Explain this
Functioning Mathematically
How the publisher describes it:
“Functioning Mathematically is a collection of mathematical activities which will help learners to develop the skills and confidence to apply, combine and adapt their mathematical knowledge to new situations in their life and work.”
Review by Piotr Zarzycki
In brief:
I found it an enjoyable read, but I would appeal to the authors to include in a second edition some examples of students’ authentic works while solving the problems. I really look forward to reading how students behave during solving mathematical tasks of such a genre.
“It is possible to teach pupils to think (to function) mathematically”
Functioning Mathematically is a collection of ten groups of activities aimed mainly at students (levels KS3 and KS4) who are interested in mathematics. Each group contains a sequence of problems of various difficulty, variations on the same theme. The authors believe that by solving such problems, as presented in the book, it is possible to teach pupils to think (to function) mathematically. Are they right? Undoubtedly yes. Although there is no precise definition of thinking (functioning) mathematically, we may agree that it means, among other things, an ability to choose a good mathematical representation for a certain problem. The authors idea is to show this process of finding such a representation; a superb example of their idea is the dominoes problem on page 13 and the graph representation for this task.
At a school level mathematics problem-solving skills are crucial. These skills could be divided into two categories; the first category is solving routine school problems (to a certain extent exam tasks) and the second consists of non-routine problems which require some creativity. Teaching students to solve problems of the first category is incomparably easier than those of the second category. So the authors undertake a very difficult task of teaching how to approach to problems of the second mentioned category. Are they successful? Definitely yes. The book is therefore a very useful source of nice school mathematical problems; ambitious math teachers could find in the book many examples how to teach their students to function mathematically. The authors help teachers by “Commentaries” part, which is a kind of didaskalia. In reviewing the book, I found it an enjoyable read, but I would appeal to the authors to include in a second edition some examples of students’ authentic works while solving the problems. I really look forward to reading how students behave during solving mathematical tasks of such a genre.
