To develop the ability of teacher students to reason mathematically

The aim of the project The project aims at developing the ability of teacher students to reason mathematically and to understand pupils' reasoning in mathematics. The problem in focus For a teacher to be able to talk to pupils in a way that suits the learning of the individual pupil she has a need to be capable of expressing herself in many different ways and to give arguments and to reason in such a way that the pupil understands. This aim is rarely reached by the ways teacher courses are structured today. A stronger focus on mathematical reasoning and communication is necessary. What is the ability to reason mathematically? Mathematics as a science is characterised among other things by the method to work with deductions and proofs which means that starting from certain given conditions you can with full certainty prove propositions and theorems. To be able to follow and develop such ways of thinking and arguing you have to develop your own ability to reason mathematically. In the school curriculum deductions and proofs have been given new importance. It is necessary for the teacher to have developed her own ability to reason mathematically in order to be able to work with the pupils to reach the aims of the curriculum in this area. The teacher must in conversations with the pupils be flexible and be able to understand different ways of thinking and reasoning. This makes it necessary for the teacher to be able to reason, to follow multiple ways of thinking, and to compare them and to value how viable they are. What do we mean by ability to reason mathematically? A good ability to reason mathematically means that you can reformulate questions and propositions in different ways, make and test conjectures, reject them or verify them, formulate counterexamples, specialise, generalise, draw conclusions, find alternative ways when you are stuck, decide if a solution is reasonable and judge the validity of arguments, describe, explain, and convince others about your arguments and to prove your claims. Mason, Burton and Stacey (1982) have demonstrated how to encourage, develop and foster the processes mentioned above, which seem to come naturally to mathematicians. They suggest a method of working that is highly practical by starting from exemplary questions and problems and involving the learner in the discussions. In this way a deeper awareness of the nature of mathematical thinking and reasoning can grow. Methods We want to take a departure in research results from mathematics education and offer the student teachers opportunities to develop their own ability to reason mathematically in a more conscious way. We want to develop the mathematics parts of the courses. Instead of starting in a traditional way by presenting the theory and then continuing with problem solving exercising the application of the theory, we want to start with open or exploratory problem solving that give the students an experiential background for the introduction of theoretical concepts. The work will be done in small groups and the focus on reporting the work will be on presenting their findings and on convincing others about the reasonableness of the conclusions they have drawn. To work with different pieces of mathematical argument, both from former teacher students and pupils, will be another type of task. Alongside they will work with a selected number of more conventional mathematical problems, but be stimulated to continue to use the group as a resource, discussing different difficulties and explaining to each other different ways of solving the problems. Comparing and valuing the viability of alternative solutions is vital here. We will construct open problems and exercises that foster reasoning and try them out in group-work with student teachers. After evaluation and reconstruction if necessary the problems will be used in future mathematics teacher training courses

Prospective mathematics teachers’ self-referential metaphors as indicators of the emerging professional identity

Ideals play a key role in a student teachers’ identity work. They form targets to strive for and a mirror for reflection. In this paper, we examine Finnish mathematics student teachers’ metaphors for the teacher’s role (N= 188). We classified the metaphors according to a model that identified teachers as subject matter experts, didactical experts, and pedagogical experts, with the addition of another two categories, self-referential and contextual. For the exploration of emerging professional identities, we studied the self-referential metaphors, which formed the most common category in the data. We observed that every third metaphor described either student teachers’ personalities or their incompleteness as teachers, or new beginnings or eras. Although these aspects were expected, they also inform us as teacher educators of the values and ideals that student teachers have in terms of teaching and being a teacher. The metaphors that mathematics student teachers produced illustrated their identity processes and their emerging identity as a mathematics teacher.Peer reviewe

Multiculturalism, Migration, Mathematics Education and Language - Teachers' Needs and Teaching Materials

The multicultural nature of modern society constitutes one of the most significant changes to have influenced schools in many European countries, especially at primary and middle school level. The teacher’s job is all the more difficult because he/she is usually not sufficiently prepared to deal with the new classroom context with pupils having a migrant background, coming from countries with different cultures and different languages. The teacher is seldom aware of the need to rethink and if necessary modify his/her methodological and pedagogical approach. This attitude is even more evident in maths teachers who often consider their subject universal and culture-free. Little has been done in Europe as far as maths teaching in multicultural contexts is concerned. The different languages and cultures present in the classroom make the teaching/learning process even more arduous than it already is, especially for pupils from minority cultures and/or with a migrant background or for Roma pupils. This project envisages the design and piloting of materials for both the initial and in-service training of middle school maths teachers who constitute the project’s primary target group. The secondary target group is their pupils, in particular those from other cultures. The materials have been produced after careful analysis of the video recordings of teaching activities. Their focus was also on the role of language in the communication of mathematical concepts and their aim was to stimulate the maths teacher’s awareness of the need to find a satisfactory balance between mathematical language and classroom language, especially when dealing with pupils with a different culture and language. The project’s training proposals aimed at promoting maths teaching strategies which are relevant to activities and problems taken from everyday life including that of different cultures in order to highlight their positive aspects

Varför och hur revideras kursplanerna för gymnasieskolan?

Skolverket har i uppdrag att kontinuerligt se över kursplanerna. Hösten 1997 började därför ett arbete med fem av programmen, bl a NV-programmet. Det innebär att alla fem kurserna A–E är berörda

Matematik och media

Hur framträder matematiken i medier och reklam? Vilket matematikinnehåll finns där? Är informationen vinklad med matematikens hjälp? Vilken matematik behövs för att man ska kunna använda informationen på ett rimligt sätt? Hur ska mottagaren vara rustad för att kunna tolka och bedöma det som presenteras

Om du hade 100 miljoner ...

NCM har fått ett regeringsuppdrag att i samarbete med Statens skolverk och Högskoleverket ”utarbeta förslag till innehåll i kompetensutvecklingsprogram för matematik och matematikdidaktik för lärare”. Matematikbiennalen 2000 avslutades med synpunkter från en panel på vad som bör prioriteras och varför? Här följer ett referat av inläggen

Om du hade 100 miljoner ...

NCM har fått ett regeringsuppdrag att i samarbete med Statens skolverk och Högskoleverket ”utarbeta förslag till innehåll i kompetensutvecklingsprogram för matematik och matematikdidaktik för lärare”. Matematikbiennalen 2000 avslutades med synpunkter från en panel på vad som bör prioriteras och varför? Här följer ett referat av inläggen

Recent Nordic research in mathematics education illustrated by examples from NORMA17

A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers, teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed