After a long six-year lapse, the Curriculum and Assessment Policy Statement introduced in 2012 included geometry as part of the South African Grade 12 Mathematics Paper 2. The first cohort of matriculation students wrote Paper 2 in 2014. This article reports on the understanding of geometry terminology with which a group of 154 first-year mathematics education students entered a rural South African university in 2015; 126 volunteered to be part of the study. Responses to a 60-item multiple-choice questionnaire (30 verbally presented and 30 visually presented items) in geometry terminology provided the data for the study. A concept’s verbal description should be associated with its correct visual image. Van Hiele theory provided the lens for the study. An overall percentage mean score of 64% obtained in the test indicated that the majority of the students had a fairly good knowledge of basic geometry terminology. The students obtained a percentage mean score of 68% on visually presented items against that of 59% on verbally presented items implying a lower level thinking as per Van Hiele theory. The findings of this study imply a combination approach using visual and verbal representations to enhance conceptual understanding in geometry. This has to be complemented and supplemented through scaffolding to fill student teachers’ content gap.

Internationally, identifying the challenges in the preparation of mathematics teachers is a growing field of research as it is one of the most urgent problems faced by those who wish to improve student learning. For example, the cross-national study on the preparation of middle school mathematics teachers by Schmidt (

In South Africa, one of the aims of teaching mathematics is to develop an understanding of spatial concepts and relationships (Department of Education,

Concept is an element of understanding and knowledge (Öksüz,

Understanding geometry is an important mathematical skill since the world in which we live is ‘inherently geometric’ (Clements & Battista,

How children develop their understanding of geometry and spatial sense has been an area of research over the past 60 years (Alex,

The research questions investigated in this study are: (1) What was the conceptual understanding of basic geometrical terminology of the sample of 2015 entry level mathematics education students in the rural university in relation to the curriculum followed by the pre-2014 matriculants and matriculants of 2014? (2) Was there a statistical difference in the overall performance of students in matching the verbal description with their correct visual images? And (3) was there a statistical difference in the performance of the students with respect to the different concepts tested?

This research adopted a positivist paradigm and a quantitative approach. This case study design mainly focused on matching the verbal description with their correct visual images in the geometrical concepts and terminology and as indicated earlier was a retrospective study.

Euclidean geometry in South African schools is usually the figures in the plane (Atebe,

For example, in

A homologous pair.

The instrument had two sections, the first one to gather biographic data and the second one consisted of the 60-item multiple choice questionnaire. The lead researcher administered the instrument during the first two-hour mathematics education lecture.

The mean average age of the students who participated in the study was 22 years. Out of the 126 students who participated in the study, who were enrolled for the year 2015 in year 1, 88 (70%) passed matric before 2014 (pre-2014 matriculants) and 38 (30%) were matriculants of 2014.

This article reports on a study that was conducted in a historically disadvantaged rural university in the Eastern Cape. To conduct the study, permission was sought from the Head of the Department of Mathematics, Natural and Consumer Sciences Education. A permission letter was obtained and approved by the Faculty of Educational Sciences Ethics Committee. Entry level mathematics education students were informed of the purpose of the test and a request for voluntary participation was made. Out of the 154 students who enrolled for the course for the year 2015, 126 (86 male students and 40 female students) voluntarily took part in the study. It was agreed that anonymity and confidentiality of the data would be guaranteed. This information was also printed on the general information of the instrument and there was space for participants to sign for informed consent. There was no reward for participation.

The scoring of the terminology section was calculated using Microsoft Excel 2013. Each item was awarded 1 mark and the total was 60 marks. For each student, the total was then converted to a percentage. The general performance of the students was calculated in terms of the overall percentage mean score as shown in

Performance of entry level mathematics education students in the geometry terminology test.

For research question (1), an overall percentage mean score of 64% obtained in the test indicated that the majority of the students (64%) in this study had a fairly good knowledge of basic geometric terminology. The study further aimed to determine the students’ ability in visually presented and verbally presented terminology items. The students obtained a percentage mean score of 68% on visually presented items against a percentage mean score of 59% on verbally presented terminology items. This meant that the students’ performance was better in dealing with visually presented terminology items than the verbally presented items for the same concept.

To answer research question (2), a further analysis was also done to find out the performance of students in the multiple choice questionnaire in relation to pre-2014 matriculants and the matriculants of 2014.

Performance of students in the multiple choice questionnaire in relation to pre-2014 matriculants and the matriculants of 2014.

Year of passing matric | Mixed items (all) (mean score %) | SD | |
---|---|---|---|

Before 2014 | 88 | 59 | 15 |

In 2014 | 38 | 76 | 12 |

Note:

From

From

Performance of students in the visually presented items in relation to pre-2014 matriculants of and the matriculants of 2014.

Year of passing matric | Visually presented items (mean score %) | SD | |
---|---|---|---|

Before 2014 | 88 | 64 | 15 |

In 2014 | 38 | 79 | 11 |

Note:

From

Performance of students in the verbally presented items in relation to pre-2014 matriculants of and the matriculants of 2014.

