Mathematics Curriculum in the Primary Grades

A vocabulary set capturing key terms, theories, models, and standards from the lecture notes on Mathematics Curriculum in the Primary Grades.

Sensorimotor Stage (0-2 years)

First Piaget stage where learning occurs through sensory experiences and motor activities; object permanence develops.

Preoperational Stage (2-7 years)

Language and symbols emerge; imaginative play; thinking is concrete and egocentric; struggles with conservation.

Concrete Operational Stage (7-11 years)

Development of logical thinking with concrete examples; understands conservation; can sort and classify.

Formal Operational Stage (12+ years)

Abstract thinking; hypothetical reasoning; systematic problem solving; capability in algebra, geometry, calculus.

Object permanence

Understanding that objects continue to exist even when not seen or heard.

Conservation

Idea that quantity remains the same despite changes in shape or arrangement.

Jean Piaget

Swiss psychologist who proposed stages of cognitive development.

Constructivist learning theory

Learning as an active process where learners construct meaning from experiences rather than passively receiving information.

Constructivist teaching

Teacher practices that invite questions, accept students’ ideas, promote discussion, test ideas, and encourage cooperation.

Traditional Classroom

Teacher-centered setting where the teacher disseminates information and students receive it.

Five Es model

Engage, Explore, Explain, Elaborate, Evaluate—an inquiry-based instructional framework.

ADIDAS model

Activity, Discussion, Input, Deepening, Activity, Summary—a sequence guiding learning activities.

The Teaching Cycle

Identify objectives, plan instruction, implement plan, check understanding, reflect on teaching, assess learning and reflect.

Identify objectives

Know what knowledge and/or skills students should learn, guided by curriculum standards.

Plan instruction

Choose strategies to meet objectives, master content, and consider students’ knowledge and learning styles.

Implement plan

Carry out planned activities while remaining flexible to necessary changes.

Check for understanding

Use formative assessments during the lesson to confirm students’ learning.

Reflect on teaching

Evaluate whether objectives were achieved and how to improve instruction.

Assess learning and reflect

Use tests or authentic assessments and reflect on results before setting new goals.

Content standards

Broad descriptions of what students should learn.

Performance standards

Outline what students should be able to do once concepts and skills are taught.

Learning competencies

Logically arranged objectives that guide classroom instruction to achieve standards.

Five content areas (K-12 Mathematics)

Numbers and Number Sense; Measurement; Geometry; Patterns and Algebra; Statistics and Probability.

Numbers and Number Sense

Concepts of numbers, properties, operations, estimation, and their applications.

Measurement

Use of numbers and measures to describe, understand, and compare objects (length, mass, capacity, time, money, temperature, perimeter, area, volume, angle).

Geometry

Properties of 2D and 3D figures; spatial reasoning; relationships; models and proofs.

Patterns and Algebra

Studying patterns and relationships; use of algebraic notations, equations, and functions.

Statistics and Probability

Collecting and organizing data; charts, tables, graphs; interpretation; dealing with uncertainty; predictions.

Growth mindset

Belief that math abilities can improve with effort, leading to enhanced learning outcomes.

Fixed mindset

Belief that math abilities are static and cannot improve, often hindering performance.

General characteristics of learners in a primary grade

Physically active; socially forming friendships (sometimes quarrels); emotionally sensitive to criticism; cognitively, pattern recognition and problem-solving with self-talk.

Elements in Lesson Planning

Content, objectives, students, physical environment, social environment, emotional environment, and availability of resources.

Difference between traditional and constructivist classrooms

Traditional: teacher-centered, focus on basics; Constructivist: student-centered, active knowledge construction through discussion and collaboration.