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Murphy S, Danaia L, Tinkler J, Collins F. Parents' experiences of mathematics learning at home during the COVID-19 pandemic: a typology of parental engagement in mathematics education. Educ Stud Math 2023:1-18. [PMID: 37362797 PMCID: PMC10068714 DOI: 10.1007/s10649-023-10224-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/09/2023] [Indexed: 06/28/2023]
Abstract
The COVID pandemic disrupted the schooling of students worldwide resulting in many having had a period of at-home learning. Many parents found themselves assuming responsibility for supporting their children's at-home learning. Parents often find it difficult to support their children's mathematics learning compared with other curriculum areas. There has been limited research exploring parental engagement in mathematics education generally, and little into parental engagement in mathematics education during the COVID pandemic. This paper examines how parents supported their child's mathematics education during the school closures and identifies the factors that impacted this engagement. The Ecologies of Parental Engagement (EPE) model was used to help describe the engagement of different parents in mathematics education during the school closures and to examine the way the home space and available capital shaped parental engagement. Eight parents were selected from a larger Australian study that explored the impact of the pandemic-induced period of at-home schooling on primary school mathematics and science. One-on-one narrative interviews were conducted online with participants. Analysis identified three categories of parental engagement: monitors, facilitators, and enhancers. Parents in each category responded to their role in at-home learning differently, and accessed and activated different capital to support their child's at-home learning in mathematics during the pandemic. Results highlight the value of emotional capital, as well as knowledge of mathematics and mathematics education, with implications for schools hoping to engage parents in mathematics learning. The study offers a typology to be explored in future research concerning parental engagement in mathematics education.
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Affiliation(s)
- Steve Murphy
- School of Education, La Trobe University, Wodonga, Victoria Australia
| | - Lena Danaia
- School of Education, Charles Sturt University, Bathurst, New South Wales Australia
| | - Jacquie Tinkler
- School of Education, Charles Sturt University, Wagga Wagga, New South Wales Australia
| | - Fiona Collins
- School of Education, Charles Sturt University, Wagga Wagga, New South Wales Australia
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Menendez D, Brown SA, Alibali MW. Some Correct Strategies Are Better Than Others: Individual Differences in Strategy Evaluations Are Related to Strategy Adoption. Cogn Sci 2023; 47:e13269. [PMID: 36960870 DOI: 10.1111/cogs.13269] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Revised: 02/22/2023] [Accepted: 02/25/2023] [Indexed: 03/25/2023]
Abstract
Why do people shift their strategies for solving problems? Past work has focused on the roles of contextual and individual factors in explaining whether people adopt new strategies when they are exposed to them. In this study, we examined a factor not considered in prior work: people's evaluations of the strategies themselves. We presented undergraduate participants from a moderately selective university (N = 252; 64.8% women, 65.6% White, 67.6% who had taken calculus) with two strategies for solving algebraic word problems and asked them to rate these strategies and their own strategy on a variety of dimensions. Participants' ratings loaded onto two factors, which we label quality and difficulty. Participants' initial evaluations of the quality of the strategies were associated with whether they used the strategies at posttest, and this effect held even when controlling for individual and contextual factors. However, people's evaluations of the difficulty of the strategies were not consistently associated with their later adoption of those strategies. We also examined individual and contextual predictors of strategy ratings and strategy adoption. Participants' need for cognition and their spatial visualization ability were associated with their strategy evaluations, and the framing of the story problems was associated with their strategy adoption. The findings highlight that strategy adoption depends on multiple interacting factors, and that to understand strategy change, it is critical to examine how people evaluate strategies.
