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Groth RE, Choi Y. A method for assessing students' interpretations of contextualized data. EDUCATIONAL STUDIES IN MATHEMATICS 2023; 114:1-18. [PMID: 37362798 PMCID: PMC10182342 DOI: 10.1007/s10649-023-10234-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 04/13/2023] [Indexed: 06/28/2023]
Abstract
Learning to interpret data in context is an important educational outcome. To assess students' attainment of this outcome, it is necessary to examine the interplay between their contextual and statistical reasoning. We describe a research method designed to do so. The method draws upon Toulmin's (1958, 2003) model of argumentation for the first stage of qualitative data analysis and the Structure of the Observed Learning Outcome (SOLO) (Biggs & Collis, 1991) model for the second stage. Toulmin analyses help identify the justifications and expressions of uncertainty students provide in their interpretive arguments. Subsequent analyses based on the multi-modal conceptualization of SOLO help characterize the quality of student arguments relative to one another. Existing literature and an empirical example are drawn upon to explain how the Toulmin and SOLO models can be used in tandem to analyze students' interpretations of contextualized data. We also explain how pairing Toulmin and SOLO can address theoretical and practical limitations that arise when using just one of the two models on its own.
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Affiliation(s)
- Randall E. Groth
- Department of Secondary and Physical Education, Salisbury University, 1101 Camden Ave., Salisbury, MD 21801 USA
| | - Yoojin Choi
- Department of Secondary and Physical Education, Salisbury University, 1101 Camden Ave., Salisbury, MD 21801 USA
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Cantoral R, Espinoza L, Gaete-Peralta C. Exponential behaviour and variational practices in Chilean newscasts: a socioepistemological view. ZDM : THE INTERNATIONAL JOURNAL ON MATHEMATICS EDUCATION 2023; 55:147-161. [PMID: 36742130 PMCID: PMC9885417 DOI: 10.1007/s11858-022-01458-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/15/2022] [Indexed: 06/17/2023]
Abstract
The research on which we report in this paper was framed within the socioepistemological theory and dealt with the fundamental role of variational practices in the understanding of COVID-19 pandemic graphs. Given the proliferation of mathematical graphs related to the pandemic in the media, we proposed to analyse the variational practices in use in the interpretation of graphs of exponential behaviour that a Chilean newscast of high rating used to inform the population about the pandemic in Chile. For this purpose, a thematic analysis intertwined with documentary analysis techniques was carried out, in order to describe the types of graphs shown in the newscast, and a variational reference system was studied to analyse the use of variational practices. To obtain our results, the types of graphs most frequently shown in the newscast at the beginning of the pandemic were identified and the use of the variational practices of comparison, seriation and prediction in such graphs was analysed. In conclusion, the need is discussed for the conceptual evolution of the exponential function to be accompanied by a pragmatic evolution in school that favours the use and development of variational practices in the student body.
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Affiliation(s)
- Ricardo Cantoral
- Centro de Investigación y Estudios Avanzados del IPN (Cinvestav, IPN), Mexico, Mexico
| | | | - Claudio Gaete-Peralta
- Departamento de Matemáticas y Ciencias de la Ingeniería, Universidad Bernardo O’Higgins, Santiago, Chile
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Melnik-Leroy GA, Aidokas L, Dzemyda G, Dzemydaitė G, Marcinkevičius V, Tiešis V, Usovaitė A. Is my visualization better than yours? Analyzing factors modulating exponential growth bias in graphs. Front Psychol 2023; 14:1125810. [PMID: 36874812 PMCID: PMC9977824 DOI: 10.3389/fpsyg.2023.1125810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Accepted: 01/20/2023] [Indexed: 02/18/2023] Open
Abstract
Humans tend to systematically underestimate exponential growth and perceive it in linear terms, which can have severe consequences in a variety of fields. Recent studies attempted to examine the origins of this bias and to mitigate it by using the logarithmic vs. the linear scale in graphical representations. However, they yielded conflicting results as to which scale induces more perceptual errors. In the current study, in an experiment with a short educational intervention, we further examine the factors modulating the exponential bias in graphs and suggest a theoretical explanation for our findings. Specifically, we test the hypothesis that each of the scales can induce misperceptions in a particular context. In addition to this, we explore the effect of mathematical education by testing two groups of participants (with a background in humanities vs. formal sciences). The results of this study confirm that when used in an inadequate context, these scales can have a dramatic effect on the interpretation of visualizations representing exponential growth. In particular, while the log scale leads to more errors in graph description tasks, the linear scale misleads people when they have to make predictions on the future trajectory of exponential growth. The second part of the study revealed that the difficulties with both scales can be reduced by means of a short educational intervention. Importantly, while no difference between participants groups was observed prior to the intervention, participants with a better mathematical education showed a stronger learning effect at posttest. The findings of this study are discussed in light of a dual-process model.
