Pauline Vos | Western Norway University of Applied Science (original) (raw)
Books by Pauline Vos
In the 20th century, assessment in mathematics classrooms mainly focused on knowledge with low co... more In the 20th century, assessment in mathematics classrooms mainly focused on knowledge with low cognitive demands, in particular on testing students on memorized calculation procedures. In the 21 st century, we need to focus more on higher order thinking (HOT), which should also be reflected in mathematics assessment. This will require quite an overhaul, not only in assessment, but also of instruction as teachers will need to carefully look at how to best prepare students for assessment formats that activate HOT. In this chapter, we will explain that assessment tasks activating HOT focus on inquiry and creativity rather than on reproduction and imitation. To assist with analysing and redesigning tasks, we explain the usefulness of the Revised Bloom's Taxonomy as a framework to conceptualize cognitive processes (e.g., summarizing, comparing, explaining, exploring, analysing, critiquing, and creating). We will validate the framework through four exemplary types of tasks: problem-posing tasks, puzzle-problems, modelling tasks based on realistic questions, and cloze paragraphs; and we will discuss how assessment tasks can be designed or redesigned based on the framework. We will review some challenges in the research and development of mathematics assessment for the 21 st century, present research-based evidence on how assessment tasks activating HOT in mathematics can be accessible tasks that lead to a better conceptual understanding of mathematics, and finally, we discuss issues of reliability and validity.
Mathematical Modelling Education in East and West, 2021
Mathematical modelling tasks increasingly feature the use of digital tools and media. In this cha... more Mathematical modelling tasks increasingly feature the use of digital tools and media. In this chapter, we discuss the wide variety of these. Until now, classifications for modelling tasks did not consider the use of tools and media. Therefore, we developed a new classification for ICT-based modelling tasks. One class relates to mathematics; the others differentiate across (1) modelling aspects unrelated to tool and media, (2) the task context, (3) the digital tools and media (CAS, Wikipedia, type of feedback, etc.) and (4) students' anticipated activities guided by task regulations, such as group work or time restrictions. The classification was validated with three example tasks. A visual presentation based on the classification system enables the evaluation of qualities of a given ICT-based modelling task and can give insight into potential adaptations.
Ark Flyt diagrammer, 2019
dette et arbeidsark for å lære om sankey diagrammer (flyt diagrammer) med elever i 8. trinn (elle... more dette et arbeidsark for å lære om sankey diagrammer (flyt diagrammer) med elever i 8. trinn (eller 7. eller 9.)
Sankey Diagrams, 2019
This is a classroom worksheet for grade 8 (or 7 or 9) to learn about data visualization, in parti... more This is a classroom worksheet for grade 8 (or 7 or 9) to learn about data visualization, in particular the use of Sankey Diagrams
Agder Mattebroer 12Oppgavene, 2019
Here are eight mathematics tasks which start from bridges in Agder, the province of South Norway
Digital Experiences in Mathematics Education, 2016
In an increasing number of mathematics classes throughout the world, technology is being used fo... more In an increasing number of mathematics classes throughout the world, technology
is being used for the teaching and learning of mathematics. But knowledge is
limited about the long-term development of students’ mathematical thinking when
learning mathematics with the use of technology. This article reports on the development
of a student and the role of the graphing calculator (GC) in his learning about derivatives
and instantaneous rate of change. This case is compelling, because the student is an
intensive user of the GC and develops flexible problem-solving techniques – techniques
which differ from those of his peers and from what he was taught in mathematics class.
We used the framework of instrumental genesis to investigate how this student’s
mathematical thinking was affected by the use of the GC. Over a 2-year period, we
administered four task-based interviews involving problems on instantaneous rate of
change situated in contexts. We found that the use of the GC may facilitate a learning
process in which instrumentation schemes involving symbolical representations develop
separately from those for the graphical and numerical use of the GC.
