Search

Many students have difficulties giving meaning to algebra. In this study, we investigated how graphing formulas by hand can help grade 11 students to give meaning to algebraic formulas, defined as the ability to “read through” an algebraic formula: i.e., to recognize its structure and to link it to graphical features. During five 90-minute lessons, 21 students worked on graphing tasks focusing on recognition and heuristic search. To assess the effects of this intervention, a graphing task, and a cardsorting task were administered to the students. In addition, six students were asked to think aloud during the graphing task. The results of the card-sorting task showed that 14 students used categories similar to the ones experts use, but had trouble in consistently categorizing all formulas. The thinkingaloud protocols showed that the students improved their recognition of basic functions and graph features, and their qualitative reasoning, which allowed them to give meaning to algebraic formulas

Interventions aimed at fostering students’ growth mindsets have been carried out in 21 classrooms (with a focus on Grade 7 and Grade 10) in the Netherlands. The intervention consisted of three main elements: introduction to neuroplasticity, the importance of learning from errors in learning processes, and growth-mindset feedback. Before and after the intervention, the students finished a questionnaire, and during the intervention, students and their teachers were interviewed. Results indicate that the students’ mindsets tended to be more towards a growth mindset after the intervention, in particular for the Grade 10 students. Students were very positive about the intervention, especially the neuroplasticity and the attention for and learning from errors. Teachers and students valued the changes in attitudes and interactions with a new language for teaching and learning mathematics.

Rationales for interdisciplinary STEM courses are often based on the fact that the problems we face in today’s world call for perspectives and knowledge from many different areas. In many cases this includes mathematics because it is used in many research fields and because it is part of everyday life. At the same time interdisciplinary literature suggests that mathematics gains the least from integration. In this paper we use a successful interdisciplinary STEM course in the Netherlands to illustrate how students and teachers think about the value of mathematics. To analyse teacher and student statements concerning the value of mathematics a model is introduced for a disciplinary mathematics perspective for interdisciplinary STEM courses and the opportunities this model ca provide are discussed.

Drawing statistical inferences (SI) is essential in a society where data are of increasing importance. Understanding the relation between data and chance, necessary to understand statistical inference, is however challenging for students. Technological innovations – such as the Sampler in TinkerPlots (TP) – enable students to investigate this relationship by modeling a population and simulating repeated samples. Along this line, the research reported here presents the results of a pilot with fourteen 9th-grade students, inexperienced with sampling, in a Learning Lab. The pilot focuses on how students use TP as a digital environment for exploring data and chance – i.e. what strengths and constraints they encounter – and how they subsequently use this information for SI. The results suggest that the participating students encountered difficulties in modeling the population, however, they were able to simulate, explore and reason inferentially through repeated sampling in TP.

In this paper, we describe the impact of a mathematics game programming project on the intrinsic motivation of eighth grade students (n = 8). We investigate which aspects of the project contributed to student motivation based on a taxonomy that distinguishes individual (e.g., challenge) and interpersonal motivation aspects (e.g., recognition). We also employ these aspects to compare the programming project to regular mathematics education. The findings reveal that students appreciated the project because it was challenging and they had freedom of choice. All group members had a positive attitude towards learning. In regular mathematics classes, they experienced a lack of challenge while the freedom of choice was minimal.

There is increasing attention for the embodied and extended nature of mathematical cognition but the bodies of literature on embodied and on extended cognition have developed mostly separately. We propose a new step in the tradition of networking theories: design research from two theoretical perspectives to promote integration. Embodied design and instrumental genesis inspired us to elicit embodied instrumentation: learning via techno-physical interaction with digital artifacts. A case study illustrates a design and subsequent problem solving by a student (aged 16), who uses her body and the designed artifact to solve trigonometric equations. We reflect on the benefits of not only analyzing but also designing from different theories to network these theories.

In this paper, we describe the impact of a mathematics game programming project on the intrinsic motivation of eighth grade students (n = 8). We investigate which aspects of the project contributed to student motivation based on a taxonomy that distinguishes individual (e.g., challenge) and interpersonal motivation aspects (e.g., recognition). We also employ these aspects to compare the programming project to regular mathematics education. The findings reveal that students appreciated the project because it was challenging and they had freedom of choice. All group members had a positive attitude towards learning. In regular mathematics classes, they experienced a lack of challenge while the freedom of choice was minimal.

Rationales for interdisciplinary STEM courses are often based on the fact that the problems we face in today’s world call for perspectives and knowledge from many different areas. In many cases this includes mathematics because it is used in many research fields and because it is part of everyday life. At the same time interdisciplinary literature suggests that mathematics gains the least from integration. In this paper we use a successful interdisciplinary STEM course in the Netherlands to illustrate how students and teachers think about the value of mathematics. To analyse teacher and student statements concerning the value of mathematics a model is introduced for a disciplinary mathematics perspective for interdisciplinary STEM courses and the opportunities this model ca provide are discussed.

Educational research is often of limited use to designers, as it typically offers descriptions of or explanations for how education was or currently is. In this paper we argue that generalizability is not enough; what deserves more attention is generativity. Designers and educators need actionable knowledge on how education could be. To substantiate the criterion of generativity, we here develop the construct of a design genre—a theory-driven class of designs targeting a particular form of learning. As an example we discuss the evolution of an action-based genre of embodied design through iterative theory-design clarifications. Initially instantiated in the form of activities for promoting the understanding of proportional reasoning, the genre has been elaborated through the process of applying it to additional notions such as parabolas and trigonometry. We argue that this genre was generative for design, theory development, and methodological innovation.

