Foundational Math Activities

• Mathematics is a socially constructed, pan-cultural practice.

Foundational Math Activities (Allan Bishop)

• Mathematics involves a way of knowing.
• Counting is a systematic way to compare discrete data.
• Locating involves using one's spatial environment, symbolizing it with drawings, symbols, and words.
• Measuring involves associating objects or tokens with their units or measuring words.
• Designing involves creating a shape or design for an object in the environment, forming a mental template.
• Playing involves participating in games with formalized rules.
• Explaining involves finding ways to prove answers.

Mathematics According to CAPS

• Mathematics uses symbols to describe numerical, geometric, and graphical relationships.
• Mathematics is a human activity involving observation, representation, and investigation of patterns physically and socially.
• Mathematics develops mental processes that benefit logical and critical thinking, accuracy, and problem-solving skills.

Aims of Teaching and Learning

• Teaching and learning mathematics aim to develop critical awareness, confidence, competence, curiosity, recognition of creativity, and a deep understanding of mathematics.

Expected Achievements in School Mathematics

• Students should be creative and look for patterns.
• Students should be able to reason and give arguments.
• Students should be able to mathematize, involving collecting data.
• Students should be able to communicate and express thoughts.

Traditional Schooling

• Traditional schooling is based on a transmission or absorption view of teaching.
• Students passively absorb information.
• Teaching consists of transmitting sets of established facts.

Approaches to Learning and Teaching Maths

• Constructivism, both radical and social, and problem-centered approaches.

Constructivism

• Constructivism explains how individuals learn.
• Constructivism includes learning theories from Piaget, Bruner, Vygotsky, and Dewey.
• Constructivism is child-centered and focuses on knowledge construction.
• Knowledge is built from personal experiences.
• Each learner's experiences are unique, requiring flexible teachers.

Radical Constructivism

• Knowledge is accessed only through senses and personal experiences.

Social Constructivism

• Knowledge is constructed socially.
• Shared learning leads to knowledge from others and sensible conversations.

Applying Constructivism

• Learners need to engage in mathematics through concrete experiences to foster curiosity.
• Active participation by children helps them become critical thinkers.
• Teachers should create engaging experiences that involve explanation, evaluation, communication, and application.

Problem-Centered Approach

• Tasks need to be accessible and engaging, building on prior knowledge.
• Teachers should encourage learners to think deeply and share their thoughts.
• Classroom culture is important.

Benefits of Learning with Understanding

• Understanding mathematics is motivating.
• Understanding promotes better comprehension.
• Understanding mathematics fosters memory.
• Understanding maths enhances transfer of knowledge.
• Understanding influences attitudes and beliefs.
• Understanding promotes autonomous learning.

Problems in Teaching and Learning School Maths

• Only one form of representation is taught.
• Teachers may not be aware of how concepts develop later.
• Only knowing producers is concerned.

Strands of Maths

• Conceptual understanding involves comprehension of mathematics.
• Procedural fluency means accurately completing calculations.
• Strategic competence involves the ability to formulate problems.
• Adaptive reasoning is the capacity for logical thought.
• Productive disposition indicates a habitual ability to engage with mathematics.

Aims for Teachers to Help Pupils

• Help pupils understand.
• Help pupils enjoy mathematics.
• Help pupils excel at mathematics.