Providing Support for Student Learning: Cornerstone findings ... · Siswa van Riesen Univerisity of...

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Scientific Research Community: WO.008.14N Developing competencies in learners: From ascertaining to intervening

Second meeting

Providing Support for Student Learning:

Cornerstone findings, implications and recommendations from Cognitive Psychology for the Teaching of STEM (Science, Technology, Engineering and Mathematics)

October 14-16, 2015, Irish College Leuven

Programme and abstracts

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Second meeting




Scientific Programming Committee

D. Gijbels (U Antwerpen, Belgium) P. Kirschner (Open University, The Netherlands) J. Star (Harvard University, Cambridge, USA) K. Struyven (VU Brussel, Belgium) M. Valcke (U Gent, Belgium) W. Van Dooren (KU Leuven, Belgium) L. Verschaffel (KU Leuven, Belgium)

Local Organizing Committee

K. Dens (KU Leuven, Belgium) F. Depaepe (KU Leuven, Belgium) J. Elen (KU Leuven, Belgium) D. Gijbels (U Antwerpen, Belgium) K. Struyven (VU Brussel, Belgium) S. Lem (KU Leuven, Belgium M. Valcke (U Gent, Belgium) W. Van Dooren (KU Leuven, Belgium) L. Verschaffel (KU Leuven, Belgium)

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Second meeting




List of participants

Julia Banhmüller Leibniz-Institut für Wissensmedien (Germany)

Sophie Batchelor Loughborough University (UK)

Leen Catrysse University of Antwerp (Belgium)

Sarah Clayton Loughborough University (UK)

Tanja Dackermann Leibniz-Institut für Wissensmedien (Germany)

Anique De Bruin Maastricht University (The Netherlands)

Mieke De Cock University of Leuven (Belgium)

Ton de Jong University of Twente (The Netherlands)

Bert De Smedt University of Leuven (Belgium)

Tine Degrande University of Leuven (Belgium)

Fien Depaepe University of Leuven (Belgium)

Jan Elen University of Leuven (Belgium)

Ursula Fischer Leibniz-Institut für Wissensmedien (Germany)

Maja Flaig University of Trier (Germany)

David Gijbels University of Antwerp (Belgium)

Minna Hannula-Sormunen University of Turku (Finland)

Paul Kirschner Open University (The Netherlands)

Ellen Kok Maastricht University (The Netherlands)

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Minna Kyttälä University of Turku (Finland)

Erno Lehtinen University of Turku (Finland)

Stephanie Lem University of Leuven (Belgium)

Koen Luwel University of Leuven (Belgium)

Jake McMullen University of Turku (Finland)

Andreas Obersteiner Technische Universität München (Germany)

Fleur Prinsen Open University (The Netherlands)

Sanne Rathé University of Leuven (Belgium)

Kristina Reiss Technische Universität München (Germany)

Michael Schneider University of Trier (Germany)

Robert S. Siegler Carnegie Mellon University (USA)

Victoria Simms Ulster University (UK)

Bianca Simonsmeier University of Trier (Germany)

Jon Star Harvard Graduate School of Education (USA)

Elsbeth Stern ETH Zurich (Switzerland)

Lieve Thibaut University of Leuven (Belgium)

Joke Torbeyns University of Leuven (Belgium)

Xenia Vamvakoussi University of Ioannina (Greece)

Wim Van Dooren University of Leuven (Belgium)

Jo Van Hoof University of Leuven (Belgium)

Siswa van Riesen Univerisity of Twente (The Netherlands)

Kiran Vanbinst University of Leuven (Belgium)

Lieven Verschaffel University of Leuven (Belgium)

Stella Vosniadou University of Athens (Greece)

Iro Xenidou-Dervou University of Leuven (Belgium)

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Second meeting




Address conference venue The Leuven Institute for Ireland in Europe Janseniusstraat 1 3000 Leuven Belgium

Phone: + 32 16 31 04 30 Fax: + 32 16 31 04 31 Email: [email protected] Website: http://www.leuveninstitute.eu/site/index.php Google Maps From Leuven train station to the conference venue: https://goo.gl/maps/cKbMv

From the conference venue to the Faculty Club: https://goo.gl/maps/cWNXv Address CIP&T Centre for Instructional Psychology and Technology Dekenstraat 2, postbox 3773 3000 Leuven Belgium Phone: +32 16 32 62 03 Fax: +32 16 32 62 74 E-mail secretariat: [email protected] Link to website conference: http://ppw.kuleuven.be/o_en_o/CIPenT/WOGCONF2015

mailto:[email protected]

http://www.leuveninstitute.eu/site/index.php

https://goo.gl/maps/cKbMv

https://goo.gl/maps/cWNXv


http://ppw.kuleuven.be/o_en_o/CIPenT/WOGCONF2014

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Second meeting




Programme

Wednesday 14.10.2015

13.00-15.00: Arrival

15.00-15.10: Welcome and opening – Wim Van Dooren (KU Leuven)

15.10-16.40: Invited lecture 1 – Bob Siegler (Carnegie Mellon University, Pittsburgh, USA): An integrated theory of numerical development, with applications to mathematics instruction [Chair: Lieven Verschaffel]

16.40-17.00: Coffee break

17.00-19.00: Paper session 1 [Chair: Andreas Obersteiner]

• Michael Schneider and Bert de Smedt (University of Trier, KU Leuven): Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis

• Minna Kyttälä1, Sophie Batchelor2, Joke Torbeyns3, Victoria Simms4, Bert De Smedt3, Camilla Gilmore2 and Minna Hannula-Sormunen1 (1 University of Turku, 2 Loughborough University, 3 KU Leuven, 4 Ulster University): Action and verbally based measures of spontaneous focusing on numerosity in relation to arithmetical skills in 4- and 7-year-old children

• Sarah Clayton, Matthew Inglis, and Camilla Gilmore (Mathematics Education Centre, Loughborough University, UK): Can non-symbolic comparison training improve mathematics achievement?

