Unit I The Mathematics Curriculum in The Intermediate Grades

 

UNIT I THE M

THEM

TICS

CURRICULUM IN THE INTERMEDI

TE GR

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This unit will give you an overview of what it means to teach and learn mathematics in the primary grades. It will provide you with basic information about the curriculum, the learners, and the learning theory that governs mathematics.

Lesson 1 Mathematics in the Intermediate Grades  

Objective To understand the purpose of learning mathematics in the intermediate grades.

Introduction Mathematics as a subject has a unique nature that demands a special and distinct approach to make learning interesting, challenging, and fun for the learners. This unique nature of mathematics must be learned and understood by mathematics teachers.

Think In the Philippines, mathematics in the Intermediate levels includes five content areas: Numbers and Number Sense, Geometry, Patterns and Algebra, Measurement, and Statistics and Probability. The contents and topics are sequentially arranged with and acquire the skills for every topic to avoid gaps and future difficulties. For example, in the elementary levels, levels , the skills in the operation on whole numbers must be learned first before the operation on decimals and fractions. Knowing that the five contents areas are just part of the whole discipline, the questions now are: what is the purpose of learning whole number up to 10,000,000? What is the purpose of learning to measure the area, perimeter, circumference, surface area, and volume of two- to three-dimensional objects? What is the purpose of learning to collect and 1

 

present data in tables, bars, and pie graphs? These learning standards in the mathematics curriculum, in intermediate levels in particular, are part of the whole mathematics education program because it has roles in achieving the goals of mathematics education  – to acquire the skills needed to be analytic, critical, and a problem solver in real life. Moreover, they are necessary prerequisites to higher level of mathematics. For instance, learning the linear equations in algebra is more than representing mathematical problems symbolically and finding the value of an unknown variable, it is finding patterns and predicting certain behaviors or phenomena, then to realizing that a certain cause will lead to a specific results. To relate the graph of equations to business supply and demand, then Mathematics lesson in the Intermediate grades should be leading to this kind of realization for the learners. Learning mathematics is more than getting good grades. It must be applied beyond the walls of the classroom. The main goal of mathematics education is to develop lifelong skills so that the students will be ready to interact with the real world. Therefore, it is a challenge for the mathematics teacher to make mathematics lesson as real as real-life situations and for the learners to acquire the skills such as a s critical thinking, analytical thinking, and problem-solving.

Experience

“I am not good at math.”  “I fear attending my math class.”   “There is an upcoming math test, I am stressed out!” 

The above are few statements given by students who experience math anxiety. Math anxiety is fear, tension, or stress associated with mathematics usually due to repetitive failures. The development of mathematics skills begins in the primary and intermediate levels, so when repeated failures and disappointments happen in these levels, the mathematics anxiety begins to manifest at the intermediate grades. If not addressed, it will have a definite d efinite influence on their future performances, future choices and decisions in mathematics. By Grade 7, when they enter junior high school, the learners have already a fix, solid mental models of mathematics learning. With their experiences in the elementary levels, the learners by Grade 7 are vocal in saying: “Mathematics is difficult.” It is therefore important that the students’ mind-set toward mathematics be address in the elementary levels.

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Assess Answer the following question to verbalize your understanding of teaching mathematics in the intermediate grades. Why is it important to learn mathematics in the intermediate grades? Cite some experiences to support your answer.

Challenge  The following questions will practice you reflective-thinking skills. As you will learn later, it is important for teachers to develop these skills as they evaluate ev aluate their lessons. Have you experienced mathematics anxiety? If not, do you know someone who did? Describe your experience below. Focus on how you viewed math, math class, and your math teacher during the times when you had mathematics anxiety.

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Harness  The following activity will require you to interact with students in the intermediate levels. This experience will give you a broader understanding of the learners in this level and will also enhance your communication skills with them. This activity will be part of the learning l earning portfolio that you will compile at the end of this module. 1.  Survey at least five students in Grades 4, 5, and 6. Ask them the following questions: Are you afraid of math? Why or o r why not? Record their response in the table below.

Are you afraid of Math? yes no

Why/why not?

Student 1 Student 2 Student 3 Student 4 Student 5

 

2. Based on the students’ responses in #1, suggest a classroom setup (including classroom rules) that will help reduce math anxiety among the students.

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Summary  Learning math in the intermediate grades is important because it provides the necessary prerequisites to learning a higher-level of mathematics. Many students develop math anxiety in these levels, so it is crucial that teachers present math in a way that does not elicit fear.

