Michiel Doorman

Utrecht University | UU · Freudenthal Institute for Science and Mathematics Education

Our current multicultural societies require that education addresses diversity and promotes cultural awareness and inter-cultural learning. Mathematics and science education can also contribute to this aspect of citizenship education and create a culture of belonging for all students. Professional development that integrates intercultural learning...

The use of carefully selected contexts can help students in providing meaning, purpose, and relevancy to mathematical concepts and skills. Moreover, contexts can show the relevance of mathematics and support students in building mathematical knowledge on their intuitions and inventions. This use of contexts—from science—is illustrated with three ca...

In March 2020, many schools worldwide were closed due to the COVID-19 pandemic. This closure confronted mathematics teachers with the challenging transition to emergency remote teaching (ERT). How did students experience ERT, and how did these experiences relate to context variables and to their teachers’ beliefs and practices? In particular, what...

The pandemic has demonstrated more than ever that citizens around the world need to understand how mathematics contributes to understanding global challenges and ways of overcoming them. People need to understand that predictions are based on models that make use of assumptions and the best inputs available. They also need to learn to critically ev...

Purpose The authors investigate the use and potential of a theoretical combination of Realistic Mathematics Education (RME) and the Theory of Didactic Situation (TDS) to support Lesson Study (LS) in upper secondary mathematics. Design/methodology/approach Case study performed by university researchers, based on theoretical analysis and case studie...

Braille readers read and comprehend mathematical expressions while moving their fingertips over braille characters. The aim of this exploratory study was to investigate the effect of an intervention that teaches braille readers who use a braille display to use finger movements with a focus on the expression’s mathematical structure. The finger move...

We study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of tasks based on embodied design, including perception-based, action-based and incorporation-based tasks. Tiago’...

The COVID-19 pandemic has confronted mathematics teachers with the challenge of developing alternative teaching practices—in many cases at a distance through digital technology—because schools were closed. To investigate what distance practices in secondary mathematics education have emerged and how teachers experienced them, we set out online ques...

Textbooks are considered to highly influence instruction in lessons, while mathematics textbooks were found not supporting constructivist pedagogy. We explored through a textbook perspective about opportunities for inquiry-based learning (IBL) provided by tasks in lower-secondary mathematics textbooks of Beijing and the Netherlands. Based on an ana...

Recent developments in cognitive and educational science highlight the role of the body in learning. Novel digital technologies increasingly facilitate bodily interaction. Aiming for understanding of the body’s role in learning mathematics with technology, we reconsider the instrumental approach from a radical embodied cognitive science perspective...

A Correction to this paper has been published: https://doi.org/10.1007/s10649-021-10061-0

The design of inquiry-based tasks and problem situations for daily mathematics teaching is still a challenge. In this article, we study the implementation of two tasks as part of didactic scenarios for inquiry-based mathematics teaching, examining teachers’ classroom orchestration supported by these scenarios. The context of the study is the Erasmu...

Braille readers use a braille display and text-to-speech synthesizer while reading and comprehending mathematical expressions and equations. Teachers need to have technological, pedagogical and content (TPACK) knowledge and skills for exploiting the potential of these devices in mathematics education. They have to understand how the use of assistiv...

This research is aimed to describe a learning trajectory for probability through game-based learning. The research employed design research consisting of three stages: preparing for the experiment, design experiment, and retrospective analysis. A hypothetical learning trajectory (HLT) using Sudoku and Snake-and-ladder games was developed by collect...

This article is based on the panel on inquiry based mathematics education and the development of learning trajectories held at the VARGA 100 Conference. After an introduction presenting the theme and organization of the panel, this article focuses on the diversity of conceptualizations of inquiry based education existing today in mathematics educat...

Introducing the slope of a curve as the limit of the slope of secant lines is a well-known challenge in mathematics education. As an alternative, three other approaches can be recognized, based on linear approximation, based on multiplicities, or based on transition points. In this study we investigated which of these approaches fits students most...

Inquiry-based learning (IBL) emphasizes learning through experiencing and constructing. Where IBL is often applied in science education, the conceptualization of IBL practices in mathematics education is less obvious. We compared students’ reports on IBL practices in two different teaching cultures as an attempt to better understand IBL practices i...

Bodily experiences are associated with powerful forms of understanding, yet not much research has investigated to what extent bodily experiences benefit the development of graphical reasoning. We examined the effectiveness of providing embodied support in a teaching sequence of six lessons on motion graphs, including both graph interpretation and g...

Indonesian students’ poor performance in the mathematics test of PISA 2015 prompted the decision by the Ministry of Education of Indonesia to pay more attention to the integration of higher-order thinking (HOT) in the curricula starting in 2018. This new regulation emphasizes the need to have a shared understanding of HOT in mathematics on many lev...

