Marja van den Heuvel-Panhuizen

• Utrecht University

Despite the generally acknowledged relevance of providing students with rich, challenging tasks that require genuine problem solving, several studies have shown that these tasks are often lacking in textbooks. Bringing new textbooks to the market might feel as a logical solution for this, but maybe there is also another way of resolving this proble...

In the large body of literature that is available about the role of motivation in mathematics education, the focus is mostly on students’ attitudes and feelings toward mathematics in general. In the current small-scale explorative study, we zoomed in on what students think about the tasks they can come across in mathematics education. To investigat...

In this paper, we use video documentation to examine fifth-grade students' use of metaphors as they in small groups in a whole-class setting are engaged in a practical learning activity about fractions in the everyday life context of a vegetable garden. Our study aims to understand how the students collaboratively conceptualise different constructs...

This chapter focuses on four national reforms that started in the second half of the past century and were influenced by international movements, some during their implementation period, others being still influential today. Each of them were led or strongly influenced by prominent mathematicians and were strongly influenced by these mathematicians...

Since the late 1960s, a reform in mathematics education, which is currently known under the name Realistic Mathematics Education (RME), has been taking place in the Netherlands. Characteristic for this approach to mathematics education is that mathematics is not seen as ready-made knowledge but as an activity of the learner. Although much has been...

In many countries, assessment and curriculum reforms came into being in recent decades. In Iran, an important educational assessment reform took place called Descriptive Assessment (DA). In this reform, the focus of student assessment was moved from a more summative approach of providing grades and deciding about promotion to the next grade to a mo...

In this study, we aimed to gain further knowledge about Brazilian primary school teachers' assessment practices and beliefs in mathematics education. For this, we carried out an analysis of curriculum documents and reviewed recent research literature on assessment in Brazil, permitting us to answer the following research question: How are the mathe...

In this study, we aimed to gain further knowledge about Brazilian primary school teachers' assessment practices and beliefs in mathematics education. For this, we carried out an analysis of curriculum documents and reviewed recent research literature on assessment in Brazil, permitting us to answer the following research question: How are the mathe...

This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020–4) of ZDM Mathematics Education. The research covers the broad spectrum of educational research focusing on different content and m...

The balance model is often used for teaching linear equation solving. Little research has investigated the influence of various representations of this model on students’ learning outcomes. In this quasi-experimental study, we examined the effects of two learning environments with balance models on primary school students’ reasoning related to solv...

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...

In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n = 30...

In this introductory chapter I give a preview of the landscape of issues concerning mathematics education in the Netherlands and the role of Realistic Mathematics Education (RME) that one can come across in this volume, which contains the reflections of twenty-eight Dutch mathematics didacticians on teaching and learning mathematics in the Netherla...

This chapter contains an overview of the most important textbook series used in the Netherlands from 1800 to 2010. We distinguish five time periods, and for each period we highlight the textbook series that are most characteristic. To describe the textbooks that were in fashion in the successive periods we distinguish three categories of textbooks:...

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...

This chapter is a synthesis of visions on and experiences with Realistic Mathematics Education (RME) described in the eighteen following chapters of this volume by forty-four authors from fifteen different countries. Through a process of synthesizing information from these chapters and combining and contrasting what the authors wrote about RME, a c...

This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, consists of 17 chapters, in which educators from the Netherlands reflect on the teaching and learning of mathematics in their country and the role of the Dutch domain-specific instruction theory of Realistic Mathematics Education. Written by mathema...

Abstract This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report why such a model is used, what types of models are used, and when they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a comprehensive overview of des...

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...

Unfortunately, the original version of the article contained an incorrect presentation in the author group due to a mistake made at the Publisher’s end. The author Marja van den Heuvel-Panhuizen was previously not included in the first page of the article. The Publisher apologize for this error.

In this study, we investigated the development of algebraic reasoning in 65 fifth-grade students who never had algebra instruction before. In the six-lesson teaching sequence on solving linear equations, a hanging mobile, a physical balance model, played the central role. We expected students’ perceptual-motor experiences with this hanging mobile t...

In this study, we explored the insights that Chinese primary mathematics teachers gained into their students’ mathematical understanding from using classroom assessment techniques (CATs). CATs are short teacher-initiated targeted assessment activities proximate to the textbook, which teachers can use in their daily practice to make informed instruc...

In a three-phase study, with a total of 40 third-grade teachers and their 830 students, teachers were supported to use classroom assessment techniques (CATs) to reveal their students’ knowledge of number operations. In phase I, four teachers and 66 third-grade students participated in five monthly workshops in which CATs were co-designed and their...

