Challenging Tasks and Mathematics Learning

Powell, Arthur B.; Borge, Inger Christin; Fioriti, Gema; Kondratieva, Margo; Koublanova, Elena; Sukthankar, Neela

doi:10.1007/978-0-387-09603-2_5

Cited by 17 publications

(8 citation statements)

References 18 publications

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“…Similarly, schema training was effective for helping middle school students solve mathematics word problems on fractions and percentages (Jitendra & Star, 2012). Schema training was also reported to assist students with future problem solving (Powell et al, 2009). Jitendra and Star (2012) reported that schema training might be effective because it provides specific strategies for students.…”

Section: Literature Reviewmentioning

confidence: 99%

Using schema training to facilitate students' understanding of challenging engineering concepts in heat transfer and thermodynamics

Yang

Streveler

Miller

et al. 2020

J of Engineering Edu

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Background: Chi and colleagues have argued that some of the most challenging engineering concepts exhibit properties of emergent systems. However, students often lack a mental framework, or schema, for understanding emergence. Slotta and Chi posited that helping students develop a schema for emergent systems, referred to as schema training, would increase the understanding of challenging concepts exhibiting emergent properties. Purpose: We tested the effectiveness of schema training and explored the nature of challenging concepts from thermodynamics and heat transfer. We investigated if schema training could (a) repair misconceptions in advanced engineering students and (b) prevent them in beginning engineering students. Method: We adapted Slotta and Chi's schema training modules and tested their impact in two studies that employed an experimental design. Items from the Thermal and Transport Concept Inventory and expert-developed multiplechoice questions were used to evaluate conceptual understanding of the participants. The language used by students in their open-ended explanations of multiple-choice questions was also coded. Results: In both studies, students in the experimental groups showed larger gains in their understanding of some concepts-specifically in dye diffusion and microfluidics in Study One, and in the final test for thermodynamics in Study Two. But in neither study did students exhibit any gain in conceptual questions about heat transfer. Conclusion: Our studies suggest the importance of examining the nature of the phenomena underlying the concepts being taught because the language used in instruction has implications for how students understand them. Therefore, we suggest that instructors reflect on their own understanding of the concepts.

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Section: Literature Reviewmentioning

confidence: 99%

Using schema training to facilitate students' understanding of challenging engineering concepts in heat transfer and thermodynamics

Yang

Streveler

Miller

et al. 2020

J of Engineering Edu

View full text Add to dashboard Cite

show abstract

“…Challenging tasks can be determined according to the effectiveness of developing the creativity of younglearners (Powell, Borge, Fioriti, Kondratieva, Koublanova, &Sukthankar, 2009). Memorization cannot help learners with mastering basic concepts, and it damages their attempts to learn mathematics.…”

Section: Findings Related To Procedural Skillsmentioning

confidence: 99%

Analysis of a Turkish Mathematics Textbook in the Late Ottoman Era with respect to the Principles of Contemporary Elementary Education

Yaprak¹,

Çorlu²,

Aydın³

2018

Sakarya University Journal of Education

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Developing an understanding of the foundations of the educational tradition of the Turkish Republic is connected to an exploration of the specifics of Ottoman education. This qualitative study explored an Ottoman mathematics textbook published in the early twentieth century. Under the influence of naturalistic inquiry, the textbook was analyzed in terms of content, organization, and principles of elementary mathematics education. It was concluded that the textbook is successfully presented multiple representations and real-life examples while the development of content did not provide opportunities to develop reasoning skills.

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“…The solvers are not aware of procedural or algorithmic tools that are critical for solving the task and therefore they have to invent mathematical actions to solve it (Powell et al, 2009). Smith and Stein (2011) describe the same thing as "doing mathematics" instead of "challenging tasks".…”

Section: Introduction: Tasks and Challenging Tasksmentioning

confidence: 99%

“…One key feature of challenging tasks is their authenticity in the sense that they are characterized by a certain degree of complexity and they are not amenable to a ready-made solution (Diezman & Watters, 2000). Students should be engaged in challenging tasks for important pedagogical, psychological and social reasons (Powell et al, 2009) even in the early years of schooling when they possess a very small fraction of formal mathematical knowledge, thus allowing students at different levels to pursue the same learning objective (Russo, 2016). Challenging tasks "engage students in cognitive processes at the level of doing mathematics and engage students in high-level thinking and reasoning" (Henningsen & Stein, 1997, p. 546).…”

Section: Introduction: Tasks and Challenging Tasksmentioning

confidence: 99%

“…The relevant literature distinguishes two different ways of grouping challenging tasks. The first way is about paradoxes, counterintuitive propositions, patterns and sequences, geometry, combinatorics, and probability (Powell et al, 2009). For the second way, Applebaum and Leikin (2014) working with teachers describe five types of challenging tasks: (i) problems that require logical reasoning, (ii) nonconventional problems, (iii) inquiry-based problems, (iv) problems that require performing different ways of solutions, and (iv) problems that require a combination of different mathematical topics.…”

Section: Introduction: Tasks and Challenging Tasksmentioning

confidence: 99%

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Using tasks to bring challenge in mathematics classroom

Papadopoulos

2020

JPR

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Rich and challenging tasks can be the vehicle to bring mathematical challenge in classroom. Challenge emerges when you don"t know how to solve the task at first but you can figure out, that is when the solvers are not aware of certain tools to solve the tasks and they have therefore to invent some mathematical actions to proceed. Some challenging tasks in the paper-and-pencil as well as in a digital environment will be presented. The aim is to highlight their potential (i) in engaging students to actions that make sense for them from the mathematical point of view, (ii) to support students in their experimentation and development of problem-solving strategies, (iii) to foster creative mathematical thinking, and (iv) to provoke students" curiosity as the starting point of meaning-making actions in mathematics.

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Challenging Tasks and Mathematics Learning

Cited by 17 publications

References 18 publications

Using schema training to facilitate students' understanding of challenging engineering concepts in heat transfer and thermodynamics

Using schema training to facilitate students' understanding of challenging engineering concepts in heat transfer and thermodynamics

Analysis of a Turkish Mathematics Textbook in the Late Ottoman Era with respect to the Principles of Contemporary Elementary Education

Using tasks to bring challenge in mathematics classroom

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