Abstract:

In 1985 it was shown by Hestenes and Hallouin [1] that the majority of college students were able to state Newton‘s third Law at the beginning of their introductory Physics courses, but not many of them fully understood it at the end of their courses. In fact, the courses changed practically nothing regarding students’ input and misconceptions about Newtonian mechanics. That made Eric Mazur, professor of physics at Harvard University, completely change his teaching approach. He abandoned classic lectures and came up with his own peer instruction strategy [2].
Peer instruction is an active learning method in which effectiveness is based primarily on group discussions that were raised by the conceptual question of the so-called ConcepTest [3]. Discussions over ConcepTests allow students to engage with one another, to teach with one another and to engage with their questions at hand. Students who understand the discussed concept know how to overcome the difficulties and speak the same language as their peers, and therefore they are more likely to help one another than the instructor [2]. Although peer instruction is one of the most surveyed teaching methods so far [4], not many studies have focused on its implementation in mathematics or in elementary school education.
The goal of our study is therefore to find answers for the following questions:
a) Is it possible to fulfil the premises of peer instruction in mathematics at lower secondary school levels (e. g. sufficient social skills to maintain fruitful group discussions)?
b) Are there similar outcomes that were promised by research studies of this method in physics or university level education (e. g. deepening of conceptual understanding, improvement of attitudes towards mathematics, etc.)??
In order to find the answers, action research has taken place since the beginning of the previous 2018/2019 school year, with a single class of thirty 8th grade participants (now 9th grade) at a Czech grammar school. The key was to compare the class with itself before and after the implementation of peer instruction, and to compare their results with global datasets (Programme for International Student Assessment (PISA), Trends in International Mathematics and Science Study (TIMSS), etc.). We used tests and questionnaires to discover pupils' attitudes toward mathematics, and their motivational structures and understanding of mathematical concepts. In the spirit of action research, several pupils were selected to form a reflexive group which met up monthly since the beginning of the study. The objective of the reflexive group was to suggest the appropriate improvements to simplify peer instruction implementation in lower secondary school mathematics, and to discuss over continuous results of the research itself.
We found that there is a relationship between normalized learning gains (introduced by Richard R. Hake in 1998 [5]) obtained by individuals and their typical role in ConcepTest group discussions. This particular result can be found in this article together with examples of several tasks from the test that were designed to measure pupils' pre/post-understanding of geometric concepts and their pre/post-argumentation skills.

Keywords:

Peer instruction, mathematical concepts, normalized learning gains, geometric concepts.