This chapter is about a change in geometry education that took place in the last century. We discuss the emergence of meaningful geometry in the Netherlands. Of course, this was not an isolated reform. Worldwide, mathematicians and mathematics educators came up with new ideas as an alternative for the traditional axiomatic approach to teaching geom...

As cognitive science reports joint action requiring tight intercorporeal coordination between two partners, we aim to evaluate the role of this coordination in computer-supported instrumental genesis for mathematics. In our dual eye-tracking design study we developed an embodied activity that potentially contributes to technologically extended prob...

Assessment is a crucial factor in the implementation of curriculum reform. Little is known, however, on how curriculum changes can be reflected adequately in assessment, particularly if the reform concerns process skills. This issue was investigated for the case of assessing mathematical thinking in a mathematics curriculum reform for 15–18-year-ol...

Firstly, this study examined changes in Indonesian high school students’ attitude towards science after the implementation of inquiry-based learning (IBL). Using a quasi-experimental approach, TOSRA questionnaires were administered before and after intervention to access changes on students’ attitude. The results indicate IBL did not have a positiv...

Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper addres...

Embodied learning environments have a substantial share in teaching interventions and research for enhancing learning in science, technology, engineering, and mathematics (STEM) education. In these learning environments, students’ bodily experiences are an essential part of the learning activities and hence, of the learning. In this systematic revi...

This study reports on a way to address twenty-first-century skills in mathematics education by organizing one-day mathematics challenges in the Netherlands. During such a day, students work in teams in school on an open-ended problem which aims to elicit skills like problem-solving, modeling, collaboration, and communication. The framework and the...

Innovation in mathematics education needs the involvement of teachers, textbook authors, policy makers and researchers. This paper sketches the role and importance of instructional design aiming at new local instruction theories in mathematics education. The approach is shown with a study that investigated how students can be supported in the devel...

Mathematical and scientific knowledge are integral to preparing our population to be actively engaged and responsible citizens. Science and mathematics education, however, has mainly focused on concepts and skills detached from societal implications. In this paper we present an interdisciplinary international design research study in which we devel...

Abstract Introduction: Braille readers encounter difficulties when reading mathematical expressions. In this exploratory study, we created a setting to investigate these difficulties. Method: Using a motion-capturing system, we analyzed the tactile strategies of three braille readers while they read mathematical expressions. To compare tactile with...

On the 22nd and 23rd November 2016, experts of European STEM curriculum gathered to discuss the question ‘What is the position of mathematics education and of informatics education in a coherent STEM curriculum?’ Nine different national perspectives were sketched in papers. These papers were used as input for international discussion groups, which...

This study investigated whether providing opportunity-to-learn can improve Indonesian students’ performance in solving context-based mathematics tasks. On the basis of an inventory of Indonesian students’ difficulties with these tasks and an analysis of textbooks and classroom practices, an intervention program for mathematics teachers was develope...

CIDREE is a network of educational organisations involved in curriculum development and/or educational research, set up in 1990 to establish closer working relationships at a European level. In November 2016, representatives of member countries gathered in order to address the research question 'What is the position of mathematics and informatics e...

Grafieken zijn krachtige middelen om gegevens op overzichtelijke wijze weer te geven. We komen ze dan ook veelvuldig tegen in tijdschriften en andere media. Grafieken zijn echter niet altijd even gemakkelijk te interpreteren. Dit geldt zowel voor kinderen als voor volwassenen. Met name grafieken waarin veranderingen in de tijd zijn afgebeeld, zoals...

In this study, we investigated teachers’ teaching practices and their underlying beliefs regarding context-based tasks to find a possible explanation for students’ difficulties with these tasks. The research started by surveying 27 Junior High School teachers from seven schools in Indonesia through a written questionnaire. Then, to further examine...

Based on the findings of an error analysis revealing that Indonesian ninth- and tenth-graders had difficulties in solving context-based tasks, we investigated the opportunity-to-learn offered by Indonesian textbooks for solving context-based mathematics tasks and the relation of this opportunity-to-learn to students’ difficulties in solving these t...

This chapter gives an overview of the current state of the art related to frameworks and principles for task design so as to provide a better understanding of the design process and the various interfaces between teaching, researching, and designing. In so doing, it aims at developing new insights and identifying areas related to task design that a...

We interpret problem posing not as an end in itself, but as a means to add quality to students’ process of learning content. Our basic tenet is that all along students know the purpose(s) of what they are doing. This condition is not easily and not often satisfied in education, as we illustrate with some attempts of other researchers to incorporate...

The intention of this study was to clarify students’ difficulties in solving context-based mathematics tasks as used in the Programme for International Student Assessment (PISA). The study was carried out with 362 Indonesian ninth- and tenth-grade students. In the study we used 34 released PISA mathematics tasks including three task types: reproduc...

