Exploring the errors committed by grade 11 learners in Euclidean geometry problem-solving

Abstract

The aim of this study was to explore the types and the causes of errors committed by learners while solving Euclidean geometry problems. Learners experience challenges in geometric problemsolving due to errors based on the misinterpretation of various geometric aspects and insufficient conceptual development. The current study enquired how do teachers’ geometric instructional practices influence errors committed by learners in geometry problem-solving? What types of errors are evident in diverse levels of geometric knowledge and understanding? What are general error types and indicators that are outstanding on learners’ problem-solving process ? What are the causes of errors in geometry problem-solving? The Van Hiele theory of geometric knowledge, together with Newman’s Error Analysis (NEA), were used to profile learners’ errors as they engaged in circle geometry evaluation. An exploratory single case qualitative case study was employed with 15 Grade 11 learners and one teacher in Amathole East district in the Eastern Cape Province of South Africa. The data were collected using a geometry test, non-participatory observation and one-on-one interviews. The findings indicated that the teacher taught geometry at a higher level of geometric knowledge which promoted memorisation and deductive learning that hindered concept and rule application during problem-solving leading to errors in geometry problem-solving. Further, the errors were analysed at each level of Van Hiele’s theory and the findings were that, on the visualisation level, limited errors were displayed with a lower number of learners committing reading and comprehension errors. The analysis level evidenced comprehension and transformation errors; the informal deduction level produced comprehension, transformation, encoding and conceptual errors; while the formal deduction level was characterised by comprehension, transformation, encoding and conceptual errors. It became evident that the comprehension error was most prevalent. In addition, findings revealed that the causes of errors in geometry problem-solving include faulty schemas, instructional practices that do not align to level of learner thinking, inappropriate geometric language and learners’ lack of knowledge from lower levels of understanding. This study revealed the prevalent error types and causes, including how teaching practices contribute to typical errors committed by learners in geometry problem-solving. Therefore, the recommendation is that teachers should be exposed to the Van Hiele theory of geometric thinking in order to classify the learners’ geometric contributions during classroom activity in accordance with the theory. This will also help the teachers to align their teaching with the level of learner comprehension. When the teacher knows the level of Van Hiele at which the learner is functioning, he/she is able to give questions that cater to learners’ levels of geometric knowledge and understanding because errors committed by learners might be a sign that the learners are not on the required level of thought. Teachers should therefore take the types of errors committed and the causes of errors into consideration during geometric problem-solving to refine their teaching practices to alleviate errors and to enable cognitive development in learning and problem-solving in Euclidean geometry.