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Affiliation(s)
- David Menendez
- Department of Psychology, University of Wisconsin - Madison
| | - Sarah A Brown
- Department of Psychological & Brain Sciences, Boston University
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Akın A. The effectiveness of web-based Mathematics instruction (WBMI) on K-16 students' mathematics learning: a meta-analytic research. Educ Inf Technol (Dordr) 2022; 27:8015-8040. [PMID: 35250352 PMCID: PMC8882714 DOI: 10.1007/s10639-022-10931-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
Given the increasing prevalence of web technology, web-based mathematics environments have been increasingly widely used in mathematics education for the past two decades. The COVID-19 pandemic has led to an urgent transition from traditional mathematics instruction (TMI) to web-based mathematics instruction (WBMI) at all levels of mathematics education. At this point, it is crucial to scrutinize the effects of WBMI on K-16 students' mathematics learning comprehensively. This meta-analysis research contained a total of 63 studies with 115 effect sizes, which aimed to investigate the effectiveness of WBMI on K-16 students' mathematics learning by incorporating potential moderators, namely mathematics topics, mathematical content standards, feedback status, type of instructional features, age (i.e., grade level), and assessment methods. Based on findings, WBMI has a significantly strong effect on K-16 students' mathematics learning (g = 1.10, p = 0.01, 95% CI [0.95, 1.27]). Moderator analyses reveal that the effect sizes of WBMI on K-16 students' mathematics learning varied significantly depending on all these potential moderators. Additionally, higher-level mathematical concepts, statistics and probability, WBMI with providing feedback, tutorial systems, undergraduate students, and traditional paper-pencil assessment are the strongest moderators in their context. The most notable results of this research are that WBMI is significantly more effective on students' mathematics learning than TMI, while even in the context of WBMI, traditional paper-pencil assessment is significantly more effective than online assessment. This meta-analytic research provides a comprehensive and up-to-date perspective on the effectiveness of WBMI on K-16 students' mathematics learning.
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Affiliation(s)
- Ayça Akın
- Alumni Association, Yunusemre Campus Student Central, First Floor, Anadolu University, 26470 Tepebaşı/Eskişehir, Turkey
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Diego-Mantecon JM, Prodromou T, Lavicza Z, Blanco TF, Ortiz-Laso Z. An attempt to evaluate STEAM project-based instruction from a school mathematics perspective. ZDM 2021; 53:1137-1148. [PMID: 34493944 PMCID: PMC8413685 DOI: 10.1007/s11858-021-01303-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/24/2021] [Indexed: 06/13/2023]
Abstract
Official documents in several educational systems reflect the importance of integrating Science, Technology, Engineering, Arts, and Mathematics (STEAM) and consider project-based learning (PBL) as a way of integrating such disciplines in the classroom. Although STEAM-PBL has been characterized and evaluated in different ways, its impact on school mathematics teaching remains unclear. Mathematics is recognized as the fundamental basis of other disciplines; however, many students still perceive it as a difficult subject and abandon it. To analyze STEAM-PBL classroom implementation from a school mathematics standpoint, we examined 41 classroom experiences from 11 Spanish secondary education teachers (five in-field mathematics teachers), who participated in a STEAM training program for more than 4 years. To frame this study, Thibaut et al.'s (J STEM Educ 3(1):02, 2018) and Schoenfeld's (Educ Res 43(8):404-412, 2014) characterizations of well-designed and implemented projects, respectively, were employed. The results showed that in-field mathematics teachers avoided transdisciplinary projects in which school mathematics is difficult to address, while out-of-field teachers tended to overlook the mathematics in interdisciplinary projects. Unlike out-of-field teachers, mathematics teachers often eluded design-based learning processes for deeply exploiting school mathematics. The latter teachers promoted high cognitive demands and positive perceptions about mathematics in projects where formative environments were generated through discussion and a meaningful feedback loop.