Drawing statistical inferences (SI) is essential in a society where data are of increasing importance. Understanding the relation between data and chance, necessary to understand statistical inference, is however challenging for students. Technological innovations – such as the Sampler in TinkerPlots (TP) – enable students to investigate this relationship by modeling a population and simulating repeated samples. Along this line, the research reported here presents the results of a pilot with fourteen 9th-grade students, inexperienced with sampling, in a Learning Lab. The pilot focuses on how students use TP as a digital environment for exploring data and chance – i.e. what strengths and constraints they encounter – and how they subsequently use this information for SI. The results suggest that the participating students encountered difficulties in modeling the population, however, they were able to simulate, explore and reason inferentially through repeated sampling in TP.

Educational research is often of limited use to designers, as it typically offers descriptions of or explanations for how education was or currently is. In this paper we argue that generalizability is not enough; what deserves more attention is generativity. Designers and educators need actionable knowledge on how education could be. To substantiate the criterion of generativity, we here develop the construct of a design genre—a theory-driven class of designs targeting a particular form of learning. As an example we discuss the evolution of an action-based genre of embodied design through iterative theory-design clarifications. Initially instantiated in the form of activities for promoting the understanding of proportional reasoning, the genre has been elaborated through the process of applying it to additional notions such as parabolas and trigonometry. We argue that this genre was generative for design, theory development, and methodological innovation.

Many students have difficulties giving meaning to algebra. In this study, we investigated how graphing formulas by hand can help grade 11 students to give meaning to algebraic formulas, defined as the ability to “read through” an algebraic formula: i.e., to recognize its structure and to link it to graphical features. During five 90-minute lessons, 21 students worked on graphing tasks focusing on recognition and heuristic search. To assess the effects of this intervention, a graphing task, and a cardsorting task were administered to the students. In addition, six students were asked to think aloud during the graphing task. The results of the card-sorting task showed that 14 students used categories similar to the ones experts use, but had trouble in consistently categorizing all formulas. The thinkingaloud protocols showed that the students improved their recognition of basic functions and graph features, and their qualitative reasoning, which allowed them to give meaning to algebraic formulas

Braille readers create an overview of an expression by reading one braille character after another or listening to a voice saying the expression or equation aloud. The specific skills and knowledge that mathematics teachers need to assist this complicated process are often lacking. The purpose of this study was to investigate the effect of an intervention consisting of a course focused on braille display support in combination with Text-To-Speech synthesizer for mathematics teachers on the mathematical performances of braille readers. A quasi-experimental approach was taken to answer this question. Five teachers of an experimental group received the intervention whereas the teacher of the control group did not. Both the experimental group, consisting of 10 braille readers, and the control group, consisting of five braille readers, took a pre- and post-test. The results indicated that there was a very small positive effect of the intervention.

Braille readers create an overview of an expression by reading one braille character after another or listening to a voice saying the expression or equation aloud. The specific skills and knowledge that mathematics teachers need to assist this complicated process are often lacking. The purpose of this study was to investigate the effect of an intervention consisting of a course focused on braille display support in combination with Text-To-Speech synthesizer for mathematics teachers on the mathematical performances of braille readers. A quasi-experimental approach was taken to answer this question. Five teachers of an experimental group received the intervention whereas the teacher of the control group did not. Both the experimental group, consisting of 10 braille readers, and the control group, consisting of five braille readers, took a pre- and post-test. The results indicated that there was a very small positive effect of the intervention.

There is increasing attention for the embodied and extended nature of mathematical cognition but the bodies of literature on embodied and on extended cognition have developed mostly separately. We propose a new step in the tradition of networking theories: design research from two theoretical perspectives to promote integration. Embodied design and instrumental genesis inspired us to elicit embodied instrumentation: learning via techno-physical interaction with digital artifacts. A case study illustrates a design and subsequent problem solving by a student (aged 16), who uses her body and the designed artifact to solve trigonometric equations. We reflect on the benefits of not only analyzing but also designing from different theories to network these theories.

Interventions aimed at fostering students’ growth mindsets have been carried out in 21 classrooms (with a focus on Grade 7 and Grade 10) in the Netherlands. The intervention consisted of three main elements: introduction to neuroplasticity, the importance of learning from errors in learning processes, and growth-mindset feedback. Before and after the intervention, the students finished a questionnaire, and during the intervention, students and their teachers were interviewed. Results indicate that the students’ mindsets tended to be more towards a growth mindset after the intervention, in particular for the Grade 10 students. Students were very positive about the intervention, especially the neuroplasticity and the attention for and learning from errors. Teachers and students valued the changes in attitudes and interactions with a new language for teaching and learning mathematics.

International audience; In this paper, we present a model for upper secondary in-service teacher courses based on the Anthropological Theory of the Didactics and explore how we can teach teachers to design and implement mathematical modelling in their classrooms. The course evolves around Study and Research Path based teaching and strives to create para-didactic infrastructures as a framework for teachers’ development of teaching practice. The novelty in this study is the sequence of shared preparation, observation and evaluation of teaching in the course. We describe the structures and their functioning through an example of a group of teachers’ work. Based on the activity we discuss the potentials of creating such structures and the needs for further research in this field.

International audience; Research on the inclusion of visually impaired (VI) pupils in mainstream classrooms is underdeveloped in mathematics education. This paper investigates mathematical discourses of a teacher and a VI pupil in a classroom episode on number sequences. We see that, while the teacher considers the pupil’s enthusiastically demonstrated mathematical contribution which differs from the institutional one, she draws on it to guide him in responding within the institutional mathematical discourse. We then see the pupil responding within the teacher’s expectations but less enthusiastically. We explore the teacher’s reaction in terms of whether it evidences valuing of the pupil’s initial mathematical contribution and whether it is potentially excluding. We propose an alternative, more explicitly inclusive way forward in which the teacher can play along with non-prevalent mathematical contributions and bring these also to the whole class, to the benefit of all.