In this paper, we describe four studies that have been done in the project Improving Classroom Assessment in China (ICA-C). The project was a sequel to the ICA project in the Netherlands. To shed light on the current situation of Chinese primary school mathematics teachers' perception and practice of classroom assessment, we first did a review stud...

The Dynamic Overlapping Waves Model (DOWM) can model strategy use in problem-solving tasks for strategies that can be construed as developmentally and hierarchically ordered (Boom, 2015). We observed children's (M age = 11 years, SD = 6 months) strategy use during a task in which they had to find the rotation direction of the last gear in a series...

This chapter highlights key aspects of the didactics of mathematics in the Netherlands. It is based on the Dutch contribution to the Thematic Afternoon session on European didactic traditions in mathematics, organised at ICME13 in Hamburg 2016. The chapter starts with a section in which mathematics education in the Netherlands is viewed from four p...

European traditions in the didactics of mathematics share some common features such as a strong connection with mathematics and mathematicians, the key role of theory, the key role of design activities for learning and teaching environments, and a firm basis in empirical research. In this first chapter, these features are elaborated by referring to...

This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research...

Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we e...

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...

This chapter provides an overview of the ICME 23 Study panel on special needs in research and instruction in whole number arithmetic. It starts with a general introduction by Verschaffel about the state of affairs in and the major issues and challenges for research and educational practice in the field of mathematical learning difficulties (MLD). A...

In this chapter, we address children’s geometry learning in the early years with a focus on visualization. We start the chapter with some background information about visualization in mathematics and geometry and its relationship with language and gestures paying special attention to the early years. The next parts of the chapter aim to give insigh...

This study investigated Chinese primary school mathematics teachers’ views on assessment in an effort to determine their assessment profiles. A large-scale questionnaire survey with 1101 teachers from 12 Chinese provinces and regions was carried out. The teachers reported to use assessment on a daily or weekly basis for different purposes. They rec...

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 paper we report on a review of papers written by teachers aimed at knowing more about teachers’ perceptions of the current situation of classroom assessment in primary mathematics education in China. The review is based on 266 papers included in the China National Knowledge Infrastructure database. We found that the teacher-authors reflecte...

Background This paper reports on the use of classroom assessment techniques (CATs) by primary school mathematics teachers in China. CATs are short, focused assessment activities that can reveal students’ understanding of specific mathematical subjects. The study involved six female third-grade mathematics teachers from Nanjing, China. The focus was...

This study examined the effects of a teacher-delivered intervention with online math-ematics mini-games on special education students’ multiplicative reasoning ability(multiplication and division). The games involved declarative, procedural, as well asconceptual knowledge of multiplicative relations, and were accompanied with teacher-led lessons an...

The use of digital tools in algebra education is expected to not only contribute to master skill, but also to acquire conceptual understanding. The question is how digital tools affect students” thinking and understanding. This paper presents an analysis of data of one group of three grade seventh students (12-13 year-old) on the use of a digital t...

In the Netherlands, most contemporary textbook series for primary school mathematics education are influenced by the so-called Realistic mathematics education (RME) reform. This reform dates back to the 1970s. In the study described in this paper we investigated what this reform means for the approach to decimal numbers. We analyzed how this conten...

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...

This paper describes a dataset consisting of longitudinal data gathered in the BRXXX project. The aim of the project was to investigate the effectiveness of online mathematics mini‐games in enhancing primary school students' multiplicative reasoning ability (multiplication and division). The dataset includes data of 719 students from 35 primary sch...

Digital technology plays an increasingly important role in daily life, mathematics education and algebra education in particular. To investigate the effect of a technology-rich intervention related to initial algebra on the achievement of 12–13 year old Indonesian students, we set up an experiment. The experimental group’s intervention focused on e...

In this paper I address a number of projects on elementary mathematics education carried out at the Freudenthal Institute. The focus is on (i) using picture books to support kindergartners’ development of mathematical understanding, (ii) revealing mathematical potential of special needs students, and (iii) conducting textbook analyses to disclose t...

This paper reports about a large-scale longitudinal field experiment investigating the effects of online mathematics mini-games on second- and third-graders’ multiplicative reasoning abilities. The study included students in regular primary education (n = 719) and special primary education (n = 81). There were three experimental conditions: playing...

This study aimed at gaining further understanding of kindergartners’ performance in imaginary perspective-taking (IPT) by examining whether they can imagine what is visible from a particular point of view (IPT type 1: visibility) and how an object or scene will look from a particular point of view (IPT type 2: appearance). The sample consisted of 4...

This paper is about an explorative study of the use of classroom assessment techniques (CATs) by primary school mathematics teachers in China. Six female teachers and 216 third-grade students from two schools in Nanjing were involved. The focus was on assessing whole number arithmetic. Teachers’ use of the CATs was investigated through lesson obser...