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Affiliation(s)
| | | | | | - Teresa F. Blanco
- University of Santiago de Compostela, Santiago de Compostela, Spain
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Hallinen NR, Sprague LN, Blair KP, Adler RM, Newcombe NS. Finding formulas: Does active search facilitate appropriate generalization? Cogn Res Princ Implic 2021; 6:50. [PMID: 34279745 PMCID: PMC8289958 DOI: 10.1186/s41235-021-00316-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 07/02/2021] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND One criterion of adaptive learning is appropriate generalization to new instances based on the original learning context and avoiding overgeneralization. Appropriate generalization requires understanding what features of a solution are applicable in a new context and whether the new context requires modifications or a new approach. In a series of three experiments, we investigate whether searching for an algebraic formalism before receiving direct instruction facilitates appropriate generalization. RESULTS (1) Searching buffers against negative transfer: participants who first searched for an equation were less likely to overgeneralize compared to participants who completed a tell-and-practice activity. (2) Likelihood of creating a correct new adaptation varied by performance on the searching task. (3) Asking people to sketch alleviated some of the negative effects of tell-and-practice, but sketching did not augment the effect of searching. (4) When participants received more elaborate tell-and-practice instruction, the advantages of searching were less notable. CONCLUSIONS Searching for an algebraic formula prior to direct instruction may be a productive way to help learners connect a formula to its referent and avoid overgeneralization. Tell-and-practice instruction that only described the mathematical procedures led to the greatest levels of overgeneralization errors and worst performance. Tell-and-practice instruction that highlighted connections between the mathematical structure of the formula and the visual referent performed at similar or marginally worse levels than the search-first conditions.
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Affiliation(s)
| | - Lauren N. Sprague
- Department of Psychology, Florida State University, 1107 W. Call St., Tallahassee, FL 32304 USA
| | - Kristen P. Blair
- Stanford Graduate School of Education, 485 Lasuen Mall, Stanford, CA 94305 USA
| | - Rebecca M. Adler
- Department of Psychology and Human Development, Vanderbilt University, 230 Appleton Place, Peabody #552, Nashville, TN 37203-5721 USA
| | - Nora S. Newcombe
- Department of Psychology, Temple University, 1701 N. 13th Street, Weiss Hall, Room 318, Philadelphia, PA 19122 USA
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Brown SA, Menendez D, Alibali MW. Strategy adoption depends on characteristics of the instruction, learner, and strategy. Cogn Res Princ Implic 2019; 4:9. [PMID: 30900063 PMCID: PMC6428876 DOI: 10.1186/s41235-019-0158-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Accepted: 02/01/2019] [Indexed: 11/29/2022]
Abstract
Why do people change their strategies for solving problems? In this research, we tested whether negative feedback and the context in which learners encounter a strategy influence their likelihood of adopting that strategy. In particular, we examined whether strategy adoption varied when learners were exposed to a target strategy in isolation, in conjunction with their own current strategy, and in conjunction with another novel strategy. We also investigated the roles of individual differences, including learners’ need for cognition and their confidence in their current strategies. In Study 1, undergraduate participants who encountered a target strategy in isolation were more likely to adopt it than participants who encountered it in the context of their own current strategy. Negative feedback, low confidence, and high need for cognition also predicted greater adoption. In Study 2, we examined whether rates of strategy adoption depended on the target strategy itself. Indeed, participants were more likely to adopt one strategy than the other, and the effects of feedback also varied across strategies. Individual differences—need for cognition and confidence—also influenced patterns of strategy adoption. These results suggest that strategy adoption depends on the confluence of many factors, including the context in which a target strategy is introduced, characteristics of the learner, and characteristics of the strategy itself.
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Affiliation(s)
- Sarah A Brown
- Department of Psychology, University of Wisconsin - Madison, 1202 W Johnson Street, Madison, WI, 53706, USA.