Report for Den Haag, Netherlands: Nederlandse Organisatie voor Wetenschappelijk Onderzoek/ProgrammaRaad voor het OnderwijsOnderzoek, 2001
Papers by Pauline Vos
Adults Learning Mathematics,an International Journal, 2024
In 2020, the COVID-19 pandemic urged authorities to share quantitative information such as infect... more In 2020, the COVID-19 pandemic urged authorities to share quantitative information such as infection and death rates. One way of disseminating was through graphs, maps, and diagrams. Such data visualizations communicate numeric data in compact ways, but also require a particular mathematical literacy from readers. We conceptualized this particular mathematical literacy as visual-numeric literacy. To study it, we interviewed two young adults with higher education but low confidence in mathematics and asked them to make sense of COVID-19 data visualizations from journalistic digital media. An in-depth analysis of their visual-numeric literacy revealed that the two participants had developed various sense-making strategies. Their lived experience in the pandemic assisted them to overcome obstacles in mathematical sense-making, and gain insights from the data visualizations. We discuss out-of-school mathematics learning and provide recommendations for improving adults’ visual-numeric literacy.
![Research paper thumbnail of Kva er matematisk modellering?[What is mathematical modelling?]](https://attachments.academia-assets.com/114455894/thumbnails/1.jpg)
](Tangenten, 2024
Kva er matematisk modellering? Kvifor matematisk modellering? Korleis ser ei modelleringsoppgåve ... more Kva er matematisk modellering? Kvifor matematisk modellering? Korleis ser ei modelleringsoppgåve ut? Er ein modell det same som ein representasjon? Modellering har vore med i norske læreplanar i fleire tiår. Ikkje alle lærarar har hatt om matematisk modellering i eiga utdanning, noko som kan føre til usikkerheit knytt til korleis ein bør undervise om det (Berget, 2023). Gjennom denne artikkelen vil vi gi nokre svar på desse spørsmåla. Målet er å få fram mangfaldet i korleis ein kan forstå omgrepet, og at mange ulike elevaktivitetar kan inngå som arbeid med matematisk modellering.
Mathematics Enthusiast, 2024
We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit o... more We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit of mathematical modeling (SoMM), which idealistically reflects core aspects of mathematical modeling. The basis of our analysis is the notion of bildung, which is an educational philosophy that strives for harmonizing heart, mind, social life and culture. We built SoMM on five descriptions of mathematical modeling: two research studies from the 1970s, two studies about the work of professional modelers, and one about an environmental school project. We captured SoMM as a collection of aspects at the micro, meso and macro level: at the micro level, we found aspects such as agency, anticipating, scrutiny and critique as part of SoMM; at the meso level, we found collaborating, consulting and navigating social norms; and at the macro level, interdisciplinarity, relevance and social justice. Through the lens of bildung-based educational philosophies, we see that instruction and assessment traditions have transposed mathematical modeling into 'teachable' practices that drift away from SoMM. We recommend focusing more on fostering mathematical modeling and to assess students through alternative formats (e.g., group projects).
Frontiers in Education, 2024
People are more motivated to put effort into learning when they know they will be able to put the... more People are more motivated to put effort into learning when they know they will be able to put the learnt content to use. These relevance perceptions play a motivating role in the learning of mathematics, a subject renowned for its abstraction, hard examinations, and usefulness in many fields in society (research, industries, etc.). In this article, we describe a study on upper secondary students in an advanced mathematics course and their perception of the relevance of mathematics in future professions, in particular regarding two concepts in their curriculum (logarithms, trigonometry). We defined relevance as a connection between an object (relevance of what?), a subject (relevant for whom?), an asserter (relevant according to whom?), and a purpose (relevant to what end?).
