Peter Gould 2011

Electronic mathematics

textbooks: old wine in new skins?

Be innovative, teachers told

• Source: MINISTRY OF INFORMATION

• Teachers are asked to improvise, be innovative in their work and not to rely a lot on textbooks.…

• “If all our schools can do this, parents need not buy a lot of textbooks.”

• FIJI SUN - JANUARY 22, 2011

Different uses of textbooks

• The use and nature of mathematics textbooks varies significantly between countries.

• In many countries use of mathematics textbooks is an expectation of teaching.

• In other countries, use of mathematics textbooks is optional, and thought to be a practice of less experienced or less confident teachers.

Textbooks in different countries

Textbooks in different countries

Maths Plus 3

Uses of textbooks

• The design of a mathematics textbook is influenced by its intended use by teacher and student. Textbook or workbook?

• How a mathematics textbook is used can relate to who owns the textbook.

• Many mathematics textbooks in Australia include a CD. If the school owns the textbook…

• One way to think about mathematics textbooks is as a series of screens.

From clay to paper

YBC 7289

30

1 24 51 10

3525

42

Interpreting screens

What we see is often a function of how we interpret or classify.

What do you see?

Looking through screens

Which has the greater area?

Giving meaning to images on screens

• Looking at screens and looking through screens can be very different experiences:

- Surface observations - as a representation of a mathematical object

- Deep observations - referring directly to the mathematics

Diagram added to the Zhou Bi ( 周髀 )

Gougu: The hook and the leg

Looking through screens

• Seeing - looking at or looking through

•Construing - learning from mathematical activity

•Doing - engaging in mathematical activity

QuickTime™ and aVideo decompressor

are needed to see this picture.

Watching or doing

What did you learn?

Educational design

• Challenge 1

Wielding the symbols

• Notation systems• In mathematics we use our symbol system

as both a means of communication and as tools for thinking.

1:30Division, fraction, ratio or time?

The power of the fraction notation system is that it turns questions into answers. Three divided by seven is .37

Wielding the symbols

• Notation systems• The textbook

challenge of the mathematics notation system is that it is very difficult to typeset.

The Evolution of Mathematics in Ancient ChinaFrank SwetzMathematics Magazine, Vol. 52, No. 1. (Jan., 1979), pp. 10-19.

• Digital textbooks may accept other forms of student recordings, such as drawings or audio responses.

Educational design

• Challenge 2

A question:Do digital textbooks need a feedback

system?

Interacting with screens

• Perceiving an affordance is recognising that some action is possible. The ‘object’ appears to suggest which interactions may be possible.

• Affordance:

• Gesturing:Many e-books use a gesture to ‘turn the page’. Multi-touch screens also appear to make interacting with digital textbooks more natural.

The diagrammatic method

Rumoured proof attributed to Bhaskara II (12th century A.D.)

Behold!

What actions are possible?

Educational design

• Challenge 3

Story frames

4 3

3

4

25 units2

What is the total area of the white squares?

9 units2

16 units2

Story frames

43

3

425 units2

What is the edge length of the white square in the centre?

??

Pythagorean story frames

The basis of a general explanation that could eventuallybecome a proof.

Diagrammatic method

Partitive division

Measurement division

Tape diagrams visually illustrate relationships among quantities in a problem.Their progressive development in a dynamic mathematics textbook would contribute to the diagrammatic method.

Educational design

• Challenge 4

Perceptual variability or constancy?

All that glisters is not gold

Old wine in new skins?

Korea’s Digital Texts

• In Korea, for both teachers and students, textbooks are the main materials for teaching and learning mathematics.

• In using the digital mathematics textbooks, input is through both keyboard and stylus.

• Digital textbooks are currently only used in the classrooms and not at home.

• The vision of Korea’s digital textbook program is large and is subject to ongoing evaluation.

Korea’s 6th Grade Digital Texts

South Korea Digital Texts

Students had to double-click to drag two pieces at the same time.

Lack of affordance.

Summing up

• Digital mathematics textbooks provide new opportunities to support learners.

• The capacity to interact with mathematical representations in mathematics textbooks poses several design challenges.

• In particular, development of a digital mathematics textbook needs to support mathematical representation.

• All that glisters is not gold!