Monday seminars will normally be arranged on Mondays at 13.15 in BU-031. If it is arranged at another place or at another time that will be specified.
by Dr. Alvaro Köhn-Luque, University of Oslo.
Alvaro Köhn-Luque and his colleagues at the University of Oslo are part of a larger network of academics and medical doctors working in cancer research.
How can we know whether it is a proof?
Tommy Dreyfus, Tel Aviv University
Proof is arguably what distinguishes mathematics most markedly from other domains of knowledge. Is it obvious what a proof is?
Mathematicians have asked some incisive questions about the nature and role of proof. Research results on students’ conceptions of proof appear inconsistent: While beginning the transition to deductive reasoning is possible already in elementary school, most high school students still have a vague notion of proof, at best. And many teachers are uncertain how to relate to non-algebraic arguments such as verbal, visual and generic ones.
This talk addresses mathematicians, mathematics teachers and mathematics educators. I will present some of the above questions and results and discuss how the community of mathematics educators deals with some of the issues raised.
13.15 Investigating similar triangles using student-produced videos
Anders Støle Fidje, CERME presentation
The task of eliciting student talk in mathematics teaching can be daunting for teachers. An approach to this is using student work actively in teaching. In this paper, the teacher moves in a lower secondary full class discussion regarding similar triangles is investigated. The results show that the teacher utilised different teacher moves to steer the discussion towards both didactical and mathematical goals.
13.45 Characterising the mathematical discourse in a kindergarten
Per Sigurd Hundeland, Martin Carlsen og Ingvald Erfjord, CERME presentation
In our presentation we will report from a study in which we investigate the mathematical discourse in a kindergarten. The mathematical learning activity engaged with was initially designed by researchers for 5-year-olds, and the kindergarten teacher orchestrated the mathematical activity. Observational data was quantitatively analysed by measuring how time and talk were distributed between the kindergarten teacher and the children. We also analysed whether the talk was focused on mathematics or not. Our analysis shows that the time elapsed during the activity was distributed unequally, the nature of the participants’ utterances shared both similarities and differences, while the engagement nurtured upon the kindergarten teacher’s request varied from each of the requests. Based on these results we characterise the mathematical discourse and hypothesise about the children’s potentials for mathematics learning.
Wednesday 21 August at 11-15 in 48-115 An introduction to Abstraction in Context
Tommy Dreyfus, Professor, Tel Aviv University
Abstraction in Context (AiC) is a theoretical framework for investigating processes of construction of abstract mathematical knowledge. It allows for analyzing social as well as cognitive aspects of these processes as well as their interaction.
This meeting is planned as a lecture – workshop – lecture combination. In the opening lecture, I will use examples from our research to introduce the basics of the framework: 1. The AiC view of knowledge construction; 2. The associated methodology as expressed in the epistemic actions model; and 3. The central role played by an a priori analysis of the intended learning activity. In the workshop, participants will carry out an a priori analysis of a learning activity and use the epistemic actions model to analyze two students’ construction of knowledge during this activity. After the break, we will discuss participants’ workshop productions. In the final lecture, I will explain how AiC takes into account the learning context, present some research achievements of AiC, and discuss further directions for AiC based research.
This meeting is intended for graduate students and researchers in mathematics education.
26 August Construction of Knowledge in Classrooms
Tommy Dreyfus, Professor, Tel Aviv University
Students’ construction of mathematical knowledge is, for methodological reasons, usually investigated in small groups of 2-3 students. However, students typically learn in much larger classrooms. In this talk, I will report on recent attempts to combine two theoretical frameworks, Abstraction in Context and Documenting Collective Activity, in order to research the construction of knowledge in inquiry-based mathematics classrooms. Abstraction in Context has successfully been used for investigating processes of construction of mathematical knowledge by small groups and individual students. Documenting Collective Activity has successfully been used for investigating how knowledge becomes normative in classrooms. Combining the two frameworks has made it possible to follow how knowledge is constructed by small groups in a classroom, and then shifts among various social settings in the classroom, as well as who are the knowledge agents for such shifts.
Examples will be chosen from an introductory course on differential equations.
This talk addresses graduate students and researchers in mathematics education.
A case study on mathematical routines in undergraduate biology students’ group-work
In this paper, we investigate the mathematical discourse of undergraduate biology students when working on biology tasks. Our data consists of students’ and the lecturer’s discussion when working on two tasks in an Evolutionary Biology course. In our analysis we make use of the commognitive framework and focus on the use of mathematical routines. We observed that although the overall aim of students’ engagement with routines was exploratory, the way they engaged with mathematical routines when working on biology tasks was ritualized. However, students were aware of the need of using construction routines when trying to mathematize a biological phenomenon although the lack of familiarity with relevant construction routines constrained their ability to deal with certain task situations.
