time comes, it is much more important for students to use it. I've learned everything we've gone through and have a deep understanding of our life.

LESSON 15: Vygotsky’s social learning theory Vygotsky’s Social Learning Theory Collaborative learning branches out from the zone of proximal development theory of Collaborative Vygotsky. Vygotsky defined the zone of proximal development as follows: • The The z zon one e of of p pro roxi xima mall dev devel elop opme ment nt is dist distan ance ce betw betwee een n tthe he actu actual al deve develo lopm pmen enta tall level as determined. •

By ind indep epen ende dent nt pro probl blem em-s -sol olvi ving ng and and lev level el o off pote potent ntia iall deve develo lopm pmen ent. t.

•

As a det deter ermi mine ned d thro throug ugh h prob proble lemm-so solv lvin ing g unde underr ad adul ultt guid guidan ance ce in in coll collab abor orat atio ion n with with

more capable peers. Vygotsky’s Social Learning Theory • In th the e zon zone e of of pro proxi xima mall d dev evel elop opme ment nt,, the the lear learne nerr IIs s clo close se to deve develo lopi ping ng th the e new new skills, but they need supervision and assistance. For example: If a student has already mastered basic addition of fractions, then basic subtraction may enter their zone of proximal development, development, that is, they have the capacity to gain mastery of subtraction of fractions with assistance. The assistance may not be directly provided by the subject teacher. A child seeks to understand the actions or instructions provided by any skillful peer and internalizes the information, using to guide or regulate their own performance. Designing Group Activities • Coll Collab abor orat ativ ive e acti activi viti ties es enc encou oura rage ge act activ ive e parti partici cipa pati tion on fro from m lear learne ners rs.. Inst Instea ead d of passively accepting information from the teachers.

 

•

Le Lear arne ners rs di disc scov over er new new ins insig ight hts s by by coo coope pera rati tive vely ly work workin ing g wit with h oth other er lear learne ners rs..

Identify the Instructional Objectives When you are deciding to use group work for a specific task. You need to reflect on the following questions:

•

What does the activity aim to achieve?

•

How How wi will ll th that at obje object ctiv ive e be be fur furth ther ered ed by aski asking ng st stud uden ents ts to work work in grou groups ps? ?

•

Is th the e acti activi vity ty co comp mple lex x enou enough gh that that it re requ quir ires es grou group p work work? ?

•

Will tth he pr project re require tr true c co ollaboration?

•

Is th ther ere e any any re reas ason on why why the the ass assig ignm nmen entt sho shoul uld dn not ot be co coll llab abor orat ativ ive? e?

•

Ar Are e th the ob objec ecti tive ves s att atta aina nab ble wit with hin a gi give ven n ti time fr fra ame? me?

Determine the Group Size •

How many many stu studen dents wil illl be ass ssiigned to eac each grou roup?

• The The s siz ize e you you choo choose se wi will ll depe depend nd on the the ttot otal al numb number er of st stud uden ents ts in in you yourr cla class ssro room om,, the size of the venue where the activity will be held. •

The The v var arie iety ty of stud studen ents ts need needed ed in a gro group up,, and and th the e tas task k ass assig igne ned. d.

Decide how you will divide the class Will you group them based on proximity? Will you group them according to their own preference? •

The The ffas aste test st way way tto o gro group up stud studen ents ts is to divi divide de th the e cl clas ass s bas based ed on prox proxim imit ity. y.

• You You mig might ht also also assi assign gn stud studen ents ts to grou group p ran rando doml mly y by by cou count ntin ing g off off and and gro group upin ing g tthe hem m according to number. • Le Lett s stu tude dent nt get get a piec piece e of of c cho hoco cola late te fro from m a bask basket et of diffe differe rent nt choc chocol olat ates es and and gro group up students according to the flavor they chose. Give a teambuilding task before assigning the actual task • Give Give a pre preli limi mina nary ry task task that that wi will ll help help each each stud studen entt e est stab abli lish sh a goo good d rap rappo port rt wit with h his/her group. • You You may may pr prep epar are e a si simp mple le acti activi vity ty li like ke aski asking ng each each memb member er to answ answer er ques questi tion ons s about his/her favorite foods, books, places, or hobbies. Delegate a specific task to each member of the group How do you get students to participate in the task?