The aim of the study was to know (1) what relevance perceptions students held regarding the advanced abstract mathematical concepts, and (2) how students can develop these considering that students do not yet know exactly what future is ahead of them. We interviewed pairs of students (n = 14, 17–19 years old) in two parts. The first part of the interview revealed that students learned mathematics within a traditional school culture that emphasized practice-and-drill of pure mathematics and that did not in any way inform students about the use of mathematics in research and workplaces. After exposing students to authentic applications of logarithms and trigonometry, the second part of the interview showed the power of imagination when it connected students to future professions for which mathematics was relevant. Instrumental in effectively prompting students’ imagination were visualizations showing applications of the mathematical concepts within workplace contexts. Drawing on Leont’ev’s version of Activity Theory, we theorize students’ assertions of the relevance of mathematics through the dialectics of self and collective (relating one’s own goals and more general motives), the dialectics of use-value and exchange-value (needing mathematics for later life or for examinations), and the dialectics of mathematization and de-mathematization (while mathematics is used in many workplaces, it is hidden in instruments).
Tangenten: tidsskrift for matematikkunder visning, 2022
I august 2020 ble den nye læreplanen (LK20) iverksatt for grunnskolens 1.–9. trinn og videregåend... more I august 2020 ble den nye læreplanen (LK20) iverksatt for grunnskolens 1.–9. trinn og videregående skoles 1. trinn (vg1). For vg1 skulle det utvikles nye kjerneelementer tilpasset den nye læreplanen. Vi har analysert hvordan set av eksempeloppgaver publisert i september 2020 og januar 2021 samsvarer med kjerneelementene. Oppsummert viser analysen at det elevene blir bedt om å gjøre i eksempeloppgaver for den teoretiske matematikken, ligger nærmere det som er formulert i kjerneelementene, enn for den praktiske matematikken. Den yrkesfaglige matematikkens oppgaver viser i enda mindre grad til handlinger som er kommunisert i kjerneelementene.
Journal on Mathematics Education, 2022
Many students do not experience usefulness in mathematics. To address this problem, we offered th... more Many students do not experience usefulness in mathematics. To address this problem, we offered them a mathematical tool, Sankey diagrams, which is a flow chart appearing in news media to visualize social, industrial or environmental processes. We carried out an Educational Design Research (EDR) to develop and evaluate lesson materials about contextualized Sankey diagrams. We tested these materials with a class of grade 8 students and evaluated these on the feasibility of students' appropriation of the diagrams. In the lesson, we observed how students were able to read the Sankey diagrams, liked the societal processes visualized, yet did not fully grasp their mathematical properties. However, weeks later, the same students skillfully used Sankey diagrams in an unrelated project, which showed they needed time for their learning. Our contributions are that (1) grade 8 students can appropriate Sankey diagrams and use these in situations relevant to them, (2) design researchers should consider long-term learning effects beyond the experimental phase in EDR. We recommend educational designers to innovate curricula and introduce diagrams from news media to make students experience usefulness in school content.
... Bespreking door: Pauline Vos Instituut voor Didactiek en Onderwijsontwikkeling Rijksuniversit... more ... Bespreking door: Pauline Vos Instituut voor Didactiek en Onderwijsontwikkeling Rijksuniversiteit Groningen Michiel Doorman Freudenthal Instituut voor Didactiek van Wiskunde en Natuurwetenschappen Universiteit Utrecht ...
In the 20th century, assessment in mathematics classrooms mainly focused on knowledge with low co... more In the 20th century, assessment in mathematics classrooms mainly focused on knowledge with low cognitive demands, in particular on testing students on memorized calculation procedures. In the 21 st century, we need to focus more on higher order thinking (HOT), which should also be reflected in mathematics assessment. This will require quite an overhaul, not only in assessment, but also of instruction as teachers will need to carefully look at how to best prepare students for assessment formats that activate HOT. In this chapter, we will explain that assessment tasks activating HOT focus on inquiry and creativity rather than on reproduction and imitation. To assist with analysing and redesigning tasks, we explain the usefulness of the Revised Bloom's Taxonomy as a framework to conceptualize cognitive processes (e.g., summarizing, comparing, explaining, exploring, analysing, critiquing, and creating). We will validate the framework through four exemplary types of tasks: problem-posing tasks, puzzle-problems, modelling tasks based on realistic questions, and cloze paragraphs; and we will discuss how assessment tasks can be designed or redesigned based on the framework. We will review some challenges in the research and development of mathematics assessment for the 21 st century, present research-based evidence on how assessment tasks activating HOT in mathematics can be accessible tasks that lead to a better conceptual understanding of mathematics, and finally, we discuss issues of reliability and validity.
