1 Some issues with learning from textbooks

Making connections between mathematical concepts is a very important part of understanding mathematics as a subject. Research suggests that teachers who make connections in their teaching are more successful than those who do not (Askew et al., 1997). Making connections is also often a joyous part of mathematics. Making connections is often lost when students are using textbook questions because the focus is on completing questions as quickly as possible, and these questions are usually only about one aspect of a concept, such as listing all factors of a number.

When students use textbooks, the purpose of the learning is not always made clear to them. They can also get so bogged-down in completing the problems correctly that they lose any perspective of the learning that is supposed to take place.

Pause for thought Think about a recent mathematics lesson in your classroom. What mathematics were your students learning? To what extent were they thinking mathematically? To what extent were they making connections between mathematical concepts and ideas? Why do you think this is?

The activities in this unit are based on problems and examples as they can be found in any textbook. Additional questions will then be asked to move the students from mechanically finding answers to really thinking about what they are doing, such as:

• How did you find that answer?
• What is the same and what is different in your answers to those questions?
• What is the same or what is different in your process of thinking?

When students are given the opportunity to think about the process of learning and making connections, they will learn to learn. However, students might initially be uncomfortable with these kinds of questions, as they might not have been required to think in this way before. Therefore, it will be necessary to have support for students, for example through working with their peers in groups or pairs.