Al Jupri

Using the Van Hiele theory to analyze primary school teachers' written work on geometrical proof problems

The lack of ability of primary school teachers in deductive thinking, such as doing geometrical proof, is an indispensable issue to be dealt with. In this paper, we report on results of a three-step of the field document study. The study was part of a pilot study for improving deductive thinking ability of primary school teachers. First, we designed geometrical proof problems adapted from literature. Second, we administered an individual written test involving nine master students of primary education program, in which they are having experiences as primary school mathematics teachers. Finally, we analyzed the written work from the view of the Van Hiele theory. The results revealed that even if about the half of the teachers show ability in doing formal proof, still the rest provides inappropriate proving. For further investigation, we wonder whether primary school teachers would show better deductive thinking if the teaching of geometry is designed in a systematic and appropriate manner according to the Van Hiele theory.

From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems – considered as tasks inviting the use of problem solving and reasoning skills – theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instan...

Investigating Primary School Mathematics Teachers’ Deductive Reasoning Ability through Varignon’s Theorem

The responsibility to promote the growth of deductive reasoning ability of school students through learning mathematics is in the hand of mathematics teachers and particularly primary school mathematics teachers. However, how we can make sure whether teachers are able to do so. To investigate this issue, we conducted a three-step of an exploratory survey study. First, we designed tasks from the Varignons theorem. Second, we administered an individual written test involving twenty master students of primary education program, in which they are prospective of and primary school mathematics teachers. Finally, we address the results in the light of Van Hiele theory. The results showed that participated students lack of deductive reasoning ability in the context of geometry. For further research, we wonder whether the designed tasks are also applicable to assess student deductive reasoning ability if the students have acquired appropriate teaching.

Learning algebra on screen and on paper: The effect of using a digital tool on students’ understanding

The use of digital tools in algebra education is expected to not only contribute to master skill, but also to acquire conceptual understanding. The question is how digital tools affect students’ thinking and understanding. This paper presents an analysis of data of one group of three grade seventh students (12-13 year-old) on the use of a digital tool for algebra, the Cover-up applet for solving equations in particular. This case study was part of a larger teaching experiment on initial algebra enriched with digital technology which aimed to improve students’ conceptual understanding and skills in solving equations in one variable. The qualitative analysis of a video observation, digital and written work showed that the use of the applet affects student thinking in terms of strategies used by students while dealing with the equations. We conclude that the effects of the use of the digital tool can be traced from student problem solving strategies on paper-and-pencil environment which are similar to strategies while working with the digital tool. In future research, we recommend to use specific theoretical lenses, such as the theory of instrumental genesis and the ontosemiotic approach, to reveal more explicit relationships between students’ conceptual understanding and the use of a digital tool.