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...

Computerspelletjes voor rekenen zijn het leerzaamst als leerlingen ze thuis spelen en op school nabespreken, blijkt uit onderzoek naar minigames voor vermenigvuldigen en delen.

This paper reports the Context-based Mathematics Tasks Indonesia (CoMTI) project that was aimed at getting a better insight into Indonesian students’ low performance on context-based tasks and identifying ways to improve it. The project addressed three main issues: (1) Indonesian students’ difficulties when solving context-based tasks; (2) possible...

We report on the results of the Improving Classroom Assessment (ICA) project in the Netherlands that was aimed at improving primary students’ mathematics achievement through improving their teachers’ classroom assessment. Towards this end we first investigated primary teachers’ assessment practice in a large-scale survey study. After having describ...

This study used a large-scale cluster randomized longitudinal experiment (N = 719; 35 schools) to investigate the effects of online mathematics mini-games on primary school students’ multiplicative reasoning ability. The experiment included four conditions: playing at school, integrated in a lesson (Eschool), playing at home without attention at sc...

Samenvatting Dit artikel beschrijft een eerste try-out van de ‘Digitale Toets Omgeving’ (DTO). Deze DTO wordt ontwikkeld in het kader van het FaSMEd project, een Europees project waarin onderzoek wordt gedaan naar het gebruik van ICT bij formatief toetsen. Deze manier van toetsen is bedoeld om leerkrachten aanwijzingen te geven voor het nemen van d...

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...

In the present study we investigated to what extent workshops aimed at improving teachers’ use of classroom assessment techniques had an effect on students’ achievement in mathematics. Ten primary school teachers participated in two consecutive small-scale studies, aimed at using and improving different classroom assessment techniques in mathematic...

This Research Forum proposal arises from a recent focus on spatial reasoning that began with a multi-year collaborative project amongst a diverse group of researchers (mathematicians, psychologists, mathematics educators) from Canada and the US, and continues to expand with the goal of: mapping out the terrain of established research on spatial rea...

This article describes a field experiment with a pretest-posttest control group design which investigated the potential of reading picture books to children for supporting their mathematical understanding. The study involved 384 children from 18 kindergarten classes in 18 schools in the Netherlands. During three months, the children in the nine exp...

Our paper examines the representational nature of number lines as they are used in instructional tasks. The examination is informed by a so-called mathedidactical analysis of the number line as a tool used in teaching students mathematics. This analysis led to the identification of a family of number line models, based on visual aspects of number l...

In Indonesia, as in many other countries, mathematics teachers, educators and researchers are confronted with student difficulties in initial algebra. To investigate and understand these difficulties, we carried out a pilot study involving 51 Indonesian grade seven students who use a digital mathematics environment for algebra. The notions of opera...

Our study investigated children’s knowledge of multiplicative reasoning (multiplication and division) at the end of Grade 1, just before the start of formal instruction on multiplicative reasoning in Grade 2. A large sample of children (N = 1176) was assessed in a relatively formal test setting, using an online test with 28 multiplicative problems...

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significa...

In recent educational research, it is well acknowledged that gestures are an important source of developing abstract thinking in early childhood and can serve as an additional window to the mind of the developing child. The present paper reports on a case study which explores the function of gestures in a geometrical activity at kindergarten level....

The aim of this study was to contribute to knowledge about classroom assessment by identifying profiles of teachers' assessment of their students' understanding of mathematics. For carrying out this study we used data of a nationwide teacher survey (N = 960) in the Netherlands. The data were collected by an online questionnaire. Through exploratory...

Mathematics textbook series largely determine what teachers teach and consequently, what students learn. In the Netherlands, publishers have hardly any restrictions in developing and publishing textbooks. The Dutch government only prescribes the content to be taught very broadly and does not provide guidelines on how content has to be taught. In th...

This paper reports on a survey of the classroom assessment practices of Dutch primary school teachers in mathematics education. We investigated, using an online questionnaire, how teachers collect information on their students’ progress and how teachers’ assessment methods, purposes, and beliefs about the usefulness of assessment are related. In to...

Hebben kinderen al kennis van vermenigvuldigen en delen, voordat ze in groep 4 beginnen met het leren van de tafels? Wat kunnen ze dan al en wat is hierop van invloed? In het BRXXX-project van het Freundenthal Instituut van de Universiteit Utrecht is hier onderzoek naar gedaan. Het is bekend dat kinderen, voordat het formele rekenwiskundeonderwijs...

In this study we investigated the role of a dynamic online game on students’ early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10–12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the students’ on...

