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The primary purpose of this study is to determine the geometric habits of mind of classroom teacher candidates and the level of these habits. The study was conducted with 55 elementary education program students studying at an education faculty in the 2017-2018 spring term. The criterion used in the determination of the study group is that the teacher candidates should have knowledge about almost all the courses in the classroom education program and have taken courses I and II in mathematics teaching. Three worksheets were distributed to the teacher candidates as a data collection tool. Since the research is like a case study, the mathematical ideas developed by the teacher candidates about quadrilaterals and their written answers were summarized and interpreted according to the predetermined themes. When the findings obtained as a result of the research are examined in general, it can be said that teacher candidates are not sufficient in finding relationships between quadrilaterals, generalizing the relationships they find by using strategies, associating the feature valid for a quadrilateral with quadrilaterals that may have that feature, namely the whole, and making judgments. [ABSTRACT FROM AUTHOR]

This article presents preliminary analysis of a test item in a large-scale study design to promote the development of geometric reasoning progression. Two sets of data were analysed to validate the item designed to assess secondary school students' knowledge of a rectangle. The first data set involved 155 Year 4–10 students from seven trial schools across social strata. The second data set involved 585 Year 7–10 students from eleven project schools situated in lower socio-economic areas. The aim was to audit Australian students' knowledge of hierarchy of shapes and document the process of validating a test item. The findings indicated that an iterative process of design, test and redesign, incorporating Sfard's mathematical discourse framework and a multi-stage Rasch analysis, is vital in validating the results. A distinct change in students' reasoning about rectangle is observed and this is not due to age. Moreover, Rasch analysis identified eight distinct thinking zones to assist in mapping out a learning progression for developing geometric reasoning. [ABSTRACT FROM AUTHOR]

Abstract: The Isis problem, which has a link with the Isis cult of ancient Egypt, asks: “Find which rectangles with sides of integral length (in some unit) have area and perimeter (numerically) equal, and prove the result.” Since the solution requires minimal technical mathematics, the problem is accessible to a wide range of students. Further, it is notable for the variety of proofs (empirically grounded, algebraic, geometrical) using different forms of argument, and their associated representations, and it provides an instrument for probing students’ ideas about proof, and the interplay between routine and adaptive expertise. A group of 39 Flemish pre-service mathematics teachers was confronted with the Isis problem. More specifically, we first asked them to solve the problem and to look for more than one solution. Second, we invited them to study five given contrasting proofs and to rank these proofs from best to worst. The results highlight a preference of many students for algebraic proofs as well as their rejection of experimentation. The potential of the problem as a teaching tool is outlined. [Copyright &y& Elsevier]

This article presents information on geometrical problems as give in the section "Media Clips" of the September 1, 2004 issue of the "Mathematics Teacher." The "Media Clips" offers the readers contemporary, authentic applications of quantitative reasoning that are based on print and electronic media. Here the problems are related to rectangles, ratios, diagonals etc.

In this article, the author, professor at College of Saint Scholastica in Duluth, Minnesota, discusses a Pythagorian theorem for a clipped rectangle. He mentions a clipped rectangle, where one corner has been removed to form a fifth side. He also represents d and e as lengths of two diagonals, which are nearest to the fifth side c. He also presents the theorem in the form of a numerical equation.

This article presents information on the solutions to geometrical problems as give in the section "Media Clips" of the September 1, 2004 issue of the "Mathematics Teacher." The "Media Clips" offers the readers contemporary, authentic applications of quantitative reasoning that are based on print and electronic media. Here the problems are related to rectangles, ratios, diagonals etc.