| | - David Menendez
- Department of Psychology, University of Wisconsin - Madison, 1202 W Johnson Street, Madison, WI, 53706, USA
| | - Martha W Alibali
- Department of Psychology, University of Wisconsin - Madison, 1202 W Johnson Street, Madison, WI, 53706, USA
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Vosniadou S, Pnevmatikos D, Makris N, Lepenioti D, Eikospentaki K, Chountala A, Kyrianakis G. The Recruitment of Shifting and Inhibition in On-line Science and Mathematics Tasks. Cogn Sci 2018; 42:1860-1886. [PMID: 29900574 DOI: 10.1111/cogs.12624] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Revised: 04/11/2018] [Accepted: 04/25/2018] [Indexed: 11/30/2022]
Abstract
Prior research has investigated the recruitment of inhibition in the use of science/mathematics concepts in tasks that require the rejection of a conflicting, nonscientific initial concept. The present research examines if inhibition is the only EF skill recruited in such tasks and investigates whether shifting is also involved. It also investigates whether inhibition and/or shifting are recruited in tasks in which the use of science/mathematics concepts does not require the rejection of an initial concept, or which require only the use of initial concepts. One hundred and thirty-three third- and fifth-grade children participated in two inhibition and shifting tasks and two science and mathematics conceptual understanding and conceptual change (CU&C) tasks. All the tasks were on-line, and performance was measured in accuracy and RTs. The CU&C tasks involved the use of initial concepts and of science/mathematics concepts which required conceptual changes for their initial formation. Only in one of the tasks the use of the science/mathematics concepts required the concurrent rejection of an initial concept. The results confirmed that in this task inhibition was recruited and also showed that the speed of shifting was a significant predictor of performance. Shifting was a significant predictor of performance in all the tasks, regardless of whether they involved science/mathematics or initial concepts. It is argued that shifting is likely to be recruited in complex tasks that require multiple comparisons of stimuli and the entertainment of different perspectives. Inhibition seems to be a more selective cognitive skill likely to be recruited when the use of science/mathematics concepts requires the rejection of a conflicting initial concept.
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Affiliation(s)
- Stella Vosniadou
- Department of Philosophy and History of Science, National and Kapodistrian University of Athens
- School of Education, Psychology and Social Work, Flinders University
| | | | - Nikos Makris
- Department of Primary Education, Democritus University of Thrace
| | - Despina Lepenioti
- Department of Philosophy and History of Science, National and Kapodistrian University of Athens
| | - Kalliopi Eikospentaki
- Department of Philosophy and History of Science, National and Kapodistrian University of Athens
| | - Anna Chountala
- Department of Philosophy and History of Science, National and Kapodistrian University of Athens
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Abstract
We review current debate regarding the core competencies that support early mathematics learning, focusing on the contributions of the inherent system for representing approximate magnitudes, and domain-general systems that facilitate learning across academic domains. The latter include the executive control system that enables explicit processing of quantitative symbols, such as Arabic numerals, and the logical problem-solving abilities (intelligence) that facilitate learning the relations among numerals. The neural systems that underlie these abilities, as related to mathematical learning, are also discussed, albeit briefly. We place the contributions of inherent quantitative abilities and domain-general mechanisms in an evolutionary context and provide some discussion as to how they interact during the learning of evolutionarily novel mathematics.
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Fyfe ER, Rittle-Johnson B. The benefits of computer-generated feedback for mathematics problem solving. J Exp Child Psychol 2016; 147:140-51. [PMID: 27082020 DOI: 10.1016/j.jecp.2016.03.009] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Revised: 03/11/2016] [Accepted: 03/12/2016] [Indexed: 10/21/2022]
Abstract
The goal of the current research was to better understand when and why feedback has positive effects on learning and to identify features of feedback that may improve its efficacy. In a randomized experiment, second-grade children received instruction on a correct problem-solving strategy and then solved a set of relevant problems. Children were assigned to receive no feedback, immediate feedback, or summative feedback from the computer. On a posttest the following day, feedback resulted in higher scores relative to no feedback for children who started with low prior knowledge. Immediate feedback was particularly effective, facilitating mastery of the material for children with both low and high prior knowledge. Results suggest that minimal computer-generated feedback can be a powerful form of guidance during problem solving.
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Affiliation(s)
- Emily R Fyfe
- Department of Psychology and Human Development, Vanderbilt University, Nashville, TN 37203, USA.
| | - Bethany Rittle-Johnson
- Department of Psychology and Human Development, Vanderbilt University, Nashville, TN 37203, USA
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Abstract
Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning.
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Affiliation(s)
- Philip J Kellman
- Department of Psychology, University of California, Los AngelesInstitute for Research in Cognitive Science, University of Pennsylvania
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