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Individualized Mathematics Instruction for Adults: The Prison Education Context
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0002-1928-7537
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Individualized instruction tailors content, instructional technology, and pace to the abilities and interests of each student. Carrying out individualized instruction for adults returning to mathematics after some years away from schooling entail special challenges. Adults have, to a greater extent than children and adolescents, various prior knowledge from former schooling. Their rationales for learning mathematics differ from children and adolescents. The main triggers for adults to study mathematics are to get qualification for further studies; to prove that they can succeed in a subject where they have previously experienced failure; to help their children and to experience understanding and enjoyment. Adults also struggle with negative affective feelings against mathematics as a subject and with mathematics anxiety to a greater extent than children and adolescent learners. 

Much is known about the special challenges in teaching adults but less is known of how to adapt this knowledge into teaching practice. This thesis addresses the aim of how to organize individual mathematics instruction for adult students without an upper secondary diploma, so that they are given opportunities to succeed with their studies and reach their individual goals. 

In the context of the Swedish prison education program four case studies were conducted to address the aim. The methods used were: development and evaluation of a student test of prior knowledge on proportional reasoning combined with clinical interviews; interviews focusing on a student’s rationales for learning; a retrospective analysis of events in relation to feedback situations; an analysis of a common student error in relation to the role of language representation as a signifier for triggering students’ schemes.

The results showed, first, that the test together with the clinical interview elicited students’ prior knowledge on proportional reasoning well and that different students could be classified in qualitatively different ways. Second, that the theoretical construct of instrumental- and social rationales for learning was useful for understanding a student’s initial and changing motivation in relation to the teaching and to the practice of mathematics the teaching entails. Third, that a delay between written and oral feedback worked as a mechanism that gave the receiver time and space to reflect on the feedback, which led to circumventing situations where the student ended up in affect that hindered him from receiving the teacher’s message. Forth, that a linguistic representation in the problem formulation led to a common error, triggering two separate schemes. As a result of the analysis, a theoretical extension of Vergnaud’s theory was suggested by detailing the relationship between schemes and semiotics.

The results are transformed into a model for individualized mathematics instruction of adults, MIMIA, in the Swedish prison education program. MIMIA consist of a flowchart for using practical- and thinking tools for individualizing instruction. The practical tools are used to elicit students’ prior knowledge and organize feedback situations for adults with negative affective feelings towards mathematics. The thinking tools are used to understand and classify adult students’ rationales for learning and to analyze students’ solution schemes in relation to language representations in the problem statements.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics and Science Education, Stockholm University , 2020. , p. 79
Series
Doctoral thesis from the department of mathematics and science education ; 22
Keywords [en]
Individualized Instruction, Mathematics, Prison Education, Adults, Tutoring
National Category
Educational Sciences
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-179978ISBN: 978-91-7911-098-7 (print)ISBN: 978-91-7911-099-4 (electronic)OAI: oai:DiVA.org:su-179978DiVA, id: diva2:1415506
Public defence
2020-05-08, Hörsal 7, hus D, Universitetsvägen 10 D, Stockholm, 13:00 (Swedish)
Opponent
Supervisors
Available from: 2020-04-15 Created: 2020-03-18 Last updated: 2022-02-26Bibliographically approved
List of papers
1. Designing a research-based detection test for eliciting students’ prior understanding on proportional reasoning
Open this publication in new window or tab >>Designing a research-based detection test for eliciting students’ prior understanding on proportional reasoning
2019 (English)In: Adults Learning Mathematics: An International Journal, ISSN 1744-1803, Vol. 14, no 1, p. 6-22Article in journal (Refereed) Published
Abstract [en]

In the Swedish Prison Education Program only two out of ten reach a passing grade in their mathematics courses. Large variation in prior knowledge makes it difficult to meet the students at their level. This paper reports on a project aiming to enhance students’ possibilities to access mathematics through individualization. Research findings on the development of the pervasive mathematical idea of proportional reasoning are used to construct a test on proportional reasoning, designed to work specifically with students with large variation in prior knowledge. The test presented here, combined with a follow-up clinical interview, can be used in adult education in general as a basis for individualizing instruction. 

