Mapping a Group of Northern Namibian Grade 12 Learners' Algebraic Non-routine Problem Solving Skills

Abstract

This article investigates the algebraic non-routine problem-solving skills of grade 12 learners of a high-achieving school in northern Namibia. The school was selected on the basis of its outstanding results and sound management style. The study followed a descriptive survey design that involved a written test to examine learners' problem-solving skills together with the solution strategies used, and structured learner interviews to get their views about the choice of strategies for solving non-routine problems. The assessment framework of the learners' problem-solving skills was based on the Trends in International Mathematics and Science Study (TIMSS) scales for Polya's problem-solving model. The results showed that learners were more successful in answering the question with a diagrammatic illustration, suggesting that the use of diagrams makes it easier to understand the problems. A significant number of learners' algebraic problemsolving skills function at or below level 2 of TIMSS scale. The algebraic strategy was the most preferred solution strategy and there were learners who encountered difficulties with the language used in the questions.

Problem Solving Heuristics and Mathematical Abilities of Heterogeneous Learners

“…Likewise, Webb [15] even pointed out that engaging learners into numerous cognitive processes augment their problem-solving abilities and understanding. Mathematics problem solving through non-routine problems plays a vital role in inculcating higher-order thinking skill that leads to the development of thinking and reasoning skills [16]. Besides, non-routine problems demand flexibility; it requires the knowledge of various problem-solving heuristics and strategies [17].…”

Mathematical Creativity of Pre-service Teachers in Solving Non-routine Problems in State University in Laguna

“…Non-routine problems are kinds of problems that require the use of different strategies and heuristics [9]. These problems are more difficult and complicated than routine problems because numerous approaches must be devised to solve an unfamiliar situation [10]. Thus, these problems require flexibility and strategic thinking to extend previous knowledge and concepts that allow having different pathways to a solution, leading to the enhancement of student's Mathematical creativity [11].…”

Comparing grades 10 – 12 mathematics learners’ non-routine problem solving

“…For example, Mogari and Lupahla (2013) found that Namibian learners most preferred the algebraic strategy to other strategies, even though they successfully solved problems that were illustrated with diagrams. The Filipino learners in Mabilangan, Limjap and Belecina (2011) used the 'making a model or diagram' strategy the most.…”

“…Elia, van den Heuvel-Panhuizen and Kolovou (2013, p607) consider NRMPs 'more complicated and difficult than routine problems' and similarly, according to Mogari and Lupahla (2013, p95), they are 'more cognitively challenging and demanding than routine problems'. NRMPs are tasks based on real life circumstances or models thereof that cannot be solved using familiar methods by replicating known procedures (see Muis, 2004;Arslan & Altun, 2007;Mogari & Lupahla, 2013). To this end, in the view of Arslan and Altun, NRMP reflects the relationship between mathematics and reality.…”

“…Furthermore, Bansilal, Brijlall and Mkhwanazi (2014) measured mathematics teacher's content knowledge and found that on average teachers scored 29% on problem solving questions. Mathematics problem solving is essential in developing thinking and reasoning skills, promotes high-order thinking and facilitates conceptual understanding and meaningful learning (see Mogari & Lupahla, 2013). Webb (2010) notes that engaging learners more on cognitively demanding mathematical tasks requiring critical thinking and reasoning tend to enhance deeper knowledge and understanding which are requisite for developing problem solving competencies.…”