Mathematical Modelling Education in East and West, 2021
Mathematical modelling tasks increasingly feature the use of digital tools and media. In this cha... more Mathematical modelling tasks increasingly feature the use of digital tools and media. In this chapter, we discuss the wide variety of these. Until now, classifications for modelling tasks did not consider the use of tools and media. Therefore, we developed a new classification for ICT-based modelling tasks. One class relates to mathematics; the others differentiate across (1) modelling aspects unrelated to tool and media, (2) the task context, (3) the digital tools and media (CAS, Wikipedia, type of feedback, etc.) and (4) students' anticipated activities guided by task regulations, such as group work or time restrictions. The classification was validated with three example tasks. A visual presentation based on the classification system enables the evaluation of qualities of a given ICT-based modelling task and can give insight into potential adaptations.
Ark Flyt diagrammer, 2019
dette et arbeidsark for å lære om sankey diagrammer (flyt diagrammer) med elever i 8. trinn (elle... more dette et arbeidsark for å lære om sankey diagrammer (flyt diagrammer) med elever i 8. trinn (eller 7. eller 9.)
Sankey Diagrams, 2019
This is a classroom worksheet for grade 8 (or 7 or 9) to learn about data visualization, in parti... more This is a classroom worksheet for grade 8 (or 7 or 9) to learn about data visualization, in particular the use of Sankey Diagrams
Agder Mattebroer 12Oppgavene, 2019
Here are eight mathematics tasks which start from bridges in Agder, the province of South Norway
Digital Experiences in Mathematics Education, 2016
In an increasing number of mathematics classes throughout the world, technology is being used fo... more In an increasing number of mathematics classes throughout the world, technology
is being used for the teaching and learning of mathematics. But knowledge is
limited about the long-term development of students’ mathematical thinking when
learning mathematics with the use of technology. This article reports on the development
of a student and the role of the graphing calculator (GC) in his learning about derivatives
and instantaneous rate of change. This case is compelling, because the student is an
intensive user of the GC and develops flexible problem-solving techniques – techniques
which differ from those of his peers and from what he was taught in mathematics class.
We used the framework of instrumental genesis to investigate how this student’s
mathematical thinking was affected by the use of the GC. Over a 2-year period, we
administered four task-based interviews involving problems on instantaneous rate of
change situated in contexts. We found that the use of the GC may facilitate a learning
process in which instrumentation schemes involving symbolical representations develop
separately from those for the graphical and numerical use of the GC.
Report for Den Haag, Netherlands: Nederlandse Organisatie voor Wetenschappelijk Onderzoek/ProgrammaRaad voor het OnderwijsOnderzoek, 2001
Adults Learning Mathematics,an International Journal, 2024
In 2020, the COVID-19 pandemic urged authorities to share quantitative information such as infect... more In 2020, the COVID-19 pandemic urged authorities to share quantitative information such as infection and death rates. One way of disseminating was through graphs, maps, and diagrams. Such data visualizations communicate numeric data in compact ways, but also require a particular mathematical literacy from readers. We conceptualized this particular mathematical literacy as visual-numeric literacy. To study it, we interviewed two young adults with higher education but low confidence in mathematics and asked them to make sense of COVID-19 data visualizations from journalistic digital media. An in-depth analysis of their visual-numeric literacy revealed that the two participants had developed various sense-making strategies. Their lived experience in the pandemic assisted them to overcome obstacles in mathematical sense-making, and gain insights from the data visualizations. We discuss out-of-school mathematics learning and provide recommendations for improving adults’ visual-numeric literacy.
