## Posts Tagged ‘Recommended Reading’

This reading discusses how an average student can benefit from a structured and ordered approach to the teaching of fractions. It could probably be applied to any mathematics topic.

The approach taken was one of understanding the needs of the child first and having an in depth idea of where her weaknesses were. There was a strong focus on the language of fractions – this relates to some of the findings I wrote about yesterday. Fractions are a relative part of maths and their outcome depends entirely on whatever the whole is.

However, we initially observed Audrey having problems in comparing the equivalent fractions 1/3 and 2/6. We therefore used the fraction-lift to clarify equivalent fractions, by making them fractions living at the same floor of the fraction-building and by introducing the metaphor of “roommates” for fractions at the same position on the number line. We now observed how Audrey used the strategy of doubling both the numerator and the denominator to generate equivalent fractions, for example by replacing 2/3 by 4/6 to compare the latter fraction with 5/6.

This gives Audrey a hook to hang her ideas on, something concrete that she can build her learning on. I’m convinced that children need to have the basics of any topic before moving on. I also think that the current approach we have to teaching in this country, based on the current Mathematics Framework, is far too fleeting and jumpy. As practitioners, I feel we need to consider the needs of our children – group parts of topics together so that they have more time to practise and consolidate their learning.

**Link (the full article)**: Ronald Keijzer and Jan Terwel: Audrey’s Acquisition Of Fractions: A Case Study Into The Learning Of Formal Mathematics.

After Study Block 1, taught session 2, we were given a reading to look through and digest.

We were given Chapter 5 (pp. 79-104) from **“Children’s mathematics 4-15: learning from errors and misconceptions”** by Julie Ryan, Julian Williams. *(McGraw-Hill International, 2007)*

The mistakes children make in mathematics are usually not just ‘mistakes’ – they are often intelligent generalizations from previous learning. Following several decades of academic study of such mistakes, the phrase ‘errors and misconceptions’ has recently entered the vocabulary of mathematics teacher education and has become prominent in the curriculum for initial teacher education.

The popular view of children’s errors and misconceptions is that they should be corrected as soon as possible. The authors contest this, perceiving them as potential windows into children’s mathematics. Errors may diagnose significant ways of thinking and stages in learning that highlight important opportunities for new learning.

This book uses extensive, original data from the authors’ own research on children’s performance, errors and misconceptions across the mathematics curriculum. It progressively develops concepts for teachers to use in organizing their understanding and knowledge of children’s mathematics, offers practical guidance for classroom teaching and concludes with theoretical accounts of learning and teaching.

Children’s Mathematics 4-15 is a groundbreaking book, which transforms research on diagnostic errors into knowledge for teaching, teacher education and research on teaching. It is essential reading for teachers, students on undergraduate teacher training courses and graduate and PGCE mathematics teacher trainees, as well as teacher educators and researchers.

Anyway, I found an online version of the text via Google Books, which is embedded below. However, pages 82, 83, 87, 88, 94, 95, 101 and 102 are not included in the preview due to copyright reasons. Although the content that is there gives a reasonable account of the subject and includes many examples of good practice. Clearly, the lack of the full chapter really doesn’t help!