• Tanja Dackermann1, Ursula Fischer1, Jonas M. Müller2, Hans-Christoph Nuerk3,1 and Michael Schneider2 (1 Knowledge Media Research Center, Tuebingen, Germany, 2 University Trier, Germany, 3 Eberhard Karls University Tuebingen, Germany): Optimizing embodied number line trainings: Preparing preschoolers for number relations

20.00: Dinner (Irish College)

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Thursday 15.10.2015

9.00-10.30: Invited lecture 2 – Elsbeth Stern (ETH, Zurich, Switzerland): Beyond silver bullets and cherry picking: How to integrate cognitive psychology in STEM-teacher education programs [Chair: Kristina Reiss]


11.00-13.00: Paper session 2 [Chair: David Gijbels]

• Ellen Kok, Anique de Bruin, Ide Heyligers, Andreas Gegenfurtner, Simon Robben, Bettina Sorger, Diana Dolmans, and Jeroen van Merrienboer (School of Health Professions Education, Maastricht University, The Netherlands): Neuropsychological correlates of observational learning in real-life tasks

• Fleur Prinsen, Marcus Specht and Olga Firssova (Welten Institute, Open University of the Netherlands): The weSPOT approach to Inquiry Based Learning; Supporting science competence development with an IBL model and modular online platform

• Siswa A. N. van Riesen, Hannie Gijlers, Anjo A. Anjewierden, and Ton de Jong (University of Twente): Scaffolding students’ investigation in online learning environments

• Leen Catrysse, David Gijbels, Vincent Donche, Sven De Maeyer, Piet Van den Bossche, and Luci Gommers (University of Antwerp): Mapping processing strategies in learning from text: an eye-tracking study

13.00-14.00: Lunch

14.00-15.30: Invited lecture 3 – Jon Star (Harvard University, Cambridge, USA): Toward an Educational psychology of mathematics learning [Chair: Fien Depaepe]


16.00-18.00: Paper session 3: [Chair: Joke Torbeyns]

• Minna Hannula-Sormunen, Anna Alanen, Jake McMullen, Minna Kyttälä and Erno Lehtinen (University of Turku): Training of kindergartners’ arithmetical skills by a computer game “Fingu” integrated with everyday activities and SFON enhancemement

• Jake McMullen, Mikko Kainulainen, Minna M. Hannula-Sormunen, and Erno Lehtinen (University of Turku): Promoting spontaneous focusing on quantitative relations in late primary school

• Xenia Vamvakoussi (University of Ioannina, Greece): Fraction learning: The importance of starting early

• Kristina Reiss and Andreas Obersteiner (Technische Universität München, TUM School of Education): Understanding mathematical competence: The interplay of mathematics education and psychometrics

20.00: Dinner (Faculty Club)

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Friday 16.10.2015

9.00-11.00: Paper session 4 [Chair: Erno Lehtinen]

• Andreas Obersteiner and Kristina Reiss (TUM School of Education, Technische Universitaet Munich): Using eye tracking to assess strategy use in fraction arithmetic

• Stella Vosniadou (University of Athens and The Flinders University of South Australia): Teaching science and mathematics: The role of executive functions in conceptual change processes

• Stephanie Lem, Patrick Onghena, Lieven Verschaffel, and Wim Van Dooren (Katholieke Universiteit Leuven, Belgium): Remedying the misinterpretation of box plots

• Ton de Jong, Janneke Bekhuis, Ellen Wassink-Kamp, and Anjo Anjewierden (University of Twente) Learning basic trigonometry with virtual manipulatives


11.30-13.00: Closing session: Invited lecture 4 – General discussion by Paul Kirschner (Open University, The Netherlands) [Chair: Jan Elen]

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CONFERENCE FORMATS

1. Invited lecture. Invited lectures are keynote presentations given by experts from the field

from outside or within the network. Invited lectures last 90 minutes. Each invited lecture

starts with a brief introduction of the speaker by the chair, followed by the keynote

presentation + 60 minutes) and a discussion with the audience (+ 30 minutes).

2. Paper session. Paper sessions provide the opportunity to present theoretical and/or

empirical work related to the major conference theme. Paper sessions last 120 minutes. Each

paper session consists of 4 paper presentations. Each paper is presented during 20 minutes,

followed by 10 minutes for questions and discussion.

3. Discussion session. The conference ends with a general discussion session (90 minutes) which

involves the active discussion of interesting research findings and relevant research

questions on the conference theme. This discussion will be introduced by one of the

members of the scientific programming committee, namely Paul Kirschner.

All keynote speakers and presenters of a paper in a paper session are requested to send their

powerpoint presentation (or at least a tentative version of it) to Mrs. Karine Dens

([email protected]) by October 7, 2015 by the latest, to allow the general

discussant to prepare his discussion.


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Invited lecture 1

An integrated theory of numerical development, with applications to mathematics instruction

Robert S. Siegler (Carnegie Mellon University, USA)

Much of the most exciting current research in the fields of developmental and cognitive psychology concerns how theories and methods from these areas can be applied to improving education. This talk provides an overview of how this is being done in the area of children's mathematics learning.

Understanding of mathematical development has grown greatly in recent years, but the sheer profusion of research areas and findings can make it difficult to perceive the coherence of the developmental process. The integrative theory of numerical development posits that a coherent theme is present – progressive broadening of the set of numbers whose magnitudes can be accurately represented – and that this theme unifies numerical development from infancy to adulthood. From this perspective, development of numerical representations involves four major acquisitions: 1) increasingly precise representations of magnitudes of numbers expressed non-symbolically, 2) linking non-symbolic to symbolic numerical representations, 3) extending understanding to increasingly large whole numbers, and 4) extending understanding to all rational numbers. Thus, the mental number line expands rightward to encompass larger whole numbers, leftward to encompass negatives, and interstitially to include fractions and decimals.

The present talk discusses and provides evidence for each of these developmental trends. It also provides illustrations of how the theory is being used to improve children's understanding of both whole numbers and fractions, and how it has helped identify gaps in teachers' knowledge that interfere with the effectiveness of their instruction. Finally, I will discuss some new ideas and data regarding how research on magnitude knowledge and arithmetic can be integrated to provide a better understanding of interactions between conceptual and procedural knowledge in the context of fractions and decimals.

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Paper session 1

Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis

Michael Schneider and Bert de Smedt (University of Trier, Germany and KU Leuven, Belgium)

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra (e.g., Fazio et al., 2014). Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17.201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non-symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school aged children and adults.

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Paper session 1

Action and verbally based measures of spontaneous focusing on numerosity in relation to arithmetical skills in 4- and 7-year-old children

Minna Kyttälä1, Sophie Batchelor2, Joke Torbeyns3, Victoria Simms4, Bert De Smedt3, Camilla Gilmore2 and Minna Hannula-Sormunen1 (1 University of Turku, Finland, 2 Loughborough University, UK, 3 KU Leuven, Belgium, 4 Ulster University, UK)

Empirical findings show that there are significant individual differences in children’s Spontaneous Focusing On Numerosity (SFON) at the age of 3-7 years, which predict domain-specific mathematical skills from two (Hannula, Lepola & Lehtinen, 2010) to six years later in elementary school (Hannula-Sormunen, Räsänen, & Lehtinen, in press; McMullen, Hannula-Sormunen & Lehtinen, 2015).

The aims of this study are to investigate whether action and verbally based measures of SFON and arithmetical skills are related to each other at the age of four and at the age of seven in this cross-cultural and cross-sectional data, and whether the relation between SFON and arithmetical skills is affected by variability in numerical experiences and formal teaching at day care, preschool, school or at home. In addition, reliability and inter-relations of four SFON tasks, two action based and two verbally based SFON tasks are investigated. Participants were 80 children; 40 four-year-olds and 40 seven-year-olds from Northern Ireland, England, Belgium, and Finland, in which formal schooling begins and written number symbols are introduced to students at different ages (4, 5, 6, and 7 years-old, respectively). This is the first time the relation between SFON and arithmetical skills is investigated using such a broad sample of children from different educational systems and cultural backgrounds.

