Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors

Abstract

The main purpose of this study is to explore the extent to which 11 selected mathematics tutors facilitate the teaching and learning of geometry at the van Hiele Levels 1, 2, 3 and 4 at the college of education level in Ghana. The van Hiele theory of geometric thinking was used to explore the type of teaching strategies employed by the mathematics tutors. The theory served as a guideline from which classroom observation protocol was developed. Results indicated that the tutors exhibit a good conceptual understanding in facilitating the teaching and learning of geometry that is consistent with van Hiele Levels 1 and 2. However, much of the geometry teaching and learning strategies of the mathematics tutors were not structured in a way that support the development of geometric thinking as described in van Hiele Levels 3 and 4. Implications for the involvement of college mathematics tutors in utilizing the van Hiele framework were discussed.

A Van Hiele Theory analysis for teaching volume of three-dimensional geometric shapes

“…A number of studies show that most teachers are not fully prepared to teach geometry, in particular, 2D and 3D shapes (Luneta, 2014;Robichaux-Davis & Guarino, 2016;Armah & Kissi, 2019). This is indicative in their subject matter knowledge in geometry and the pedagogical content knowledge which is mostly below the requirements of the curriculum for the students they are supposed to teach.…”

“…It is used in our daily lives by architects, engineers, physicists, land surveyors, and many more professions (Russell, 2014). http://journals.ums.ac.id/index.php/jramathedu Because of its importance, a number of research studies have been conducted in either investigating the teachers' geometric pedagogical content knowledge, their subject matter knowledge, and the impact of instruction on students' understanding by using Van Hiele theory of geometric thought (Abu & Abidin, 2013;Luneta, 2014;Alex & Mammen, 2016;Robichaux-Davis & Guarino, 2016;Armah et al,2018;Armah & Kissi, 2019). Luneta (2014) investigated student teachers' conceptual knowledge of some basic geometric shapes(polygons, polyhedrons, and their properties) through tests and interviews.…”

“…Abu and Abidin (2013), Alex and Mammen (2016), Armah et al (2018), and Connolly (2010) studied the impact of Van Hiele based instruction on students' understanding of geometry by giving the students both the pre-test and post-test to find out how the teaching based on the Van Hiele theory impacted their learning. Armah and Kissi (2019) and Robichaux-Davis and Guarino (2016) investigated teachers' geometric pedagogical content knowledge. Armah and Kissi made some classroom observations while Robichaux-Davis and Guarino gave the teachers some test items to respond to.…”

“…The type of questions in the form of interviews that were posed to the teacher after instruction enabled the teacher to reflect more on areas of improvement in teaching. Such discussions were beneficial as they within the framework of the theory that has proved to be useful in teaching geometry (Abu & Abidin, 2013;Armah et al, 2018;Armah & Kissi, 2019, Atebe & Schäfer, 2011.…”

Measuring Spatial Ability and Geometric Thinking Level of Prospective Elementary School Teachers Using the Rasch Model

“…It is learned from the primary to higher education level. In several countries like Ghana (Akayuure et al, 2016;Armah & Kissi, 2019), United States (Bergstrom & Zhang, 2016), Malaysia (Mdyunus & Hock, 2019), and Indonesia (Prayitno, Suryadi, & Mulyana, 2019;Syamsuddin, 2019), geometry learning is essential as it is related to other disciplines. In addition to its importance, geometry is internationally acclaimed as difficult, seen from the many students who faced problems.…”