Education Sciences

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20 pages, 6784 KiB

Open AccessArticle

Analyzing Difficulties in Arithmetic Word Problem Solving: An Epistemological Case Study in Primary School

by Roberto Capone, Federica Filiberti and Alice Lemmo

Educ. Sci. 2021, 11(10), 596; https://doi.org/10.3390/educsci11100596 - 30 Sep 2021

Cited by 3 | Viewed by 2667

This paper focuses on difficulties that primary school students have in facing mathematical word problems. In particular, we are interested in exploring how they develop in the transition from grade 2 to grade 5. The research basis of the hypothesis is that some [...] Read more.

This paper focuses on difficulties that primary school students have in facing mathematical word problems. In particular, we are interested in exploring how they develop in the transition from grade 2 to grade 5. The research basis of the hypothesis is that some difficulties detected in grade 5 are already predictable in grade 2. Starting from the data collected in grade 5 by the National Standardized Assessment, we carry out a quantitative analysis looking for word problems in which students experience difficulties. Subsequently, we conduct a backward analysis of the grade 2 test of the same cohort of students in order to identify a set of word problems linked with those selected in grade 5 test. The analysis shows the presence of many common difficulties in the two grades. We design and carry out specific educational activities concerning word problem-solving in grade 2. These activities produce positive changes in the experimental class compared to the control class. This could suggest that a previous intervention in grade 2 could allow overcoming future difficulties in word problem text comprehension in grade 5. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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12 pages, 261 KiB

Open AccessArticle

Basic Geometric Concepts in the Thinking of In-Service and Pre-Service Mathematics Teachers

by Alessandro Gambini and István Lénárt

Educ. Sci. 2021, 11(7), 350; https://doi.org/10.3390/educsci11070350 - 14 Jul 2021

Cited by 3 | Viewed by 2006

Abstract

This paper discusses a model of a mathematics teacher professional development implemented in Italy and Hungary with in-service and pre-service mathematics teachers. The model focuses on comparative geometry, and it develops with the use of an artifact: the Lénárt spheres. The teacher training [...] Read more.

This paper discusses a model of a mathematics teacher professional development implemented in Italy and Hungary with in-service and pre-service mathematics teachers. The model focuses on comparative geometry, and it develops with the use of an artifact: the Lénárt spheres. The teacher training model is the result of several years of experience of the two authors both as regards the activities in the classroom with the Lénárt spheres and as regards the training of teachers in this field. The proposed teachers’ professional development, in addition to providing ideas for activities to be implemented in the classroom, has the objective of proposing reflective activities from a community of inquiry perspective; during the activities, mediated by the artifact, both the Pedagogical Content Knowledge and the Mathematical Content Knowledge are taken into consideration (Ball et al., 2008). The model has been implemented in Italy in more than 15 training courses taught in the last 5 years, both with primary school teachers and with secondary school teachers. In Hungary, the model is at the basis of elective courses under the title ‘Ball Geometry’ at ELTE University, Budapest, for decades. These courses have been aimed at prospective preschool and elementary school teachers at the Faculty of Primary and Preschool Education, as well as future secondary teachers at the Faculty of Natural Sciences. The subject of the teachers’ professional development paths corresponds to the comparative geometry between the plane and the sphere. After the presentation of the model, some examples of activities implemented in Hungary during the pandemic period will be illustrated and commented from a didactic point of view, which will serve to exemplify the path described. The described path was carried out remotely in online mode through synchronous and asynchronous activities. The distance obviously changed the way we interacted with the artifact, but it did not prevent the achievement of the courses’ objectives. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

17 pages, 527 KiB

Open AccessArticle

Making Good of a Pandemic: A Long-Distance Remedial Summer Course in Calculus

by Ottavio G. Rizzo

Educ. Sci. 2021, 11(7), 327; https://doi.org/10.3390/educsci11070327 - 30 Jun 2021

Cited by 1 | Viewed by 2204

Abstract

What do you do when a change in enrollment policies leaves you with more than 600 students in a first-term university calculus class, three-quarters of those students had a failing mark in mathematics in the pre-enrollment test, you planned a series of remedial [...] Read more.

What do you do when a change in enrollment policies leaves you with more than 600 students in a first-term university calculus class, three-quarters of those students had a failing mark in mathematics in the pre-enrollment test, you planned a series of remedial activities for the second term, and the COVID-19 pandemic shuts the university down with a two-day notice? The pandemic hit instruction with might, forcing schools and universities that were timidly experimenting with digital tools to reinvent themselves in days. The pandemic also offered incentives for creative solutions that, in normal times, would have been considered fit for submission to the committee for recursive committee submissions at best. This paper narrates a teaching experience of how we proposed and managed an at-distance remedial course in August that not only catered to more than twice the number of students expected by our best forecasts, but was a very good success once its effectiveness was compared to the outcomes predicted by the pre-enrollment test scores. We expose the design of the course and link its measured effectiveness with both its design and student engagement; in particular, we show that a different approach to the examination of cognitive load and to fostering student–teacher and student–student communication thanks to digital mediation could be effective in countermanding the math-induced drop-out phenomenon in STEM. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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21 pages, 1651 KiB

