A study of the phenomena of conjoining terms and related aberrant transformations in the simplification of algebraic expressions by Grade 8 learners of two secondary schools in the Western Cape

Adonis-Maarman, Bronwyn

A study of the phenomena of conjoining terms and related aberrant transformations in the simplification of algebraic expressions by Grade 8 learners of two secondary schools in the Western Cape

Thesis / Dissertation

2025

Publisher

University of Cape Town

Department

School of Education

Faculty

Faculty of Humanities

Abstract

Mathematics education research on conjoining has been inconsistent with regard to the study of the phenomenon and the use of the term conjoining. This study aimed to identify justifications for the procedures implicated in producing instances of what we refer to as aberrant conjoining in early school algebra. The study took a rationalist view of knowledge acquisition and used a computational approach to analyse data obtained through a written test and semi-structured interviews with a selection of research subjects. The rationalist research orientation used rests on the proposition that humans possess biologically endowed, core domain knowledge of number, as is evident in the results of experiments carried out on human infants as well as other animals. Seventy-six Grade 8 students at two secondary schools in the Western Cape were given a test in which they were required to simplify ten algebraic expressions, all of which were sums. Eight students were selected for interviews on the basis that they had either displayed aberrant conjoining in their responses or that they had answered most items correctly. The computational analysis identified four computational principles employed in instances of aberrant conjoining: the use of type-specific computations, the treatment of constituents of terms as sets, the implicit use of string operations, and the use of addition-like monoids. Furthermore, the biologically endowed cognitive operation, merge, is implicated as generative of the concatenation of the results of type-specific computations central to aberrant conjoining, and as the ground for the system of addition-like monoids used by students. The analysis also found the use of a pedagogically exploited structure-preserving mapping between distributivity and indirect distributivity that enables students to simplify algebraic expressions, but which inadvertently contributes to the production of aberrant conjoining in its reliance on the typographically legitimate conjoining of symbols to form written algebraic expressions. Finally, the description and analysis of aberrant conjoining in the literature is interrogated, and a more robust explication of the phenomenon is offered.