Using our Mathematical kitbag

Anne ReayPhillip Linsell

Senior Lecturers in Primary Mathematics Education

Bradford College

The United Kingdom remains one of the few advanced nations where it is socially acceptable, fashionable even, to profess an inability to cope with mathematics. That is hardly conducive to an environment in which mathematics is seen by children as an essential and rewarding part of their everyday lives.’

Sir Peter Williams, Chancellor of the University of Leicester

What is the area of each piece of this tangram?

10 cm

10 cm

Two kinds of understanding of mathematics arepossible… Instrumental understanding is knowing a

particularmethod or rule for getting an answer. Relational understanding is having a cognitive

mapof relevant sections of the interconnected networkof concepts which constitute mathematics.

Skemp, R. (1989) Mathematics in the Primary School. London: Routledge.

Using your mathematical kitbag....

Putting things in context

Compare two problems related to tangrams:

Either:

The teacher shows the class a set of 7 tangram pieces and

says that they should try to put the pieces together to make

a square... Extension work is provided e.g. Trying to make

a triangle, a rectangle, etc.

Or:

Story is used as a stimulus and meaningful context...

Tan was a poor potter in Ancient China. He was so poor

that he only had one set of clothes, could only afford one

meal a day, and could not afford the dowry he needed to

marry the woman he loved. However, Tan was well-known

for his ability to make beautiful tiles.

One day the Emperor of China asked Tan to make him a

beautiful square floor tile . Tan did so while thinking his

fame and fortune would be secured if the Emperor liked his

tile....

Schiro, M.S. (2004) Oral storytelling and teaching Mathematics. London: Sage Publications.

Oral Storytelling and Teaching Mathematics (Schiro, M. 2004)Using stories to teach Mathematics can:

refocus from highly literate school mathematics (which uses the written word and pictures) to engage with the more oral traditions of many urban communities;

interweave a multicultural perspective into mathematics;

ensure a problem solving model, through which children gain understanding of Mathematical concepts AND develop core skills. ( organising, selecting, checking, communicating, presenting).

Teaching As Story Telling (Egan, K. 1986)

The process of teaching can be an objective led model. (Egan refers to it as an assembly line!)

The Story Form Model (p.41). Stories can organise and communicate meaning in a more powerful, pervasive way.

Links to SEAL curriculum in harnessing children’s feelings and imagination.

Elements of learning that are evident in activities based upon stories.

Listening skillsSpeaking skillsCollaborationProblem SolvingDevelopment of key Mathematical ideasContextualisationUse of ICTCross-curricular links

Three Hat Day QuestionsFor how many days can Mr.Pootle wear different three hat towers if he owns three hats?

For how many days can Mr. Pootle wear different two-hat towers if he owns five hats?

For how many days can Mr. Pootle wear different four-hat towers if he owns four hats?

Using the outdoor environment.RHS Gardens Harlow Carr, Harrogate

Using natural materials to createsymmetrical pictures.

World On A Plate

How would you exploit ‘The world

on a plate’ resource as a starting-

point for mathematical and cross-

curricular work in primary?

Three orientations towards teaching mathematics

Connectionist e.g. makes connections between different areas of mathematics, with other subjects and with everyday life.

Transmission e.g. emphasises one method even though another method may be more apt in this case.

Discovery e.g. priority is given to children developing their own strategies.

Thompson, I. (1999) Issues in teaching numeracy in primary schools, Chapter 8. Buckingham: Open University Press.

Summary

Learning is most effective when children meet concepts in a range of meaningful contexts e.g. story, local environment, etc.

Effective mathematics teaching develops children’s subject specific skills and transferable skills;

Two kinds of understanding e.g. instrumental and relational (Skemp);

There is some evidence that the most effective teachers of mathematics adopt a connectionist approach to their teaching.