 

• Come Come up wi with th a ttas ask k whe where rein in diffe differe rent nt role roles s are are assi assign gned ed to th the e gro group up memb member ers ss so o that they are all involved in the process. • Each Each memb member er shou should ld feel feel resp respon onsi sibl ble e ffor or the the s suc ucce cess ss of th thei eirr gro group upma mate tes s and and realize their individual success depends on the group’s success. Have a contract signed by your participants

• Esta Establ blis ish h how how grou group p mem membe bers rs shou should ld inte intera ract ct wi with th one one anot anothe her. r. Make Make th them em si sign gn an agreement that explicitly their expectations of one another. • The The c con ontra tract ct shou should ld also also incl includ ude e the the beh behav avio iors rs th that at you you wan wantt them them to avoi avoid d and and th the e values that you want them to observe and uphold. Share your reason/s for doing collaborative activities •

Stud Studen ents ts mus mustt unde unders rsta tand nd the the ben benef efit its s of of col colla labo bora rati tive ve lear learni ning ng..

• Thes These e act activ ivit itie ies s can can con conne nect ct lar large gerr cla class ss the theme mes s and and lear learni ning ng outc outcom omes es when whenev ever er possible.

Give your instructions clearly •

Givi Giving ng in inst stru ruct ctio ions ns is not not som somet ethi hing ng that that yo you u tak take e for for grant ranted ed..

• Give Give th them em a clea clearr set set of of in inst stru ruct ctio ions ns con contr trib ibut utes es to the the good good perf perfor orma manc nce e of of stu stude dent nts s in an activity. Go around and keep your ears open  As students accomplish accomplish their group group task: •

Go ar arou ound nd and and ans answe werr que quest stio ions ns abou aboutt the the ta task sk.. Mak Make e sur sure e your your ears ears are are ope open. n.

•

Listen to their collaborative dialogue.

• Pay Pay atte attent ntio ion n to to the the inte intere rest stin ing g poi point nts s tha thatt wil willl s sur urfa face ce fr from om th the e dis discu cuss ssio ion. n. • Talk Talk ab abou outt thes these e iint nter eres esti ting ng poin points ts dur durin ing g tthe he subs subseq eque uent nt clo closi sing ng/p /pro roce cess ssin ing g of of activity.

Provide Closure to the group activities •

Conc Conclu lude de the the act activ ivit ity y by by hav havin ing gas ses essi sion on wher wherei ein ns stu tude dent nts s giv give e a repo report rt..

•

You You can can ask ask eac each hg gro roup up to giv give e an an ora orall rrep epor ortt or or s sub ubmi mitt a wri writt tten en repo report rt..

•

The The rre eport portiing sh sho ould uld re revo vollve arou round the their iin nsi sig ght hts. s.

• •

You You may may al also so ask ask the them m tto o ref refle lect ct on how how the they yp per erfo form rmed ed in th the e gro group up Relate the points raised to your current lesson and the objectives of the activity.

 

Reflection:

In this lesson, I learned how to determine how long kids think and how to assess what they demonstrate in their behaviours when they are asked to complete a difficult task. I also discovered that each activity allows children to express themselves cognitively. To boost their cognitive growth, it must be widely distributed and encourage encouraged. d.

LESSON 16: Teaching by Asking OBJECTIVE • Formulate purposeful questions that encourage students to participate in classroom discussions. INTRODUCTION  In mathematics class, effective questioning questioning is essential. Students will get bored if his/ her teacher merely states facts. An effective teacher does not just tell the definitions and theorems but rather asks meaningful questions that lead the learners to the correct ideas.  Also the teacher teacher gets to identify students students who are having having a hard time time with the lesson, lesson, and those with more advanced skills through questioning. It is through t hrough questioning questioning that teacher get to know the misunderstanding misunderstanding of the learners. If the teachers is knowledgeable knowledgeable about the misunderstanding misundersta nding of the learners, then the teacher will have the greatest understanding understanding of his/her learners. It is therefore necessary, that teachers deliber deliberately ately frame questions that will keep the class discussion moving. THINK This goal of this strategy is to keep the learners voices at the forefront of every classroom session. session. Here are the challenges challenges to think of questions that you

Discussion vs. Lecture Art of Questioning Questioning

Could ask that would get your student engage: DISCUSSION VS. LECTURE • In the the di disc scus ussi sion on-b -bas ased ed stra strate tegy gy,, th the e ttea each cher er’s ’s role role is to enga engage ge th the e llea earn rner ers s to a question-oriented dialogue. • The The te teac ache herr spen spends ds a sign signif ific ican antt amou amount nt of of time time to to ask ask sca scaff ffol oldi ding ng ques questi tion ons s to help help students understand an idea deeply. •

In a le lect ctur ure, e, the the teac teache herr is the the ch chie ieff s sou ourc rce e of info inform rmat atio ion. n.

