TRAINING ON THE �REVISED K-10 CURRICULUM
MATHEMATICS
Pedagogical Approaches
At the end of the session, the participants are expected to:
1. examine the alignment of pedagogical approaches in Mathematics to a given learning competency and
2. align pedagogical strategies with the learning competency
Session Objectives
ACTIVITY: Dance and Tell
1. A ball will be passed while the music is being played.
2. Once the music stops, the person who holds the ball will be asked to mention a teaching strategy/ pedagogical approach that he/she used in his/her math class.
3. The selected teacher shall also be asked to describe how he used the strategy.
ACTIVITY: Dance and Tell
4. Steps 1-3 shall be repeated for 5 minutes. Once a pedagogy is mentioned, it must not be repeated by the next selected participant.
5. As an additional task, participants will be asked to take note of the pedagogical approaches mentioned.
ANALYSIS
1. What are the pedagogical approaches mentioned?
ANALYSIS
6. What preparations must a teacher have to efficiently implement a pedagogical approach?
7. Do you know of the pedagogical approaches in mathematics suggested in the REVISED K to 12 K10 Curriculum? Do you want to know these?
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Grades 1 to 10 Mathematics Curriculum Framework
Instructional Design Framework
The K to 10 Instructional Design Framework
SUGGESTED PEDAGOGICAL APPROACHES
ABSTRACTION
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
EXAMPLE
APPROACH
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
CONSTRUCTIVIST
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Using our prior knowledge, we build new knowledge by drawing comparisons and making connections.
5 Core Principles of Constructivism
Knowledge is Constructed
To learn, students must be part of the process in order to understand new content.
Active Learning
We learn best by doing something together and interacting with it socially
Social Learning
Subjectivity of experience dictates that each will differ in how we learn and comprehend a given concept
Knowledge is personal
5 Core Principles of Constructivism
Received knowledge is both socially tempered and subjective in nature. As we learn more, we update our mental models of the world, thus changing how we see and interpret reality.
Reality and the Mind
5 Core Principles of Constructivism
Concrete-Representational-Abstract (CRA) Model
CRA It is a three-part constructivist process that transitions students from hands-on instruction to the symbolic math we use as adults. This brings both meaning and context for how and why we use math to solve problems.
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
SAMPLE LCs
APPROACH
Learners are given actual manipulatives to learn the concept.
After, they can be given pictures to replace the manipulatives. Then, they are given word problems to solve without the aid of concrete objects and pictures.
LC: recognize, using models, and draws a point, line, line segment, and ray.
LC: represent numbers up to 10 000 using pictorial models and numerals.
*note: all LCs that make use of models or pictorials
CONCRETE PICTORIAL ABSTRACT (CPA)
LC: represent numbers up to 10 000 using pictorial models and numerals
CONCRETE
REPRESENTATIONAL
ABSTRACT
5000
= 1000
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
EXAMPLE
APPROACH
Learners are engaged in the process of asking questions, exploring ideas, and finding solutions
LC: identify and draw line segments of equal length using a ruler.
The class will be divided into groups with complete materials. The task is to explore on how to draw lines of equal length. The teachers can pose questions to trigger critical analysis. Learners are also asked to ask questions leading to the development of correct understanding of the topic. The learners will explain their questions in coming up with the idea, methods and ways on how the task is accomplished.
INQUIRY-BASED
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When students solve problems themselves, they internalize conceptual processes. Inquiry-based teaching prioritizes process over product.
Characteristics of Inquiry-based Learning
Process Focus
The teacher may pose a problem derived from the class content or students’ questions. The students then investigate the issue to find an answer.
Investigation
Students may work in small groups when exploring a problem. Students assist one another throughout the learning process, enabling them to share and build upon ideas and articulate how they arrived at a solution.
Characteristics of Inquiry-based Learning
Group Learning
As the students work together, the teacher can move from group to group, listening to their discussions. Teachers may ask questions to gauge students’ understanding and correct any misconceptions.