PRIMARY MATHEMATICS CLASSROOM ARGUMENTATION CONTEXT
The review of the related literature has revealed that researchers in mathematics education investigate the argumentation in mathematics classrooms either through the aspect of social and socio-mathematical norms in classroom participation or of mathematical argument and classroom interaction. In theorizing these two strands of the literature, I developed the “Mathematics Classroom Interactional Model” (MCIM) (Dallas, 2019, in press, see attached CERME11 paper). In this presentation, an attempt is made to operationalize the MCIM model by formulating the research questions of the study and operationalizing them through the development of the conceptualization of the methodological framework. As a result, I discuss the operationalization of the methodological framework (in relation to the research questions and the MCIM model) using one (or two) argumentation episode(s) of a 4th-grade primary mathematics classroom to illustrate both the approach to analysis and the rationale for the project.
Thursday 5 september at JU-071
Nils F. Buchholtz, associate professor at UiO will talk about MathTrails
9 September at 13.15 - 14.15
Ten years journey in mathematics education: Iran, New Zealand, and Norway
Farzad Radmehr, postdoc
In this presentation, I will talk about the research projects that I have conducted in the past ten years in Iran and New Zealand that include several quantitative, qualitative, and mixed method studies. In quantitative studies between 2009 to 2013, I have explored how different psychological factors (e.g., mathematics anxiety, mathematics attitudes, working memory capacity, and cognitive style) impact on students’ mathematical performance and problem solving. The qualitative and mixed methods studies that I have conducted with colleagues since 2014 mainly focus on how the quality of teaching, learning, and assessment of mathematics could be improved, particularly at the tertiary level. I will briefly describe the frameworks, theories, and approaches that I have used in the past few years in my second PhD, and also in collaborations with my postgraduate students. In particular, I will talk about my studies in mathematics education in relation to Revised Bloom’s taxonomy, facets of metacognition, APOS theory, problem-posing, puzzle-based learning, and flipped classroom approaches. I hope this introduction will inspire opportunities for research collaborations with my new colleagues at UiA. At the end of my presentation, I will briefly describe the research project that I am now developing that focuses on university students’ perceptions of effective mathematics teaching at higher education.
13.15 Bruk av podcasts i et matematikkurs ved UiA og analyse av eksamensresultat, Kirsten Bjørkestøl
13.45 Comparative judgement as a learning tool in university mathematics: Students’ views of benefits and drawbacks, Niclas Larson
Comparative judgement (CJ) draws on the idea that it is easier to judge which of two objects weighs more, than to judge the weight of one object. In education, CJ can be used to rank students’ responses to a task, rather than evaluate responses due to marking rubrics. Research has shown rankings made by students to be valid and reliable, and hence possible to use as a base for summative assessment. Moreover, research has indicated that assessment by CJ can serve as a learning activity for students.
This paper reports from an exercise in a calculus course, where the students judged each other’s responses by CJ. One of the purposes of the exercise was to explore whether the CJ-process would provide a learning opportunity for the students. The exercise was compulsory, but the results did not count towards their final grade. First, the students were required to respond to the conceptual task “How would you describe the derivative?” Their one-page responses were uploaded to the web engine No More Marking (NMM). NMM randomly selects pairings of responses, where students by a mouse click should judge which response shows the best understanding of the derivative. Each student should fulfil at least 11 such pairwise judgements.
The research data reported in this paper contain students’ responses to the task (N = 64), output from NMM based on students’ judgements (N = 61), and student interviews (N = 5). Data from the interviews support that CJ can improve students’ learning. Despite this, output from NMM indicates the students spent only a small amount of time on their judgements. This ambiguity shows the question of whether active participation in CJ can improve students’ learning still needs further exploration.
13.15 Students of Development Studies learning about modelling and simulations as a research approach in their discipline, Amrit Poudel
13.45 Grade 8 students learning to visualize and mathematically model industrial processes through Sankey diagrams, Pauline Vos
13.15 Developing a survey instrument to explore the incidence of active learning approaches in higher mathematics education, Simon Goodchild
At the annual meeting of the Norwegian Mathematics Council (NMR) held September 2018 Professor David Bressoud spoke about the research evidence associating students’ performance in STEM (MNT) subjects and teacher’s use of active learning approaches. Bressoud also presented an overview of the use of active learning approaches in mathematics teaching in universities in the USA. Following this presentation, the leader of NMR approached Simon Goodchild (Leader of MatRIC) with the request that MatRIC might lead a Norwegian study to explore the incidence of active learning approaches in higher mathematics education in Norway. A working group was set up drawing from both NMR and MatRIC researchers. In this presentation we will describe the development of a survey instrument to find out the extent to which teaching approaches that might promote active learning are used in mathematics in Norwegian Higher Education Institutions. We will describe the two stage Delphi-Study process leading to the construction of the instrument that was first trialled in the early summer 2019. The instrument has since been revised and recently presented at the 2019 Annual Meeting of NMR. We will further report the reaction of NMR members after having the opportunity to respond to the survey.
