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Introducing density histograms to grades 10 and 12 students : Design and tryout of an intervention inspired by embodied instrumentation

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Title: Introducing density histograms to grades 10 and 12 students : Design and tryout of an intervention inspired by embodied instrumentation
Authors: Boels, Lonneke, Onderzoeker, Shvarts, Anna, Onderzoeker
Contributors: Wiskundig en Analytisch Vermogen van Professionals, Hogeschool Utrecht@@@Kenniscentrum Leren en Innoveren
Source: G.F. Burrill, L. De Oliveria Souza & E. Reston (Eds.), Research on reasoning with data and statistical thinking: International perspectives. Advances in Mathematics Education.. :143-167
Publisher Information: Hogeschool Utrecht, 2023.
Springer.
Publication Year: 2023
Subject Terms: density histograms, design-based research, embodied design, statistics education
Description: Density histograms can bridge the gap between histograms and continuous probability distributions, but research on how to learn and teach them is scarce. In this paper, we explore the learning of density histograms with the research question: How can a sequence of tasks designed from an embodied instrumentation perspective support students’ understanding of density histograms? Through a sequence of tasks based on students’ notions of area, students reinvented unequal bin widths and density in histograms. The results indicated that students had no difficulty choosing bin widths or using area in a histogram. Nevertheless, reinvention of the vertical density scale required intense teacher intervention suggesting that in future designs, this scale should be modified to align with students’ informal notions of area. This study contributes to a new genre of tasks in statistics education based on the design heuristics of embodied instrumentation.
Document Type: book Part
Language: English
Access URL: https://surfsharekit.nl/public/7eb518d4-dbd4-4d16-8961-bc27a56261cf
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Accession Number: edshbo.sharekit.hu.oai.surfsharekit.nl.7eb518d4.dbd4.4d16.8961.bc27a56261cf
Database: HBO Kennisbank
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  Data: Introducing density histograms to grades 10 and 12 students : Design and tryout of an intervention inspired by embodied instrumentation
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  Data: <i>G.F. Burrill, L. De Oliveria Souza & E. Reston (Eds.), Research on reasoning with data and statistical thinking: International perspectives. Advances in Mathematics Education.</i>. :143-167
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  Data: Density histograms can bridge the gap between histograms and continuous probability distributions, but research on how to learn and teach them is scarce. In this paper, we explore the learning of density histograms with the research question: How can a sequence of tasks designed from an embodied instrumentation perspective support students’ understanding of density histograms? Through a sequence of tasks based on students’ notions of area, students reinvented unequal bin widths and density in histograms. The results indicated that students had no difficulty choosing bin widths or using area in a histogram. Nevertheless, reinvention of the vertical density scale required intense teacher intervention suggesting that in future designs, this scale should be modified to align with students’ informal notions of area. This study contributes to a new genre of tasks in statistics education based on the design heuristics of embodied instrumentation.
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            – TitleFull: G.F. Burrill, L. De Oliveria Souza & E. Reston (Eds.), Research on reasoning with data and statistical thinking: International perspectives. Advances in Mathematics Education.
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