 ART OF QUESTIONING QUESTIONING • Not Not a all ll qu ques esti tion ons s are are cr crea eate ted d equ equal al.. Some Some ques questi tion ons s can can be answ answer ered ed by a sim simpl ple e yes or no. Some questions would require students to think more meaningfully. • Aski Asking ng the the ri righ ghtt ques questi tion ons s wil willl help help you you u und nder erst stan and d wha whatt your your lear learne ners rs kno know, w, do not not know, and need to know.

 

This lesson will enumerate general ideas for your careful consideration consideration when framing essential questions: •

Avoid one-word response’ questions

•

Fost Foste er a cli climate mate co con nduc uciv ive e tto o lle earni rning an and qu quest stio ion ning

•

My questions, my answer is no-no!

• •

Fr Fra ame questio stion ns tth hat ar are acc acce ess ssiible ble to to all lle earne rners Learners should be be active questioners too!

 AVOID `ONE-WORD `ONE-WORD RESPONSE’ QUESTIONS QUESTIONS Refrain from asking questions which only requires a yes or no answer. In general, questions that would require one-word answers do not provide much information to check your learners thought processes. FOSTER A CLIMATE CONDUCIVE TO LEARNING AND QUESTIONING • Make Make sure sure that that your your lear learne ners rs,, fee feell com comfo fort rtab able le to expr expres ess s his his// h her er idea ideas s and and /o /orr ask ask questions at any time. • Some Some st stud uden ents ts are are re relu lucta ctant nt to spea speak k up up bec becau ause se th they ey are are afr afrai aid d of of wha whatt tthe he te teac ache herr or classmates might think if they give an incorrect response. • Li List sten en at atte tent ntiv ivel ely y to what what you yourr lea learn rner ers s have have to say say,, if your your lea learn rner ers s fe feel el th that at you you are are listening to their ideas, then a good working relationship relationship with them will develops. •

Cr Crea eate te a cl clas assr sroo oom m env envir iron onme ment nt wher where e lea learn rner ers s ffee eell h hea eare red d and and reco recogn gniz ized ed..

MY QUESTIONS, MY ANSWER IS A NO-NO! • Do no nott answ answer er your your ow own n que quest stio ions ns.. If you you are are not not a abl ble e tto o eli elici citt resp respon onse ses s from from your your students, try rephrasing your questions. •

Do not rush rush learne rners to giv give resp respo ons nses es insta stant ntlly.

•

Give Give stud studen ents ts so some me time time to pond ponder er and and h hyp ypot othe hesi size ze deep deeply ly abou aboutt iide deas as..

• You You mig might ht also also give give some some lead leadin ing g que quest stio ions ns to help help th them em leve levell up up tthe heir ir conc concep eptu tual al understanding. FRAME QUESTIONS THAT ARE ACCESSIBLE TO ALL LEARNERS 1. Remind Remind your your stud student ents s that that the qu quest estio ions ns iis s for for all all memb members ers of the class. class. Try no nott label label degree of difficulty of a question. 2.

Avoid Avoid sayin saying: g: I expe expect ct my fast fast lea learne rners/ rs/cha chall lleng enged ed ones ones tto o answ answer er this this que questi stion. on.

3. Give Give open open-en -ended ded questi questions ons from from ttime ime to time. time. The answe answers rs to op openen-end ended ed questi questions ons vary from person to person. LEARNERS SHOULD BE ACTIVE QUESTIONERS TOO! •

Dema Demand nd you yourr s stu tude dent nts s to ask ask que quest stio ions ns.. Lear Learne ners rs shou should ld prac practi tice ce dire direct ctin ing g que quest stio ions ns

not only to you but also to their co-learners. co-learners.

 

• You You sho shoul uld d giv give e oth other er stud studen ents ts the the time time to deve develo lop p an an ans answe werr to th the e que quest stio ions ns th that at their co-learners have posed. •Keep in mind that in a discussion, you do not always provide a ready answer. You want you the voices of students to be at the center of every classroom session.

