Utilizing analogical reasoning to aid children’s proportional reasoning understanding

Abstract

Proportional reasoning is an important skill that relates to fraction learning and math achievement. Because both proportional and analogical reasoning involve comparing relations, we hypothesized that supports for analogical reasoning (multiple exemplars and labels) would help children match discrete proportions. Fourth and 5th graders (N = 119) completed a 16-item proportional equivalence choice task in a 2 (exemplars: one, two) x 3 (script type: juice mixing narrative, novel adjectives, no labels) x 2 (trial type: part-foil, whole-foil) mixed-effects design. The juice mixing script included common labels and a story paradigm, whereas the novel adjectives script only utilized common labels. The least-informative no-labels script served as a baseline. Results showed a significant three-way interaction between exemplars, script type, and trial type. Viewing two exemplars led to no significant differences across the other factors. However, when viewing one exemplar, children exhibited a part-matching bias with novel adjectives and no labels, but not the juice narrative. In sum, multiple exemplars and the juice narrative reduced children’s part-matching bias; we conclude that supports for analogical reasoning can aid proportional reasoning as well.

Spatial skills, but not spatial anxiety, mediate the gender difference in number line estimation.

“…However, gender differences were found on mental rotation and proportional reasoning and not on mental transformation or visuospatial working memory. We did not expect to find a gender difference in proportional reasoning because several prior studies with children of similar ages to those in the current study reported a lack of gender difference (Boyer al., 2008;Ham & Gunderson, 2019;Hansen et al, 2015;Möhring et al, 2018Möhring et al, , 2015. This discrepancy might be attributable to the specific tasks used to measure proportional reasoning, given that most prior studies assessed proportional reasoning with a matching task, in which children were asked which of two proportions matched a target proportion (Boyer et al, 2008;Ham & Gunderson, 2019;Hansen et al, 2015), whereas we used an estimation task.…”

“…We did not expect to find a gender difference in proportional reasoning because several prior studies with children of similar ages to those in the current study reported a lack of gender difference (Boyer al., 2008;Ham & Gunderson, 2019;Hansen et al, 2015;Möhring et al, 2018Möhring et al, , 2015. This discrepancy might be attributable to the specific tasks used to measure proportional reasoning, given that most prior studies assessed proportional reasoning with a matching task, in which children were asked which of two proportions matched a target proportion (Boyer et al, 2008;Ham & Gunderson, 2019;Hansen et al, 2015), whereas we used an estimation task. Moreover, some studies using different proportional reasoning tasks and with older students have found better proportional reasoning among boys than girls (Linn & Pulos, 1983;Sophian & Wood, 1997).…”

“…A recent meta-analysis on the development of gender differences in mental rotation showed an effect size of Hedge's g = .20 at around 6 years old and increased to Hedge's g = .50 at around 14 years old (Lauer et al, 2019). In contrast, studies using proportional reasoning tasks and visuospatial working memory tasks frequently report a lack of gender differences (Boyer et al, 2008;Ham & Gunderson, 2019;Hansen et al, 2015;Möhring et al, 2018Möhring et al, , 2015Robert & Savoie, 2006;Vuontela et al, 2003). For example, Vuontela et al (2003) reported that 6-to 13-year-old boys were faster but less accurate than girls on visuospatial working memory tasks.…”

Current Knowledge and Future Directions: Proportional Reasoning Interventions for Students with Learning Disabilities and Mathematics Difficulties

“…We focused on fifth to ninth grades for a few reasons. (Christou & Philippou, 2001;Ham & Gunderson, 2019;Lamon, 2007); in addition, we considered studies with fifth grade participants in an attempt to (a) gather studies conducted prior to the broad adoption of the CCSS; (b) gather studies with mixed grade level groupings of students without disaggregated data (e.g., fifth and sixth grade); and (c) gather studies conducted in non-U.S. countries who may introduce proportional reasoning knowledge and skills earlier than the United States. 3.…”

What does ‘three’ look like? Analogical reasoning in early number word acquisition

“…Because the challenge of learning number words is that set size is an abstract relational concept, learning may be facilitated if we draw on mechanisms that children use to learn other abstract relational concepts (Gentner, 1983;Gentner & Markman 1997;Gentner, 2010). Learning of words that refer to abstract relational concepts such as 'triangle', 'twothirds' or 'increasing' can be facilitated if examples enable structural alignment Ham & Gunderson, 2019;Smith et al, 2014). Structural alignment is a mechanism of cognitive inference that is enabled if examples fulfill two functions: 1) Highlighting a common relational structure and 2) Highlighting alignable differences Gentner, 2010;Gentner & Asmuth, 2019;Kotovsky & Gentner, 1996).…”