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Grade 11 Students' Proof Construction Ability in Relation to Classroom Resources

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Title: Grade 11 Students' Proof Construction Ability in Relation to Classroom Resources
Language: English
Authors: Shongwe, Benjamin
Source: International Electronic Journal of Mathematics Education. 2020 15(2).
Availability: International Electronic Journal of Mathematics Education. Suite 124, Challenge House 616 Mitcham Road, CR0 3AA, Croydon, London, UK. Tel: +44-208-936-7681; e-mail: iejme@iejme.com; Web site: https://www.iejme.com
Peer Reviewed: Y
Page Count: 15
Publication Date: 2020
Document Type: Journal Articles
Reports - Research
Education Level: Grade 11
High Schools
Secondary Education
Descriptors: Grade 11, Secondary School Mathematics, Mathematical Logic, Validity, Secondary School Students, Educational Resources, Mathematics Instruction, Teaching Methods, Foreign Countries, Textbooks, Educational Technology, Gender Differences, Age Differences, Institutional Characteristics, Racial Differences, Socioeconomic Status
Geographic Terms: South Africa
ISSN: 1306-3030
Abstract: Despite proof being fundamental to the mathematics discipline and its role as a means to convey mathematical content, little is known about the effect of resources on influencing students' proof construction ability. The purpose of this study was to compare two didactic environments, one regarded as resourced (favored) and the other under-resourced (disadvantaged), in relation to the construction of a mathematical proof. Motivated by the discrepancies in the literature on the influence of school resources on students' performance and the unfortunately prevalent view that the sole function of proof in mathematics is verification by using confirmatory cases, this study sought to examine the differences (if any) between resourced and under-resourced classrooms in relation to students' proof construction ability. To this end, data were drawn from a proof-related task performed by 78 Grade 11 students in the Ethekwini Metropolitan area, South Africa. A modified version of the Proof Construction Assessment tool showed that students in resourced schools significantly performed better than those in under-resourced schools in relation to proof construction. In addition, there was an observable and noticeable effect of this. Specifically, at an alpha = 0.05, the t-test for independent means revealed a significant difference between the two groups, t(76) = 2.749, p < 0.01, d = 0.624 SD. The practical significance of the results emphasizes the importance of taking into account the role of resources when investigating the learning and teaching of proofs. Further, preliminary results also suggested that most students struggled to even begin to prove the proposition. Recommendations and implications for the students' careers and future research are raised and discussed.
Abstractor: As Provided
Entry Date: 2019
Accession Number: EJ1235398
Database: ERIC
FullText Text:
  Availability: 0
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  Data: Despite proof being fundamental to the mathematics discipline and its role as a means to convey mathematical content, little is known about the effect of resources on influencing students&#39; proof construction ability. The purpose of this study was to compare two didactic environments, one regarded as resourced (favored) and the other under-resourced (disadvantaged), in relation to the construction of a mathematical proof. Motivated by the discrepancies in the literature on the influence of school resources on students&#39; performance and the unfortunately prevalent view that the sole function of proof in mathematics is verification by using confirmatory cases, this study sought to examine the differences (if any) between resourced and under-resourced classrooms in relation to students&#39; proof construction ability. To this end, data were drawn from a proof-related task performed by 78 Grade 11 students in the Ethekwini Metropolitan area, South Africa. A modified version of the Proof Construction Assessment tool showed that students in resourced schools significantly performed better than those in under-resourced schools in relation to proof construction. In addition, there was an observable and noticeable effect of this. Specifically, at an alpha = 0.05, the t-test for independent means revealed a significant difference between the two groups, t(76) = 2.749, p &lt; 0.01, d = 0.624 SD. The practical significance of the results emphasizes the importance of taking into account the role of resources when investigating the learning and teaching of proofs. Further, preliminary results also suggested that most students struggled to even begin to prove the proposition. Recommendations and implications for the students&#39; careers and future research are raised and discussed.
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    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
    Subjects:
      – SubjectFull: Grade 11
        Type: general
      – SubjectFull: Secondary School Mathematics
        Type: general
      – SubjectFull: Mathematical Logic
        Type: general
      – SubjectFull: Validity
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      – SubjectFull: Secondary School Students
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      – SubjectFull: Educational Resources
        Type: general
      – SubjectFull: Mathematics Instruction
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      – SubjectFull: Teaching Methods
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      – SubjectFull: Foreign Countries
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      – SubjectFull: Textbooks
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      – SubjectFull: Educational Technology
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      – SubjectFull: Gender Differences
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      – SubjectFull: Socioeconomic Status
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      – SubjectFull: South Africa
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      – TitleFull: Grade 11 Students' Proof Construction Ability in Relation to Classroom Resources
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