Discussion Monitoring
Students solve math problems that have a meaningful life application.
Characteristics of Inquiry-based Learning
Real-life Application
Inquiry-based Learning- Checking for Understanding
1. What should the teacher pose to start IBL?
2. Which is a preferred strategy when students answer an inquiry, independently done or by small groups?
3. When students are answering a certain inquiry, what should the teacher do? Why?
4. If students have derived the process, what must be given to them to test their understanding?
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
EXAMPLE
APPROACH
Helps learners to become more aware of their strengths and weaknesses, and to develop strategies for improving their learning
LC: all LCs applicable
After teaching the concept, the teacher can ask reflective questions:
1.What are the difficulties you have encountered?
2.What can be done to help you understand the concept?
3.What can you do for you to master this concept?
REFLECTIVE
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R – Recall the events
E – Examine your responses
F – Acknowledge feelings
L – Learn from the experience
E – Explore options
C – Create a plan of action
T – Set timescale
7 Stages of Reflective Learning Model
When mistakes are made, take a moment to process the mistake as a learning opportunity.
Enough wait-time for learners to reflect when responding to inquiries.
Classroom activities that are relevant to real-world situations and provide integrated experiences.
Authentic (real) problems that require teachers and learners to deeply think about solutions.
Reflective journal to write down learners’ positions
Affect, Behavior, and Cognition questions to prompt reflective thinking
Activities that promote reflective learning
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
EXAMPLE
APPROACH
Learners learn better through collaboration than solo experiences (Vygotsky)
LC: recognize and draw parallel, intersecting, and perpendicular lines
The teacher will give a worksheet and illustrations of lines. The teacher will group the learners and describe each line. Note: the teacher has not defined yet parallel, intersecting and perpendicular lines
COLLABORATIVE
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CHARACTERISTICS OF COLLABORATIVE LEARNING
GROUP
DYNAMICS
Students work on groups of two or more
INTERACTION
INTERDEPENDENCE
SHARED RESPONSIBILITY
FEEDBACK
Group members rely on one another to achieve their shared goal
Interact with one another to share ideas, challenge perspectives, provide explanations and negotiate meanings
Every student is responsible for their learning and the learning of their peers
Give and receive feedback allowing them to reflect and adjust accordingly
STRATEGIES FOR EFFECTIVE COLLABORATIVE LEARNING
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Establish Clear Objectives
Create Heterogeneous Groups
Assign Roles
Use Suitable Tasks
Assess Group Process
COLLABORATIVE ACTIVITIES FOR MATHEMATICS
Problem Solving
Math Games
Jigsaw Puzzles
Peer Tutoring
Mathematical Projects
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
EXAMPLE
APPROACH
This approach encourages connections between different learning areas, various contexts, promoting integrated learning
LC: compare numbers up to 10 000 using the symbols =, >, and <.
After using the symbols, the teacher can ask learners where they can use these symbols in real life. For example, if the normal body temperature is 36.5°, what is the implication if your body temperature is greater than 36.5°? (integration to science & health)
INTEGRATIVE
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TYPES OF INTEGRATIVE LEARNING
Intra-disciplinary
Multidisciplinary
Interdisciplinary
Transdisciplinary
Within subject areas
Between subject areas
Beyond the subject areas
Principles of Integrative Learning
Integrated learning helps the children to expand the knowledge . Then build and extend their previous knowledge and experiences.
Open ended learning style.
Helps to develop problem solving ability.
Collaboration
CHARACTERISTICS OF INTEGRATIVE LEARNING
Holistic way of learning
Encouraging peer group work
Develop problem solving ability
Develop the social skills of the children
Directly connected with the real world
Emphasis on projects that goes beyond text
Combinations of the subjects
Helps the child to think creatively and critically
Collaboration is the main feature of integrated learning
Ensures the active participation of the learners
OTHER PEDAGOGICAL APPROACHES
(mapping the LC and the pedagogical approaches)
ABSTRACTION
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
SAMPLE LCs
APPROACH
Teachers provide resources, guidance, and support. They create an environment that encourages exploration and discovery, allowing learners to take the lead in their learning.
