Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; "Good practice in primary mathematics: evidence from 20 successful schools," was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a "high…

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

During Mathematics Teaching Course-I (MT-I), the author was given the opportunity to teach a primary mathematics class at a Government school in Karachi, Pakistan while on teaching practice. The author was lucky to be able to share the lesson planning with a friend, and they found the sharing of ideas a supportive process. The focus of the lesson…

The authors document their experience of working with 6-year-olds over several weeks. They share some observations that arise from weekly sessions they conducted which have been under way for several years and which have been widely reported. These observations show the payoff of a problem-solving approach to learning.

The publication in June of Sir Peter Williams' review of mathematics teaching in early years' settings and primary schools came at a time when the thoughts of many teachers were turning towards a well-earned summer break. However, the report has attracted much attention and promises a fundamental shake-up of attitudes and approaches to the…

Over the past three years this author has spent a good deal of time in primary classrooms, working with teachers on problem solving approaches to the teaching and learning of mathematics. He has also worked part-time on an initial teacher training course and an NCETM/Yorkshire Forward funded project entitled "Inspiring Mathematics Champions". Thus…

Implications for teachers from Piagetian-oriented piagetian-oriented research on problem solving reported in an article by Eleanor Duckworth are presented. Edward de Bono's Children Solve Problems,'' a collection of examples, is also discussed. (MS)

An anecdote shows why children studying mathematics should be given freedom to explore, generalize, classify, and originate proofs. (RS)

Research done with ten year olds on problem solving, generalization, and proof is outlined. (MK)

Suggestions for teaching problem solving which include the use of general models, variation of illustrations and terminology, and diagrams are illustrated for comparison multiplication word problems. (MN)

Portions of interviews with children who are engaged in a problem solving activity are presented. The problem used is an "eel question" taken from the work of Piaget. The verbal responses of children are seen as a part of effective teaching, and this method of assessment is encouraged. (MP)