Using Visual Representations as an Alternative in Teaching Simultaneous Equations

Abstract

Abstract:It is widely known that students normally struggle in the mathematics topic of algebra. They tend to steer away from algebraic problems such as solving linear equation with one variable, let alone simultaneous equations, which require them to determine the values of two variables. This action research study investigates the effect of replacing the common symbolic representations with pictorial (static visual) representations in simultaneous equations lessons of 38 low-performing Year 10 students. The data for the study was collected by means of pre-and post-tests and facilitated by three worksheets as the intervention instruments. During the lessons, pictorial representations were used in solving simultaneous equations questions. These entailed drawing several pictorials that were given in the equations. In particular, drawings of burgers, fries, cheese slices, gift boxes and sweets were used as these were generally relatable to the students in real-life. The students were then provided with fresh worksheets and subsequently translated their workings from the pictorial part to x and y. And thus forms the symbolic part of the intervention. From the students' pre-test and posttest scores, it was evident that the pictorial representations helped the students in making significant improvements in the topic.

Performance Analysis of Simulated Annealing and Genetic Algorithm on systems of linear equations

“…These comprise a set of equations, which is finite in nature and should meet at a common point in space. 22 These equations should have functions of at least two variables and can either have a linear or a non-linear characteristic.…”

Ascertaining Grade 10 learners’ levels of mathematical modelling competency through solving simultaneous equations word problems

“…Simultaneous equations word problems as mathematics content is considered an important aspect of algebra (Johari & Shahrill, 2020) in the Grade 10 mathematics curriculum, according to the Curriculum and Assessment Policy Statement (CAPS) (Department of Basic Education [DBE], 2011), which constitutes the current South African school curriculum. Solving these systems of simultaneous equations is essentially viewed as problem-solving (Nordin et al, 2017;Ugboduma, 2006Ugboduma, , 2012Yunus et al, 2016) which also involves certain procedures (for instance addition, subtraction, multiplication, division, substitution, etc.). This research is pitched at the Grade 10 level specifically, since this grade forms the first year of a three-year Further Education and Training (FET) mathematics phase (Grade 10 to Grade 12).…”

“…Consequently, it is essential that Grade 10 learners acquire a sound knowledge, and basic understanding of mathematical content essential to successfully complete the final summative Grade 12 (also referred to as Matric) final assessment. From anecdotal evidence and research literature (Johari & Shahrill, 2020;Nordin et al, 2017;Ugboduma, 2006Ugboduma, , 2012Yunus et al, 2016), many learners clearly encounter difficulties solving simultaneous equation systems, that is, they always make some or other error. These said errors may be the result of misconceptions, which Johari and Shahrill (2020, p. 263) refer to as 'mathematical error [s] and irrational error[s]', procedural inaccuracies such as 'wrong substitution of the subject' (Johari and Shahrill, 2020, p. 263), or unforced errors through negligence, involving the basic operations such as multiplication, subtraction or division, involving mathematical tools such as additive inverse and multiplicative inverse.…”