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Papers by Arthur Bakker
Diversity Dimensions in Mathematics and Language Learning
STATISTICS EDUCATION RESEARCH JOURNAL, 2017
Measurement activities were designed in this study on the basis of authentic professional practic... more Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17–18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities? Analysis of students’ reasoning during these activities in one classroom (N = 13) suggests that students considered variability in four ways: noticing and acknowledging variability, measuring variability, explaining variability, and using investigative strategies to handle variability. We conclude that the measurement tasks based on authentic professional practices helped students to reason with relevant aspects of variability. Finally, we discuss curricular and research implications. First published November 2017 at Statistics Education Research Journal Archives
Pedagogische Studien
Creating coherence between mathematics and science, and making these school subjects meaningful a... more Creating coherence between mathematics and science, and making these school subjects meaningful are still topical challenges. This study investigated how students made meaningful connections between mathematics, statistics, science and applications when they engaged in a specially developed unit. This unit is based on professional practices in which mathematical, statistical and scientific knowledge is used. The central question is to what extent professional practices can serve as meaningful contexts for senior high school students (aged 16-17) to help them make connections between mathematics, statistics, science and professional practices. Surveys on the opinions of students (388 before and 27 after completing two chapters of the unit) on the educational strategy, and student work are used to answer this question. The analysis of responses to surveys shows that students consider an educational strategy based on authentic professional practices meaningful. The results indicate tha...
Developing Students’ Statistical Reasoning
Developing mathematical inquiry practices requires that teachers are explicit about classroom nor... more Developing mathematical inquiry practices requires that teachers are explicit about classroom norms that support these practices. In this study, we asked: How can a teacher scaffold the development of norms and practices in mathematical inquiry over time? Analysis of classroom video over a year showed that the teacher constantly diagnosed classroom norms and responsively used strategies to improve them. By the end of the year, there was evidence of inquiry norms and practices independent of the teacher’s presence.
Measurement activities were designed in this study on the basis of authentic professional practic... more Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17–18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities? Analysis of students' reasoning during these activities in one classroom (N = 13) suggests that students considered variability in four ways: noticing and acknowledging variability, measuring variability, explaining variability, and using investigative strategies to handle variability. We conclude that the measurement tasks based on authentic professional practices helped students to reason with relevant aspects of variability. Finally, we discuss curricular and research implications.
The Wiley Handbook of Vocational Education and Training
Vocational education and training (VET) is a heterogeneous field, which is organized in diverse w... more Vocational education and training (VET) is a heterogeneous field, which is organized in diverse ways in different countries. Part of VET is school‐based: Students are at school most of the time and do an internship at the end of their vocational education. Part of VET is work‐based: Employees work most of the time, but receive training to qualify better for their current or future work. Both school‐based education and work‐based training have been studied a lot, but far less is known about the transitions that students and employees make between school and work. Yet these transitions are crucial. If learners cannot connect what they learn in different settings, it is very likely that what they have learned in educational settings remains inert. What they have learned in an internship or regular work may not be enriched by what they gained in education or training. It is therefore crucial to think through what implications follow for curriculum and pedagogy in VET when we ask how to support VET learners to make such transitions and connections. Such transitions and making connections have been conceptualized in terms of boundary crossing.
Thinking Skills and Creativity
The importance of promoting mathematical creativity in education is increasingly acknowledged. Se... more The importance of promoting mathematical creativity in education is increasingly acknowledged. Several strategies have been recommended to foster mathematical creativity such as creating an open atmosphere in the classroom, offering open lessons and possibly enriching mathematics education with ideas from other disciplines and experiences from out-of-school contexts. However, it is not yet clear in what way recommended pedagogical strategies promote pupils’ mathematical creativity. Therefore, the purpose of this case study was to gain an in-depth understanding of promoting mathematical creativity in educational practice. To this end, interactions between a teacher and her 22 fourth-grade pupils in three different types of mathematics lessons were investigated. An ‘open’ in-school mathematics lesson, an ‘open’ out-of-school mathematicslesson and a regular (‘closed’) mathematics lesson were video recorded and interactions were transcribed verbatim. Subsequently, dialogic episodes were identified in the video transcripts and were coded on mathematical creative expressions of pupils and strategies used by the teacher. Furthermore, after each lesson the teacher was interviewed regarding her experiences with the given lesson. Interviews were audiotaped, transcribed verbatim and analysed by using constant comparison analyses. Findings indicate that mathematical creativity was only promoted in the two open mathematics lessons. More specifically, mathematical creative expressions were related to longer whole class dialogues in which the teacher created an open atmosphere; she created opportunities for pupils to express their ideas and took these ideas seriously. Although in some episodes of the regular mathematics lesson this open atmosphere was also created, no mathematical creativity occurred.