Reflection:  As I realized in this this lesson, it has a greater greater significance significance in our lives. lives. This is required required in order to expand our knowledge and better explain the issues. It's important to state that we're not embarrassed to ask for aid because what we're asking for is a meaningful contribution and should be treated as such. Teaching it to children is considerably more vital nowadays nowaday s ffor or their mental and social development.

LESSON 17: Assessing Learning  ASSESSING LEARNING LEARNING •

The pr process of of ga gathe thering d da ata and ev evidences.

•

To identi entify fy stu students ents’’ stre trength gths and and weakn eakne ess sse es.

•

To dete terrmine/me /measure learners’ progress.

OBJECTIVES •

Demo Demons nstr trat ate e und under erst stan andi ding ng and and app appre reci ciat atio ion n of of ass asses essm smen ents ts..

•

Diff ffer eren enti tia ate form forma ative tive and and su summa mmativ tive ass asse ess ssme men nts ts..

INTRODUCTION •

Demands ur urgent at attention is is tth he a as ssessment.

•

Cl Clas assr sroo oom m ass asses essm smen entt sho shoul uld d be be wi with thin in the the KK-12 12 Basi Basic c Edu Educa cati tion on Fram Framew ewor ork. k.

•

Depa Depart rtme ment nt of Educ Educat atio ion n iss issue ued d tthe he DepE DepEd d Ord Order er No No.. 8, 8, s. s. 201 2015 5 - (The Policy Guidelines on Classroom Assessment for K-12 Basic Education Curriculu Curriculum) m)

THINK •

Asse Assess ssme ment nt is defi define ned d as as a proc proces ess s tha thatt is is u use sed d to to tra track ck of lear learne ners rs’’ p pro rogr gres ess. s.

•

A par partt o off n new ew K-12 K-12 educ educat atio ion n ffra rame mewo work rk is is the the deve develo lopm pmen entt o off 2 21s 1stt c cen entu tury ry skil skills ls..

• The The p pro roce cess ss of asse assess ssme ment nt is anch anchor ored ed to the the fram framew ewor ork ko off Zon Zone e of of Pro Proxi xima mall Development Develop ment of (Vygotsky). •

The The n nat atu ure of th the le learner rner is tth he ce center ter of of th the proc rocess ss..

•

Asse Assess ssm ment ent s sha halll re reco cogn gniize the the di dive vers rsiity of le learner rners s.

•

A lea learn rner er-c -cen ente tere red da ass sses essm smen entt sup suppo port rts s the the lear learne ners rs’’ s suc ucce cess ss..

- (knowledge, understanding, skills, and assimilation in future situations)

 

• Le Lear arni ning ng and and tea teach chin ing g shou should ld not not be be di diff ffic icul ultt yet yet chal challe leng ngin ing g and and faci facili lita tate tes s ulti ultima mate te objectives of the K-12 program in the t he 21st century skills. PRINCIPLES OF ASSESSMENT 1.

Asse Assess ssme ment nt shou should ld be cons consis iste tent nt wi with th the the cur curri ricu culu lum m sta stand ndar ards ds..

2.

Format Formativ ive e asse assessm ssmen entt nee needs ds to scaffo scaffold ld the studen students ts in the summa summativ tive e asse assessm ssmen ent. t.

3.

Asse Assess ssme ment nt res resul ults ts mus mustt be used used by by teac teache hers rs to to hel help p stud studen ents ts lea learn rn bet bette ter. r.

4.

Asse Assess ssme ment nt is is not not use used d to thre threat aten en or int intim imid idat ate e lea learn rner ers. s.

EXPERIENCE There are two fundamental types of assessments - FORMATIVE AND SUMMATIVE

FORMATIVE ASSESSMENT - Assessment for learning (Teacher) and Assessment as learning (Learner)  A formative assessment assessment is effective when when instruction is embedded in in it to promote learning learning (McMillan, (McMilla n, 2007). Steps: 1. Orientation about the learning goals (black arrow) 2. Determine the current status of learners or evidence of prior understanding. 3. Providing clear, specific and on-time feedback 4. Instructional corrections/adjustments corrections/adjustments based on the needs of learners 5. Move the learners close to the goals/learning standards. 6. Evaluate the learner’s progress 7. Provide feedback of the learner’s status. In a case where learner; 1. Orientation of learning goals. 2. Determine the status/prior understanding of learners 3. To provide feedback 4. Instructional Instructional corrections/adjustments corrections/adjustments 5. Evaluation of students’ progress 6. The process end in the same step which is provide feedback after evaluation of students progress. DEPED GUIDELINES OF ASSESSMENT’S PURPOSES BEFORE, DURING, AND AFTER THE LESSONS.