Open AccessArticle

Interactive Feedback for Learning Mathematics in a Digital Learning Environment

by Alice Barana, Marina Marchisio and Matteo Sacchet

Educ. Sci. 2021, 11(6), 279; https://doi.org/10.3390/educsci11060279 - 05 Jun 2021

Cited by 27 | Viewed by 4786

Abstract

The COVID-19 pandemic has evidenced a need for tools and methodologies to support students’ autonomous learning and the formative assessment practices in distance education contexts, especially for students from challenging backgrounds. This paper proposes a conceptualization of Interactive Feedback (IF) for Mathematics, which [...] Read more.

The COVID-19 pandemic has evidenced a need for tools and methodologies to support students’ autonomous learning and the formative assessment practices in distance education contexts, especially for students from challenging backgrounds. This paper proposes a conceptualization of Interactive Feedback (IF) for Mathematics, which is a step-by-step interactive process that guides the learner in the resolution of a task after one or more autonomous tentative. This conceptualization is grounded on theories and models of automatic assessment, formative assessment, and feedback. We discuss the effectiveness of the IF for engaging students from low socio-economic contexts in closing the gap between current and reference performance through a didactic experimentation involving 299 Italian students in grade 8. Using quantitative analyses on data from the automatic assessment, we compared the results of the first and last attempts in activities with and without IF, based on algorithmic parameters so that the task changes at every attempt. We found that IF was more effective than other kinds of activities to engage learners in actions aimed at improving their results, and the effects are stronger in low socio-economic contexts. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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17 pages, 1639 KiB

Open AccessArticle

Assessment Practices and Beliefs: Teachers’ Perspectives on Assessment during Long Distance Learning

by Federica Ferretti, George Richard Paul Santi, Agnese Del Zozzo, Marzia Garzetti and Giorgio Bolondi

Educ. Sci. 2021, 11(6), 264; https://doi.org/10.3390/educsci11060264 - 27 May 2021

Cited by 12 | Viewed by 3628

Abstract

The COVID-19 crisis has strongly affected the school system. In Italy, at-distance forms of didactics have been activated, changing the physiognomy of schools in terms of social interaction, practices and the identity of the individuals. In this paper, we address the issue of [...] Read more.

The COVID-19 crisis has strongly affected the school system. In Italy, at-distance forms of didactics have been activated, changing the physiognomy of schools in terms of social interaction, practices and the identity of the individuals. In this paper, we address the issue of how teachers are facing the crisis: our focus is on assessment, as a key variable catalyzing personal history; beliefs; the interface between students; teachers and the school system. We study teachers’ beliefs as part of their identities and assessment as a fundamental variable of beliefs. A qualitative content analysis of the open-ended answers to an online questionnaire is carried out to understand the main characteristics associated with assessment by teachers and the obstacles to overcome in the context of long distance learning (LDL). The data show that teachers did not identify valid assessment methods for LDL during the lockdown, especially due to the lack of control over the students. A misconception emerges concerning the definition of formative assessment together with a new awareness of the possibilities offered by digital technologies regarding the individualization of didactics. This study helps to understand which teachers’ beliefs are related to assessment are and how they are shaped. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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18 pages, 2356 KiB

Open AccessArticle

Secondary Mathematics Teachers’ Perception of Their Readiness for Emergency Remote Teaching during the COVID-19 Pandemic: A Case Study

by Luis J. Rodríguez-Muñiz, Diego Burón, Álvaro Aguilar-González and Laura Muñiz-Rodríguez

Educ. Sci. 2021, 11(5), 228; https://doi.org/10.3390/educsci11050228 - 11 May 2021

Cited by 26 | Viewed by 5568

Abstract

The coronavirus disease 2019 (COVID-19) pandemic caused a worldwide unexpected interruption of face-to-face teaching and a sudden conversion to emergency remote teaching (ERT). In this exploratory study, a sample of 244 secondary mathematics teachers was considered to analyze their perception of their readiness [...] Read more.

