This paper reports on the ways in which textbooks highlight the relationships between mathematical concepts, in the topic of number patterns, and the implications this can have on fostering innovative pedagogical practices. More specifically the idea was to show the relationship between mathematical concepts to propose methods of teaching two different concepts relationally and to advance students’ understanding.

Research done by the South African department of education highlights that much of the student difficulties in number patterns arises from questions that requires students to use ‘relational understanding’ between concepts. For example, a question that requires students to find the minimum value of a quadratic sequence requires them to make connections between the sequence and a quadratic function. The connection is essential to understand the general term of the quadratic sequence in relation to a quadratic function, the constitutive elements of the two separate formulas and to perform operations. Literature highlights that textbooks are a major resource and often the only resource that most teachers have access to, with embedded pedagogical approaches in their structure (content), organisation of content and their sequencing of the content.

Our research was guided by the question of whether learning resources, such as textbooks, do explicitly highlight connections between concepts to advance relational understanding and provide an opportunity for teaching mathematical concepts simultaneously? The investigation included an analysis of two well-known South African grade 12 textbooks that are currently used in secondary schools: The Classroom Mathematics and the Siyavula textbook. Skemp’s (1976) theory of relational understanding was adopted as a theoretical base and used to investigate the explanations, examples and representational affordance of connections in these textbooks. A coding scheme was specifically developed for the study with the following codes: R0, representing zero or no relational affordance in textbook explanations, examples or representations, R1, representing relational affordance or a connection instance of the number pattern concept to only one other mathematical concept, R2, representing connections with two other mathematical concepts, and R3, representing connections with three or more other mathematical concepts.

The high frequent occurrence of code R0 detected in both textbook explanations, examples and representations signify the lack of relational affordance, implying high chances that the students or teachers who use these textbooks to perceive the topic of number patterns in isolation, viz having no relationship or connection with other mathematical concepts. Our analysis showed some detection of code R1, but codes R2 and R3 were not detected at all, which is a concern. The contribution of the study lies in highlighting the relationship between number patterns and its relational mathematical concepts in the textbooks. More generally, the results from the study suggest the possibility of an innovative pedagogical practice where two different concepts can be taught at the same time, and it suggest how highlighting the relationship between mathematical concepts can advance students’ understanding.

Keywords: Number patterns, Textbooks, Pedagogical practices, Relational understanding.