 

SUMMATIVE ASSESSMENT •

Assessment of learning

•

Al Alw ways give at th the end o off a parti rticu cullar un unit or or p per erio iod d.

•

Ai Aims ms to meas measur ure e wha whatt the the lear learne ners rs have have acqu acquir ired ed af afte terr tthe he lear learni ning ng proc proces ess. s.

•

Meas Measur ures es if the the lea learn rner ers s hav have e met met the the sta stand ndar ards ds set set iin n the the curr curric icul ulum um guid guide. e.

• Form Format ativ ive e ass asses essm smen entt pre prepa pare res s tthe he lear learne ners rs in ta taki king ng summ summat ativ ive e ass asses essm smen ent. t. • Meas Measur ures es the the dif diffe fere rent nt ways ways lear learne ners rs use use and and appl apply y all all th the e rel relev evan antt know knowle ledg dge, e, understanding, and skills. •

In the fo forrm of unit test, and quarterly test.

• It has has th thre ree e com compo pone nent nts; s; W Wri ritt tten en Work Work,, Perf Perfor orma manc nce e Tes Test, t, and and Quar Quarte terl rly y  Assessment.  These components are the bases of computing the grade and different learning areas, have unique ways to assess, and set different percentage. percentage.

The DepEd Guidelines provide a list of assessment tools per learning area.

 

Shown below is for Mathematics. 

Reflection: You will gather information on the students' knowledge and abilities in order to to assess the school's strengths and weaknesses weaknesses in this lesson. I've learnt to cherish it so that I can help people meet their wants and desires through teaching. Where the student is weak, he or she must pay attention in order to be taught and gain what he or she requires. This is vital to ensure that the student is not distracted by the teacher's t eacher's word

LESSON 18: Traditional Assessment INTRODUCTION:  Assessment has specific specific purpose, purpose, namely, to monitor monitor student’s progress progress to gather data for instructional instructional decisions, to evaluate student’s achievement achievement and performance, performance, and to evaluate the program. There are many critiques on the use of traditional assessment tools. Included is that the tools overemphasis upon narrowly skills/abilities skills/abilities and content, the mismatch between the standardized standardize d tests and student’s experience in the learning activities, as well as student’s motivation to complete such tests. Some issues are relative and apparent vis-à-vis comparison with the authentic assessment.

 At present, tradi assessment assessme nt may have many manyare critiques but still still have advantages. advan tages. To. name some,traditional thetional traditiona traditional l assessment measures more objectives, valid, and reliable. reliable This is especially true for standardize standardized d tests and other types of multiple choice tests (Law

 

&Eckes, 1995) while these advantages of traditional assessment measures are the critiques to authentic assessment especially the reliability and subjectively issues.   PRINCIPLE OF TRADITONAL ASSESSMENT 1. THE PURPOSE OF THE ASSESSMENT AND WHETHER THE TASK FULFILLS THAT PURPOSE. - An essential starting point is to be aware of the reasons why you are assessing the students, and how to design an assessment that will fulfil your needs. 2. THE VALIDITY AND RELIABILITY OF THE ASSESSMENT THAT YOU ARE CONTRUCTING - to ensure that you are constructing, get out of the t he assessment results is and honest as possible, it is crucial to make sure that the assessment is both valid and reliable. 3. THE REFERENCING OF THE ASSESSMENT - To make the assessment meaningful, meaningful, it is important to compare the candidate’s abilities with a common measure.

4. THE CONSTRUCTION QUALITY OF ASSESSMENT ITEMS. - For the assessment to become effective, the assessment items must be constructed to an appropriate appropria te quality. 5. THE GRADING OF THE ASSESSMENT

- The grades of the assessment results are very concise summaries of a student’s abilities. EXPERIENCE The following are the most widely used traditional assessment assessment tools that can be lead in class.

1. TRUE OR FALSE TEST

 

True or false items required students to make decisions and find out which of two potential responses is true. 2. MULTIPLE CHOICE TEST - According to Bailey (1998), this type of test is commonly utilized by teachers, schools, and assessment organizations for the following reasons. a). Fast, easy, and economical to score. Machines can be used in scoring. b). this measure can be scored objectively, thus given an impression of being must fair f air and/or more reliable than other forms of tests. c). Compared with true or false test, the multiple choice test reduces the chances of learners guessing the correct items. 3. ESSAY - an essay is an effective assessment tool because the answer is flexible and measures higher- order learning skills- written communication and or organization of ideas. 4. SHORT- ANSWER TEST - in a short- answer test, the items are written either a s a direct questions requiring the learner fill in a word, phrase, or statement in which a space is been left blank for a brief written answer.