Tangenten, 2024
Kva er matematisk modellering? Kvifor matematisk modellering? Korleis ser ei modelleringsoppgåve ... more Kva er matematisk modellering? Kvifor matematisk modellering? Korleis ser ei modelleringsoppgåve ut? Er ein modell det same som ein representasjon? Modellering har vore med i norske læreplanar i fleire tiår. Ikkje alle lærarar har hatt om matematisk modellering i eiga utdanning, noko som kan føre til usikkerheit knytt til korleis ein bør undervise om det (Berget, 2023). Gjennom denne artikkelen vil vi gi nokre svar på desse spørsmåla. Målet er å få fram mangfaldet i korleis ein kan forstå omgrepet, og at mange ulike elevaktivitetar kan inngå som arbeid med matematisk modellering.
Mathematics Enthusiast, 2024
We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit o... more We mark the 50th anniversary of mathematical modeling education by reviving the term the spirit of mathematical modeling (SoMM), which idealistically reflects core aspects of mathematical modeling. The basis of our analysis is the notion of bildung, which is an educational philosophy that strives for harmonizing heart, mind, social life and culture. We built SoMM on five descriptions of mathematical modeling: two research studies from the 1970s, two studies about the work of professional modelers, and one about an environmental school project. We captured SoMM as a collection of aspects at the micro, meso and macro level: at the micro level, we found aspects such as agency, anticipating, scrutiny and critique as part of SoMM; at the meso level, we found collaborating, consulting and navigating social norms; and at the macro level, interdisciplinarity, relevance and social justice. Through the lens of bildung-based educational philosophies, we see that instruction and assessment traditions have transposed mathematical modeling into 'teachable' practices that drift away from SoMM. We recommend focusing more on fostering mathematical modeling and to assess students through alternative formats (e.g., group projects).
Frontiers in Education, 2024
People are more motivated to put effort into learning when they know they will be able to put the... more People are more motivated to put effort into learning when they know they will be able to put the learnt content to use. These relevance perceptions play a motivating role in the learning of mathematics, a subject renowned for its abstraction, hard examinations, and usefulness in many fields in society (research, industries, etc.). In this article, we describe a study on upper secondary students in an advanced mathematics course and their perception of the relevance of mathematics in future professions, in particular regarding two concepts in their curriculum (logarithms, trigonometry). We defined relevance as a connection between an object (relevance of what?), a subject (relevant for whom?), an asserter (relevant according to whom?), and a purpose (relevant to what end?).
The aim of the study was to know (1) what relevance perceptions students held regarding the advanced abstract mathematical concepts, and (2) how students can develop these considering that students do not yet know exactly what future is ahead of them. We interviewed pairs of students (n = 14, 17–19 years old) in two parts. The first part of the interview revealed that students learned mathematics within a traditional school culture that emphasized practice-and-drill of pure mathematics and that did not in any way inform students about the use of mathematics in research and workplaces. After exposing students to authentic applications of logarithms and trigonometry, the second part of the interview showed the power of imagination when it connected students to future professions for which mathematics was relevant. Instrumental in effectively prompting students’ imagination were visualizations showing applications of the mathematical concepts within workplace contexts. Drawing on Leont’ev’s version of Activity Theory, we theorize students’ assertions of the relevance of mathematics through the dialectics of self and collective (relating one’s own goals and more general motives), the dialectics of use-value and exchange-value (needing mathematics for later life or for examinations), and the dialectics of mathematization and de-mathematization (while mathematics is used in many workplaces, it is hidden in instruments).
Tangenten: tidsskrift for matematikkunder visning, 2022
I august 2020 ble den nye læreplanen (LK20) iverksatt for grunnskolens 1.–9. trinn og videregåend... more I august 2020 ble den nye læreplanen (LK20) iverksatt for grunnskolens 1.–9. trinn og videregående skoles 1. trinn (vg1). For vg1 skulle det utvikles nye kjerneelementer tilpasset den nye læreplanen. Vi har analysert hvordan set av eksempeloppgaver publisert i september 2020 og januar 2021 samsvarer med kjerneelementene. Oppsummert viser analysen at det elevene blir bedt om å gjøre i eksempeloppgaver for den teoretiske matematikken, ligger nærmere det som er formulert i kjerneelementene, enn for den praktiske matematikken. Den yrkesfaglige matematikkens oppgaver viser i enda mindre grad til handlinger som er kommunisert i kjerneelementene.