Our development of the survey instrument has been presented at the MNT Conference in Tromsø (March 28-29, 2019) and at the NMR Annual Meeting in Stavanger (September 18-20, 2019). The Monday seminar presentation will be based on the latter of these.
13.45 First-year engineering students’ reflections on integration and the Fundamental Theorem of Calculus, Hans Kristian Nilsen
From an institutional perspective, my study so far focuses on first-year engineering students at university and their use and justification of techniques when solving a task involving integration by parts. A second part of the study aims to investigate how these same groups of calculus students reflect on integration as a concept and the Fundamental Theorem of Calculus (FTC). Students’ discussions are analyzed through observations of group work and interviews. For the first part of the study, despite encouraging the students to justify their techniques, findings indicate that the discourse focused on rules and formulas without mathematical justifications. Hence, the applied techniques became almost exclusively of pragmatic value, focusing on whether or whether not they led to an answer. This suggests that even for university students, techniques applied for simple routine tasks in integration, to a large extent become “de-mathematicised”. For the second part of the study, the students demonstrated reluctance and confusion related to the algebraic sense-making of notations. Although all students somehow associated integration with “area under a curve” a great deal of variation seems to be the case concerning conceptual aspects like limits of Riemann sums, infinitesimals and the relation between anti-derivatives and integration.
13.15 Introduction to MERGA, PAMAR, MatRIC and Department
21 October 13.15-15.00
Mathematics crossing borders: Integrating mathematics with other disciplines in teacher education
Professor Merrylin Goos , University of Limerick, Ireland
This presentation will explore ways in which the discipline of mathematics underpins, illuminates, or can be integrated with other disciplines in the context of mathematics teacher education. Drawing on my experience as a mathematics teacher educator and mathematics education researcher, I will compare different models of integration I have used or observed in pre-service and in-service teacher education. These include mathematical modelling, curriculum integration, and numeracy across the curriculum approaches. My analysis will investigate the theoretical and philosophical rationales for these different approaches, the positioning of mathematics and assumptions about the relationship of mathematics to other disciplines, barriers to and enablers of integration, and implications for both teacher education and classroom practice more generally.
Disciplinary border crossing in mathematics education is sometimes conceived of in terms of making connections between mathematics, other disciplines, and the real world. Mathematics curriculum documents in many countries stress the value of such connections for enriching student understanding and engagement. Rather than giving priority to connections, an alternative view defines the border between disciplines and disciplinary communities as a marker of sociocultural difference, giving rise to a discontinuity that needs to be negotiated. This view draws on sociocultural theories of learning in communities of practice (Wenger, 1998) and boundary crossing between communities (Akkerman & Bakker, 2011). Boundaries and boundary crossing are thought to carry potential for learning involving dialogical interactions between multiple perspectives and multiple actors. Taking a boundary crossing theoretical perspective permits a deeper and more critical investigation of the types of connections and discontinuities that might exist between mathematics, other disciplines, and the real world.
Starts at 14.15 in BU-031
Deparment meeting with rector and vice-rectors. The rectorate leads the meeting and start by presenting themselves and some of their main aims, followed by prepared question from them to us and discussion.
4 November at J1-064
13.15 First year seminar, Yusuf Feyisara Zakariya
Undergraduate students’ performance in mathematics: Singular and combined effects of learning approaches, self-efficacy, and prior mathematics knowledge.
Reactor: Professor Matthew Inglis, Mathematics Education Centre, Loughborough University, United Kingdom.
This project concerns with an exploration of factors that affect learning outcomes of students in higher education mathematics. It is framed within a quantitative research methodology in which the existence of personal traits such as prior knowledge, self-efficacy, learning approaches, etc., are not questioned and that these traits may be operationalised and measured. Two well-established psychological theories are knitted together to form the conceptual framework for justifying appropriateness and usefulness of chosen constructs under investigation coupled with hypothesized relationships among them. These theories are student approaches to learning theory and self-efficacy theory. A cross-sectional survey research design was adopted with a focus on first-year engineering students aimed at addressing three research questions. These research questions are:
In the seminar, I will present an overview of the project including the adopted theoretical and methodological stances as well as preliminary results of two analysed data sets. The preliminary findings have established a differential classification of the students’ approaches to learning into deep and surface. Thus, the first research question is addressed. It has also exposed the relationship between calculus self-efficacy and approaches to learning. Students with high sense of self-efficacy have been identified with deep approaches and those with low sense of self-efficacy have been identified with surface approaches. Some of these results have been published in level 1 journals and some submitted for conferences. You may follow this LINK to access the published articles.
