Relationship between Computational Estimation and Problem Solving

Abstract

The present study attempted to explore the relationship between computational estimation and problem solving in a sample of Year 6 children and adults (N=72). For this purpose, participants were presented with two tasks which asked them to estimate the computational result in eight arithmetic operations (Computational Estimation Task) as well as to provide solution to eight mathematical word problems, all coming from four different areas of mathematics (Problem Solving Task). The analysis of the results showed that adult participants accomplished more successful estimations compared to children, mostly with the use of rounding and algorithm strategies in both age groups. Age differences were also found in the Problem Solving Task with geometry and arithmetic problems being the most difficult for children and adults, respectively. Last, a significant positive correlation was revealed between estimation computational ability and problem solving ability: participants who had great success in computational estimation tended to indicate high success rates in problem solving. Educational implications are further discussed in terms of the role of computational estimation and problem solving in mathematics learning.

Does this Answer Make Sense? Primary School Students and Adults Judge the Reasonableness of Computational Results in Context-Based and Context-Free Mathematical Tasks

“…Students were found to be particularly weak in contextualised problems where algorithms did not suffice for a correct answer or when the results generated from them were incomplete and needed adaptation to make sense. This is in line with previous findings suggesting that students often rely too heavily on algorithms to solve mathematical tasks (Desli & Lioliou, 2020;Heirdsfield & Cooper, 2002), even when algorithms are insufficient or inappropriate to generate correct responses (Masingila et al, 1996;Menon, 2004).…”

“…As an illustration, only 41% placed the decimal point correctly into the result of 15.24 × 4.5 displayed as 6858 in a "broken" calculator, while only half of them chose computational estimation over algorithms to do so. As illustrated by this example, students' difficulties in achieving reasonable results often stem from their weakness in using mental computations and computational estimation flawlessly or their reluctancy to do so altogether (Desli & Lioliou, 2020;Heirdsfield & Cooper, 2002). In another item of Menon's (2004) study, more than half of the participants (56%) considered 2¼ as the correct answer to the number of vehicles required for the transportation of 9 passengers.…”

Neural Correlates of Numerical Estimation: The Role of Strategy Use

“…(1) the AC strategy involves rounding and multiplication procedures [18,27,31]; (2) the SOM strategy is based on intuitive approximate magnitude representations for the results, without any calculation. To test the neural network that associates with each of these strategies, during an fMRI scan, we asked participants to solve the computation estimation task in the no-choice paradigm: in one block using AC strategy only and in the other block using the SOM strategy only.…”

Investigation of the computational estimation skills of and strategies employed by pre-service primary school teacher

“…Recent studies reveal that specialists such as scientists, engineers, or mathematicians employ estimation before actually using assessment tools to reach to exact results (Jones & Taylor, 2009;Jones et al, 2012). Educators who emphasize the importance of estimation skills (Brade, 2003;Desli & Lioliou;Reys, 1984;Reys & Bestgen, 1981;Reys et al, 1991;Sowder & Wheeler, 1989;Van den Heuvel-Panhuizen, 2001) note that it is a skill required not only for a few occupations and daily life, but also helps develop numerous mathematical skills, such as mental activities, spatial visualization, assessments, and understanding quantities (Kose, 2013). That is why it is imperative and necessary to instill skills such as reasoning, interpreting, mental calculus, creative thinking, and estimation in the students, from their earliest years on.…”