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A Van Hiele Theory analysis for teaching volume of three-dimensional geometric shapes Moru, Eunice Kolitsoe; Malebanye, Maqoni; Morobe, Nomusic; George, Mosotho Joseph
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 6 Issue 1 January 2021
Publisher : Department of Mathematics Education, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v6i1.11744

Geometry is among the cornerstones of mathematics because of its applicability in real life and its connection to other areas of mathematics. The reported study explored how the volume of 3D geometric shapes was taught in one high school in Lesotho. One male teacher and an intact class of sixty high school students were the participants of the study. The study was exploratory in nature. This was in order to understand the phenomenon under study so as to suggest ways on how to make some improvements for the future. Data were collected through classroom observations, photo shootings, note-taking, and interviews. Classroom observations enabled the researchers to start the analysis while also observing. The photos taken captured the nature of the tasks given to students, some explanations, and class interactions. The Van Hiele theory of geometric thought was used as the framework of analysis. The findings of the study show that at level 1, the teacher focused mainly on the vocabulary of the concept at hand, the information phase. Another phase which was dominant in the teaching at the same level is the direct orientation. The free-orientation phase was not fully realized. The analysis level was achieved through the information phase and the direct orientation phase. Thus the progression from one level to another by students occurred having some phases of learning being skipped due to the way the instruction was organized. It is postulated that lack of proper understanding of some concepts in geometry by students may result from this kind of instruction.

INVESTIGATING SOCIAL SCIENCE STUDENTS’ UNDERSTANDING OF LIMITS THROUGH THE LENS OF THE PROCEPT THEORY Moru, Eunice Kolitsoe; Essien, Anthony A
JOHME: Journal of Holistic Mathematics Education Vol 7, No 1 (2023): JUNE
Publisher : Universitas Pelita Harapan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19166/johme.v7i1.5900

The idea of limit is central to both differential and integral calculus. It is also applicable in other disciplines such as physics, engineering, economics, etc. Because of this, conducting a study to further improve teachers’ knowledge about how social science students (whose major is economics) understand limits is of utmost importance. The reported study sought to find out how students understand the idea of limit with regard to the use of its symbolism. Sixty first year university students in the social sciences acted as the sample of the study. An adapted procept theory was used to analyse data obtained from these students through their solution to tasks on limit and explanations on their thinking and solution processes. Qualitative analysis of data indicated that some students understood the limit symbolism to be a procept while others did not. When solving the mathematical tasks, students’ difficulties emanated from: (i) their inability to coordinate the two processes, and , or and (ii) the proper use of the limit operator, and (iii) inability to realise that the simplification has led to the same response as they could not see the relationship between the results. This resulted in misalignment between their reasoning and their choice of answers where justification was required. The results also show that limits at infinity were more problematic than those of the form as where a is a constant. Students’ choice of method used depended mostly on how much efficient the method was in terms of saving time and not really on promoting understanding. The lesson learnt from the study is that when using the adjusted procept theory, the yes or no answers do not qualify to be used in concluding the level of thinking at which students are at. It is recommended that students be asked to show their working and also explain their answers so that the type of understanding that leads to their choices come to fore

A Van Hiele Theory analysis for teaching volume of threedimensional geometric shapes Moru, Eunice Kolitsoe; Malebanye, Maqoni; Morobe, Nomusic; George, Mosotho Joseph
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 6 Issue 1 January 2021
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v6i1.11744

Geometry is among the cornerstones of mathematics because of its applicability in real life and its connection to other areas of mathematics. The reported study explored how the volume of 3D geometric shapes was taught in one high school in Lesotho. One male teacher and an intact class of sixty high school students were the participants of the study. The study was exploratory in nature. This was in order to understand the phenomenon under study so as to suggest ways on how to make some improvements for the future. Data were collected through classroom observations, photo shootings, note-taking, and interviews. Classroom observations enabled the researchers to start the analysis while also observing. The photos taken captured the nature of the tasks given to students, some explanations, and class interactions. The Van Hiele theory of geometric thought was used as the framework of analysis. The findings of the study show that at level 1, the teacher focused mainly on the vocabulary of the concept at hand, the information phase. Another phase which was dominant in the teaching at the same level is the direct orientation. The free-orientation phase was not fully realized. The analysis level was achieved through the information phase and the direct orientation phase. Thus the progression from one level to another by students occurred having some phases of learning being skipped due to the way the instruction was organized. It is postulated that lack of proper understanding of some concepts in geometry by students may result from this kind of instruction.

A constructivist analysis of Grade 8 learners’ errors and misconceptions in simplifying mathematical algebraic expressions Moru, Eunice Kolitsoe; Mathunya, Motlatsi
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 7 Issue 3 July 2022
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v7i3.16784

Algebra is an important branch of mathematics which applies to many fields related to mathematics. However, many studies show algebra as posing problems even to the most gifted students. This phenomenon, therefore, necessitates more studies to be conducted in this area. As such, the study explored the types of errors that Grade 8 learners committed in simplifying algebraic expressions and the misconceptions that might have given rise to such errors. Ninety-five Grade 8 learners were selected as the subjects of the study at one high school in Lesotho. Within the framework of the Qualitative case study design, the study used tasks and interviews for data collection. The thematic approach to data analysis within the framework of the constructivist theory was adopted. The study identified most errors committed by the learners as persistent. Overgeneralizing the rules of prior knowledge to new knowledge, particularly in different contexts, was the most frequent cause of the errors. In addition to this was the misunderstanding and misinterpretation of correct meanings in the given context. Some of the identified errors overlapped with those in the reviewed literature while others did not.

INVESTIGATING SOCIAL SCIENCE STUDENTS’ UNDERSTANDING OF LIMITS THROUGH THE LENS OF THE PROCEPT THEORY Moru, Eunice Kolitsoe; Essien, Anthony A
JOHME: Journal of Holistic Mathematics Education Vol. 7 No. 1 (2023): JUNE
Publisher : Universitas Pelita Harapan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19166/johme.v7i1.5900

The idea of limit is central to both differential and integral calculus. It is also applicable in other disciplines such as physics, engineering, economics, etc. Because of this, conducting a study to further improve teachers’ knowledge about how social science students (whose major is economics) understand limits is of utmost importance. The reported study sought to find out how students understand the idea of limit with regard to the use of its symbolism. Sixty first year university students in the social sciences acted as the sample of the study. An adapted procept theory was used to analyse data obtained from these students through their solution to tasks on limit and explanations on their thinking and solution processes. Qualitative analysis of data indicated that some students understood the limit symbolism to be a procept while others did not. When solving the mathematical tasks, students’ difficulties emanated from: (i) their inability to coordinate the two processes, and , or and (ii) the proper use of the limit operator, and (iii) inability to realise that the simplification has led to the same response as they could not see the relationship between the results. This resulted in misalignment between their reasoning and their choice of answers where justification was required. The results also show that limits at infinity were more problematic than those of the form as where a is a constant. Students’ choice of method used depended mostly on how much efficient the method was in terms of saving time and not really on promoting understanding. The lesson learnt from the study is that when using the adjusted procept theory, the yes or no answers do not qualify to be used in concluding the level of thinking at which students are at. It is recommended that students be asked to show their working and also explain their answers so that the type of understanding that leads to their choices come to fore

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