Journal on Mathematics Education, 2022
Many students do not experience usefulness in mathematics. To address this problem, we offered th... more Many students do not experience usefulness in mathematics. To address this problem, we offered them a mathematical tool, Sankey diagrams, which is a flow chart appearing in news media to visualize social, industrial or environmental processes. We carried out an Educational Design Research (EDR) to develop and evaluate lesson materials about contextualized Sankey diagrams. We tested these materials with a class of grade 8 students and evaluated these on the feasibility of students' appropriation of the diagrams. In the lesson, we observed how students were able to read the Sankey diagrams, liked the societal processes visualized, yet did not fully grasp their mathematical properties. However, weeks later, the same students skillfully used Sankey diagrams in an unrelated project, which showed they needed time for their learning. Our contributions are that (1) grade 8 students can appropriate Sankey diagrams and use these in situations relevant to them, (2) design researchers should consider long-term learning effects beyond the experimental phase in EDR. We recommend educational designers to innovate curricula and introduce diagrams from news media to make students experience usefulness in school content.
... Bespreking door: Pauline Vos Instituut voor Didactiek en Onderwijsontwikkeling Rijksuniversit... more ... Bespreking door: Pauline Vos Instituut voor Didactiek en Onderwijsontwikkeling Rijksuniversiteit Groningen Michiel Doorman Freudenthal Instituut voor Didactiek van Wiskunde en Natuurwetenschappen Universiteit Utrecht ...
PME conference research report, 2002
TDbeta, 2009
Transdisciplinary domain-specific educational research: the case of mathematical relationships in... more Transdisciplinary domain-specific educational research: the case of mathematical relationships in science.
Many people recognize that teaching basic skills in primary schools (reading, writing, and arithm... more Many people recognize that teaching basic skills in primary schools (reading, writing, and arithmetic) is no longer sufficient for pupils in the digital age. Therefore, governments now increasingly ask schools to add other skills (oral, digital) and to create connections between subjects (e.g., use mathematics in history lessons). In this study, we explored how social simulations can be used in primary education to meet these new goals. We conducted an expert appraisal (a qualitative Delphi method) with four experts specializing in innovating primary education. We selected three simulations that were freely available on the web, relevant for pupils’ lives and had a limited number of parameters. They dealt with segregation, gossip spread and population dynamics. We asked the experts to critically discuss these. Afterward, we analyzed the videotaped discussions in terms of affordances and constraints. The results showed that the affordances of social simulations include their broad ap...
Hoe begrijpen en gebruiken docenten van de schoolvakken natuurkunde, scheikunde en economie het w... more Hoe begrijpen en gebruiken docenten van de schoolvakken natuurkunde, scheikunde en economie het wiskundige concept 'afgeleide'?
This paper reports on the role of the graphing calculator (GC) in the learning of derivatives and... more This paper reports on the role of the graphing calculator (GC) in the learning of derivatives and instantaneous rate of change. In a longitudinal study, we administered task based interviews before and after the introduction of calculus. We analyzed students’ use of the GC in these interviews. This paper reports on the case of one student, Andy, who is a resilient user of the GC while he develops into a flexible solver of problems on instantaneous rate of change. His case demonstrates that, although the GC is meant to promote the integration of symbolical, graphical and numerical techniques, it can facilitate a learning process in which symbolical techniques develop separately from other techniques.
ABSTRACT: For many years the mathematics curricula for junior secondary schools in Belgium (Fland... more ABSTRACT: For many years the mathematics curricula for junior secondary schools in Belgium (Flanders) and the Netherlands were similar. Then, in 1993, a totally innovative curriculum was established in junior secondary schools in the Nether-lands, based on the principles of ...
