This paper will provide an informative backdrop for some professional discussion for teachers of mathematics who teach middle years students in their classrooms. It will also attempt to draw out some likely implications of the generic discussion presented for mathematics teaching in the middle years. It also provides some much needed information…

Before primitive man had grasped the concept of number, the written word or even speech, he was able to count. This was important for keeping track of food supplies, sending messages, trading between villages and even keeping track of how many animals were in their herd. Counting was done in various ways, but in all cases, the underlying principle…

Reports the importance of effective classroom management in creating a classroom environment in which teachers could concentrate on instruction. Examplary teachers used a variety of activities and strategies to monitor understanding and enhance learning. Exemplary teachers were characterized by their ability to maintain an environment which…

This paper was written as a discussion guide for participants at an Australian conference. How calculators and computers might affect the curriculum is discussed, with questions focused on what mathematics should be taught, when, why, where, and how. (MNS)

Research reviewed indicated calculator use: (a) significantly improves computational ability with conflicting evidence in other areas; (b) has no significant effects on retention or attitudes towards mathematics; and (c) does help in teaching and learning at all levels with no detrimental effect. Conclusions were drawn in part from examination of…

Notes that problem solving may become the focus of school mathematics to an extent never before experienced. It is felt much more systematic research is needed. Studies which focus on perception and cognitive processing ability are viewed to have potential for producing important results of wide applicability. (MP)

Presented is a review of the research on the benefits of using writing to evaluate students' understanding of mathematics. Results indicate that student writing provides a rich resource for assessing student understanding, can have a direct influence in teachers' instructional practices, and can positively influence student-teacher interaction…

The relationship between mental models used in problem solving and strategies children use when problem solving with manipulative materials are discussed. Teaching strategies for bridging the gap between the two are suggested. (CW)

Discussed is the situation of the ability, participation, and achievement of girls in mathematics in Australia. Reasons for the concern of many educators about this situation are presented. A few research explanations are suggested. (CW)

Research findings concerning student learning difficulties in algebra are discussed. A teaching approach which takes into consideration these findings is suggested. Encouraging students to see patterns and to develop flexibility in their thinking are stressed. (CW)

Historical movements in the development of the use of computers in mathematics education are highlighted. The development of more efficient interfaces between users and machines are discussed. Future trends in this area are identified. (CW)

Discussed is the case for problem solving in mathematics classrooms. The characteristics of "good" questions are identified. The assessment of questions and questioning techniques is considered. (CW)

Described is a study designed to extend a theoretical model of children's progression from a perceptual to an abstract concept of number. The implications of this research for the design of mathematics curricula are discussed. (CW)

The experience of several different female mathematicians in the male domain of mathematics is discussed. The implications of the barriers experienced by these mathematicians for girls in mathematics are discussed. (CW)