The International Academy of Education (IAE) is a not-for-profit scientific association that promotes educational research,its dissemination , and the implementation of its implications. Founded in 1986, the Academy is dedicated to strengthening the contributions of research, solving critical educational problems throughout the world, and providing better communication among policy makers, researchers and practitioners. The seat of the Academy is at the Royal Academy of Science, Literature and Arts in Brussels, Belgium, and its coordinating centre is at The general aim of the IAE is to foster scholarly excellence in all fields of education. Towards this end, the Academy provides timely syntheses of research-based evidence of international importance. The Academy also provides critiques of research, its evidentiary basis, and its application to policy. The current members of the Board of Directors of the Academy are: 3 Preface This booklet has been adapted for inclusion in the Educational Practices Series developed by the International Academy of Education (IAE) and distributed by the International Bureau of Education (IBE) and the Academy. As part of its mission, the Academy provides timely syntheses of research on educational topics of international importance. This booklet is the fourth in the series on educational practices that generally improve learning. The material was originally prepared for the Handbook of research on improving student achievement, edited by Gordon Cawelti and published in a second edition in 1999 by the Educational Research Service (ERS). The Handbook, which also includes chapters on subjects such as generic practices and science , is available from ERS (and website:www.ers.org). ERS is a not-for-profit research foundation serving the research and information needs of educational leaders and the public. As Vice-President of the Academy and editor of the present series, I thank ERS officials for allowing the IAE and the IBE to make available the material adapted from the Handbook to educators around the world. mathematics teaching and learning (Macmillan,1992) and has a large number of other publications on research in mathematics education to his credit. He has made invited research pre-and the United Kingdom. He has directed several research projects for the National Science Foundation (NSF) and other agencies in the areas of mathematical problem-solving and classroom teaching practices. His current NSF work involves mathematics and technology. He received his Ph.D. The second author, Kristin J. Cebulla, is a mathematics education doctoral student at the University of Iowa.She previously taught middle-school mathematics. Before teaching, she worked …

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Improving student achievement in mathematics

Prompted by ongoing concerns over standards of numeracy, eight mathematics teachers from four secondary schools in south Wales formed a teacher inquiry group to research the impact of introducing whole-class interactive teaching strategies into their own practice. Possible teaching approaches and activities were developed and agreed during group meetings. These were trialled by the teachers during their normal mathematics lessons. Lesson observations, interviews with teachers and discussions at the group meetings, however, indicated that the implementation of the approaches varied significantly across teachers. This paper analyses the variation in interpretations and teaching styles, and discusses their impact on the quality of the classroom discourse. The determining features discerned within the classroom dialogue included the extent to which pupils were encouraged to reflect on their mathematical knowledge, and the ways in which teachers were able to scaffold pupils' learning.

Teachers' Interpretations of Effective Whole-class Interactive Teaching in Secondary Mathematics Classrooms

The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification.

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Visualisation and proof: a brief survey of philosophical perspectives

In this chapter we propose re-conceptualizing the field of mathematics education research as that of a design science akin to engineering and other emerging interdisciplinary fields which involve the interaction of “subjects”, conceptual systems and technology influenced by social constraints and affordances. Numerous examples from the history and philosophy of science and mathematics and ongoing findings of M&M research are drawn to illustrate our notion of mathematics education research as a design science. Our ideas are intended as a framework and do not constitute a “grand” theory. That is, we provide a framework (a system of thinking together with accompanying concepts, language, methodologies, tools, and so on) that provides structure to help mathematics education researchers develop both models and theories, which encourage diversity and emphasize Darwinian processes such as: (a) selection (rigorous testing), (b) communication (so that productive ways of thinking spread throughout relevant communities), and (c) accumulation (so that productive ways of thinking are not lost and get integrated into future developments).

https://hs.umt.edu/math/research/technical-reports/documents/2010/08_Sriraman.pdf

Re-conceptualizing Mathematics Education as a Design Science

This paper presents a non-experimental, exploratory and descriptive study of learners and educators from seven Soshanguve secondary schools in order to learn more about factors that possibly contribute to lack of success in mathematics and physical sciences in the 11th grade. The paper focuses primarily on the learners’ and educators’ perceptions of why learners perform badly in Grade 11 and 12 mathematics and physical science. The methodology used includes data collected through unstructured interviews and the use of matric results made available by the Department of Education. The following categories of factors contributing to poor performance of learners in mathematics and physical science were identified: laboratory apparatus, teacher's content knowledge, time management, parents’ commitment to children's education, motivation and interest and teaching strategies.

Factors associated with poor performance of learners in mathematics and physical science in secondary schools in Soshanguve, South Africa

Didactics of mathematics as a scientific discipline

Une approche heuristique de l'analyse.

Vers l'infini pas à pas : approche heuristique de l'analyse (AHA) - Notions pour élèves

Vers l'infini pas à pas : approche heuristique de l'analyse (AHA) - Guide méthodologique

Plane representations as a guideline for the teaching of geometry. Learning space geometry rests on plane representations of solids, whereas realizing such representations relies on some notions of geometry. That is why these representations have a substantial and constant relation to geometry. They range from children's drawings to orthogonal and parallel projections, and to linear perspective, that is from naive perceptions to more and more advanced and complex representations. For such reasons, they constitute an interesting guideline for geometry learning. The workshop will illustrate this point of view by a sequence of questions appropriate to geometry learning from early childhood to adulthood. Resume. D'une part, l'etude de la geometrie de l'espace s'appuie sur des representations planes de solides, et d'autre part on ne realise de telles representations qu'en s'appuyant sur des notions de geometrie. Ainsi, ces representations entretiennent avec la geometrie un lien substantiel et constant. Elles vont des dessins d'enfants a la perspective centrale, en passant par les projections orthogonales et paralleles, c'est-a-dire du dessin naif vers des formes de projection de plus en plus evoluees et complexes. Pour ces diverses raisons, elles constituent un fil conducteur interessant pour l'apprentissage de la geometrie. Dans cet atelier, nous illustrerons ce point de vue par quelques questions jalonnant l'enseignement de la prime enfance a l'âge adulte. Mots-cles. Geometrie, representations planes, ombres, projections, perspectives, enseignement maternel, primaire et secondaire.

Christiane Hauchart

Papers

Didactics of mathematics as a scientific discipline

Une approche heuristique de l'analyse.

Vers l'infini pas à pas : approche heuristique de l'analyse (AHA) - Notions pour élèves

Vers l'infini pas à pas : approche heuristique de l'analyse (AHA) - Guide méthodologique

Les représentations planes comme un fil conducteur pour l'enseignement de la géométrie