Review of factors of influence for implementing large scale development projects

This work is part of grant 2020-04090 under the Swedish Research Council

Students' formal written communication

This work is part of Swedish Institute for Educational Research grant 2020-00066

Designing a research-based detection test for eliciting students’ prior understanding on proportional reasoning

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.

Research Findings' Impact on the Representation of Proportional Reasoning in Swedish Mathematics Textbooks

This article investigates the impact of research findings on the representation of proportional reasoning in two commonly used Swedish mathematics textbook series for grades 7-9. A research-based framework that identifies five learning goals for understanding of proportional reasoning was used to analyse the textbooks. The results brought to surface a gap between research findings of important issues to address and the actual design of mathematics textbooks. Both textbook series make use of an effective range of representations. Besides that, the analysis shows low impact from research findings concerning the importance of given opportunities to compare and contrast additive and multiplicative situations, identify multiplicative structures and proportional thinking, make use of meaningful symbolic representations, and connect and relate fraction knowledge. The main conclusion is that there are possibilities for improvement in textbook design in relation to understanding proportional reasoning

Individualized Mathematics Instruction for Adults : The Prison Education Context

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

Research Findings' Impact on the Representation of Proportional Reasoning in Swedish Mathematics Textbooks

This article investigates the impact of research findings on the representation of proportional reasoning in two commonly used Swedish mathematics textbook series for grades 7-9. A research-based framework that identifies five learning goals for understanding of proportional reasoning was used to analyse the textbooks. The results brought to surface a gap between research findings of important issues to address and the actual design of mathematics textbooks. Both textbook series make use of an effective range of representations. Besides that, the analysis shows low impact from research findings concerning the importance of given opportunities to compare and contrast additive and multiplicative situations, identify multiplicative structures and proportional thinking, make use of meaningful symbolic representations, and connect and relate fraction knowledge. The main conclusion is that there are possibilities for improvement in textbook design in relation to understanding proportional reasoning

Bill’s Rationales for Learning Mathematics in Prison

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

The role of language representation for triggering students’ schemes

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

Distance mathematics education as a means for tackling impulse control disorder : the case of a young convict

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