A constructivist analysis of Grade 8 learners’ errors and misconceptions in simplifying mathematical algebraic expressions

Abstract

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.

Argumentation Using the Indigenous Language as a Strategy to Reduce Misconceptions: Addition and Subtraction of Directed Numbers Classroom

“…Persistent errors and misconceptions in addition and subtraction of directed numbers Misconceptions are unavoidable stages in the learning process (Moru & Mathunya, 2022). The result that the misconception leads to persistent errors has been shared by the several studies, for example, Iddrisu et al (2017) and Moru and Mathunya (2022). In the study conducted by Aydin-Guc and Aygun (2021) and Kim et al (2016), it was reported that the students made a reversal error where they map the order of words from the question.…”

“…This was followed by the advantage and disadvantages of argumentation and indigenous language used in learning and teaching of mathematics. Persistent errors and misconceptions in addition and subtraction of directed numbers Misconceptions are unavoidable stages in the learning process (Moru & Mathunya, 2022). The result that the misconception leads to persistent errors has been shared by the several studies, for example, Iddrisu et al (2017) and Moru and Mathunya (2022).…”

“…These results resemble those of Iddrisu et al (2017) where the participants did not mind the subtrahend and the minuend in the question. In this case, the student has the misconception of direct translation (Kim et al, 2016;Mathunya, 2022). The misconception of direct translation is where the students match the order of words that appear in the question (Kim et al, 2016).…”

Orthographic Errors Analysis of English as a Second Language Learners’ writing: lessons from the use of WhatsApp language

“…The constructivists argue that learners bring into the classroom concepts they may be using outside the classroom. As pointed out by Moru and Mathunya (2022), learners do not come to class as empty vessels; rather, they bring with them prior knowledge from previous classes and other interactions with the environment. In this view, as they communicate in an informal manner on WhatsApp out of classrooms, the language used on this platform is then internalized and reproduced by them in their academic essays.…”

“…The persistent use of social media language by learners also indicate that teachers should develop skills in analysing learners' errors. Teachers should be able to identify, diagnose and remedy errors learners frequently commit (Moru & Qhobela, 2013;Moru et al, 2014;Moru & Mathunya, 2022). Once the diagnosis is posed, remediation should be carried out by teachers (Booth et al, 2014;Makonye, 2016;Makonye & Fakude, 2016).…”