Per Nilsson - Academia.edu (original) (raw)

Papers by Per Nilsson

STATISTICS EDUCATION RESEARCH JOURNAL

A design experiment where students in Grade 5 (11–12 years old) play the Color Run game constitut... more A design experiment where students in Grade 5 (11–12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space reasoning over idiosyncratic reasoning when the sample space was changed between color runs. In the second and third steps, students used degrees of variation in the distribution of the mode across samples to infer whether an unknown sample space was uniform. Students’ reasoning disclosed the logic: the larger the variation, the greater the reason for rejecting a uniform sample space.

Journal of Mathematics Teacher Education

Professional learning communities (PLC) have increasingly attracted attention in research on teac... more Professional learning communities (PLC) have increasingly attracted attention in research on teachers’ professional development. The aim of this study is to identify contradictions that can occur and be manifested in PLCs in mathematics. Identifying contradictions in PLCs are important, as the identification and resolution of contradictions are crucial to developing PLCs. We have conceptualized PLCs and contradictions within the Cultural Historical Activity Theory. Our data consist of two iterations of interviews with four teacher leader coaches with extensive experience of coaching teacher leaders of PLCs in mathematics. The study distinguishes 26 manifestations of contradictions, taking the overall forms of dilemmas and conflicts. Our results can be used in designing PLCs in mathematics: they can be used to make visible and increase participants’ awareness of contradictions involved in PLCs and thereby increase the possibility that the contradictions serve as sources of support ra...

Digital Experiences in Mathematics Education, 2021

The purpose of this study is to further our understanding of orchestrating math-talk with digital... more The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective exploration. We use the construct of instrumental orchestration to conceptualize a teacher’s intentional and systematic organization and use of digital technology to guide math-talk in terms of a collective instrumental genesis. We consider math-talk as a matter of inferential reasoning, taking place in the Game of Giving and Asking for Reasons (GoGAR).The combination of instrumental orchestration and inferential reasoning laid the foundation of a design experiment that addressed the research question: How can collective inferential reasoning be orchestrated in a technology-enhanced learning environment? The design experiment was conducted in low...

Mathematics Education Research Journal, 2021

The aim of the present study is to explore strategies in enumerating units of three dimensional (... more The aim of the present study is to explore strategies in enumerating units of three dimensional (3D) arrays. We analyse enumeration strategies of students in grade 3 (ages 8 to 9) in situations of cubical and spherical representations of units of 3D arrays. By exploring students’ strategies in these two situations, we find that difficulties in enumerating units in 3D arrays can be traced to difficulties in units-locating, with the consequence of applying double and triple counting. Our results also indicate that spherical units can serve as perceptual clues in units-locating and in assembling units into relevant composites. With input from our findings, we suggest research to investigate the following three hypotheses: (i) spherical units can turn students away from double and triple counting, (ii) spherical units can support students’ units-locating process and their ability to assemble units into relevant composites and (iii) teaching of enumerating 3D arrays should start with sph...

International Handbook of Research in Statistics Education, 2017

Theories have a significant role for scientific work-also for statistics education research (SER)... more Theories have a significant role for scientific work-also for statistics education research (SER). This paper elaborates on the use of theories in SER, based on findings of a literature review on the nature and use of theories in SER. In particular, we address theoretical issues and possible directions to further theory development in SER. Subsequently, we discuss five themes that in our view need further attention in SER.

Education Sciences, 2020

Mathematical reasoning is gaining increasing significance in mathematics education. It has become... more Mathematical reasoning is gaining increasing significance in mathematics education. It has become part of school curricula and the numbers of empirical studies are growing. Researchers investigate mathematical reasoning, yet, what is being under investigation is diverse—which goes along with a diversity of understandings of the term reasoning. The aim of this article is to provide an overview on kinds of mathematical reasoning that are addressed in mathematics education research. We conducted a systematic review focusing on the question: What kinds of reasoning are addressed in empirical research in mathematics education? We pursued this question by searching for articles in the database Web of Science with the term reason* in the title. Based on this search, we used a systematic approach to inductively find kinds of reasoning addressed in empirical research in mathematics education. We found three domain-general kinds of reasoning (e.g., creative reasoning) as well as six domain-sp...

