Electronic mathematics textbooks old wine in new skins

Electronic mathematics textbooks: old wine in new skins? Peter Gould 2011

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 30 1 24 51 10 35 42 25 YBC 7289

Interpreting screens What do you see? What we see is often a function of how we interpret or classify.

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 • Doing - engaging in mathematical activity • Construing - learning from mathematical activity

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: 30 Division, fraction, ratio or time? The power of the fraction notation system is that it turns questions into answers. Three divided by seven 3 is. 7

Wielding the symbols • • Notation systems The textbook challenge of the mathematics notation system is that it is very difficult to typeset. • Digital textbooks may accept other forms of student recordings, such as drawings or audio responses. The Evolution of Mathematics in Ancient China Frank Swetz Mathematics Magazine, Vol. 52, No. 1. (Jan. , 1979), pp. 10 -19.

Educational design • Challenge 2 A question: Do digital textbooks need a feedback system?

Interacting with screens • Affordance: • Perceiving an affordance is recognising that some action is possible. The ‘object’ appears to suggest which interactions may be possible. • 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 (12 th century A. D. ) What actions are possible? Behold!

Educational design • Challenge 3

Story frames 4 3 9 units 2 3 25 units 2 16 units 2 4 What is the total area of the white squares?

Story frames 3 4 ? ? 25 units 2 3 4 What is the edge length of the white square in the centre?

Pythagorean story frames The basis of a general explanation that could eventually become 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 6 th 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!