57 research outputs found
Interest-enhancing approaches to mathematics curriculum design: Illustrations and personalization
No full textTwo common interest-enhancement approaches in mathematics curriculum design are illustrations and personalization of problems to students’ interests. The objective of these experiments is to test a variety of illustrations and personalization approaches. In the illustrations experiment, students (n = 265) were randomly assigned to lessons with story problems containing decorative illustrations, contextual illustrations, diagrammatic illustrations, misleading illustrations, or no illustrations (only text [control condition]). Students’ problem-solving performance and attitudes were not affected by illustration condition, but learning was better in the control compared with contextual illustrations. In the personalization experiment, students (n = 223) were randomly assigned to story problems that were either personalized based on: a survey of their interests, their choice of interest topics, a randomly assigned interest topic, or the original nonpersonalized story problem (control). The findings indicated there were benefits for choice personalization both for performance in the problem set as well as on a later learning assessment
Exploring an Interactive Technology for Supporting Embodied Geometric Reasoning
No full textRecent advances in research on mathematical cognition have demonstrated how mathematical thinking is embodied – tied to perception, action, spatial systems, and physical motions like gestures. For example, research shows that multisensory perceptions can help learners perceive structures in math that might not be available from symbolic representations (Gerofsky, 2007; Sinclair, 2005) and that math knowledge is revealed through gesture (Edwards, 2009; Kim, Roth & Thom, 2011; Pier et al., 2019; Ng & Sinclair, 2015a, b), action-oriented language (Nathan et al., 2014), and body-based and spatial metaphors (Lakoff & Núñez, 2000; Roth, 2011). However, theories of embodiment (e.g., Nathan & Walkington, 2017; Abrahamson & Sánchez-García, 2016; Hostetter & Alibali, 2008) seldom address the collaborative nature of embodiment that occurs in classrooms as students are learning in physical proximity. This is in part because much of the experimental work on embodiment and gesture in mathematics has been conducted with lab studies (e.g., Abrahamson & Trninic, 2015; Cook, Mitchell, & Goldin-Meadow, 2008; Edwards, 2009; Nathan & Walkington, 2017; Pier et al., 2019). Gesture research (e.g., Goldin-Meadow, 1999) present evidence and synthesize prior studies showing that the presence of multiple learners fundamentally changes the nature of how mathematical ideas can be embodied, in a way that is not describable as the sum of each individual’s actions. A theory of shared embodiment in mathematical domains – which we refer to as “collaborative embodiment”– is vital to understand mathematical cognition as it unfolds in classrooms and with increasingly prevalent technological innovations for collaborative learning.
Currently secondary and post-secondary geometry student use a mix of paper and pencil and computer-based Dynamic Geometry Systems (DGSs), interactive systems for making and manipulating shapes using a mouse, tablet or interactive whiteboard. We plan to recruit 200 undergraduates from a large Midwestern University in the United States..
It will contribute basic knowledge about collaborative embodied
cognitive processes while reasoning about mathematical conjectures. This study will use a randomized block design based on spatial ability pre-test scores. Pairs will be matched by spatial ability score and randomly selected and assigned to either work alone or work together. Participants will be asked to prove 8 geometry conjectures and no resources other than gesture for the first four and a GeoGebra simulation to the last four. Order will be counter-balanced using a Latin Square. Students will be asked to give oral proofs to each conjecture as they work through the conjecture set, and then will individually take a written posttest where they supply a proof for each conjecture. Students’ participation, movements, and verbal responses will be video recorded during the session for analysis
Using the UTeach Observation Protocol (UTOP) to understand the quality of mathematics instruction
No full textRecommended from our members
'Playing the game' of story problems : situated cognition in algebra problem solving
No full texttextThe importance of mathematics instruction including "real life" contexts relevant to students’ lives and experiences is widely acknowledged (Common Core State Standards Initiative, 2010; National Council of Teachers of Mathematics, 2000; 2006; 2009), however questions about why contextualized mathematics is beneficial and how different types of contextualization impact problem solving have yet to be fully addressed by research. Common justifications for contextualized mathematics include the idea that relevant contexts may help students to apply what they learn in school to out-of-school situations, and that relevant contexts may scaffold learning by providing a bridge between what students understand and the content they are trying to learn. The present study investigates these justifications, as well as students' beliefs and problem-solving methods, using story problems on linear functions. A situated cognition theoretical framework (Greeno, 2006) is used to interpret student behavior in the complex, social system of "school mathematics." In a series of interviews, students from a low-performing urban school were presented with algebra problems. Some problems were personalized to the ways in which they described using mathematics in their everyday lives, while others were normal story problems, story problems with equations, or abstract symbolic equations.
Results showed that students rarely explicitly used situational knowledge when solving story problems, had consistent issues with verbal interpretation of stories, and engaged in non-coordinative reasoning where they bypassed the intermediate step of understanding the given situation before trying to solve the problem. After completing most of Algebra I, students still had considerable difficulty with symbolic representations, and struggled to coordinate formal and informal mathematical reasoning. Problems with the same mathematical structure with different amounts of verbal and symbolic support elicited different strategies from students, with personalized problems having high response rates and high use of informal strategies. This suggests that students can use sophisticated, situation-based reasoning on contextualized problems, and that different problem framings may scaffold learning. However, results also demonstrated that the culture of schooling, and story problems as an artifact of this culture, undermines many of the justifications for contextualizing mathematics, and that students need more authentic ways to develop their mathematical reasoning.Curriculum and Instructio
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Exploring the Assistance Dilemma: The Case of Context Personalization
No full textClassroom Observation and Value-Added Models Give Complementary Information About Quality of Mathematics Teaching
No full textHoloLens Collaboration Structure Study
No full textThis within-subjects study compares approaches to facilitating collaboration between students using AR holograms. The research questions are: (1) What models of collaboration in embodied activities are most effective for promoting intuition, insight and proof? (2) How is their effectiveness mediated or moderated by factors like gesture, action, and language
Flatland XR iPad versus Headset Study
No full text. This study is a within-subjects study testing whether simulations of 3-dimensional shapes better leverage the affordances of AR than simulations of 2-dimensional shapes. It also has a between-subjects element where some students will be solving problems using an iPad DGS, while others experience holograms with AR goggles. This it is a 2 by 2 design with task type (2D or 3D) crossed with modality (AR or iPad DGS). The research questions are: How does learners’ gesture, actions, language, and performance when proving differ when engaging with geometric simulations in AR versus using a DGS on an iPad? How is this effect moderated by whether the simulation involves a 2-dimensional or 3-dimensional shape
How to Create an Academic Poster
No full textGuidelines to prepare you poster for the Get Published! Research Conferenc
Research into how different stakeholders value geodiversity within Malta's coastal environment
No full textGeodiversity refers to the variety of geological, geomorphological and soil features, and their assemblages, properties, relationships, systems and interpretations[1].For years geodiversity conservation has come second to biodiversity, with many finding it difficult to define the two separately[2].The research conducted aimed to explore the diverse set of ways geodiversity was valued between tourists and locals, and whether coastal sites were treated differently to others. The question ‘Do tourists and locals value geodiversity differently in three separate coastal environments’ was used throughout the study
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