Reflection:

The methods that have been used up to this point are covered in this lesson. This is an effective idea since it allows the learner to respond while still allowing them to develop their skills. Here, I learned more about how to use and operate with these tools so that I could better educate others how to use and work with them. Because it's how we've always done things in the past.

 

LESSON 19: Authentic Assessment Objective; Construct a performance task in mathematics. INTRODUCTION; The criticisms of the traditional traditional assessment measures and the new focus of learning standards of acquiring and essential skills needed in today’s society pushed the need to rethink the criteria and nature of the learning assessment. The proposal was to use openended problems, hands-on problems, computer simulations of real-world problems, and the use of portfolio in learners work. These types of measures are called authentic assessment where learners are asked to perform real-world tasks, and the criteria are based on actual performance in the field of work (Wiggins (Wiggins,, 1989; Archibald &Newman, 1988)  Authentic assessment assessment is also known known as the “per “performance formance assessment” assessment” or “performance “performance task” where the students must complete real-life activities e g,,preparing g,,preparing memo or policy recommendation, which involves reviewing and evaluating a series of documents. Performance assessment measures the demonstration ability to interpret, analyse, and synthesize informations (Silva, 2009). Think Mathematics education education aims to develop learners with critical and analytical thinking skills to solve real-life problems. Thus, mathematics classes must have tasks and activities the same with how the mathematics use mathematics outside the classroom. How the students learn mathematics inside inside the classroom shall not be different on how they will use it outside the classroom. Principles of Authentic Assessment; 1. Authen Authentic tic mathem mathemati atics cs requ require ires s es essen sentia tiall skil skills ls whi which ch can can be measur measured ed by the ab abili ility ty to communicate and ask questions, to assimilate unfamiliar information, and to work cooperatively with the team the mathematical skills for lifelong learning with the computer literacy. Related to communication is the ability of learners to articulate what they understand and do not. Communication can be fostered in school if learners learn and use the language of mathematics, activities provide opportunities opportunities to make conjectures and reasons. 2.

In aut authe hent ntic ic ass asses essm smen ent, t, tthe he use use of of mult multip iple le typ types es of of meas measur ures es is pos possi sibl ble. e.

3. Auth Authen enti tic c asse assess ssme ment nt is is buil builtt on the the acc accur urac acy y of the the mat mathe hema mati tica call cont conten entt and and interdisciplinary interdiscip linary integration. In geography, there are opportunities to use scaling, proportions and ratio. In genetics, there are opportunities to apply statistics and probability. 4. Authen Authentic tic assess assessmen mentt measu measures res the comple complete te pict picture ure of learn learner’ er’s s iinte ntell llect ectual ual growth growth.. It measures the various kinds of knowledge, knowledge, measures either group or individu individual al for different purposes. An authentic assessment is a combination of many measures. Small group

Situations may be useful to measure the ability to talk and listen, while individual individual assessment can be used to measure the ability to synthesize knowledge.

 

5. Authentic assessment uses the dynamic and adaptive form of feedback. This is also called scaffolding feedback feedback where the learner can identify the skills to model and reflect and connect on their performances. performances. Thus, assessment becomes learning opportunities opportunities and assessment aims to measure not only the actual performance but more important the potential. 6.

Auth Authen enti tic c asse assess ssme ment nt mus mustt take take pla place ce in in th the e cont contex extt of the the lea learn rnin ing g proc proces ess. s.

