**Siobhan King is a Mathematics Adviser at Herts for Learning**

I have been thinking about maths text books: what they add to lessons and how they can be used effectively. I am a firm believer in not reinventing the wheel and know that teacher time is finite and exceptionally valuable. Furthermore, I agree with Tim Oates’ assertion that “high quality textbooks ** support **both teachers and pupils – they free teachers up to concentrate on refining pedagogy and developing engaging, effective learning.” (Oates, 2014, p4)

My problem is, that I see very few of these ‘high quality textbooks’ and I have come to the conclusion that we need to be clever about making the best of the resources available to us. With this in mind, I have tried to pick out what I think are some of the pitfalls and come up with some suggestions as to how maths texts books could be used most effectively.

**Use visual representations cleverly**

For me, one of the best things about maths text books is that they often provide visual models for calculations or concepts, which help me to support children in understanding the maths they are learning. Of course, it is important not to be tempted to completely miss the concrete exploration which is so vital for children to develop their mathematical understanding. As Bruner (1966) identifies it is the shift between representations and the ability to ‘translate’ between models which is so crucial to develop depth.

To use visuals in maths textbooks cleverly, I think that it is useful to introduce them to children without the precision of labels and numbers, in the first instance. By showing a model which does not lead pupils to immediately calculate an answer, mathematical discussions can be opened up from questions such as:

- “What do you notice?”
- “What could the problem be about?”
- “What questions would you like to ask?”
- “What other information would you need to work that out?”

I have found that these key areas of discussion can uncover misconceptions, develop precise use of mathematical vocabulary and offer the chance for creativity in mathematical thinking. In addition, I have seen how working in this way can really help children to see themselves as mathematicians and to help everyone to feel that they have something to say and truly engage them in their learning. NCTM’s Dan Meyer (2016) exemplifies how this technique, which he calls “deleting the textbook”, can be used to help pupils connect with maths more fully, in his talk which can be found here:

By taking away the detail and then adding it back to a visual, you can then model and reason with children about how to unpick the problem. This element of working mathematically can otherwise be difficult to develop from textbooks where worked examples, with labelled visuals, move quickly to a bank of abstract problems. Moving from visual to abstract and becoming very precise too quickly – children can’t help themselves but head straight for the “plug in the numbers to the worked example and off we go” mentality and the deeper understanding is lost. This becomes an even bigger problem, if there isn’t enough variety in the problems presented. I would wholeheartedly agree that children need to practise their maths skills, but when does doing more of the same become pointless?

**Develop teaching sequences from your children**

One potential pitfall that I have found with some textbooks is how they are organised in terms of curriculum coverage, for example with operations being taught completely separately. I don’t want to teach addition on Monday and subtraction on Tuesday as I want to develop children’s understanding of the connectivity between these operations. I certainly don’t want a lesson focused around a bank of addition word-problems because I know my children will just work out that they need to find the numbers in the text and add them together and where is the maths in that?

In fact, I would argue that text book writers are going to find it hard to develop a teaching sequence which best meets the needs of the children we teach, by virtue of the fact that they don’t know them. Teachers know their children: their daily experiences; the topics they are covering this year; their mathematical strengths and areas for development. For me, textbooks are best used therefore to support teachers in seeing how concepts can be developed and the range of experiences and activities which could be used to support pupils in gaining deeper understanding. Fundamentally, I believe that it is not the textbooks that will make the difference, but what we as teachers, do with them.

My thoughts about how to use maths text books effectively:

- Remember to explore concrete, visual and abstract models.
- “Delete the textbook” by using visuals without the labels and numbers so that you can develop a mathematical curiosity and so you can ask questions, generate discussion and engage pupils before adding back in the detail (See Dan Meyer, 2016).
- Use examples selectively, to bring out misconceptions and to offer opportunities for rich reasoning.
- Check that examples do what you want them to do: that there is exposure to “the tricky bits” and they are not just offering more and more and more of the same.
- Make sure all children are getting opportunities to problem solve rather than this being a challenge for the more able or the quick finishers.
- Draw out mathematical connections and get children to make and articulate links between concepts.
- Use examples or activities to develop the sequence of learning that you want.
- Don’t be constrained by the organisation of your text books and use AfL so that you teach what your children need next.

**References:**

Bruner, J. S. (1961), The act of discovery. Harvard Educational Review.

Dan Meyer talk at NCTM annual meeting (April 13-16 2016) San Fransisco. Available from:

Oates, T. (2014) , Why textbooks count – A policy paper, Cambridge Assessment