Abstract

This study examined the Van Hiele geometric thinking levels attained by Year Three Senior High School students in the Asante Akim South Municipality of Ghana. A quantitative descriptive cross-sectional design was adopted.

A total of 320 students were selected using purposive and proportionate stratified random sampling. Descriptive statistics were used to analyze the data.

The findings revealed that 110 students (34.38%) attained Level 1 (Visualization), 140 students (43.75%) attained Level 2 (Analysis), and 70 students (21.88%) attained Level 3 (Informal Deduction).

The study adopted the numbering convention in which the first Van Hiele level is designated as Level 1 rather than Level 0. No student attained Level 4 (Deduction); consequently, Level 5 (Rigor) was also not attained. The mean Van Hiele geometric thinking level was 1.875 (SD = 0.741) as reported in the abstract of the published article, indicating that the largest proportion of students operated at the Analysis level.

The findings underscore the need for instructional approaches that promote students' progression to higher levels of geometric reasoning.

Keywords

Research Objective

To describe the Van Hiele geometric thinking levels of Year Three Senior High School students in the Asante Akim South Municipality.

Methodology

A quantitative descriptive cross-sectional design was employed to assess the geometric thinking levels of the students using the Van Hiele Geometry Test (VHGT).

The study was conducted in the Asante Akim South Municipality of the Ashanti Region, Ghana. The target population comprised all Year Three (SHS 3) students enrolled in the three public senior high schools in the municipality during the 2024/2025 academic year.

The total population of Year Three students across the three schools was 898: School A (515), School B (298), and School C (85).

A combination of purposive and proportionate stratified random sampling techniques was employed. The final sample consisted of 320 students: 184 from School A, 106 from School B, and 30 from School C. The sample comprised 186 females (58.13%) and 134 males (41.88%).

The Van Hiele Geometry Test (VHGT), developed by Usiskin, was used to assess students' geometric thinking levels. The instrument consists of 25 multiple-choice items, with five items measuring each of the five hierarchical Van Hiele levels.

A pilot study involving 37 Year Three students produced a Kuder-Richardson Formula 20 (KR-20) reliability coefficient of 0.77. Face and content validity were established through expert review by two experienced mathematics educators.

The VHGT was administered in February 2025 under standardized examination conditions. Students were given 45 minutes to complete the 25-item multiple-choice test. Each student was assigned the highest Van Hiele level attained after correctly answering at least three of the five items associated with that level.

Van Hiele Levels Reported in the Study

Key Findings

Of the 320 students, Level 2 (Analysis) was the most frequently attained level, representing 43.75% of the participants. Students at this level are able to identify and describe the properties of geometric figures but may experience difficulty constructing logical arguments and formal geometric proofs.

Although 21.88% of the students attained the Informal Deduction level, the relatively small proportion indicates that many learners have not yet developed the higher-order reasoning skills required for advanced geometric problem-solving.

Conclusion

The study concludes that the majority of Year Three Senior High School students in the Asante Akim South Municipality operate at the Analysis level (Level 2) of the Van Hiele geometric thinking model.

Although some students have progressed to the Informal Deduction level (Level 3), relatively few have attained higher levels of geometric reasoning. Many students have developed the ability to identify and analyse the properties of geometric figures but require further instructional support to develop higher-order reasoning and deductive thinking.

Recommendations

Mathematics educators and curriculum planners should design and implement geometry instruction explicitly aligned with the Van Hiele theory. Instruction should be sequenced to support students' progression through the hierarchical levels of geometric thinking, particularly from Analysis to Informal Deduction.

Teachers should incorporate instructional activities that promote spatial reasoning, visualization, exploration, and logical reasoning. Learner-centred approaches, including the use of manipulatives, dynamic geometry software, and collaborative problem-solving activities, should be employed to enhance students' understanding of geometric concepts.

School administrators should organize regular professional development programmes and workshops to strengthen teachers' knowledge of the Van Hiele theory and effective instructional strategies for promoting higher levels of geometric thinking.

Future studies should examine instructional interventions that facilitate students' progression from the Analysis level to the Informal Deduction and Deduction levels.

Cite This Article

About the Author

Charles Siaw Obeng is a mathematics educator and researcher whose research interests include mathematics education, geometry and geometric thinking.

Affiliation: Department of Teacher Education, Kwame Nkrumah University of Science and Technology (KNUST), Kumasi, Ghana.

ORCID: 0009-0003-7313-3250