Semantic, Executive, and Visuospatial Abilities in Mathematical Reasoning of Referred College Students

Abstract

Semantic retrieval (SR) and executive-procedural (EP), but not visuospatial (VS) skills, have been found to be uniquely predictive of mathematical calculation skills in a sample of clinically referred college students. This study set out to cross-validate these results in an independent sample of clinically referred college students (N = 337) as well as extend them by examination of the contributions of these cognitive domains to math reasoning skills. Results indicate that these cognitive domains were able to predict 30% of the variance in calculation skills and 50% of the variance in math reasoning; however, in both cases, only the domains of semantic retrieval and visuospatial skill contributed uniquely. Differences between studies, and the lack of unique contribution of the EP domain to either type of math skill, may be due to measurement and sampling differences, the degree of shared relations among domains, and the choice of measures that represent the EP domain. Implications and future directions are explored.

Students’ semantic reasoning characteristics on solving double discount problem

“…S1 : You are free to use letters or use the price of the shoes Problem-solving strategies must be determined in advance so that the desired solution is suitable to answer the problem (Davis, 2013). Interpreted strategy is influenced by the problem solver's ability to solve problems (Cirino et al, 2007;Davis, 2013;Littlefield & Rieser, 1993;Polya, 1973) and prior mastered knowledge. In this case, S1 gave meaning to variable x as the shoe price, which showed S1's abstract thinking.…”

“…At the Matahari store, S1 multiplied variable x by 70% and then deducted the initial price of the shoe to obtain the 0.3x. S1 provided the proof of calculation for each store to help S1 to get the solution and continued implementing the strategy through a calculation process (Cirino et al, 2007;Hegarty et al, 1995). S1 gave meaning to every problem-solving stage as in previous studies reported (Mairing, 2017;Pape, 2004).…”

“…In addition to involving the representation system, giving meaning to the problem is also influenced by prior knowledge and followed by the processing of each text element from the problem based on the mental model of the situation (Murphy, 2015;Pape, 2004). After interpreting the given problem, each subject uses his strategy as an effort to get a solution to the problem (Davis, 2013;Hegarty et al, 1995;Polya, 1973) then proceed with applying the chosen strategy, such as carrying out the calculation process (Cirino et al, 2007;Hegarty et al, 1995;Polya, 1973). Each subject interpreted this strategy in their own ways (Cirino et al, 2007;Davis, 2013;Littlefield & Rieser, 1993;Polya, 1973).…”

“…Semantic reasoning is the process of thinking to understand the meaning of each stage of the problem-solving process to find a solution to the problem (Davis, 2013;Liang et al, 2016;Littlefield & Rieser, 1993;Murphy, 2015;Prayitno et al, 2018). The study about semantic reasoning has been focused on different things, such as semantic reasoning in computer programs (Patelli et al, 2014;Shi et al, 2015), physics education (Mao & Sen, 2018;Uhden et al, 2012), proofing (Alcock & Inglis, 2008), analyzing errors or obstacles (Kaur & Yeap, 2001;Nesher & Katriel, 1977;Prayitno et al, 2018), and problem-solving (Cirino et al, 2007;Davis, 2013;Liang et al, 2016;Littlefield & Rieser, 1993;Murphy, 2015). Besides, there are also semantic reasoning in word numeracy problems (Davis, 2013), statistical math word problems (Liang et al, 2016), puzzles (Murphy, 2015), word problems with irrelevant information (Littlefield & Rieser, 1993) number word problems (Cirino et al, 2007;Shi et al, 2015), and calculation (Cirino et al, 2007;Patelli et al, 2014).…”

“…This situation raises a gap to examine characteristics of semantic reasoning in solving problems with incomplete information. Problem-solvers need to maintain the semantic structure of the problems (Cirino et al, 2007;Davis, 2013;Liang et al, 2016;Littlefield & Rieser, 1993;Murphy, 2015) to solve problems. The goal is to maintain the selected representation meaning (Bassok et al, 1998;Prayitno et al, 2018) and get the right solution.…”