This paper describes a case study, measuring the implementation of a totally overhauled mathemati... more This paper describes a case study, measuring the implementation of a totally overhauled mathematics curriculum. The case was the Netherlands, where in 1993 a new mathematics curriculum for the lower grades of secondary school was legislated, which differed in many respects from its p redecessor. The current paper describes a quantitative, large-scale trend study, measuring indicators of the extent to which grade 8 mathematics teachers were changing towards the intentions of the new curriculum, and whether students í performance changed accordingly. The paper has a strong methodologigal component on measuring teachers í curriculum implementation on a large scale. Measurements were carried out in 1999 in such a way that data analysis allowed (a) for a trend comparison with data from 1995, and (b) for a between-country comparison with Belgium (Flandres), where the curriculum had not changed. The results show that the match between intentions of the new mathematics curriculum and its im...
International Perspectives on the Teaching and Learning of Mathematical Modelling, 2017
In this chapter, we report on multiple-choice tasks for assessing mathematizing competences of gr... more In this chapter, we report on multiple-choice tasks for assessing mathematizing competences of grade 9 students. The task format is complex, consisting of two layers. In the first layer, students are asked to consider a holistic modelling problem. In the second layer, they are asked for an atomistic competence (making assumptions, assigning variables, etc.) related to the same modelling problem. We conducted a qualitative study to investigate the validity of these tasks based on students’ response processes. Eight students worked in pairs solving the tasks collaboratively. The results show that all students were able to handle the layered task format. They reflected meta-cognitively on the holistic modelling problem, but none of them started solving it in itself. All students considered the remainder of the task, which made them focus on a specific mathematizing activity.
Avances de Investigación en Educación Matemática,, 2020
Students often do not experience the relevance of learning mathematics. This paper reports on an ... more Students often do not experience the relevance of learning mathematics. This paper reports on an exploratory case study, in which a class of grade 8 students (n=35) was introduced to Sankey diagrams. The aim was to explore to what extent these students could appropriate Sankey diagrams, meaning: they could describe these as objects in themselves and they could use them to model and visualize phenomena relevant to them. Based on Cultural-Historical Activity Theory, we developed an analytical construct defined as the object-tool duality, coordinating mathematics as a set of objects and as a set of tools. The analysis of students’ answers showed that they could use these diagrams as tools to visualize phenomena. When asked to describe the object, all mentioned the tool-side. So, in their appropriation the tool-side came before the object-side. Our contribution is that teaching the tool-side of mathematics before the object-side may increase students’ sense of the relevance of mathematics, which is a topic to develop for future research.
CERME-12 conference paper, 2022
The modelling cycle is a theoretical construct frequently applied in research studies on mathemat... more The modelling cycle is a theoretical construct frequently applied in research studies on mathematical modelling. On the one hand, the modelling cycle highlights essential aspects of modelling, which makes it a tool for conceptualizing. On the other hand, the modeling cycle can be used as a research tool for analysis of students' work. In the latter case, it has the limitation of primarily yielding results of a cognitive nature. We sought ways to include other aspects to analyze, such as metacognitive strategies, tool use, and social norms. These aspects support and change the cognitive activities involved in mathematical modelling practice. Rather than the standard modelling cycle, we propose an enriched modelling cycle with overarching layers for analysis of results. The enriched modelling cycle is a wider theoretical framework with interacting dimensions that affect the phases in the modelling cycle. We discuss potentials and challenges of this framework for new research studies.
Mathematics Teacher, 2021
Pauline Vos and Eric Oziegbe Omobude share their experience of teaching Sankey diagrams. Sankey d... more Pauline Vos and Eric Oziegbe Omobude share their experience of teaching Sankey diagrams. Sankey diagrams are useful for modeling and
visualizing industrial processes. They are also useful tools for visualizing relationships within complex data sets. This allows teachers to
visualize how false positive and false negative test results are related.