The test battery consisted of SFON and arithmetical tasks. Two different versions of action based imitation tasks were used for SFON assessments (Hannula & Lehtinen, 2005). In addition, two picture description tasks were used (Batchelor, 2014). Arithmetical tests included assessments of verbal and written arithmetic skills. In addition, a digit naming test was used. The testing lasted approximately 1 hour, broken into two approximately 30-minute testing sessions with a break in between. Children’s socio-economic background information and information about their home and day care or school numeracy experiences were gathered by a questionnaire from their parents and teachers.

The data will be gathered by the middle of May in all participating countries. The preliminary results including 23 children’s sub-sample indicate promising variability in the battery of tasks. The final results will be presented in the Workshop at Leuven in October, 2015. The findings from this cross-cultural study will further our understanding of the relation between children’s SFON tendency and the development of arithmetical skills and the possible effect of numerical experiences and teaching at school or at home. In addition, it will inform us about the similarities and differences in verbally based and action based SFON tasks.

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Paper session 1

Can non-symbolic comparison training improve mathematics achievement?

Sarah Clayton, Matthew Inglis, and Camilla Gilmore (Mathematics Education Centre, Loughborough University, UK)

Non-symbolic comparison tasks are widely used as a tool to measure numerical representations of quantity, or Approximate Number System (ANS) acuity, in both adults and children. Many researchers have found a correlation between dot comparison task performance and formal mathematics achievement (see Chen & Li, 2014 for a meta-analysis). This has led to the development of intervention studies employing non-symbolic task practice with the aim of improving ANS acuity and, in turn, mathematics achievement (DeWind & Brannon, 2012; Hyde, Khanum, & Spelke, 2014; Park & Brannon, 2013). Although modest success has been demonstrated with non-symbolic arithmetic task training (Park & Brannon, 2013), there has not yet been any evidence to suggest that training using the dot comparison paradigm can improve mathematics achievement. This is likely due to different cognitive skills underpinning performance on the two tasks.

Recently, evidence has demonstrated that dot comparison task performance can be substantially influenced by changes to the visual characteristics of the stimuli, such as the size of the dots or the convex hull of the array. Some researchers have also suggested that dot comparison judgements may be entirely independent of numerosity processing and instead participants rely solely on the basis of the visual characteristics of arrays (Gebuis & Reynvoet, 2012). The purpose of this study was to investigate whether participants used numerosity information as well as visual cues when comparing dot arrays, and whether there were any developmental differences. Here we analysed 124 children’s and 120 adult’s (N=244) dot comparison accuracy scores from three separate studies. On a trial-by-trial basis for each participant, we used the ratios of the numerosities and the ratios of the visual characteristics of the stimuli in each trial to predict accuracy scores for each participant using hierarchical binary logistic regression. Visual cue information (convex hull size and average dot size) was entered intro the regression at step one, and numerosity information was entered at step two. We found that adults were significantly more likely than children to use numerosity judgements over and above visual cue information (70.0% of adults, 30.6% children). Most children did not use numerosity information over and above visual cues when completing the dot comparison task. This finding was consistent across studies, including where trials were created with different visual controls.

Our results have important implications for researchers exploring the relationship between the ANS and formal mathematics, which has often been studied in children. Specifically, if dot comparison tasks are not measuring numerosity processing over and above visual cues for most children, it seems unlikely that the commonly-reported correlation with mathematics stems from ANS acuity. Crucially, this finding suggests that training studies involving exposure to the dot comparison paradigm are unlikely to succeed at improving mathematics competence in children.

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Paper session 1

Optimizing embodied number line trainings: Preparing preschoolers for number relations

Tanja Dackermann1, Ursula Fischer1, Jonas M. Müller2, Hans-Christoph Nuerk3,1 and Michael Schneider2 (1 Knowledge Media Research Center, Tuebingen, Germany, 2 University Trier, Germany, 3 Eberhard Karls University Tuebingen, Germany)

The number line estimation task, in which participants have to estimate the position of a given number on an empty number line (Siegler & Opfer, 2003), has received enormous research interest over the past years. This is at least in part attributable to replicated findings that children’s performance in this task is associated with their numerical as well as mathematical competencies. Due to this association, a variety of successful number line trainings were created that revealed positive direct and also transfer training effects (e.g., Link et al., 2013). In one of the first lines of research dedicated to number line trainings, Siegler and colleagues (e.g., Siegler & Ramani, 2009) trained children with linear number board games that mirrored the ordering of numbers on a number line. They found that linear board games were more effective than circular ones, and argued that the linear ordering of numbers increased training effectiveness.

This concept was taken up and enriched by recent research suggesting not only the linear ordering of numbers, but also the physical experience of the associated numerical magnitude to be pivotal in helping children acquire an understanding for number line estimation (e.g., Fischer et al., 2011). In a prior study (Link et al., 2013), we observed beneficial training effects for children who walked along a number line and estimated the position of a number with their entire body compared to placing their estimates on a computer screen.

Based on these prior findings, we attempted to combine all of the factors known to enhance number line training effectiveness in a linear, embodied number line game for preschool children. A number line was laid out on the floor, and children were introduced to the linear ordering of numbers up to 20. They were then asked to estimate where a certain numbers was. After walking along the number line and standing at their estimate, they received feedback about the actual position of the number.

Twenty preschoolers (9 girls, mean age: 5;5 years) were trained over three training sessions in either the embodied linear number line game (experimental group) or a non-embodied non-linear number board game (control group). Before and after training, children’s performance in number line estimation (0-10/0-20), calculation (addition/subtraction), counting, and number comparison was evaluated.

Repeated measure ANOVAs with factors group (experimental/control) and time point (pretest/posttest) revealed significantly greater improvements in the experimental group in number line estimation, calculation, and counting performance. Even more importantly, simple effects showed that the experimental group outperformed the control group in the posttest in number line estimation, calculation, and marginally in counting.

The results revealed that an optimized number line training combining linear layout, direct feedback, and physical experience of number magnitude can enhance preschooler’s performance in a variety of numerical tasks, even such tasks that were not directly trained. This further highlights the importance of number line trainings that convey linear relations between numbers and suggests that an embodied experience of numerical magnitude can further enhance training effects.

