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Elementary students’ conditional reasoning skills: The case of mathematics
Elementary students’ conditional reasoning skills: The case of mathematics
Reasoning about conditional “if..then” statements is a central component of logical reasoning. However, a research link between conditional reasoning and mathematics has been reported only for late adolescence and adults (Attridge & Inglis, 2013; Stylianides, Stylianides, & Philippou, 2004; Durand-Guerrier, 2003), despite claims about the pivotal importance of conditional reasoning, i.e. reasoning with if-then statements, in mathematics. To address this issue and shed some light on the the area of conditional reasoning within mathematics in elementary school, three studies were conducted to measure students conditional reasoning and alternative generation skills in two contexts (everyday and mathematical) and investigate various factors (i.e, age, logical form, working memory capacity, alternative generation skills) that might affect conditional reasoning skills at these ages, as well as the potential scaffolding function of different trainings on these skills. Firstly, after having approached the background that frames conditional reasoning in mathematics and everyday context, we reported on a study that explored if it is feasible to survey conditional reasoning skills in everyday contexts and mathematics with primary school students. The findings shown that the applied instrument was accessible to students, and reflected central predictions of Mental Model Theories of conditional reasoning for differences between the two contexts. Moreover, the question, if the ability to generate examples of mathematical concepts, and to generate multiple alternative models for a given premise, has an influence on students ’ conditional reasoning with these concepts, was raised at that point. In this direction this pilot study also aimed at investigating students’ alternative generation outcomes in both contexts. Based on the aforementioned pilot study, the first study addressed the open question, to which extent conditional reasoning with mathematical concepts differs from conditional reasoning in familiar everyday contexts. This study also examined the role of alternatives generation skills on conditional reasoning within an everyday and a mathematical context. The results of study 1 suggest that, consistently with previous findings, even 2nd graders were able to make correct inferences on some logical forms. Controlling for WM, there were significant effects of grade and logical form, with stronger growth on MP and AC than on MT and DA. The main effect of context was not significant, but context interacted significantly with logical form and grade level. The pattern of results was not consistent with the predictions of MMT. The study also indicates that deductive reasoning skills arise from a combination of knowledge of domain-general principles and domain-specific knowledge. In addition, it extends results concerning the gradual development of primary students' conditional reasoning with everyday concepts (Markovits & Barrouillet, 2002) to reasoning with mathematical concepts adding to our understanding about the link between mathematics and conditional reasoning in primary school. Moreover, alternatives generation skills predict correct conditional reasoning in both contexts, but interesting differences occurred. The findings from the everyday context mirror previous results, predicting correct AC and DA reasoning and inhibiting correct MT reasoning. In the mathematical context, alternatives generation predicted correct reasoning in all forms. The main contribution of study 1 is the emphasis on the specific role of mathematical knowledge in conditional reasoning with mathematical concepts. The results of the latter studies inspired the development of a short-term educational intervention. This goal was addressed in study 2 by investigating the effects of two short-term trainings based on alternative generation priming within two contexts (contrary-to-fact and mathematical contexts). The results of this study were mixed, revealing a decrease of definite reasoning scores after the short interventions and an increase in DA reasoning; however, further analysis is required. Ultimately, the studies in this dissertation aimed to gain some evidence in the area of conditional reasoning within mathematics in primary school and contribute to future research on this research field.
conditional reasoning, mathematics, elementary students, alternatives generation process, training
Datsogianni, Anastasia
2020
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Datsogianni, Anastasia (2020): Elementary students’ conditional reasoning skills: The case of mathematics. Dissertation, LMU München: Faculty of Psychology and Educational Sciences
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Abstract

Reasoning about conditional “if..then” statements is a central component of logical reasoning. However, a research link between conditional reasoning and mathematics has been reported only for late adolescence and adults (Attridge & Inglis, 2013; Stylianides, Stylianides, & Philippou, 2004; Durand-Guerrier, 2003), despite claims about the pivotal importance of conditional reasoning, i.e. reasoning with if-then statements, in mathematics. To address this issue and shed some light on the the area of conditional reasoning within mathematics in elementary school, three studies were conducted to measure students conditional reasoning and alternative generation skills in two contexts (everyday and mathematical) and investigate various factors (i.e, age, logical form, working memory capacity, alternative generation skills) that might affect conditional reasoning skills at these ages, as well as the potential scaffolding function of different trainings on these skills. Firstly, after having approached the background that frames conditional reasoning in mathematics and everyday context, we reported on a study that explored if it is feasible to survey conditional reasoning skills in everyday contexts and mathematics with primary school students. The findings shown that the applied instrument was accessible to students, and reflected central predictions of Mental Model Theories of conditional reasoning for differences between the two contexts. Moreover, the question, if the ability to generate examples of mathematical concepts, and to generate multiple alternative models for a given premise, has an influence on students ’ conditional reasoning with these concepts, was raised at that point. In this direction this pilot study also aimed at investigating students’ alternative generation outcomes in both contexts. Based on the aforementioned pilot study, the first study addressed the open question, to which extent conditional reasoning with mathematical concepts differs from conditional reasoning in familiar everyday contexts. This study also examined the role of alternatives generation skills on conditional reasoning within an everyday and a mathematical context. The results of study 1 suggest that, consistently with previous findings, even 2nd graders were able to make correct inferences on some logical forms. Controlling for WM, there were significant effects of grade and logical form, with stronger growth on MP and AC than on MT and DA. The main effect of context was not significant, but context interacted significantly with logical form and grade level. The pattern of results was not consistent with the predictions of MMT. The study also indicates that deductive reasoning skills arise from a combination of knowledge of domain-general principles and domain-specific knowledge. In addition, it extends results concerning the gradual development of primary students' conditional reasoning with everyday concepts (Markovits & Barrouillet, 2002) to reasoning with mathematical concepts adding to our understanding about the link between mathematics and conditional reasoning in primary school. Moreover, alternatives generation skills predict correct conditional reasoning in both contexts, but interesting differences occurred. The findings from the everyday context mirror previous results, predicting correct AC and DA reasoning and inhibiting correct MT reasoning. In the mathematical context, alternatives generation predicted correct reasoning in all forms. The main contribution of study 1 is the emphasis on the specific role of mathematical knowledge in conditional reasoning with mathematical concepts. The results of the latter studies inspired the development of a short-term educational intervention. This goal was addressed in study 2 by investigating the effects of two short-term trainings based on alternative generation priming within two contexts (contrary-to-fact and mathematical contexts). The results of this study were mixed, revealing a decrease of definite reasoning scores after the short interventions and an increase in DA reasoning; however, further analysis is required. Ultimately, the studies in this dissertation aimed to gain some evidence in the area of conditional reasoning within mathematics in primary school and contribute to future research on this research field.