Year of passing matric | Verbally presented items (mean score %) | SD | |
---|---|---|---|

Before 2014 | 88 | 54 | 17 |

In 2014 | 38 | 72 | 15 |

Note:

From

Performance of pre-2014 matriculants in relation to the verbally presented and visually presented items in the test.

Year of passing matric | Verbally presented items (mean score %) | SD | Visually presented items (mean score %) | SD | |
---|---|---|---|---|---|

Before 2014 | 88 | 54 | 17 | 64 | 15 |

Note:

From

Performance of matriculants of 2014 in relation to the verbally presented and visually presented items in the test.

Year of passing matric | Verbally presented items (mean score %) | SD | Visually presented items (mean score %) | SD | |
---|---|---|---|---|---|

In 2014 | 38 | 72 | 15 | 79 | 11 |

Note:

To address research question (3), students’ mean scores in the terminology test were calculated separately for items on geometric terminology associated with the concepts in three categories: lines, circles, and triangles and quadrilaterals.

The different concepts tested in the terminology test.

Concept | Question numbers | Total number of questions |
---|---|---|

Lines | 4, 8, 13, 16–19, 21, 22, 25, 27, 31, 32, 34–37, 39–43, 49, 50, 52, 55, 58, 60 | 28 |

Circles | 1–3, 5–7, 10, 14, 15, 23, 24, 29, 30, 38, 56, 59 | 16 |

Triangles and quadrilaterals | 9, 11, 12, 20, 26, 28, 33, 44–48, 51, 53, 54, 57 | 16 |

The results were analysed using Microsoft Excel 2013 and are shown in

Performance of entry level mathematics education students in the multiple choice questionnaire according to concepts.

Performance of entry level mathematics education students in the multiple choice questionnaire according to concepts.

It was found that the students performed better in the terminology associated with lines (70%) followed by circles (64%) and the terminology in triangles and quadrilaterals were the worst performed (52%).

It was found that the matriculants of 2014 performed better in the terminology associated with lines (83%) followed by circles (75%) and the terminology of triangles and quadrilaterals (63%) than the pre-2014 matriculants who scored 64%, 60% and 48% respectively.

From

Performance of students in the line concepts in relation to pre-2014 matriculants and matriculants of 2014.

Year of passing matric | n | Lines (mean score %) | SD |
---|---|---|---|

Before 2014 | 88 | 64 | 18 |

In 2014 | 38 | 83 | 15 |

Note:

From

Performance of students in the circles concepts in relation to pre-2014 matriculants and matriculants of 2014.

Year of passing matric | n | Circles (mean score %) | SD |
---|---|---|---|

Before 2014 | 88 | 60 | 17 |

In 2014 | 38 | 75 | 15 |

Note:

From

Performance of students in the triangles and quadrilaterals concepts in relation to pre-2014 matriculants and matriculants of 2014.

Year of passing matric | n | Triangles and quadrilaterals (mean score %) | SD |
---|---|---|---|

Before 2014 | 88 | 48 | 17 |

In 2014 | 38 | 63 | 16 |

Note:

It is noted from

This study found that students’ performance was better in dealing with visually presented terminology items than verbally presented ones. This could lead to the conclusion that the students in the study, although high school graduates, could probably be operating at lower Van Hiele levels of geometric thinking. According to Couto and Vale (

In support of the Van Hiele theory, Couto and Vale (

The results from this study were inconsistent with the study by Bozkurt and Koç (

The data show that the matriculants of 2014 outperformed, with a significant statistical difference, the pre–2014 matriculants. The present study revealed a very significant gap in the performance of the pre-service student teachers in geometry at the university entry level in favour of students who came through a compulsory geometry curriculum. This might also be due to the constraints in the secondary school mathematics curriculum originating from curriculum reforms. This is in support of the inference put forward by Wilburne and Long (

This study investigated the knowledge of basic geometric terminology with which pre-service student teachers enter the rural university. Even though it was found that the majority of the students had a fairly good knowledge of the geometric terminology, the students performed better in dealing with visually presented terminology items than verbally presented ones. This raised a concern that the majority of students were operating at the Visualisation level of Van Hiele’s geometrical thinking. The study revealed that the matrics of 2014 performed better in all aspects tested than pre-2014 matriculants. It can be concluded that curriculum constraints due to the ongoing changes in the school mathematics curriculum might have adversely affected students’ performance in geometry. The study also gives insight into the quality of students received by universities for teacher education courses which reflects the quality of geometry learning in our schools.

Visual and verbal representations in geometry should complement and supplement each other to enhance conceptual understanding. The use of multiple representations carefully built into the geometry curriculum will ensure that students meaningfully understand the concepts they are learning. Pre-service students and their educators need to adopt a combination approach since visual representations enhance spatial understanding and verbal representations promote mathematical terminology and mathematical language development besides general vocabulary and language development. The curriculum of the universities should include more opportunities for mathematics education students to familiarise themselves with school geometry content so as to allow them to teach it with understanding and meaning-making to learners in their careers as future teachers.

The authors gratefully acknowledge Marc Schäfer for giving permission to use the test constructed by Humphrey Atebe.

The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.

J.A. conducted the research and wrote the manuscript. K.M. made conceptual contributions and provided critical revision, guidance, editing and final approval of the document.