The integration of digital technology into secondary mathematics education is not yet a widespread success. As teachers are crucial players in this integration, an important challenge is not only to attract early adopters, but also to support mid-adopting teachers in their professional development on this point. The questions addressed in this Chap...

Online resources are widely used for educational purposes, such as the training of skills. For algebra education in particular, online resources are expected to contribute to skill mastery in an efficient and effective way. However, studies that underpin these claims through a randomized experiment are scarce. To experimentally investigate the effe...

This paper describes an attempt to design, analyse and refine professional development (PD) resources that encourage the implementation of inquiry-based learning (IBL). We describe the iterative development of the resources in England with over 100 mathematics teachers from secondary, tertiary and adult education and then analyse the impact these r...

Digital resources offer opportunities to improve mathematics teaching and learning, but meanwhile may question teachers’ practices. This process of changing teaching practices is challenging for teachers who are not familiar with digital resources. The issue, therefore, is what teaching practices such so-called ‘mid-adopting’ mathematics teachers d...

Innovative teaching practices such as inquiry-based learning (IBL) have long been topics of discussion amongst mathematics and science educators. However, it is not easy to change day-to-day teaching on a large scale. The relevant question of how to promote a widespread uptake of IBL in day-to-day teaching therefore needs more consideration. In ord...

The book "Educational design research" (http://international.slo.nl/edr/) comprises two parts. Part A provides an introduction into educational design research as a suitable research approach either to address complex problems in educational practice or to develop or validate theories (e.g.) about learning processes, learning environments and the l...

The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how the use of computer tools may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a point of depa...

Insight into spatial structures (e.g., dice dot configurations or double structures) is important for learning numerical procedures such as determining, comparing and operating with quantities. Using design research, a hypothetical learning trajectory was developed and an instruction experiment was performed to gain a better understanding of how yo...

In this paper, we describe the way in which traditional Indonesian games can support the learning of linear measurement. Previous research has revealed that young children tend to perform measurement as an instrumental procedure. This tendency may be due to the way in which linear measurement has been taught as an isolated concept, which is separat...

The availability of technology in the mathematics classroom challenges the way teachers orchestrate student learning. Using the theory of instrumental orchestration as the main interpretative framework, this study investigates which types of orchestrations teachers develop when using technology and to what extent these are related to teachers’ view...

Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in desi...

The availability of technology in the mathematics classroom challenges the way teachers orchestrate student learning. Using the theory of instrumental orchestration as the main interpretative framework, this study investigates which types of orchestrations teachers develop when using technology and to what extent these are related to teachers' view...

In this paper we focus on an instructional sequence that aims at supporting students in their learning of the basic principles of rate of change and velocity. The conjectured process of teaching and learning is supposed to ensure that the mathematical and physical concepts will be rooted in students’ understanding of everyday-life situations. Stude...

This paper deals with the challenge to establish problem solving as a living domain in mathematics education in The Netherlands. While serious attempts are made to implement a problem-oriented curriculum based on principles of realistic mathematics education with room for modelling and with integrated use of technology, the PISA 2003 results sugges...

Students in secondary education experience mathematics and physics as strictly separate disciplines. They do not realise for instance that the mathematics used to describe change (calculus) is used in the topic kinematics in physics. The goal of this research was to examine whether it is possible to develop understanding of both subjects and of the...

In reform mathematics the constructions of students play an important role, in contrast with the traditional view in which teaching mathematics was seen as a process of teaching mathematics according to a pre-designed hierarchy. This paper focusses on how problems and tools are used both to support a reinvention process by the students, and to ensu...

This article discusses the role of context problems, as they are used in the Dutch approach that is known as realistic mathematics education (RME). In RME, context problems are intended for supporting a reinvention process that enables students to come to grips with formal mathematics. This approach is primarily described from an instructional-desi...

This article covers a project conducted by the Freudenthal Institute from August 1991 to September 1994 entitled “The graphics calculator in mathematics education.” The theory of realistic mathematics education was taken as the point of departure for formulating the hypotheses. The developmental research design was used. Observation of the students...

We are going to reconsider the existence property in intuitionistic first order logic (IQC) with function symbols, as presented in Dag Prawitz': "Natural Deduction, A Proof Theoretical Study." That is, we will examine its formulation, and try to give a constructive proof of the theorem. I mention in particular the function symbols in IQC, because t...

The function is a special kind of dependence, that is, between variables which are distinguished as dependent and independent. (…) This – old fashioned – definition stresses the phenomenologically important element: the directedness from something that varies freely to something that varies under constraint. (Freudenthal, 1983, p. 496).

Surnmary In dit arükel beschrijven we een hypothetische leerroute waarlangs leer- lingen formele wiskunde kunnen her-uitvinden. Het betreft een leenoute voor differentiaal- en integraalrekening die is geïnspireerd door de ge- schiedenis van de wiskunde en de kinematica. Centraal in deze geschie- denis staat het modelleren van bewegingen met discret...