An exploration of grade 11 mathematical literacy learner's engagement with start-unknown and result-unknown type problems set in a variety of real life contexts.

Abstract

With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject might develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is taught and assessed, which influences the focus of ML in the classrooms. One of the differences between the respective subjects of Mathematics and Mathematical Literacy is that when it comes to the latter, there has been less emphasis on carrying out algebraic procedures, and a greater focus on working with contexts. However, algebraic skills can be advantageous even when solving problems set within contexts. One area, which surfaces the distinction between arithmetic and algebraic skills, is in the substitution and computation of a formula, as compared to the solution of equations. In this study, I focus on this distinction by examining Grade 11 ML learner skills in solving both result-unknown problems and start-unknown problems, where the former involves substituting and computing the result of a formula or equation for which the input is given. The latter involves re-arranging the equation or formula in order to solve for the input when the output is given. With this in mind, this study sets out to explore the strategies used by Grade 11 learners to solve result-unknown and start-unknown problems set in real life contexts. This is a qualitative study, carried out with three hundred and forty Grade 11 Mathematical Literacy learners from rural and urban school in North Durban. Data was gathered from a document analysis of 340 learners’ written responses to the research instrument, along with interviews with ten of these learners. There were four tasks in the research instrument, each of which had a result-unknown, a start-unknown and a reflection question. In the four tasks with the exception of Question 1.2.1 and 1.2.2 in tasks one, were set around a linear equation, while Question 1.2.1 and 1.2.2 involved a hyperbolic equation. Semi-structured interviews were conducted individually with ten learners and the audio recorded. The purpose of the interviews was to explore some of the factors that influenced their written responses. The findings revealed the solving of start-unknown questions to be a serious problem for learners. On average, the success rate at result-unknown questions was 75%, while it was 26% for start-unknown questions. For start-unknown questions based on linear equations only, the success rate was a mere 19 percent. Some strategies used by learners in responding to start-unknown questions included number grabbing, systematic guess and test, conjoining, symbol manipulation and working backwards. On average, over the four tasks based on linear equations, only nine percent of learners successfully used strategies based on algebraic skill. Most learners who obtained correct answers in the start-unknown questions used the guess and test strategy. Strategies identified in result-unknown questions included direct arithmetic strategy. The study recommends that for ML learners, teachers need to impress upon learners that the location of the formula in the question is not an indication that certain questions would be answered using the formula, because the formula is placed next to them. It also recommends that teachers create opportunities for learners to continue to practice the algebraic skills they learned in the GET band, particularly in the area of transforming and solving simple linear equations.