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Affiliation(s)
- Gerda Ana Melnik-Leroy
- Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
| | - Linas Aidokas
- Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
| | - Gintautas Dzemyda
- Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
| | - Giedrė Dzemydaitė
- Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
| | | | - Vytautas Tiešis
- Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
| | - Ana Usovaitė
- Institute of Data Science and Digital Technologies, Vilnius University, Vilnius, Lithuania
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Lim VY, Peralta LMM, Rubel LH, Jiang S, Kahn JB, Herbel-Eisenmann B. Keeping pace with innovations in data visualizations: A commentary for mathematics education in times of crisis. ZDM : THE INTERNATIONAL JOURNAL ON MATHEMATICS EDUCATION 2022; 55:109-118. [PMID: 36532825 PMCID: PMC9734678 DOI: 10.1007/s11858-022-01449-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 10/31/2022] [Indexed: 06/17/2023]
Abstract
The mathematical medium of data visualization and other data representations (DV) has served as a primary means of communicating about the COVID-19 crisis. DVs about the pandemic are highly visible across news journalism and include an increasingly innovative and diverse set of representational forms. These representational forms employ multimodal, interactive, and narrative elements, among others, that create new possibilities for data storytelling. Building on current efforts to expand the teaching and learning of data practices in K-12 mathematics education, we argue that innovative DVs create new opportunities for teaching and learning mathematics, particularly during times of crisis. We illustrate our argument using three examples of innovative DVs from news journalism. We discuss how these DVs could serve as complementary resources alongside conventional graphs to support students as they use mathematics and mathematical representations to make sense of crises such as the COVID-19 pandemic. Our commentary seeks to bring current trends in data representation to bear in mathematics education. Leveraging such trends offers artifacts useful for teaching and opens up space for elevating emotion and experience as important aspects of mathematics curricula.
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Graven M, Venkat H, Bowie L. Analysing the citizenship agenda in Mathematical Literacy school exit assessments. ZDM : THE INTERNATIONAL JOURNAL ON MATHEMATICS EDUCATION 2022; 55:1-16. [PMID: 36407036 PMCID: PMC9648886 DOI: 10.1007/s11858-022-01448-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 10/25/2022] [Indexed: 06/16/2023]
Abstract
Assessments, in particular high stakes assessments, impact the nature of teaching and learning. Given this, the goal of citizenship if seen as important needs to feature within high stakes school exit assessments rather than only as part of curriculum and assessment policy rhetoric. South Africa's Mathematical Literacy (ML) curriculum foregrounds critical democratic citizenship. We analyse the ML Grade 12 exit assessments from their start in 2008 to 2020 to understand the emphasis placed on critical citizenship and how this emphasis has shifted over time. The literature base links critical citizenship orientations with reasoning and reflecting questions, so we focused on examination questions in this category. Our findings show shifts away from critical citizenship related agendas towards foregrounding a life preparation orientation for the self-managing person. Linked with this shift, we note a move away from general societal contexts towards more personal/individual contexts and moves from almost entirely national contexts to inclusion of global contexts. We noted movement from more open-phrased questions towards closed 'check figure calculated is valid'-type questions. Assessment memoranda suggest assessors view these questions as reasoning items, eroding the critical citizenship agenda. While increasing numbers of students are taking ML rather than Mathematics, average performance stands at around 40%. This points to limited and diminishing access to mathematical reasoning and reflecting for critical democratic citizenship. The paper highlights ways in which analysis of examinations over time can provide a window into the presence or absence of the citizenship agenda in mathematics education.
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Affiliation(s)
| | - Hamsa Venkat
- CASTeL Dublin City University and University of the Witwatersrand, Dublin, Ireland
| | - Lynn Bowie
- OLICO and University of the Witwatersrand, Johannesburg, South Africa
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Siller HS, Elschenbroich HJ, Greefrath G, Vorhölter K. Mathematical modelling of exponential growth as a rich learning environment for mathematics classrooms. ZDM : THE INTERNATIONAL JOURNAL ON MATHEMATICS EDUCATION 2022; 55:17-33. [PMID: 36249126 PMCID: PMC9549845 DOI: 10.1007/s11858-022-01433-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 09/11/2022] [Indexed: 06/16/2023]
Abstract
Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Our contribution has the aim of showing that basic mental models about exponential growth are important for understanding media reports of Covid-19. Furthermore, we highlight how the coronavirus pandemic can be used as a context in mathematics classrooms to help students understand that they can and should question media reports on their own, using their mathematical knowledge. Therefore, we first present the role of mathematical modelling in achieving these goals in general. The same relevance applies to the necessary basic mental models of exponential growth. Following this description, based on three topics, namely, investigating the type of growth, questioning given course models, and determining exponential factors at different times, we show how the presented theoretical aspects manifest themselves in teaching examples when students are given the task of reflecting critically on existing media reports. Finally, the value of the three topics regarding the intended goals is discussed and conclusions concerning the possibilities and limits of their use in schools are drawn.
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Chan MCE, Sabena C, Wagner D. Mathematics education in a time of crisis-a viral pandemic. EDUCATIONAL STUDIES IN MATHEMATICS 2021; 108:1-13. [PMID: 34934249 PMCID: PMC8536895 DOI: 10.1007/s10649-021-10113-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/19/2021] [Indexed: 06/14/2023]
Affiliation(s)
- Man Ching Esther Chan
- Melbourne Graduate School of Education, The University of Melbourne, Ground floor, 234 Queensberry Street, The University of Melbourne, VIC 3010 Australia
| | - Cristina Sabena
- Department of Philosophy and Education Sciences, University of Torino, Turin, Italy
| | - David Wagner
- Faculty of Education, University of New Brunswick, Fredericton, Canada
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