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Lesson 2 Mathematics Curriculum in the Intermediate Grades

Objectives  To understand the features of the Philippine mathematics curriculum and the learning standards for Grade 4 to 6

Introduction  The mathematics curriculum framework of the Philippines put critical thinking and problem-solving skills as the goals of learning and teaching mathematics. The following lesson will give you a deeper understanding of this curriculum that is currently implemented in the country.

Think  The figure below presents the framework of the mathematics curriculum in the Philippines.

K to 12 BASIC EDUCATION CURRICULUM CURRICULUM 6

 

Critical thinking and problem-solving are the goals across the levels in each topic of the mathematics contents. The important principles in teaching and learning mathematics (such as reflective learning, active and student-centered teaching/learning, communications allowing the learnings to articulate their understanding or express their thoughts, and making connections) are important that prior learning/attaining prerequisite skills is always considered. Moreover, mathematics in the context of real-life situation is always the main consideration in designing mathematic mathematicss activities. Mathematics education in the Philippines contains five general contents: Numbers and Number Sense, Measurement, Geometry, Patterns and Algebra, and Statistics and Probability. These general contents are the same across level, from Kinder to Grade 10. The key stage standards for the intermediate grades are shown below.

KEY STAGE STANDARDS

4-6 At the end of Grade 6, the learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers, number theory, fractions, decimals, ratio and proportion, percent, and integers); measurements (time, speed, perimeter, circumference and area of plane figures, volumes and surface area of solid/space figures, temperature and meter reading); geometry (parallel and perpendicular lines, angles, triangles, quadrilaterals, polygons, circles, and solid figures); patters and algebra (continuous and repeating patterns, number sentences, sequences, and simple equations); statistics and probability (bar graphs, line graphs and pie graphs, simple experiment, and experimental probability) as applied  – using appropriate technology  – in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

For better understanding, let us look at the standards per grade of the intermediate levels.

GRADE 4

The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 100,000, multiplication and division of whole numbers, order of operations, factors and multiples, addition and subtraction of fractions, and basic concepts of decimals including money); geometry (lines, angles, triangles, and quadrilaterals); patterns and algebra (continuous and repeating patterns and number sentences); measurement (time, perimeter, area, and volume); and statistics and probability (tables, bar graphs, and simple experiments) as applied  –  using appropriate technology  –  in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decision in real life. 7

 

GRADE 5

The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 10,000,000, order of operations, factors and multiples, fractions and decimals including money, ratio and proportion, propo rtion, percent); geometry (polygons, circles, solid figures); patterns and algebra (sequence and number sentences); measurement (time, circumference, area, volume, and temperature); and statistics and probability (tables, line graphs and experimental probability) as applied  – using appropriate technology – in critical thinking, problem solving, reasoning, communicating, making connections, representations, and and decision in real life.

GRADE 6

The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (divisibility, order of operations, fractions and decimals including money, ratio and proportion, percent, integers); geometry (plane and solid figures); patterns and algebra (sequence, expression, and equation); measurement (rate, speed, area, surface area, volume, and meter reading); and statistics and probability (tables, pie graphs, and experimental and theoretical probability) as applied  – using appropriate technology  –  in critical thinking, problem solving, reasoning, communicating, making corrections, representations, and decisions in real life.

Notice that there is a spiraling progression design in the curriculum standards. Spiral progression ensures seamless integration of content standards. Each content and topic is a piece of the overall curricular landscape. Hence, learning each mathematics content is fundamental because each is related to the previous content and a prerequisite to the next higher one. Moreover, a misconception of concept and skills means a gap or discord n the whole mathematics curriculum.

Experience

Study the k  – 12 mathematics curriculum. What key components do you notice? The mathematics curriculum is not simply a list of competencies. It is logically arranged and organized. For the teachers’ reference, the content standards, the performance standards, and the learning competencies are explicitly stated. See the following example:

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Content

Content Standards

The learner…  Grade 6 – FIRST QUARTERS Numbers and Demonstrates Number Sense understanding of the four

fundamental operations involving fractions and decimals.

Performance Standards The learner… 

Learning Competency The learner… 

Is able to apply the four fundamental operations involving

Adds and subtracts simple fractions and mixed numbers

fractions and decimals in mathematical problems and reallife situations.

without or with regrouping.

The content standards are broad descriptions of what the students should learn. The performance standards outline what the students should be able to do once the concepts and skills are taught. The learning competencies are logically – arranged objectives that must be aimed in classroom instruction for the students to achieve the required content and performance standards.

Assess  Many teachers in the field are confused about the difference between content standards, performance standards, and learning competencies. It is important that you understand them in their importance because they serve as the skeleton of the mathematics curriculum. In your own understanding, explain the difference among content standards, performance standards, and learning competencies. What is the importance of each? e ach?

