Math- Instructional Approaches, Methods, and Strategies

approach

the teacher’s overall belief or philosophy about teaching

method

the general way or system used to teach

strategy

the specific technique or activity used during teaching

teaching approach

the broad philosophy or guiding principle about how teaching and learning should happen.

teaching approach

It reflects the teacher’s beliefs about learners, learning, and instruction.

•learner-centered approach

•constructivist approach

•inquiry-based approach

Examples of Teaching Approaches in Mathematics

teaching method

organized way a teacher delivers instruction based on a chosen approach

methods

more practical and structured than approaches.

•lecture method

•cooperative learning method

•problem-solving method

Examples of Teaching Methods in Mathematics

learner-centered approach

Students actively participate in learning.

learner-centered approach

Students explore patterns and discover formulas themselves instead of listening to long lectures.

constructivist approach

Students build knowledge from experiences

constructivist approach

Students use manipulatives to understand fractions before solving equations symbolically.

inquiry-based approach

Students learn through questioning and investigation.

inquiry-based approach

Students investigate rectangles using grid paper to discover

Lecture Method

Teacher explains concepts directly.

Lecture Method

Teacher demonstrates how to solve a problem.

Cooperative Learning Method

Students work in groups to solve tasks.

Cooperative Learning Method

Groups solve geometry problems collaboratively.

Problem-Solving Method

Students solve mathematical problems systematically.

Problem-Solving Method

Students solve word problems using Polya’s steps: Understand the problem, Devise a plan, Carry out the plan, Look back.

teaching strategy

specific technique, activity, or tool used during instruction to help students learn better.

Strategies

the most specific among the three.

•Think-Pair-Share

•Math Games

•Use of Manipulatives

Examples of Teaching Strategies in Mathematics

Think-Pair-Share

Think individually

Discuss with a partner

Share with the class

Math Games

Math Bingo for multiplication facts

Use of Manipulatives

Students use physical objects.

Use of Manipulatives

using fraction strips to compare fractions

interactive and learner-centered

Through ____ approaches, students become more engaged, confident, and motivated in learning mathematics.

diverse teaching strategies

The use of ______ helps address the different learning styles, abilities, and interests of learners.

explore, reason, communicate, and apply

Effective mathematics instruction should not only focus on computation but also encourage learners to ______ mathematics meaningfully in everyday situations.

varied instructional methods

Teaching Intermediate Mathematics requires teachers to use ____ that promote conceptual understanding, problem-solving skills, critical thinking, collaboration, and real-life application of mathematical ideas.

conceptual understanding, problem-solving skills, critical thinking, collaboration, and real-life application

Teaching Intermediate Mathematics requires teachers to use varied instructional methods that promote ______ of mathematical ideas.

Concrete-Representational-Abstract (CRA) Approach

A sequential instructional method that helps learners understand mathematical concepts gradually.

Concrete-Representational-Abstract (CRA) Approach

This strategy is highly effective because many learners struggle when mathematics is introduced immediately through abstract symbols without concrete understanding.

Concrete Stage

Start with tangible items like blocks or counters to solve problems, allowing students to physically manipulate the math

Representational Stage

Transition students to drawing pictures or diagrams of the problems they previously solved with physical objects.

Abstract Stage

Introduce traditional symbols and numbers to represent mathematical concepts, building on the solid understanding developed in the earlier stages

Problem-solving

develops analytical thinking, logical reasoning, and perseverance.

Step 1: Understand the Problem

Step 2: Devise a Plan

Step 3: Carry Out the Plan

Step 4: Look Back

Problem-Solving Process

Drawing diagrams

Making tables

Looking for patterns

Guess and check

Working backward

example strategies in problem solving

Step 1: Understand the Problem

Students identify:

What is asked?

What information is given?

What operation may be needed

Step 2: Devise a Plan

in this stage, students think of possible strategies or methods that can help solve the problem. Teachers should encourage learners to explore different ways of solving instead of relying on one fixed procedure

Step 3: Carry Out the Plan

In this stage, students implement the strategy they selected during the planning stage.

They carefully perform the mathematical operations, follow the steps systematically, and solve the problem accurately.

Step 4: Look Back

This is the final stage of problem-solving where students review, analyze, and verify their solution.

Many students tend to stop once they obtain an answer, but this stage is essential because it helps learners confirm accuracy, reflect on their thinking, and deepen understanding

Cooperative learning

instructional strategy in which students work together in pair or small groups to accomplish shared learning goals and solve mathematical tasks collaboratively.

•Think-Pair-Share

•Jigsaw Method

•Group Problem-Solving

Common Cooperative Learning Strategies

Repetition

Repeating and reviewing previous formulas, lessons, and information helps students understand concepts more clearly and learn them faster.

Timed testing

Taking a short test and then grading the test in class will help teachers assess student understanding

Pair Work

Group work is a simple strategy that allows students to work and problem solve with a buddy. They can discuss the problems and work together

Manipulation Tools

The use of blocks, fruits, balls, help students learn the basics of place value, addition, subtraction, and other areas of basic math

Math games

Teachers should be sure to incorporate a strategy into games