Keywords
proportional reasoning, adult education, prison, individualized instruction
National Category
Educational Sciences
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-179868 (URN)
Available from: 2020-03-11 Created: 2020-03-11 Last updated: 2024-03-06Bibliographically approved
2. Bill’s Rationales for Learning Mathematics in Prison
Open this publication in new window or tab >>Bill’s Rationales for Learning Mathematics in Prison
2021 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 65, no 4, p. 633-645Article in journal (Refereed) Published
Abstract [en]

This paper reports on a case study of a student’s rationales for learning mathematics. We operationalize Stieg Mellin-Olsen’s educational concept of rationales for learning and apply the concept on data consisting of three semi-structured interviews with a student in the Swedish prison education program. Our analysis shows that the student’s rationales vary in character over time as a reaction to his educational contexts. We conclude that Mellin-Olsen’s construct of rationales is useful for understanding students’ changing motivation in relation to the teaching and to the practice of mathematics the teaching entails. Teachers may use the concepts from our analysis as cognitive tools, related to students’ rationales for learning. By identifying students’ different rationales, opportunities arise for an individualized instructional design.

Keywords
Individualized instruction, motivation, rationales, prison education
National Category
Educational Sciences
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-179869 (URN)10.1080/00313831.2020.1739133 (DOI)000519710800001 ()
Available from: 2020-03-11 Created: 2020-03-11 Last updated: 2022-02-26Bibliographically approved
3. Distance mathematics education as a means for tackling impulse control disorder: the case of a young convict
Open this publication in new window or tab >>Distance mathematics education as a means for tackling impulse control disorder: the case of a young convict
2017 (English)In: For the Learning of Mathematics, ISSN 0228-0671, Vol. 37, no 3, p. 27-32Article in journal (Refereed) Published
Abstract [en]

While distance education (DE) is often considered as a means to provide mathematical education to students in remote locations or to promote the professional development of mathematics teachers, this article reports a case showing that DE may also be useful in providing mathematical instruction to individuals who are marginalized or disadvantaged due to their psychological or social conditions. In particular, we present the case of a young male convict with impulse control disorder (ICD) to whom DE made it possible to follow mathematical instruction adapted to a prison environment, which again helped him to modify his attitude towards the study of mathematics. Furthermore, the DE-setting provided him with an environment in which he could control his ICD-related outbursts originally triggered by the mathematics lessons and the associated feedback processes. We argue that DE has unforeseen potentials in terms of mathematical education for learners who are disadvantaged due to their psychological and social conditions.

Keywords
adult education, mathematics, feedback, distance education, affect
National Category
Educational Sciences
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-179857 (URN)
Available from: 2020-03-11 Created: 2020-03-11 Last updated: 2022-02-26Bibliographically approved
4. The role of language representation for triggering students’ schemes
Open this publication in new window or tab >>The role of language representation for triggering students’ schemes
2018 (English)In: Perspectives on professional development of mathematics teachers: Proceedings of MADIF / [ed] Johan Häggström, Yvonne Liljekvist, Jonas Bergman Ärlebäck, Maria Fahlgren, Oduor Olande, Gothenburg: Swedish Society for Research in Mathematics Education , 2018, p. 49-59Conference paper, Published paper (Refereed)
Abstract [en]

Schemes were Piaget’s most important concept. Through work of Vergnaud, schemes were connected to representations and theoretical models from Piaget were connected to principal insights from Vygotsky. We suggest that the scheme concept can be elaborated further by detailing the relationship between schemes and semiotics. We consider a case of an adult student’s work on a situation involving average speed. Linguistic representations in the problem formulation triggers two separate schemes for the student, one associated to the speed concept and one to the arithmetic average. By identifying exemplary phenomena in the presented case, we show how previous theory connecting schemes and representations can be extended to allow alternative explanations for a well-known class of students’ errors.

Place, publisher, year, edition, pages
Gothenburg: Swedish Society for Research in Mathematics Education, 2018
Series
Skrifter från svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 13
Keywords
adult education, mathematics, speed, rate, language representation
National Category
Educational Sciences
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-179867 (URN)
Conference
The eleventh research seminar of the Swedish Society for Research in Mathematics Education, Karlstad, Sweden, January 23–24, 2018
Available from: 2020-03-11 Created: 2020-03-11 Last updated: 2022-02-26Bibliographically approved

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