SERJ EDITORIAL …, 2008
130 STATISTICAL INFERENCE AT WORK: STATISTICAL PROCESS CONTROL AS AN EXAMPLE 9 ARTHUR BAKKER Freu... more 130 STATISTICAL INFERENCE AT WORK: STATISTICAL PROCESS CONTROL AS AN EXAMPLE 9 ARTHUR BAKKER Freudenthal Institute, Utrecht University & Institute of Education, University of London a. bakker@ fi. uu. nl PHILLIP KENT Institute of Education, University of London ...
61 6 Design research in statistics education Arthur Bakker 6.1 Introduction The project '... more 61 6 Design research in statistics education Arthur Bakker 6.1 Introduction The project 'Symbolizing in statistics education'1 reported upon here was carried out in 1998-2003. It is a case of research on the integration of information technol-ogy (IT) into education, and on its influence on ...
Educational Researcher
Educational research is repeatedly confronted with the question of its relevance. Current interpr... more Educational research is repeatedly confronted with the question of its relevance. Current interpretations of relevance narrowly focus on outcomes and impact of research. In this essay, we propose an alternative, ontological conceptualization of relevance, arguing that more is at stake than outcomes and impact. We characterize the ontology of education and learning in terms of people’s meaningful movements in an always changing world and propose that relevance of educational research resides in what we call “ontological synchronization”—continuous attunement to what is happening and matters at hand, and what future is being generated, including what values and judgments researchers themselves perpetuate in society. Such synchronization, we conclude, hinges on a disciplinary and ethical commitment to principles of actuality and generativity. We discuss what such conceptualization of relevance implies for educational research.
Educational Research Review
Diversity Dimensions in Mathematics and Language Learning
STATISTICS EDUCATION RESEARCH JOURNAL, 2017
Measurement activities were designed in this study on the basis of authentic professional practic... more Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17–18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities? Analysis of students’ reasoning during these activities in one classroom (N = 13) suggests that students considered variability in four ways: noticing and acknowledging variability, measuring variability, explaining variability, and using investigative strategies to handle variability. We conclude that the measurement tasks based on authentic professional practices helped students to reason with relevant aspects of variability. Finally, we discuss curricular and research implications. First published November 2017 at Statistics Education Research Journal Archives
Pedagogische Studien
Creating coherence between mathematics and science, and making these school subjects meaningful a... more Creating coherence between mathematics and science, and making these school subjects meaningful are still topical challenges. This study investigated how students made meaningful connections between mathematics, statistics, science and applications when they engaged in a specially developed unit. This unit is based on professional practices in which mathematical, statistical and scientific knowledge is used. The central question is to what extent professional practices can serve as meaningful contexts for senior high school students (aged 16-17) to help them make connections between mathematics, statistics, science and professional practices. Surveys on the opinions of students (388 before and 27 after completing two chapters of the unit) on the educational strategy, and student work are used to answer this question. The analysis of responses to surveys shows that students consider an educational strategy based on authentic professional practices meaningful. The results indicate tha...
Developing Students’ Statistical Reasoning
Developing mathematical inquiry practices requires that teachers are explicit about classroom nor... more Developing mathematical inquiry practices requires that teachers are explicit about classroom norms that support these practices. In this study, we asked: How can a teacher scaffold the development of norms and practices in mathematical inquiry over time? Analysis of classroom video over a year showed that the teacher constantly diagnosed classroom norms and responsively used strategies to improve them. By the end of the year, there was evidence of inquiry norms and practices independent of the teacher’s presence.
Measurement activities were designed in this study on the basis of authentic professional practic... more Measurement activities were designed in this study on the basis of authentic professional practices in which linear regression is used, to study considerations of variability by students in Grade 12 (aged 17–18). The question addressed in this article is: In what ways do secondary students consider variability within these measurement activities? Analysis of students' reasoning during these activities in one classroom (N = 13) suggests that students considered variability in four ways: noticing and acknowledging variability, measuring variability, explaining variability, and using investigative strategies to handle variability. We conclude that the measurement tasks based on authentic professional practices helped students to reason with relevant aspects of variability. Finally, we discuss curricular and research implications.
