Discovering and addressing errors during mathematics problem-solving—A productive struggle?

Granberg, Carina

doi:10.1016/j.jmathb.2016.02.002

Cited by 42 publications

(33 citation statements)

References 17 publications

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“…1) in this study was based on these principles. It was used in our earlier studies (Granberg 2016;Olsson 2018;Olsson and Granberg 2018) and was designed for users with limited experience with GeoGebra. It was shown that they could receive guidance with respect to how to enter algebraic expressions into GeoGebra and in how to use the angle-measuring tool combined with instructions to focus on m-values (the x-coefficient) and test the solution, but still have to construct parts of the solution themselves.…”

Section: Design Of the Tasksmentioning

confidence: 99%

“…Despite research into the potential of dynamic software to support problem solving and reasoning, it is not yet clear how task design may affect students' utilization of the software. In our previous studies (Granberg and Olsson 2015;Granberg 2016;Olsson 2018), we designed tasks to encourage the use of GeoGebra features to support reasoning and problem solving. In these studies, in which the users were GeoGebra novices and the teacher interactions were limited merely to providing instructions for how to use it, we found that guiding students to use general formulas and strategies did not prevent them from engaging in productive reasoning.…”

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confidence: 99%

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Relations Between Task Design and Students’ Utilization of GeoGebra

Olsson

2019

Digit Exp Math Educ

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This study contributes insights into how task design with different elements of guidance may influence students' utilization of dynamic software for problem solving and reasoning. It compared students' solving of two tasks with different designs supported by the dynamic software GeoGebra. Data analysed examined students' approaches to utilizing GeoGebra, the characteristics of their reasoning and their ability to prove the validity of their solutions after solving the problems. The results showed that students who solved the task with less guidance (without instructions about a specific solving method) were better able to utilize GeoGebra's potential to support their reasoning and problem solving. These students reasoned more creatively and presented more advanced proofs for their solutions than the more guided ones. Keywords GeoGebra. Creative reasoning. Task design. Non-routine tasks A recurrent question in educational research is whether and how technology may support students' learning mathematics. Dynamic software, in this case GeoGebra, invites students to create and manipulate geometric and algebraic representationsfeatures that are considered to have the potential to support problem solving and reasoning (Falcade et al. 2007; Preiner 2008). In situations where students make use of these potentials, they create mathematical objects based on questions or hypotheses. They then interpret, assess and transform the outcomes to proceed in their problem solving. The results, however, are assumed to come from the students' engaging in problem solving and reasoning, and their use of the features of the software to do so. However, it is important to know, rather than simply to assume, what students do when they use dynamic software such as GeoGebra and what guides them in using the

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Section: Design Of the Tasksmentioning

confidence: 99%

mentioning

confidence: 99%

Relations Between Task Design and Students’ Utilization of GeoGebra

Olsson

2019

Digit Exp Math Educ

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“…In the learning of mathematics, struggle is defined as the "intellectual effort [that] students expend to make sense of mathematical concepts that are challenging but [that] fall within the students' reasonable capabilities" (Zeybek 2016, 396). Students' struggles are triggered when their prior knowledge is inadequate to cope conceptually with a given task or to assimilate a new concept, and thus necessitates restructuring of what they already know (Granberg 2016). Struggling students are inclined to be aware of their own knowledge gaps, and they may actively seek appropriate ways of addressing such knowledge gaps, for example, by engaging a peer or a tutor (Bullmaster-Day 2015;Loibl and Rummel 2014).…”

Section: Conceptual Frameworkmentioning

confidence: 99%

Exploring undergraduate students’ productive struggles in a quantitative literacy course: Implications for the development of tutoring

Mhakure

Jaftha

Rughubar-Reddy

et al. 2019

SAJHE

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The present study explores undergraduate students' productive struggles in a Quantitative Literacy (QL) course, when doing exercises on the statistical concept of confidence intervals (CIs) within the context of odds ratios (ORs), embedded in everyday authentic contexts. The research methodology employed in this study is lesson study, in which tutors and researchers work together to plan the research tutorial, observe and teach it, and reflect on the instruction in general within the research tutorial. Data for this study comprises video-and audio-recorded transcriptions of the observation and teaching, and reflections of tutors on research tutorials. In addition, samples of students' work and their achievements in assessments were analysed. Results from the study showed that the students' struggles were initiated when their prior knowledge was not sufficient for them to understand the concept of CIs in relation to ORs. The results also highlight some of the ways in which tutors can notice and address students' productive struggles during tutorials.Future researchers should focus on identifying which instructional approaches can promote and support prolific productive struggles for students during tutoring.

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“…In other words, the struggle becomes a process in which students restructure their existing knowledge while moving towards a new understanding of what is being taught [14][15][16]. Students' struggles become productive in classrooms where they are afforded opportunities to solve complex problems, while being encouraged to try various approaches; even though in these classrooms, students can still fail and struggle, they will feel motivated and good about solving complex problems [17].…”

Section: Introductionmentioning

confidence: 99%

Students’ Productive Struggles in Mathematics Learning

Sayster¹,

Mhakure²

2020

Pedagogy in Basic and Higher Education - Current Developments and Challenges

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Using a predetermined framework on students' productive struggles, the purpose of this study is to explore high school students' productive struggles during the simplification of rational algebraic expressions in a high school mathematics classroom. This study is foregrounded in the anthropological theory of the didactic, and its central notion of a "praxeology"-a praxeology refers to the study of human action, based on the notion that humans engage in purposeful behavior of which the simplification of rational algebraic expressions is an example. The research methodology comprised a lesson study involving a sample of 28 students, and the productive struggle framework was used for data analysis. Findings show that the productive struggle framework is a useful tool that can be used to analyze students' thinking processes during the simplification of rational algebraic expressions. Further research is required on the roles that noticing and questioning can play for mathematics teachers to respond to and effectively support the students' struggles during teaching and learning.

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Discovering and addressing errors during mathematics problem-solving—A productive struggle?

Cited by 42 publications

References 17 publications

Relations Between Task Design and Students’ Utilization of GeoGebra

Relations Between Task Design and Students’ Utilization of GeoGebra

Exploring undergraduate students’ productive struggles in a quantitative literacy course: Implications for the development of tutoring

Students’ Productive Struggles in Mathematics Learning

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