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Invited lecture 2

Beyond silver bullets and cherry picking: How to integrate cognitive psychology in STEM-teacher education programs

Elsbeth Stern (ETH Zürich, Switzerland)

Psychological research related to child development and education usually generates great interest among media, policy makers and the broader public. Psychologists moreover have good opportunities to inform educational practice because they are part of teacher education programs at most universities, and they often get invitations to participate in professional development projects for in-service teachers. However, the popularity of psychological research often is a double-edged sword. Many core concepts of the discipline are either trivialized or misunderstood by outside observers, and scientific findings often raise unrealistic expectations among parents and teachers, who are looking for recipes and silver bullets. In addition the enormous amount of lab-experiments, quasi-experiments and large-scale studies that have been published in recent years may cause confusion – also because of seemingly contradictory findings. This too often results in the cherry picking fallacy, which means to concentrate on findings that support already existing beliefs and to ignore counterfactual evidence. Having these quite unpleasant effects in mind, and being at the same time aware of the valuable insights from cognitive psychology that are ready to inform STEM education, my colleagues and I have developed a teacher education program that integrates psychological insights in content specific curricula. In my talk I will focus on the psychological concepts of working memory and psychometric intelligence, and I will show how we use them to help teachers understand failure and success of learning physics and mathematics.

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Paper session 2

Neuropsychological correlates of observational learning in real-life tasks

Ellen Kok, Anique de Bruin, Ide Heyligers, Andreas Gegenfurtner, Simon Robben, Bettina Sorger, Diana Dolmans, and Jeroen van Merrienboer (School of Health Professions Education, Maastricht University, The Netherlands)

Observational learning is an important mechanism in many different motor tasks, for example learning to use tools such as saws and drills. When an individual learns a new motor task, the learner will have to transform the observed action (visual information) into internal motor commands that will allow the learner to also perform the task, a process called visuomotor transformation.

The mirror neuron system is considered to be the neurophysiological basis for observational learning (Rizzolatti & Craighero, 2004). This mirror neuron system consists of specialized neurons that are active when an individual performs an action, but also when an individual observes someone else performing the same action. This activation when observing can be considered as mentally simulating the action.

Learning surgical procedures is an example of a complex task in which observational learning is particularly prevalent. Learners in surgery are not allowed to practice the procedure early on, because this poses significant risks to the patients. They therefore observe experienced surgeons for extended periods of time before being allowed to practice a procedure.

When someone is observing an action that is part of his/her own motor repertoire (e.g. when a ballet dancer observes another ballet dancer; (Calvo-Merino, Glaser, Grèzes, Passingham, & Haggard, 2005)), the mirror neuron system is active. The system is less active, however, when the action is not part of the motor repertoire (e.g. when a ballet dancer observes a capoeira dancer).

Learners in surgery, however, have a long experience in observing action. It is not yet known whether extended observation of action can already activate the mirror neuron system.

In the current experiment, we investigate the neurophysiological basis of observational learning in surgery. Experienced surgeons, beginning surgeons and medical students with no experience in surgery will be watching video fragments of surgical procedures while lying in a 3T fMRI scanner. Additionally, a task will be executed that is known to activate the mirror neuron system (Spunt & Lieberman, 2012). Such a task is called a localizer task. We will analyze the activation of the cells related to the mirror neuron system when participants watch the videos of surgical procedures. It is hypothesized that experienced surgeons will show activation in the mirror neuron system when they observe the actions of another surgeon. Little activation of the mirror neuron system is expected when medical students, who do not have a lot of experience in watching surgical procedures, observe the videos. If the participants who have a lot of experience watching the procedures show mirror neuron activation already, then this might imply that extended observation prepares the participants for eventual execution of the motor action.

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Paper session 2

The weSPOT approach to Inquiry Based Learning; Supporting science competence development with an IBL model and modular online platform

Fleur Prinsen, Marcus Specht and Olga Firssova (Welten Institute, Open University of the Netherlands)

In the context of Inquiry Based Learning, there are many opportunities for students to develop science competencies, like critical thinking skills, analytical and metacognitive skills. These skills are practiced in the execution of inquiry activities.

For teachers to adequately set up such activities and assess skills, they need a sound pedagogical model. Several reviews have revealed the level of uncertainty and complexity that IBL approaches provoke, when teachers implement it at school (Phelan, 2005; Leikin & Rota, 2006; Bruder & Prescot, 2013; Maab & Artigue, 2013).

An online platform based on the weSPOT IBL model (see figure 1) was developed to support teachers in setting up and assessing inquiry activities.

A configuration interface supports teachers in setting up an inquiry with IBL activities (see Figure 2). The IBL activity widgets are linked to skills, so that a diagnostic instrument can track the progress of students (see Figure 3).

A pilot was conducted at a Dutch school for lower vocational education. The teacher wanted to implement the weSPOT approach as an alternative way to engage students in an essay assignment, which was part of their regular educational program. He wanted to know if the use of (mobile) weSPOT tools could improve student-teacher interaction, reduce cognitive load and raise levels of metacognitive awareness. Alongside, the teacher agreed to take extra empirical measures for the weSPOT project.

The teacher created an experimental set up with weSPOT and randomly divided 48 students into a control and an experimental group.

The teacher was interviewed about his experience with setting up the inquiry based learning activities according to the weSPOT model, and students filled out questionnaires assessing the usability of the weSPOT platform, metacognitive awareness, epistemic beliefs, cognitive load and motivation. Learning analytics from the weSPOT platform were explored to track student development.

Results show enthusiasm of the teacher for certain features of the weSPOT model and tools, but also points for improvement. The student results show mixed outcomes, which can partly be explained by the newness of the approach. Specifically, the results on metacognitive awareness show that the students did not feel they could rely on their usual learning strategies and were not certain about the outcomes their usual strategies would yield in the new situation.

With the low number of participants no definite claims can be made about the role of weSPOT pedagogy in the development of science competences, but the case study of this teachers’ implementation holds valuable lessons for both educational designers and teachers, wanting to implement an IBL approach. More pilots are underway in several European countries, to test results in

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a larger sample. It is expected that students will show more positive competence development after prolonged exposure to a new inquiry pedagogy approach.

Figure 1: The weSPOT pedagogical model

* Based on the steps required for good research, steps described in scientific literature (Crawford & Stucki, 1990; Hunt & Colander, 2010) and closely related to the inquiry model by Mulholland et al. (2012)

Figure 2: The configuration interface

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Figure 3: The diagnostic instrument

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Paper session 2

Scaffolding students’ investigation in online learning environments

Siswa A. N. van Riesen, Hannie Gijlers, Anjo A. Anjewierden, and Ton de Jong (University of Twente, The Netherlands)

Inquiry learning is an important teaching approach in science education that has been found to be effective when learners are guided properly (Alfieri, Brooks, Aldrich, & Tenenbaum, 2011; Minner, Levy, & Century, 2010). Learners participate in inquiry activities and use methods similar to those used by professional scientists to build their own knowledge (Keselman, 2003; Pedaste et al., 2015). The investigation phase during which experiments are designed and conducted is one of the core phases of inquiry learning (Osborne, Collins, Ratcliffe, Millar, & Duschl, 2003). Learners need to carefully select and specify independent, control, and dependent variables for their experiments so that they can test their hypothesis or answer their research question (Arnold, Kremer, & Mayer, 2014). A well-known and applied strategy is to vary one variable and keep all other affecting variables constant across experiments (Klahr & Nigam, 2004; Schunn & Anderson, 1999; Tschirgi, 1980).