LC : recognize and draw parallel, intersecting, and perpendicular lines
LC : illustrate and estimate the area of a square or rectangle using square tile units.
LC: explore inductively the derivation of the formulas for the areas of a square and a rectangle using square tile units.
DISCOVERY LEARNING
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
SAMPLE LCs
APPROACH
The teacher gives a familiar story. The problem will be reflected in the story. The learners will be asked to propose solution and solve. They will present their solutions. The teacher guides learners.
Any LC that involves problem solving
PROBLEM-BASED LEARNING
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
SAMPLE LCs
APPROACH
This method works best for development of particular skills, and not necessarily those that require experimentation. It is considered teacher-centered.
ALL LCs are applicable
EXPLICIT INSTRUCTION
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
SAMPLE LCs
APPROACH
It is a backward design process, which means that it starts with the end goal in mind and works backward to create instructional activities
ALL LCs are applicable
EXPLORE, FIRM UP, DEEPEN, TRANSFER
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
SAMPLE LCs
APPROACH
It involves drawing conclusions or generalizations from specific examples. In education, this means starting with a broad concept or theory, verifying and applying it to specific examples or situations.
LC: describe the position of objects using ordinal numbers up to 100th
LC: identify and draw line segments of equal length using a ruler
DEDUCTIVE
LC: find the areas of squares and rectangles in sq. cm and sq. m.
The teacher will give small square models, and objects that are in the shape of square or rectangle. The task of the learners is to give the areas of the square and rectangle.
Note: The teacher did not discuss the formula for area of rectangle and square yet.
Learners build their own understanding of mathematics by exploring concepts and making sense of them, and engaging in meaningful activities, problem-solving, and reflection.
DESCRIPTION
SAMPLE LCs
APPROACH
Includes using educational technology. The goal is to create a more dynamic and engaging learning environment that better meets the needs of today's learners.
ALL LCs are applicable
TECHNOLOGY-INTEGRATED
Which among these approaches have been mentioned in our Dance & Tell activity?
Are you familiar with these approaches? Have you used them in teaching Mathematics?
Processing
SYNTHESIS
In selecting the pedagogical approach, consider the intention of the learning competency. For example, if the competency requires models, then the approach to be selected should be the one espousing the use of models. Consider also the level of ability of the learners. For teachers, you should know how to properly implement it. Learn it!
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"Feedback is the breakfast of champions. It’s the crucial element that helps learners understand how they can improve and excel.“
— John Hattie
References:
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Department of Education. 2023. K to10 Instructional Design Framework
Department of Education. 2023. MATATAG Mathematics Curriculum Framework
DepEd Order No. 8, s. 2015 Policy Guidelines on Classroom Assessment for the K to 12 Basic Education Program
References:
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DepEd Order No. 31, s. 2020 Interim Guidelines for Assessment and Grading in Light of the Basic Education Learning Continuity Plan
DepEd Order No. 42, s. 2016 Policy Guidelines on Daily Lesson Preparation for the K to 12 Basic Education Program
Classroom Assessment Resource Book
References:
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Kustra, Erika and Potter, M.K. A Primer on
Learning Outcomes and the SOLO Taxonomy.
Centre for Teaching and Learning, University of Windsor, 2012
Nasib, T. , “Instructional Methods: What factors are you as a teacher to consider when choosing a teaching strategy?” Somi, 2018.
References:
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Oligario, L.M. C., et. al. Pedagogical Approaches in Education: Theories, Practices, and Applications in the Classrooms. SEAMEO INNOTECH, 2022.�
Rocher, T. & Hastedt, D. International large-scale assessments (ILSAS) in education: a brief guide. IIEP Learning Portal, 2022.
“Teaching kids to count is fine, but teaching them what counts is best.” –Bob Talbert.”
Closure
MARAMING SALAMAT!