7. It mus mustt c cons onside iderr both both the learne learnerr and and the situat situatio ion n in in whic which h the the lea learne rnerr iis s asse assesse ssed. d. 8. It mus mustt p prov rovid ide e info informa rmatio tion n on on wha whatt the the lear learne nerr k know nows, s, wha whatt he/sh he/she e does does no nott know know,, and on the development of changes in such learning. 9. Repea Repeated ted measur measure e of of appro appropri priate ate learn learnin ing g ind indica icator tors sm mus ustt b be e made made to ob obtai tain n a clear clear picture of the learner’s knowledge. knowledge. 10 10.. Indica Indicator tors s must must inclu include de cogn cogniti itive ve and and conati conative ve abil abiliti ities es to cap captur ture e di diffe fferen rentt perspectives. 11 11.. Authen Authentic tic asse assessm ssmen entt will will requi require re instr instrume ument nt that that provid provide e in depth depth pers perspe pecti ctives ves on on learning.. For example, the use of paper and pen test, video and computer used jointly to learning have an authentic understanding of the learner. Paper and pencil can use to measure the student’s knowledge knowledge of fact’s, concepts, procedures, and text comprehension comprehension abilities. It can also be used to measure how well the students can critique the quality of other documents. Computers can be used to simulate realistic situations inside the classroom, can effectively track the process of learning and the learner’s response to adaptive feedback. Computers can make possible the dynamic assessment of the relevant criteria. 12 12.. The purp purpose ose of asses assessme sment nt must must be consid considere ered. d. If th the e asses assessme sment nt resul results ts will will be used by the student or the teacher, then the tool must be available in the classroom on a regular basis, which promotes the integration of instruction and assessment.  Authentic Assessment Assessment Tools • Pr Pres esen enta tati tion ons, s, deba debate te,, e exh xhib ibit itio ion, n, w wri ritt tten en repo report rts, s, vi vide deot otap apes es of perf perfor orma manc nce, e, demonstrations, demonstratio ns, open-ended questions, computer simulation, simulation, hands-on execution of experiments, experimen ts, portfolios, and projects. •

In In-- dep depth th eva evalu luat atio ion n in the the cont contex extt of prob proble lemm-so solv lvin ing. g. It It invo involv lves es ind indiv ivid idua uall and and

cooperative problemproblem- solving activities. This projects provides an example of how to t o examine both the individual and cooperative group problem- solving activities, provides insight on how students form their hypotheses by comparing there with other hypotheses, and how to get generalize generali ze concepts from f rom one problem situation to another. • Use Use of of o ope penn-en ende ded d que quest stio ions ns wi will ll prov provid ide e opp oppor ortu tuni niti ties es fo forr lea learn rner ers s to th thin ink k ffor or themselves and express their ideas. Communication Communication is fostered as well as writing task. This is also an opportunity to measure learner’s misconceptions and reasoning abilities. •

De Lange (1987) designed mathematical problem situation composed of multiple items with varying levels of difficulty. There are five task: a timed written task, two-stage tasks, a takehome examination, an essay task, and an oral tasks. Stage one includes open-

 

Ended and essay questions. These items are scored and returned to the students. In stage two, students are provide with their scores in the stage one, they are also allowed to take again the stage on tests at home as long as they t hey accomplish them with within in the agreed time. The final assessment includes includes the scores of the stage one and stage two tests. The assessment process becomes interactive interactive and helps assists the students in reaching their potential. • Port Portfo foli lio o ass asses essm smen entt is is als also o a reco recomm mmen enda dati tion on fo form rm of auth authen enti tic c or or per perfo form rman ance ce based assessment. However, However, there is a caution in creating Portfolio assessment is also recommended recommende d form of authentic or performance guidelines guidelines on how to score the portfolios because of the existence of multiple audiences. • Pr Proj ojec ects ts is is an an exa examp mple le of auth authen enti tic ca ass sses essm smen entt ((Si Simo mon n et et a al, l, 2000 2000). ). Thi This s can can made made individually individua lly or as a group. The project can possess authenticity, real-life related concep concepts, ts, and prior experience of the learners. The learners may provide their findings in various forms like multimedia presentation, role-play, or written report.

 According to Elliot Elliot (1995, to increase increase the effectiveness effectiveness of performan performance ce or authentic assessment, teachers must pay attention to the following details: •

Sele Select ct ass asses essm smen entt tas tasks ks that that are are cle clear arly ly alig aligne ned d or or c con onne nect cted ed to what what has has bee been n

taught. • In Invo volv lve e the the lea learn rner er in the the for formu mula lati tion on f scor scorin ing g crit criter eria ia fo forr the the ass asses essm smen entt task task and and share the final criteria prior to working on the task. • Pr Prov ovid ide e and and exp expla lain in,, if nece necess ssar ary, y, the the cl clea earr stat statem emen ents ts of of lear learni ning ng st stan anda dard rds s and/ and/ or other models of acceptable/ best performance prior to engagement on assessment tasks. • Pr Prov ovid ide e exa examp mple les s of of int inter erpr pret etin ing g tthe he stud studen ent’ t’s s per perfo form rman ance ces s by by com compa pari ring ng it to learning standards that are developmentally developmentally appropriate or compare it to other student’s performances.