It has been found that learners have difficulties setting up well-designed experiments (de Jong, 2006). Their design often does not match the research question or hypothesis (de Jong & van Joolingen, 1998) or contains too many varied variables (Glaser, Schauble, Raghaven, & Zeit, 1992). Guiding students in the investigation phase helps overcome these difficulties and has found to be fruitful (Furtak, Seidel, Iverson, & Briggs, 2012; Minner et al., 2010).

For the current study a scaffold was developed, Figure 1, to guide students in the investigation phase. Heuristics and scaffolding elements from other studies that have proven to be fruitful were integrated.

We were interested in students’ conceptual knowledge gain when working with learning environments that contained different levels of support for planning and conducting experiments in online learning environments. Three online learning environments were compared in which 120 third grade pre-university students planned and conducted experiments in a virtual laboratory to answer research questions about buoyancy and Archimedes’ principle. The learning environments, Figure 2, differed from each other in the support offered to students. In one condition students were provided with main research questions and Splash without additional guidance. In a second condition students received guiding questions providing them with a direction to help them solve the main questions. In the third condition students received the same guiding questions and were additionally guided by the developed scaffold called the Experiment Design Tool (EDT).

All students participated in four sessions of 50-60 minutes each within their own class. During the first session their prior knowledge regarding buoyancy and Archimedes’ principle was measured with a pen-and-paper test. During the second and third session they worked with the learning environment they were randomly assigned to. In the final session their knowledge was measured again with a parallel pen-and paper test.

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Figure 1: The EDT

Results showed no differences in knowledge gain between the conditions. However, when we only analyzed results of students with low prior knowledge, a significant difference was found in favor of the learning environment containing the EDT.

Figure 2. Two learning environments

Step 2

Step 3

Step 4

Step 1

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Paper session 2

Mapping processing strategies in learning from text: an eye-tracking study

Leen Catrysse, David Gijbels, Vincent Donche, Sven De Maeyer, Piet Van den Bossche, and Luci Gommers (University of Antwerp, Belgium)

Learning from text is one of the most important skills in our modern society and the ability to understand challenging textbooks is an important key to success in science learning (Mason, Tornatora, & Pluchino, 2013). One of the research traditions that is interested in how students learn from text is the Student Approaches to Learning tradition (Gijbels, Donche, Richardson, & Vermunt, 2014). Research in the SAL tradition in general distinguishes between deep and surface processing strategies. However, research that investigated the kind of processing strategies that are used by students in different learning environments across different disciplines in higher education has led to contradictory results (see e.g. Baeten, Kyndt, Struyven, & Dochy, 2010). In recent debates there is a growing consensus that an important explanation for these contradictory findings is related to the way deep and surface learning have been measured (see e.g. Dinsmore & Alexander, 2012; Richardson, 2013). In past research, self-report measures such as self-report questionnaires or interviews with students have been the dominant way to describe differences in students’ processing strategies. The present study aims to extend current research on processing strategies by using eye-tracking methodology to map differences in processing strategies. This more direct and online way of measuring processing strategies allows us to learn more about the actual behaviour of students while learning from text.

For this study we conducted adapted versions of the seminal studies by Marton, Dalgren, Saljö & Svensson (1975). Students were asked to study a series of 3 study texts about research on happiness. After each text they received a series of questions. In one condition students received reproduction-oriented questions after each text (Surface Processing Condition - SPC), in the other condition students’ received questions that asked them to think of relations between concepts in the text and make inferences from the texts (Deep Processing Condition DPC). In the original study, Marton et al. (1975) interviewed and tested the students after the third text and found that in the first condition, students adopted more so called surface learning strategies while students in the second condition adopted more so called deep learning strategies.

We replicated this study while all students’ eyes were tracked with a Tobii 300 XT eye-tracker during the whole experiment (only the data recorded in the third text were used for further analyses) and used the replay-function of the eye-tracker to conduct a stimulated recall interview at the end of the experiment. In this way the participants had the opportunity to compare his or her perception with the results of the eye-tracking and could explain striking results. A total of 28 university students participated in the experiment. Respondents were divided in 2 groups (surface versus deep processing). The analyses of the eye-tracking and stimulated recall data partly confirmed the hypotheses that students in the DPC focus their attention longer and more on the essentials (key phrases and words) in the text and also more of the return back more to these essentials compared to students in the SPC while students in the SPC focus their attention longer and more on facts and details (e.g. names) and also return back more to these facts and details compared to students in the DPC.

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Invited lecture 3

Toward an educational psychology of mathematics learning

Jon R. Star (Harvard University, USA)

In the past several years, there has been a flurry of publications attesting to renewed interest among cognitive scientists in bringing psychological findings to education in general and education in STEM subjects such as mathematics and science in particular. In this presentation, I begin by reviewing some of recommendations emerging from these recent publications, to identify a range of findings that psychologists have identified as being ready, productive, and appropriate for use in mathematics classrooms. I then select a subset of these findings for more careful examination, with the intent of reflecting more generally on how the discipline of psychology can be brought to bear on problems in mathematics education in interesting ways that take seriously the realities of classroom teaching and learning. In particular, I argue that for psychological research to be maximally relevant for improving mathematics teaching and learning, the following features should be present. (1) The work must be firmly situated within the domain of mathematics; (2) Studies must be conducted within the ‘messy’ realm of authentic classroom environments; (3) Research should incorporate topics and methods that take into consideration actual and current problems of teaching practice; and (4) The work must be undertaken by interdisciplinary teams of scholars who bring expertise not only in psychology but also mathematics and mathematics education.

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Paper session 3

Training of kindergartners’ arithmetical skills by a computer game “Fingu” integrated with everyday activities and SFON enhancemement

Minna Hannula-Sormunen, Anna Alanen, Jake McMullen, Minna Kyttälä and Erno Lehtinen (University of Turku, Finland)

This study is based on previous studies demonstrating substantial individual differences in children’s own spontaneous focusing on numerosity (SFON) suggesting that the quantity and quality of children’s own numerical activities can make a difference in the development of numerical skills from early childhood to the end of primary school (e.g., Hannula & Lehtinen, 2005; Hannula-Sormunen, Lehtinen & Räsänen, 2015; McMullen, Hannula-Sormunen & Lehtinen, 2015). Furthermore, providing deliberate variation in the aspect of number occurring in everyday surroundings can be an effective way of enhancing children’s focusing on numerosity and subsequent development of numerical skills (Hannula, Mattinen & Lehtinen, 2005). Finally, bodily experience of numbers and number combinations has been successfully promoted in a computer game, which aims at developing children’s awareness of arithmetical combinations of numbers from one to ten (Lindström, Marton, Emanuelsson, Lindahl, & Packendorff, 2012).