We investigated children’s informal knowledge of multiplicative reasoning. Data were collected at the end of first grade, before this mathematical domain was explicitly taught. A large sample of children (n = 1176) was assessed in a relatively formal test setting, through an online test containing 28 multiplicative problems with and without context...

Die Diskussionen über neue Formen des Lernens sind häufig vom Kern des Lernens weit entfernt. Im Gegensatz dazu wird in diesem Beitrag Lernen unter einer als solche erachteten Schlüsselfrage der Mathematikdidaktik überdacht: Wie können wir Lernende dazu veranlassen, auf der Basis ihres vorhandenen Wissens ein neues Verständnis auszubilden? Exemplar...

Effects of online mini-games on second-graders’ multiplicative abilities This study used a large-scale randomized experiment (n = 1005; 46 schools) to investigate the effects of mathematical mini-games on 2nd-graders’ multiplicative abilities. Four conditions were included: playing at school (E1), playing at home without attention at school (E2),...

This study investigated whether an intervention including an online game contributed to 236 Grade 6 students' performance in early algebra, that is, solving problems with covarying quantities. An exploratory quasi-experimental study was conducted with a pretest-posttest-control-group design. Students in the experimental group were asked to solve at...

In this chapter we address the role of picture books in kindergartners’ learning of mathematics. The chapter is based on various studies we carried out on this topic from different perspectives. All studies sought to provide insight into the power of picture books to contribute to the development of mathematical understanding by young children. We...

This study used a large-scale randomized experiment (n = 1005; 46 schools) to investigate the effects of mathematical mini-games on 2nd-graders' multiplicative abilities. Four conditions were included: playing at school (E1), playing at home without attention at school (E2), playing at home with debriefing in school (E3) and, in the control group,...

Research has shown that high expectations of teachers about their students’ academic development have a positive influence on how these students actually develop. Therefore, when aiming to improve students’ learning results it is essential to know how teachers think about their students’ abilities. The present study was meant to investigate what pe...

Also appeared in 2013 in Tijdschrift voor Didactiek der Betawetenschappen, 30 (1 & 2).

In this study, we examined special education students’ use of indirect addition (subtraction by adding on) for solving two-digit subtraction problems. Fifty-six students (8- to 12-year-olds), with a mathematical level of end grade 2, participated in the study. They were given a computer-based test on subtraction with different types of problems. Al...

The purpose of this study was to investigate what experts in the use of picturebooks in mathematics education consider powerful characteristics of such books in the support of young children's learning of mathematics. The study started by investigating experts’ views of such characteristics, as reflected in academic and professional publications on...

Developing knowledge and understanding of multiplicative relations is a main goal of primary school mathematics education. It is important that students consolidate basic multiplication table facts as well as learn how to flexibly apply this knowledge in more complex multiplicative problems [e.g., 1, 2]. Mathematical computer games are considered t...

Computer games are a powerful medium to learn mathematics [1]. They are used in several mathematical domains and in particular for the learning of basic skills in the domain of number. In this field, very often so-called 'mini-games' are used. In general, these games consist of small, focused activities, which students play for fun and in which the...

This paper addresses: firstly, kindergartners’ performance in length measurement, the components of their performance and its growth over time; secondly, the possibility to develop kindergartners’ performance in length measurement by reading to them from picture books. To answer the research questions, an experiment with a pretest–posttest experime...

The focus of this study was to investigate primary school students’ achievement in the domain of measurement. We analyzed a large-scale data set (N=6,638) from German third and fourth graders (8- to 10-year-olds). These data were collected in 2007 within the framework of the ESMaG (Evaluation of the Standards in Mathematics in Primary School) proje...

In this study, we examined special education students' use of indirect addition (subtraction by adding on) for solving two-digit subtraction problems. Fifty-six students (8-to 12-year-olds), with a mathematical level of end grade 2, participated in the study. They were given a computer-based test on subtraction with different types of problems. Alt...

This study explores the potential of game-generated feedback to support primary school students' problem solving processes in non-routine contextual number problems with interrelated values. The students were invited to play an online game at home that was extended with some additional problems. A paper-and-pencil test was used as a pre and posttes...

This paper reports on a research project on information and communication technology (ICT)‐based dynamic assessment. The project aims to reveal the mathematical potential of students in special education. The focus is on a topic that is generally recognised as rather difficult for weak students: subtraction up to 100 with crossing the ten. The stud...

The present study examines the cognitive activity that is evoked in young children when they are read a picture book that is written for the purpose of teaching mathematics. The focus of this study is to explore the effects of pictures on children's spontaneous mathematical cognitive engagement. The study is based on the assumption that the picture...