Maxim Bruckheimer

Bio: Maxim Bruckheimer is an academic researcher from Weizmann Institute of Science. The author has contributed to research in topics: Primary education & Education. The author has an hindex of 7, co-authored 21 publications receiving 142 citations.

A model of the function concept in a three-fold representation

Abstract: The present paper describes an attempt to alleviate some of the difficulties and misconceptions about the concept of function, by integrating a computer implemented learning environment with specifically designed activities in a curriculum covering functions This curriculum-the TRM curriculum integrates open-ended activities with a “conventional” approach to the concept of function, and “computer” sessions with normal classroom activities Typical problems and comments on student activities are given Comparative investigations led to a cognitive classification of functional reasoning Some practical issues arising from teaching about functions and pedagogical engineering are described at the end of the paper

Farey series and pick’s area theorem

Abstract: In this article, we compare the historical notes and references in wel l -known texts with what wou ld seem to be the reality as exhibited by the original sources, in the case of Farey series, Pick's area theorem, and the connection between them. Although one might suppose that we have chosen a particularly "unfor tunate" example, in which the historical notes and texts are a lmost totally misleading, it is our experience in prepar ing historical activities for the classroom that, more often than not, the information readily available to nonprofessional historians is unreliable. There are signs that history is playing a greater role in the mathematics classroom, and there is a need for readily available reliable historical information relevant to the school curriculum. Errors in printed histories are relatively costly to correct, and the significance of the error relative to the whole justifies neither the expense nor the effort, and, thus, the errors achieve more or less pe rmanent status. Perhaps in these days of flexible electronic data handling and storage, some historians will devise an electronic historical retrieval system, to which corrections and additions can be made as they are d i s c o v e r e d a sort of electronic Tropfke [1].

A Herrick Among Mathematicians or Dynamic Geometry as an Aid to Proof

Abstract: This column will publish short (from just a few lines to a couple of pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain teasers involving the use of computers or computational theory. Snapshots are subject to peer review. This issue’s snapshot presents a proof of a beautiful but not commonly known theorem in Euclidean geometry. The nuggets needed for the proof of Morley’s theorem can be dug up through systematic exploration with dynamic geometry software. These empirically excavated nuggets can then be assembled into a deductive proof. The authors reflect on how such exploratory computational environments can generate more powerful interplay between empirical explorations and formal proofs.

The role of visual representations in the learning of mathematics.

Abstract: Visualization, as both the product and the process of creation, interpretation and reflection upon pictures and images, is gaining increased visibility in mathematics and mathematics education This paper is an attempt to define visualization and to analyze, exemplify and reflect upon the many different and rich roles it can and should play in the learning and the doing of mathematics At the same time, the limitations and possible sources of difficulties visualization may pose for students and teachers are considered

The gains and the pitfalls of reification — The case of algebra

Abstract: Algebraic symbols do not speak for themselves. What one actually sees in them depends on the requirements of the problem to which they are applied. Not less important, it depends on what one is able to perceive and prepared to notice. It is this last statement which becomes the leading theme of this article. The main focus is on the versatility and adaptability of student’s algebraic knowledge

Integrating history of mathematics in the classroom: an analytic survey

Abstract: An analytical survey of how history of mathematics has been and can be integrated into the mathematics classroom provides a range of models for teachers and mathematics educators to use or adapt.