In this paper seventh-grade pupils' ways of handling aspects of probability have been investigate... more In this paper seventh-grade pupils' ways of handling aspects of probability have been investigated. The aspects in question were embedded in a dice game, based on the total of two dice. Four different setups of dice were included in the situation in which they were up to explore optimal strategies for winning the game. How children understand concepts is regarded from the perspective of how the pupils' understanding varies with their interpretation of the situation, in which the concepts are embedded. Empirical data have been analyzed with intentional analysis, a method by which we regard pupils' act as intentional. The results show approaches of extremes and of a number model, as consequences of how the pupils process and bring to the fore information in the situation. BACKGROUND Two research perspectives are seen in the area of chance encounters. First there is the psychology/cognitive perspective including the works by Kahneman and Tversky, quoted and developed in Gilovich et al. (2002), with focus on analyzing patterns in order to identify misconceptions and judgmental heuristics. The second perspective is that of mathematicians and mathematics educators, with focus more on learning probability from a mathematical point of view (Shaughnessy, 1992).

The Proceedings of the 12th International Congress on Mathematical Education, 2015

Probability has strong roots in the curricula of many countries but is relatively new in others. ... more Probability has strong roots in the curricula of many countries but is relatively new in others. And although probability has been introduced into the mainstream school mathematics curricula in many countries, research does not necessarily support a rapid inclusion into the curriculum because many problems in teaching and learning probability are still unsolved. For example, should probability be taught to all students? When should students be introduced to probability? What is probability literacy? How is probability literacy developed? What kind of knowledge do teachers need in order to teach probability in more concrete, meaningful and effective ways? How do we facilitate the development of such teaching knowledge? How could investigating students' conceptions of probability from various perspectives further inform our teaching? At ICME 12 in Seoul, Topic Study Group 11 provided a forum for presentations and discussion from an international view about the current state and important new trends in research and practice related to the teaching and learning of probability. Traditionally, the teaching of probability concerns two different interpretations of probability: (1) a classical conception, where probability is based on combinatorics or formal mathematics, and (2) a frequency conception, where probability is

Educational Studies in Mathematics, 2012

Analyzing and designing productive group work and effective communication constitute ongoing rese... more Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from 12 to 13-year old students playing a dice game as well as from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms is crucial in students' attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and of links between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.

Educational Studies in Mathematics, 2011

The authors of this paper are involved in an ongoing project with the aim of investigating ICT-su... more The authors of this paper are involved in an ongoing project with the aim of investigating ICT-supported activities for the learning of mathematics where realworld images are mixed with computer-generated 3D images. The present paper explores the ways in which four students (15 years old) try to make sense of a task that calls for reflection on the concept of scale. The analysis shows how this specific kind of learning activity can challenge students to vary and coordinate among representations offered within the activity, thereby creating ...

STATISTICS EDUCATION RESEARCH JOURNAL, 2020

This study examines informal hypothesis testing in the context of drawing inferences of underlyin... more This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning environment, and what role processes of data production play in their investigations. The study outlines aspects of students’ informal understanding of hypothesis testing. It shows how students with no formal education can follow the logic that a small difference in samples can be the effect of randomness, while a large difference implies a real difference in the underlying process. The students distinguish the mode and the size of differences in frequencies as signals in data and used these signals to give data-based reasons in processes of informal hypothesis testing. The study also highlights the role of data production and points to a need f...

The Journal of Mathematical Behavior, 2019

In this paper we investigate the different ways in which students in lower secondary school (14-1... more In this paper we investigate the different ways in which students in lower secondary school (14-15 year-olds) reason about compound stochastic events (CSE). We ask students during clinical interviews to respond to CSE-tasks in a spinner context, where two linked spinners display equal or different sizes of red and white areas. We seek to enrich our knowledge of how students make sense of CSE by not focusing exclusively on sample-space grounded reasoning. We open up the analysis to how students' reasoning can reflect aspects of multiplicative reasoning in relation to The Product Law of Probability. Our results show that students have difficulty in applying well-grounded combinatorial reasoning as well as multiplicative reasoning to the tasks, but they do show intuitive reasoning that reflect aspects of The Product Law of Probability. Two ways of reasoning identified in the current study are area-based part-whole reasoning and lowestchance reasoning.