The coronavirus disease 2019 (COVID-19) pandemic caused a worldwide unexpected interruption of face-to-face teaching and a sudden conversion to emergency remote teaching (ERT). In this exploratory study, a sample of 244 secondary mathematics teachers was considered to analyze their perception of their readiness to ERT during the COVID-19 pandemic based on their technological pedagogical content knowledge (TPCK), their previous training in digital teaching tools, their level of digital competence for teaching mathematics, and their adaptation to ERT. An online questionnaire was applied, and the answers were quantitatively analyzed. Given the use of a large number of digital resources and the high percentage of self-developed materials using educational software, secondary mathematics teachers reflected adequate digital competence and TPCK for teaching mathematics. The sudden transition to ERT forced teachers to slow down the pace of teaching and to reduce the content taught. Significant differences were observed based on gender and age with respect to teachers’ perception of their adaptation to ERT. Despite the positive influence of previous training on their perception of readiness for ERT, in general, teachers recognized that they need more training. The demand for preparation for video editing and online quiz composition can be considered for the design of future training programs. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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18 pages, 5563 KiB

Open AccessArticle

Changing the Order of Factors Does Not Change the Product but Does Affect Students’ Answers, Especially Girls’ Answers

by Clelia Cascella, Chiara Giberti and Giorgio Bolondi

Educ. Sci. 2021, 11(5), 201; https://doi.org/10.3390/educsci11050201 - 25 Apr 2021

Cited by 2 | Viewed by 1976

Abstract

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with [...] Read more.

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with the same mathematical content and question intent) were formulated differently and administered to a probability sample of 1647 students (grade 8). All the achievement tests were anchored via a set of common items. Students’ answers, equated and then analysed using the Rasch model, confirmed that different formulations affect students’ performances and thus the psychometric functionality of items, with discernible differences according to gender. In particular, we explored students’ sensitivity to the effect of a typical misconception about multiplication with decimal numbers (often called “multiplication makes bigger”) and tested the hypothesis that girls are more prone than boys to be negatively affected by misconception. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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20 pages, 9062 KiB

Open AccessArticle

Learning Mathematics in an Inclusive and Open Environment: An Interdisciplinary Approach

by Heidrun Demo, Marzia Garzetti, George Santi and Giulia Tarini

Educ. Sci. 2021, 11(5), 199; https://doi.org/10.3390/educsci11050199 - 24 Apr 2021

Cited by 8 | Viewed by 3467

Abstract

In this article, we present the first results of the project OPEN-MATH. The research project aims at acknowledging the need for learning environments with differentiation strategies for all. We developed a model for inclusive mathematics learning, based on the Theory of Objectification and [...] Read more.

In this article, we present the first results of the project OPEN-MATH. The research project aims at acknowledging the need for learning environments with differentiation strategies for all. We developed a model for inclusive mathematics learning, based on the Theory of Objectification and a broad idea of differentiation realized through Open Learning. It poses an interdisciplinary research issue that requires the collaboration of two sub-disciplines pertaining to the area of educational studies: Inclusive Education and Mathematics Education. The results we present here are related to the dialogue between theory and practice, whose outcome is a teaching and learning model for inclusion in mathematics. The construction of the teaching and learning model moves along two complementary paths: (1) concerning the theoretical point of view, we implemented connecting theory strategies to network Open Education and the Theory of Objectification; (2) concerning the methodological point of view, we implemented Educational Design Research. The new teaching–learning model is the result of theoretical and methodological validation in real contexts according to an interdisciplinary approach. This study shows the strengths of interdisciplinary research for the pursuit of inclusive mathematics and high standards of learning. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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21 pages, 407 KiB

Open AccessArticle

Teaching Mathematics in a Context of Lockdown: A Study Focused on Teachers’ Praxeologies

by Gilles Aldon, Annalisa Cusi, Florian Schacht and Osama Swidan

Educ. Sci. 2021, 11(2), 38; https://doi.org/10.3390/educsci11020038 - 22 Jan 2021

Cited by 27 | Viewed by 6607

Abstract

This study aims to explore how teachers from four countries—France, Israel, Italy, and Germany—manage their teaching–learning activity in the context of lockdown due to the COVID-19 pandemic. About 700 teachers from the four countries participated in this study. They were given an online [...] Read more.

This study aims to explore how teachers from four countries—France, Israel, Italy, and Germany—manage their teaching–learning activity in the context of lockdown due to the COVID-19 pandemic. About 700 teachers from the four countries participated in this study. They were given an online questionnaire that involved 22 open-ended items, in which they were requested to complete the items that were structured taking into account the relationships between teacher, students, mathematics and resources. The qualitative analysis of teachers’ answers was carried out, referring to both the meta-didactical transposition model and Bishop’s framework on values to investigate teachers’ teaching–learning activities and the reasons underlying their choices. The empirical analysis suggests four tasks corresponding to the main challenges that teachers had to face during the time of lockdown: (a) managing distance learning to support students’ learning through specific methodologies; (b) managing distance learning to develop assessment; (c) managing distance learning to support those students that face difficulties and/or are living a difficult situation/developing inclusive teaching; and (d) managing distance learning to exploit its potentialities for fostering typical mathematical processes. The values that motivated the teachers to change their teaching–learning activities are discussed, conclusions of how the time of lockdown affects the mathematics teaching is drawn, and finally, recommendations and insights from this study are shared. Full article

(This article belongs to the Special Issue Teaching and Assessing Mathematics in a Digital World)

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