Attempting to unpack mathematics teacher education: Competencies for reflection
By Cengiz Alacaci
Mathematics teacher education has evolved into a professional field with its own tools, processes, theories and models. In this presentation, I will describe a research project on developing mathematics teacher educator competencies, as an attempt to look back and better understand the field. I will present what we found out using Delphi method regarding mathematics teacher educator competencies. I will contextualize some of the contending issues by giving examples from the field. Then I use the opportunity to reflect upon the development of mathematics teacher education as a field based on related literature and my own experiences.
By Angelika Bikner-Ahsbahs, professor at University of Bremen
In the past decades, the diversity of theories has grown providing more and more sources for innovating the field of mathematics education; but also entailing the danger of extending its fragmentation into separated research and developmental cultures. Therefore, communicating research and its results has become increasingly challenging. Reasons do not only lie in the general complexity of research itself but rather in the diverse cultures of the educational systems worldwide, in the broad diversity of reference disciplines of mathematics education and the complexity of the teaching and learning of mathematics in the classroom – just to name a few. In 2005 at CERME4, the networking of theories emerged as a new research practice that explores how to handle these problems scientifically.
In the talk and some exercises, I will make explicit what we mean when we talk about the networking of theories and what we do not mean. Examples will show that the roots of this kind of research go back to the 70s and 80s. However, the subsequent increasing diversity of theories in the field piled pressure on the field to find a way of coping with this diversity in a scientific manner. Thus in 2006, a group of researchers began to explore and develop the networking of theories as a research practice. By telling the story of the research journey of this group (the so-called (Bremen-) networking theories group) and how it proceeds today, I will show how research in the networking of theories strand was done, what it revealed and wherefore it may or may not be relevant for contemporary and future research.
13.15 Celestine Ifeanyi Nnagbo
Assessing the Affordances and Constraints of Numbas for Mathematics Teaching and Learning.
Emergent technologies like computer-based assessment systems (CBAS) are gaining more importance in mathematics education. CBAS provide new learning potentialities through formative and summative assessments. Amongst many CBAS is the software tool, Numbas, which was developed at the school of mathematics and statistics, university of Newcastle, and is currently being used in more than thirty universities within the United Kingdom and across the globe. Numbas places emphasis on formative assessment and feedback to students’ actions. Numbas primarily enables a student to enter mathematical answer in the form of algebraic expression and then gets immediate feedback, which would impact his/her mathematical engagement.
This thesis aims at assessing the affordances, and constraints of Numbas in mathematics teaching and learning. The study adopts a socio-cultural stance, the concept of affordance developed by Gibson (1977), and Norman (1988), and Hadjerrouit’s evaluation instrument and affordance model to form the theoretical framework. Multiple-case studies design was adopted focusing on student-teachers, teachers and the developer of Numbas. The participants’ perceptions and experiences with Numbas will be studied in-depth using both survey questionnaires and interviews. Based on the findings, didactical implications will be drawn for learning mathematics using Numbas, and recommendations for future work will be proposed.
Academic advisor: Said Hadjerrouit
13.45 Besjona Shkurti
Using eye-tracking to understand inductive reasoning
One of the topics of school mathematics is inductive reasoning. Many inductive reasoning problems are composed of series of shapes, and other visuals or symbols connected with logical and semantic links. The tasks consist in (a) detecting regularities, (b) abstracting relations, and (c) deriving general rules. Eye-tracking technology gives us information about the cognitive activity of students, which, if discovered, helps us understand the learning better and improve the teaching.
The aim of this thesis is to understand students’ work with inductive reasoning tasks by using eye-tracking methodology and to discover the characteristics of the skill of generalizing involved in inductive reasoning. This study is being done within the qualitative research approach. I am planning to give a series of visual inductive reasoning tasks to students in computer environment. Data from eye-tracking equipment, analyzed with required software, and interviews will be used as data collection methods. The purpose of this study is to contribute to the improvement of teaching methods by gaining a better understanding of how students think in inductive reasoning tasks. Methodologically, it is expected that the use of eye-tracking methods in my research will open a new window into the understanding of student’s thinking in the context of inductive reasoning tasks.
Academic advisor 1: Yuriy Rogovchenko
Academic advisor 2: Cengiz Alacaci
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