Reflection: You will observe a student's abilities during a performance in this lesson. The student performance reveals reveals it has a suggestion, if I am what the observer can say. And the errors will continue to be made. Allow kids to further develop their talents with tthese hese tools, as they will require them when the time comes for them to apply them.

 

LESSON 20: Designing Learning Portfolio Introduction Portfolio assessment is a detailed, unique, and personalized evaluation of what the t he learners know and can do. A portfolio is a collection collection of pieces of evidences of efforts, learn learnings, ings, development, developm ent, growth, and achievement. It emphasizes a learner’s milestone on his/her development developm ent of concepts and skills. It contains not only outputs and work-in- progress but also reflections on the learner’s strength and progress towards the learning goals. Purposes of a Learning Portfolio • The The p por ortf tfol olio io guid guides es the the lear learne nerr and and teac teache hers rs to to set set and and esta establ blis ish h goa goals ls ali align gned ed in th the e learning objectives. • The The p pro roce cess ss of of ma maki king ng a portf portfol olio io ensu ensure res s th the e act activ ive e par parti tici cipa pati tion on of of the the lea learn rner ers s and and helps learners examine growth and development over the time •

The The p por ortf tfol olio io proc proces esse ses s pro provi vide de chan chance ces s for for self self-e -eva valu luat atio ion n and and refl reflec ecti tion on..

• The The p por ortf tfol olio io enha enhanc nces es the the stud studen ent’ t’s s llea earn rnin ing g and and curr curren entt ach achie ieve veme ment nt and and showcases and documents the development and growth in a more contextualized manner. • The The po port rtfo foli lio o can can eval evalua uate te teac teachi hing ng eff effec ecti tive vene ness ss.. The The port portfo foli lio o prov provid ides es flex flexib ibil ilit ity y in curriculum and instructions planning because it considers the developmental developmental domains of the learners and content the subject matter. •

The The p por ortf tfol olio io ca can n help help eval evalua uate te and and im impr prov ove e the the cu curr rric icul ulum um..

•

The The p por ortf tfol olio io re rein info forc rces es hand handss-on on and and co conc ncre rete te expe experi rien ence ces. s.

• The The p por ortf tfol olio io can can mot motiv ivat ate e par paren ents ts and and othe otherr s sta take keho hold lder ers s to beco become me invo involv lved ed in th the e learner’s evaluation plan. Types of Learning Portfolio DOCUMENTARY DOCUMEN TARY PORTFOLIO Involves a collection of work overtime showing the growth and improvement improvement reflecting students learning of identified outcomes. It is also called growth portfolio. The collection and exhibit of items can be based on specific educational goals or experiences of particular learning areas. PROCESS PORTFOLIO Demonstrate all facets or phases of the t he learning process, hence the arrangement is based on the learner’s stages of metacognitive processing. This portfolio contains reflective  journals, think think logs, and other other related evidences. evidences.

SHOWCASE PORTFOLIO  Is the kind that shows only the best of students’ outputs and Products?

 

EVALUATION PORTFOLIO  Includes some work that had not previously been submitted. CLASS PORTFOLIO   Contains a student student grade and evaluate assessment assessment of the student by the teacher. IDEAL PORTFOLIO  Contain all the work a student has completed. ESSENTIAL CHARACTERISTICS CHARACTERISTICS OF PORTFOLIO ASSESSMENT 1. Portfolio is an assessment that is done together by the learners and the teacher. The teacher guides the learner from planning, execution, and evaluation of contents of learning portfolio, hence the interaction and discourse are important elements of the process. 2. The portfolio should be an opportunity to exhibit the samples of work or outputs which shows the growth, development, and achievement achievement over time. 3. The criteria for selecting and assessing the portfolio especially the contents must be clear both to the teachers and students at the outset of the t he process.

Reflection: I learned in this lesson that you must save the objects you have acquired so that you can construct a documentary at the end; it is vital that you return with items or information that will help you remember or serve as a reminder. I discovered that you should create a portfolio so that you can reflect on your achievements and pursue your goals. It will be compressed to only be used when absolutely necessary.

 

CLOSING PRAYER  

We praise you for giving us life,

 

Or saving us in Christ, and for choosing us to be your people.

 

As we come to the end of this school year,

 

We voice our gratitude for the good things you have Done in us, and we praise you for all who have shared in the Work of this school.