Psychology for Learning 2 Examining the way people learn and the implications for learning mathematics

How people learn Changes in performance – valuing repetitive practice and feedback Development of conceptual understanding – reflecting, cognitive conflict and discussion Socialisation process – where the learner is an apprentice

Theories about learning Developed from different political and philosophical orientations Most are not theories in the strictest sense of the word but ‘perspectives’ that offer alternate ways of discussing teaching and learning

Theories about learning The theories are descriptive not prescriptive Not a theory of teaching but do provide alternative orientations and approaches to teaching practice and curriculum design

Behaviourism Dominant until 1970’s Assumes a stimulus-response mechanism for learning Thorndike, Skinner, Gagne

Constructivism From the 1960’s a student-centred focus emerged Teacher’s role is to promote this by providing stimulating environments as catalysts Strongly influenced by the work of Piaget Sequence of stages of cognitive development Based upon schema, four stages and transition from one to another

Social Constructivism Lev Vygotsky Zone of Proximal Development (ZDP) – relevant to learning in school through social interactions Based on the idea that children play an active role in learning and that internal developmental processes operate when students interact with and co-operate with others

Contemporary Theories of Learning Bruner Skemp – realtional Blooms Taxonomy of Educational Objectives Lave and Wenger – situated cognition

Theory of Multiple Intelligences Howard Gardner – Frames of Mind (1983, 1993) Intelligence understood as the capacity or potential to learn in various connections rather than… view intelligence as a single property of the human mind So, adopts a wider and more universal set of human intelligences than previously considered and not measureable by the standard verbal methods that rely on a blend of logical and linguistic abilities.

Theory of Multiple Intelligences – 7 Types Linguistic Musical Logical-mathematical Spatial Bodily-kinesthetic Personal intelligences- intrapersonal and the interpersonal Naturalistic

Implications for Educators Overall educational approach that every person should master a central body of curricula material and approaches Assume a range of individual differences – no one arrives at school as a ‘blank slate’ Both complicates and provides opportunity for teachers

Entry Points Provide ways to engagement students and centralise them within the topic Different types of student are likely to respond intelligently to different modes

Different Entry Points Narrative Quantitative/numerical Foundational/existential Aesthetic Hands-on Social

Your Turn Golden Ratio and Ancient Greece Pythagoras and the Egyptians Fibonacci Fractals

Habits of Mind “Develop mental habits that allow students to develop a repertoire of general heuristics and approaches that can be applied in many different situations” (Cuoco et al., 1996, p.3) A curriculum that is organised around habits of mind encourages students to be involved in processes of creating, inventing, conjecturing and experimenting – looking for connections between new and old ideas.

Students should be… pattern sniffers experimenters describers tinkerers inventors visualizers conjecturers guessers

Mathematicians… talk big and think small talk small and think big use functions use multiple points of view mix deduction and experiment push the language use intellectual chants

References Bruner, J (1960) The process of education. Harvard University Press, Cambridge Cuoco, Goldenberg & Mark ( 1996) Daniels, H (Eds)(2005) An introduction to Vygotsky. Routledge, London Gardner, H. (1983). Frames of mind. New York: Basic Books Labinowicz, E (1980) The Piaget primer. Addison-Wesley Publishing, Menlo Park Skemp, R (1987) The psychology of learning mathematics. Routledge, New York Smith, L., Dockrell, J., & Tomlinson, P (Eds)(1997) Piaget, Vygotsky and beyond. Routledge, London Thornton, M.C (1982) Piaget and mathematics students (Paper from the ADAPT Program) Wertsch, M (1985)Vygotsky and the social formation of mind. Harvard University Press, Cambridge