In the current study, we aim to design activities that bridge the skills trained in the computer game with children’s everyday activities and investigate whether children’s arithmetical skills and their SFON tendency develop as a result of a four week intensive playing of Fingu iPad game integrated with everyday activities and SFON enhancement. Particularly, it will be studied, whether the possible training effect is specific to the skills trained, and if it will last after the training period has ended?

Participants were 15 children (7 pre-kindergartners and 8 kindergartners) in a private daycare centre and an age- and skill-matched group of 15 children from two other private daycare centres in the same neighborhood in Finland.

A quasi-experimental design with training and “business as usual” control group and pre-, post-, and delayed post-tests was used. The training period lasted four weeks and the delayed post-tests were completed three months after the post-tests. The assessments in each measurement point involved an action-based SFON Imitation task (Hannula & Lehtinen, 2005), verbally-based SFON Photo description task (modified from Hannula et al., 2009 and Batchelor, 2015), number sequence production and elaboration tasks (Hannula & Lehtinen, 2005), digit and letter naming tasks (TEMA 3) and verbal arithmetical tasks (e.g. “What will you get if you add 2 and 2 together?” from Lindström et al., 2012).

In the Fingu game (http://ipkl.gu.se/english/Research/research_projects/codac/fingu), the player has to place the same number of fingers on the screen as the sum of all the objects that are displayed on the iPad. Fingers can be placed anywhere on the screen and there are no restrictions to the combinations or order of fingers pressed. The player gets feedback for accuracy. In the current study, the children were playing individually with head phones and they said aloud the total number of objects on the screen. Children played 15-minute sessions four times a week for four weeks.

The SFON enhancement included encouragement and guidance for focusing on numerosities and combinations of numerosities in practically all activities several times per day at the kindergarten.

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Children were, for example, asked to search for certain numerosities in their environment, and take their Fingu avatar next to a certain numerosity in the “Number Hunt game” and demonstrate the numerosity they saw with their fingers and say the numerosity aloud to their pairs or to the whole group of children.

The results of pre- and post-tests show a clear developmental advantage for the training group over the control group in arithmetical skills. The training group demonstrated a positive trend towards a better development in SFON and number sequence elaboration, while there were no differences in digit or letter naming. The delayed post tests are in May, and their results will be presented in the workshop. If the delayed post tests show similar effects, it can be concluded that an intensive period of SFON enhancement integrated with arithmetic training in a computer game and everyday activities may be an effective and motivating mathematics learning environment for kindergartners.

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Paper session 3

Promoting spontaneous focusing on quantitative relations in late primary school

Jake McMullen, Mikko Kainulainen, Minna M. Hannula-Sormunen, and Erno Lehtinen (University of Turku, Finland)

Spontaneous Focusing On quantitative Relations (SFOR) has been found to be a unique contributor to the development of rational number conceptual knowledge in late primary school children (McMullen et al., submitted). It is expected that a higher SFOR tendency facilitates more self-initiated practice with quantitative relations in students’ everyday environments (McMullen, 2014). This practice with quantitative relations is expected to then support the development of rational number conceptual knowledge. However, due to their correlational design, previous studies have been unable to examine this explicit connection between SFOR tendency and rational number conceptual knowledge. Previous studies have found that spontaneous focusing on numerosity can be enhanced through social interaction (Hannula, Mattinen, & Lehtinen, 2005). The present study therefore aims to determine if SFOR tendency can be enhanced in late primary school children, and if this enhancement has an impact on their rational number conceptual knowledge.

To this end two 6th grade classrooms (N = 43; Mage = 13y, 0m) took part in a pilot, pre- and post-test, experimental study over a seven-week period in Spring 2015. One classroom was assigned to the experimental condition, in which students participated once a week for five weeks activities aimed at enhancing their SFOR tendency. The other classroom continued with normal mathematics instruction, which was about rational numbers.

The SFOR intervention activities are mainly carried out within the ActionTrack, a mobile application in which “scavenger hunt”-like activities can be created for participants to follow. In the first of five sessions students were introduced to the idea of finding quantitative relations in everyday situations and some basic instructions on the use of ActionTrack (taking photos and videos, typing in responses). In the second, third, and fifth session students completed the core activity of the intervention, namely the Find-the-Relation scavenger hunt. This activity involved two main tasks, following routes which were given in relational terms and finding and describing quantitative relations in the surroundings. In the fourth session students designed their own routes, which would be completed by their classmates the following week.

Routes began at a certain point and contained directions to a second and third point that involved quantitative relations (e.g. “The task can be found halfway between the starting and ending point.” “You have now gone 1/3 of the way to the end-point, guess where the end is.”). At each checkpoint students had to scan a QR-code in order to get directions to the next route and confirm they were in the right spot. At the end of each route, students were given an additional task to describe quantitative relations of some everyday situation. Students were asked either to take a photo and write a description of the quantitative relations, take a video and verbally describe at least three quantitate relations, or describe quantitative relations of a given photo.

Pre-test results suggest no differences between the classrooms in rational number size conceptual knowledge, F(1, 41)=0.00, p=.97, or SFOR tendency F(1, 41)=0.21, p=.89. Post-test data will be available by May 2015.

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Paper session 3

Fraction learning: The importance of starting early

Xenia Vamvakoussi (University of Ioannina, Greece)

The development of rational number knowledge has been studied extensively by mathematics education researchers, cognitive-developmental psychologists, and recently by neuroscientists as well (Vamvakoussi, 2015). One pervasive finding is the adverse effects of natural number knowledge in rational number learning, namely the natural number bias. This bias has been studied from conceptual change perspectives as well as from the perspective of the dual process theories to reasoning and is considered a major source of difficulty for students.

An overarching principle for instruction aiming at moderating the effects of the natural number bias is long-term planning (Greer, 2004). Consistently with this principle it has been suggested to start fraction instruction early (Ni & Zhou, 2005); to exploit children’s informal fraction experiences, instead of starting with the part-whole aspect of fractions (e.g., Moss, 2005; Ni & Zhou, 2005); and to reconsider early natural number instruction with a view to narrowing the gap between natural and rational numbers (Sophian, 2004).

Research evidence on early fraction understanding and on early predictors of mathematical competence is in line with these suggestions. It appears that young children, and even infants, are sensitive to information about discrete as well as continuous quantity (Mix, Huttenlocker, & Cohen Levine, 2002). However, children have more opportunities to acquire symbolic tools (e.g., number words and symbols) and structured experiences (e.g., finger counting) pertaining to natural numbers than to fractions. Such early experiences do matter: children who are lacking them lag behind their peers already at the kindergarten, differences increasing with grade (Ramani & Siegler, 2008). Young children also have experiences with actions such as sharing and splitting and competences such as perceiving of proportionality, but they are typically not encouraged to express and systematize them (Greer, 2004). Thus, children do not have much opportunity to form an experiential base that will allow them to realize the common relational basis of diverse situations, a critical aspect of fraction learning (Davis, 1991). Yet, the early tendency to notice multiplicative relations spontaneously-arguably enhanced by exposure to appropriate experiences- predicts students’ conceptual knowledge of fractions three years later (McMullen, Hannula-Sormunen, & Lethinen, 2014).