The Wiley Handbook of Vocational Education and Training
Vocational education and training (VET) is a heterogeneous field, which is organized in diverse w... more Vocational education and training (VET) is a heterogeneous field, which is organized in diverse ways in different countries. Part of VET is school‐based: Students are at school most of the time and do an internship at the end of their vocational education. Part of VET is work‐based: Employees work most of the time, but receive training to qualify better for their current or future work. Both school‐based education and work‐based training have been studied a lot, but far less is known about the transitions that students and employees make between school and work. Yet these transitions are crucial. If learners cannot connect what they learn in different settings, it is very likely that what they have learned in educational settings remains inert. What they have learned in an internship or regular work may not be enriched by what they gained in education or training. It is therefore crucial to think through what implications follow for curriculum and pedagogy in VET when we ask how to support VET learners to make such transitions and connections. Such transitions and making connections have been conceptualized in terms of boundary crossing.
Thinking Skills and Creativity
The importance of promoting mathematical creativity in education is increasingly acknowledged. Se... more The importance of promoting mathematical creativity in education is increasingly acknowledged. Several strategies have been recommended to foster mathematical creativity such as creating an open atmosphere in the classroom, offering open lessons and possibly enriching mathematics education with ideas from other disciplines and experiences from out-of-school contexts. However, it is not yet clear in what way recommended pedagogical strategies promote pupils’ mathematical creativity. Therefore, the purpose of this case study was to gain an in-depth understanding of promoting mathematical creativity in educational practice. To this end, interactions between a teacher and her 22 fourth-grade pupils in three different types of mathematics lessons were investigated. An ‘open’ in-school mathematics lesson, an ‘open’ out-of-school mathematicslesson and a regular (‘closed’) mathematics lesson were video recorded and interactions were transcribed verbatim. Subsequently, dialogic episodes were identified in the video transcripts and were coded on mathematical creative expressions of pupils and strategies used by the teacher. Furthermore, after each lesson the teacher was interviewed regarding her experiences with the given lesson. Interviews were audiotaped, transcribed verbatim and analysed by using constant comparison analyses. Findings indicate that mathematical creativity was only promoted in the two open mathematics lessons. More specifically, mathematical creative expressions were related to longer whole class dialogues in which the teacher created an open atmosphere; she created opportunities for pupils to express their ideas and took these ideas seriously. Although in some episodes of the regular mathematics lesson this open atmosphere was also created, no mathematical creativity occurred.
SERJ EDITORIAL …, 2008
130 STATISTICAL INFERENCE AT WORK: STATISTICAL PROCESS CONTROL AS AN EXAMPLE 9 ARTHUR BAKKER Freu... more 130 STATISTICAL INFERENCE AT WORK: STATISTICAL PROCESS CONTROL AS AN EXAMPLE 9 ARTHUR BAKKER Freudenthal Institute, Utrecht University & Institute of Education, University of London a. bakker@ fi. uu. nl PHILLIP KENT Institute of Education, University of London ...
61 6 Design research in statistics education Arthur Bakker 6.1 Introduction The project '... more 61 6 Design research in statistics education Arthur Bakker 6.1 Introduction The project 'Symbolizing in statistics education'1 reported upon here was carried out in 1998-2003. It is a case of research on the integration of information technol-ogy (IT) into education, and on its influence on ...
Educational Researcher
Educational research is repeatedly confronted with the question of its relevance. Current interpr... more Educational research is repeatedly confronted with the question of its relevance. Current interpretations of relevance narrowly focus on outcomes and impact of research. In this essay, we propose an alternative, ontological conceptualization of relevance, arguing that more is at stake than outcomes and impact. We characterize the ontology of education and learning in terms of people’s meaningful movements in an always changing world and propose that relevance of educational research resides in what we call “ontological synchronization”—continuous attunement to what is happening and matters at hand, and what future is being generated, including what values and judgments researchers themselves perpetuate in society. Such synchronization, we conclude, hinges on a disciplinary and ethical commitment to principles of actuality and generativity. We discuss what such conceptualization of relevance implies for educational research.
Educational Research Review