Students' ability to visualize set expressions: An initial investigation

Hodgson, Ted

doi:10.1007/bf00302628

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…The spatial ability in the model affects mathematics achievement both directly and indirectly via problem solving skills. There are many studies within the relevant literature indicating that one's spatial ability is correlated with mathematics achievement (Delialioğlu & Aşkar, 1999;Fennema & Tartre, 1985;Guay & McDaniel, 1977;Kayhan, 2005) and problem solving skill (Booth & Thomas, 1999;Hodgson, 1996;Markey, 2009;Smith, 1964). A common point of those studies investigating the relationship between spatial ability and problem solving skills is that those students with effective problem solving skills effectively use the visualization and depiction method.…”

Section: Discussion and Suggestionsmentioning

confidence: 99%

A Structural Equation Model Explaining 8th Grade Students’ Mathematics Achievements

Yurt¹,

Sünbül²

2014

ESTP

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Today, in a time when extraordinary and rapid developments occur daily and because foundations of daily life are increasingly becoming mathematical, knowing and understanding mathematics have gained considerable importance. In such a changing world, individuals able to understand and use mathematics will have more say in enhancing opportunities and occasions that may shape their future (NCTM, 2000). In this context, understanding and being successful in mathematics have gained further importance.

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Section: Discussion and Suggestionsmentioning

confidence: 99%

A Structural Equation Model Explaining 8th Grade Students’ Mathematics Achievements

Yurt¹,

Sünbül²

2014

ESTP

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“…In the process of transition between representation ways of algebraic reasoning, most of the PMSMT follow all ways of representation of algebraic reasoning emerged in the study in order or from the second way to the third one or from the first way to the second one. When the topic of set is considered in our education system from secondary education to college level, it can be concluded that algebraic reasoning in sets is important since it is related to algebraic reasoning and the topics of the undergraduate course of Abstract Algebra (Hodgson, 1996). Therefore, it is important to help the PMSMT produce formal justifications for set expressions and they can be educated in a way explained in the present study.…”

Section: Discussionmentioning

confidence: 91%

“…Moreover, this type might also be linked to the structuring layer of Harel (2008) because the learners focus on arithmetical structures and symbols. However, the usage of Venn-diagrams and shading regions have been examined in previous research and they have stated the important place of visualization in problem solving and explaining reasoning process (Hodgson, 1996;Giordano, 1990;Tall & Thompson, 1989).…”

Section: Discussionmentioning

confidence: 99%

Representation of Algebraic Reasoning in Sets through Argumentation

Uygun¹,

Güner

2022

Int. J. of Cont. Edu. Res.

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The purpose of the current study is to examine the ways in which preservice middle school mathematics teachers (PMSMT) apply and represent algebraic reasoning in their solution processes for the problems in the concept of sets. This model provides detailed information about the reasoning made through the process of the solution of set problems. The study group of this case study was composed of 20 preservice mathematics teachers. The data were collected through written documents and whole class discussions. Based on the findings of the study, three ways to represent algebraic reasoning in sets emerged; context-based representation of algebraic reasoning, generalization-based representation of algebraic reasoning and formulization-based representation of algebraic reasoning. These ways determined based on the argumentations that they formed. They produced different warrants since they reasoned differently.

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“…Previous research studies have found a positive relation between the spatial visualization ability and the mathematics performance (Usiskin, 1987;Herskowithz, 1989;Hodgson, 1996, Presmeg, 1997. Gutierrez (1985) mentions that he usefulness of visualization and graphical representations in the teaching of mathematics had been recognized by most mathematics educators and teacher of mathematics.…”

Section: Introductionmentioning

confidence: 99%

A Case Study on the Ways How Engagement with Spatial Visualization Problem Solving Activities Helps Pre-Service MathematicsTeachers in Solving Mental Rotation Problems

Kirmaç¹,

Bulut²

2013

BUEFAD

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The purpose of the present study is to investigate in what ways engagement with spatial visualization problem solving activities helps pre-service mathematics teachers in solving mental rotation problems. To achieve this purpose, a case study is conducted and the case of the study is the group of five pre-service mathematics teachers studying in a public university in Ankara. Spatial Ability Test (SAT) and task-based interviews are used as data collecting instruments. The results of the study show that participants use different ways in solving mental rotation problems; mentally rotating the figure or comparing the relative positions or patterns of the parts of the given figure. Additionally, solving spatial problems help participants in exploring, practicing or shifting their ways of solving problems to cope with the difficulties in solving spatial visualization problems requiring mental rotation accurately and practically.

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Students' ability to visualize set expressions: An initial investigation

Cited by 4 publications

References 10 publications

A Structural Equation Model Explaining 8th Grade Students’ Mathematics Achievements

A Structural Equation Model Explaining 8th Grade Students’ Mathematics Achievements

Representation of Algebraic Reasoning in Sets through Argumentation

A Case Study on the Ways How Engagement with Spatial Visualization Problem Solving Activities Helps Pre-Service MathematicsTeachers in Solving Mental Rotation Problems

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