Starting fraction instruction early is still a controversial idea: Some researchers recommend starting already at the kindergarten (e.g., Clements, 2004; Baroody, 2004); others do not take a position (e.g., Sophian, 2004); yet others discard the idea as unwise (e.g. Engelmann & Engelmann, 2004). The latter view is shared also by many early childhood educators on the grounds that fractions are not an age-appropriate topic. Despite arguing in favor of early fraction instruction, I am concerned about early educators’ readiness to incorporate fraction ideas in their classrooms. They need to be adequately prepared by professional development programs so that they are convinced that it is possible and worth-trying; and informed about ways to exploit the vast range of opportunities to build experiences with fraction ideas offered by a typical kindergarten curriculum (measurement, sharing, simple probability notions, etc.). Else, they will either not commit to doing it; or they will just transfer traditional fraction teaching in the kindergarten.

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Paper session 3

Understanding mathematical competence: The interplay of mathematics education and psychometrics

Kristina Reiss and Andreas Obersteiner (Technische Universität München, TUM School of Education, Germany)

Initiated by international large-scale assessments like TIMMS, PIRLS, or PISA, there has been an intensive discussion on the outcomes of classroom instruction in the last years. In many countries, standards for selected school subjects were defined and introduced in schools (e.g., Common Core State Standards Initiative, 2010). In this context, the notion of competence gained significance thus emphasizing the role of applicable knowledge for students’ learning (Weinert, 2001). Moreover, the development of standards was accompanied by testing in order to ensure that these standards were not only considered by the teachers but were met by their students. The definition of standards was mostly based on theoretical ideas and specifics of the subjects. They relied on aspects regarded as important or indispensable in order to understand a subject. Accordingly, standards as well as tests took hardly into account neither students’ understanding and actual competencies, nor psychological aspects of mathematical development.

Reiss, Heinze, and Pekrun (2007) also started from this theoretical perspective and suggested a competency model for mathematics in the primary school. For grades 1 to 4, students’ aspired competencies were described also with respect to their development. In a pilot study, this theoretical model could be supported by data of an empirical study. This study provided evidence how mathematical competence can be described and how it develops during the first years of school. Moreover, the results of the study were used to adapt the model to students’ actual competencies. In a further step, this competency model built the basis for a larger study, which provided more insights in the nature of mathematical competencies. Based on piloting data of a nationwide survey, Reiss, Roppelt, Haag, Pant, and Köller (2012) suggested a competency model for grade 4. With the parameters M=500 and SD=100, the results of Reiss, Heinze, and Pekrun (2007) suggested to set the beginning of the lowest level at 390 and to define higher levels at an equal distance of 70 each. Finally, the levels were interpreted from a mathematics education perspective. In consequence, Reiss et al. (2012) provided a general competency model and five sub-models, which are based on the specific content area of primary school mathematics, namely numbers, geometry, measuring, patterns structures, as well as data and probability.

In this paper, we discuss how competency models based on mathematics education and psychometrics can contribute to our better understanding of the nature and development of mathematical competencies. Firstly, the data suggest strong correlations between different sub-domains of mathematics (Roppelt & Reiss, 2012). Interpreting these correlations on the basis of one-dimensional and of multi-dimensional models leads to the assumption that sub-domains of mathematics might be similarly appropriate when mathematical competency in general is assessed. Secondly, the data are apt to serve for purposes of test development. Understanding the different levels of competency from a subject-specific point of view supports the development of tests that meet psychometrical standards. Thirdly, the model may build the basis for understanding mathematical procedures and their development, such as reasoning (cf. Reiss & Moll, 2015) or problem-solving.

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Paper session 4

Using eye tracking to assess strategy use in fraction arithmetic

Andreas Obersteiner and Kristina Reiss (TUM School of Education, Technische Universitaet Munich, Germany)

Fraction arithmetic is an essential component of mathematical competence in the domain of numbers, and it has been found to be predictive of later mathematical achievement (Siegler et al., 2012). At the same time, many studies have shown that fraction arithmetic is exceptionally difficult for many students. This seems to be largely due to inappropriate strategies, which may be applied to whole numbers but not to fractions. A widespread mistake while adding two fractions seems to be the result of a componential strategy, where numerators and denominators of the fractions are simply added (e.g., 1/2+2/3=3/5). When adding fractions, this is the most frequent mistake of German sixth-graders as well as of students of other countries, such as the United States or England (Padberg, 2009).

Diagnosing students’ strategy use in mathematical problems is a methodological challenge. On the one hand, it is important to know a student’s result of a specific problem. On the other hand, analyzing this answer will probably not allow conclusions with respect to the strategy actually used. As a consequence, methods providing information about processes are important in order to understand a student’s answer in depth. There are a number of methods used in educational research, however many have severe constraints with respect to their objectivity and reliability. For example, verbal self-reports have been used frequently but are not regarded a specifically reliable or objective method of measurement. Response time measures, which have been used in recent studies, are more objective but give an only indirect measure of strategy use. Moreover, brain imaging methods have been used to identify brain activation patterns, but these methods are quite invasive and restrictive, which limits their applicability in educational contexts.

A method that is more objective than verbal reports, more informative than response time measures, and less invasive than brain imaging, is eye tracking. Eye tracking has already been used successfully for assessing individual strategies in comparing the numerical values of fractions (e.g., which is larger, 1/2 or 2/3; Huber, Moeller, & Nuerk, 2014; Obersteiner et al., 2014; Obersteiner & Tumpek, submitted). The present study goes one step further and assesses eye movements in fraction addition tasks. Twenty-three university students were asked to solve fraction addition tasks of different types, which were assumed to require different comparison strategies. We found that fixation times on numerators and denominators corresponded to the expected strategies. Individual scan paths also allowed distinguishing strategies for different item types. Based on these results, we discuss the feasibility of using eye tracking for assessing strategy use in fraction arithmetic also in primary and secondary school students.