Challenge The following question will challenge your research and reasoning skills. It was discussed that the Philippine math curriculum is primarily concerned with critical thinking and problem-solving skills. Why do you think this is so? Research on the importance of these skills and synthesize your learning.

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Harness In every math lesson, the teacher must keep three things in mind: (1) what is to be learned. (2) Where the students are coming from. And (3) where the students are going with what they will learn. The following activity will help you develop the skill of mapping every competency you teach. This will be part of the learning portfolio that you will compile at the end of this module. Choose three learning competencies in Grade 5. In each competency, find the prerequisite competencies in Grade 4 and competencies in Grade 6 wherein your chosen Grade 5 competency is prerequisite of.

Prerequisite Grade 4 Competency

Grade 5 Competency

Future Grade 6 Competency

Summary The Philippine Mathematics curriculum under the K  – 12 program promotes critical thinking and creativity. Moreover, content standards, performance standards, and learning competencies are explicitly stated to guide teachers in developing their lessons.

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Lesson 3  Constructivist Theory in Teaching Mathematics in the Intermediate Grades

Objectives  • •

  Demonstrate understanding and appreciation of the constructivist learning theory.   Determine how the constructivist learning theory is applied in teaching mathematics in the early grades.

Introduction DepEd (2016) specifically noted constructivist theory as the backbone of the curriculum. According to DepEd, knowledge is constricted when the learner is able to draw ideas from his/her own experiences and connect them to new ideas. In this lesson, you will learn about the constructivist learning theory and how h ow it is applied in teaching mathematics in the intermediate grades.

Think  Constructivism was conceptualized by educational theorist Jean Piaget. Do you remember him for your psychology classes? Piaget believed that young children learn by constructing knowledge from experiences rather than from adults telling them about the world. According to Piaget and others who p practice ractice constructivist education, education, the method that is the most likely to educate the students is the one in which they experience their world. Constructivism is appropriately applied in teaching mathematics since math is a cumulative and vertically structured discipline. One learns new math by building on the math that has been previously learned. Constructivist learning is described as follows: •

  Learning builds on the learner’s prior knowledge  and the approach is a constructive process.

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  Learner involves in the processes to ensure self-regulated self -regulated and self-directed process.   Learning is grounded in the context of the learners and fundamentally social process. Interaction and communication communication are open and basic elements of learning process.

•

  Learning is more than the acquisition of knowledge. It is collaborative, involves interaction and enculturation with community of practitioners. Collaboration with experts is basic.

•

  The learning processes do not apply only require cognitive but also motivational and emotional domains.

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Experience In a constructivist mathematics class, knowledge is constructed by the learners. To teach is not to explain, not to lecture, not to transfer mathematical knowledge; instead, teaching is to create situations that allow the learners to form the mental construction. The following are some recommendations on how to apply constructivism in teaching mathematics: • •

  Pose problems that is relevant to the learners;   Use big concepts than segmented or disjointed. It invites the learners to participate irrespective of learning styles and dispositions;

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  Create situations that will reveal learner’s point of view. The teacher must create opportunities for this to occur and mus t be willing to listen to the learner’s reasoning and thinking processes; and

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  Use authentic assessments, which includes interaction between the teacher and learner and learner and peer.

Assess  Answer the following questions to verbalize your understanding of the constructivist learning theory. 1.  What is the constructivist theory? Explain it in your own words.

2.  Expound why the constructivist theory is applicable in teaching mathematics.

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Challenge  There is no perfect theory. The following questions will challenge your critical thinking skills as they raise criticisms on the constructivist learning theory. 1.  What do you think could be the possible challenges in using constructivism in teaching mathematics?

2.  What other learning theories could be implemented in teaching math that could complement the down sides of constructivism?

Harness  The next activity will expose e xpose you to an actual mathematics class. You will do numerous classroom observations throughout this module. In this activity, direct your observation skills to the teaching style of the teacher. Note that this is not an activity to criticize the teacher. The purpose is for you to develop keen observation skills on teaching styles implemented in the classroom and later suggests ways to improve the learning activities. This activity will be part of the learning portfolio that you will compile at the end of this module. Observe a Grade 6 mathematics class. Did the lesson develop in a constructivist way? If yes, describe the part of the lesson that followed constructivism. Otherwise, explain how you would revise the lesson in order to facilitate a constructivist constructivist lesson.

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Summary The constructivist learning theory states that learning takes place when we would build on what the students already know. Moreover, it is student-centered, allowing the students to take ownership of their own learning.

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