STATISTICS EDUCATION RESEARCH JOURNAL, 2013

This study investigates the relationship between deterministic and probabilistic reasoning when s... more This study investigates the relationship between deterministic and probabilistic reasoning when students experiment on a real-world situation involving uncertainty. Twelve students, aged eight to nine years, participated in an outdoor teaching activity that called for reflection on the growth of sunflowers within the frame of a sunflower lottery, where students were involved in the process of creating their own empirical data of the growth. However, the study shows not only that the students do not make use of data for predicting the outcome of an uncertain event, but also how this can be explained by students’ attention to deterministic features of the situation, brought to the fore within an ecology context and connected to a conceptual principle of ‘sharing’. First published November 2013 at Statistics Education Research Journal Archives

The study reported in the present paper is part of a larger project, which aims to explore possib... more The study reported in the present paper is part of a larger project, which aims to explore possibilities and challenges in developing a teaching practice that supports students ' INTRODUCTION Models are essential to mathematics. We develop mathematical models to understand the world and to predict the behavior of phenomena we encounter in the world A frequentist modeling approach is based on the assumption that we can repeat a random experiment a large number of times under exactly the same conditions each time. However, in practice it is often impossible to repeat an experiment a very large number of times and to achieve exactly the same conditions in each trial. Think, for instance, of the simple experiment of throwing one die. Is it possible to throw the die from exactly the same angle and height each time? We guess not! Moreover, many situations involve the assessment of a probability when we only have data from a single, or a short termed, sample. Consider, for example, th...

The Journal of Mathematical Behavior, 2009

... In practice, the framework of contextualization has helped to account for students' ways... more ... In practice, the framework of contextualization has helped to account for students' ways of dealing with learning tasks in a variety of ... is found in a study by Wistedt and Brattström (2005), where undergraduate students were presented with a task on the concept of mathematical ...

Scandinavian Journal of Educational Research, 2013

ABSTRACT Balancing content and students' participation in the mathematics classroom is an... more ABSTRACT Balancing content and students' participation in the mathematics classroom is an area of both practical and theoretical interest. In this article we relate and contribute to these two interests by analyzing classroom data from an intervention project aiming at teaching mathematics through problem solving. The study shows that several aspects such as mediating tools, the teacher's conceptual accountability and interactional moves play important roles in the nature of the co-construction of critical dimensions of variation. We therefore suggest that an analysis of content and participation in the mathematics classroom would benefit from drawing on several theoretical sources. As such, the study could be seen as a contribution to recent elaborations on developing variation theory for analyzing the enacted object of learning.

Educational Studies in Mathematics, 2007

The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 ... more The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 and 13 years old) handle chance encounters. Four groups of students working in pairs participated in the study. In the group discussions, which were taperecorded and fully transcribed, the students were encouraged to explore strategies for winning a specifically designed dice game based on the sum of two dice. The dice game included four different setups of dice designed to bring to the fore different aspects of probability modelling and to offer the student the opportunity to encounter small differences in the mathematical structure of the sample space and of the probability distribution between the four different setups. The study describes strategies that the students use when confronted with these different setups , what their activities imply in terms of resources in handling random phenomena and what the dice game offers in terms of opportunities for learning probability. In order to explain such meaning-making processes the students' activities are viewed from a perspective that takes into consideration how the students' understanding varies with their interpretations of the situation they are confronted with, i.e., how they contextualize the different setups of the dice game. The results show how the students, during the course of the game, reorganize their interpretations of the mathematical content confronting them, and how a variation of guiding principles becomes the object of exploration. Approaches of extremes and a number model are described as a means for the students to identify and assign probabilities for the total of two dice.