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Paper session 4

Teaching science and mathematics: The role of executive functions in conceptual change processes

Stella Vosniadou (University of Athens, Greece, and The Flinders University of South Australia)

One of the main reasons why children find it hard to understand many concepts in science and mathematics is because these concepts are incompatible with their prior knowledge and require major conceptual changes to take place. It has been generally assumed that when counter-intuitive scientific or mathematical concepts are learned they replace the naïve conceptions students have formed on the basis of their everyday experience. However, recent research in the learning of science and more recently in the learning of mathematics suggests that naïve conceptions are not replaced by scientific ones but continue to exist and to influence problem solving even when conceptual change has been achieved (DeWolf & Vosniadou, 2015; Shtulman & Valcarcel, 2012). If naive conceptions continue to exist alongside the more recently acquired scientific concepts and are easier and faster to activate, it then follows that access to scientific concepts may require the inhibition of naive conceptions and the continuous shifting between naive and scientific views and explanations. In this case, the learning of science and mathematics would implicate the types of cognitive abilities known as Executive Functions (EFs). EFs are a set of processes responsible for the regulation and monitoring of complex cognitive tasks that require deliberate planning, impulse control, goal-directed behaviour, and flexible strategy employment. Together with my colleagues (Vosniadou et al., 2015) we have initiated a research program to investigate the hypothesis that Executive Functions (EFs) are implicated in the learning of science and mathematics. For this purpose two computer-based reaction time Conceptual Understanding and Conceptual Change (CU&C) tasks have been developed to access conceptual change processes in science and mathematics. Elementary and high school students’ performance in these tasks and in two Stroop-like Inhibition and Shifting EF tasks was examined The results showed high correlations between accuracy performance in the CU&C and EF tasks even when Intelligence Ability (IA) and Age were partialed out. A path analytic model showed that performance in the CU&C tasks could be explained by performance in the EF and IA tasks, which were positively related to each other. Further analyses showed that accuracy of performance particularly in the CU&C tasks could be predicted by performance in the EF tasks, with high or medium EF scores being a prerequisite for placement in the group of high CU&C achievers. The implications of these results for the design of learning environments that promote learning in science and mathematics will be discussed.

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Paper session 4

Remedying the misinterpretation of box plots

Stephanie Lem, Patrick Onghena, Lieven Verschaffel, and Wim Van Dooren (KU Leuven, Belgium)

Boxplots are frequently used to represent the distribution of quantitative variables. However, research shows that they are frequently misinterpreted (e.g., Bakker, Biehler, & Konold, 2005). So far, educational attempts to correct these misinterpretations have not been successful. In this study we focus on a specific misinterpretation of box plots, namely the area misinterpretation: Students often think that a larger area in a box plot represents a larger proportion of data than a smaller area, while a larger area actually represents the same amount of data but spread out over a larger interval, thus representing a lower density. For example, if the figure below represents the exam marks of two equally large groups of pupils, students will believe that in the upper group there are more students with a mark of 10 or higher than in the bottom group.

Lem et al. (2013) studied this misinterpretation in depth using a dual processing perspective (relying on the distinction between heuristic and analytic processes). Using accuracy and reaction time data on different item types, it was found that the area misinterpretation indeed can be characterized as fast but incorrect heuristic reasoning. Traces of this incorrect heuristic reasoning were also found in experts (Lem et al., 2014). This paper presents two studies aimed to investigate the effect of instruction focused on this area misinterpretation.

In this study, we tested the effect of two instructional techniques in a large group of first year university students. In condition 1, we used multiple external representations (Ainsworth, 1999): Histograms were used as an overlay on box plots in order to give students a better insight in the way box plots represent data distributions. In condition 2, we used refutational text (Tippett, 2010) to explicitly name and invalidate the area misinterpretation of box plots. In condition 3, we combined multiple external representations and refutational text. Condition 4 was a control group. Results showed that refutational text led to significant learning gains, while only a trend could be observed for using multiple external representations. Also combining both did not lead to significant extra learning gains.

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In a second study, a small group of students were individually involved in a teaching session along the same lines: The box plot was linked to a dot plot to reveal the frequencies of observations in each part of the graph, and the area misinterpretation was refuted. While the intervention had a strongly positive effect on students’ understanding of box plots, a reaction time posttest showed that even though many participants obtained a completely correct understanding of box plots, their reasoning was still affected by the heuristic processed of the area. This means that under some circumstances, such as under time pressure or when less attentive, these participants could still be prone to reason heuristically and hence interpret box plots incorrectly.

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Paper session 4

Learning basic trigonometry with virtual manipulatives

Ton de Jong, Janneke Bekhuis, Ellen Wassink-Kamp, and Anjo Anjewierden (University of Twente, The Netherlands)

Constructive approaches to instruction emphasize the importance of students’ activity in the learning process. This idea is related to more fundamental psychological theories that state that all human cognition emerges from human bodily activities. This idea of ‘embodied cognition’ entails that all cognitions are influenced by physical experiences sometimes assuming a fairly direct relation, sometimes proposing that this relation is mediated by other cognitive processes (see e.g., Barsalou, Simmons, Barbey, & Wilson, 2003). Studies that use fMRI to plot brain activities underscore these assumptions by showing that activation of specific sensorimotor brain systems mediates between students’ learning experiences (physical experience vs observing) and performance on a conceptual knowledge test for the physics domain of torque and angular momentum (Kontra, Lyons, Fischer, & Beilock, 2015). Under the influence of developing computer techniques, an upcoming debate is whether activity needs to be rooted in actual physical manipulations or that virtual manipulations are sufficient of even more effective than physical ones (de Jong, Linn, & Zacharia, 2013). Other approaches say that combinations of physical and virtual activities should be preferred, using alternation of the two (Jaakkola, Nurmi, & Veermans, 2011) or a combination of kinetic and virtual interfaces (Lindgren & Johnson-Glenberg, 2013). In the field of learning mathematics there is often no direct physical manipulative like there is in physics. There are, however, interesting attempts to introduce bodily but still virtual interactions with mathematical concepts, for example by using motion-controlled input for angle representations (Smith, King, & Hoyte, 2014). Another approach to link activity to math learning can be in the form of touch device (e.g., iPad) interfaces that require a finger-based manipulation of mathematical objects and/or functions. In the current study we developed an iPad based intervention (Ziggy) for learning about trigonometry and we compared the effects of this intervention with a “traditional” lesson on the same topic. In this Ziggy application students can manipulate geometrical figures (triangles, angles) and trigonometry formulas (Pythagorean Theorem, sine, cosine etc.) with their fingers and also move symbols between figures and formulas. This creates an environment in which there is genuine virtual activity with math representations. In the study, 54 third grade students, who followed a pre-university track, participated. The experiment followed a quasi-experimental design with an iPad class as experimental group (n = 25) and a traditional class (n = 29) as control group. Both groups participated in two lessons and a third lesson in which a procedural and a conceptual knowledge test were administered. Both groups did not differ in performance on a prior trigonometry test and general math grades. The results showed a significant difference on the procedural knowledge test in favor of the traditional group; the iPad group outperformed the traditional group on conceptual items measuring insight. We see this study therefore as a first indication that using virtual manipulatives for math education can be a promising route for acquiring deeper mathematical knowledge.

http://go-lab.gw.utwente.nl/production/ziggy/labs/ziggy/screen.html?lang=en

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