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Innovations in Mathematics Education: Evaluation, Research and Practice

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A special issue of Education Sciences (ISSN 2227-7102). This special issue belongs to the section "STEM Education".

Deadline for manuscript submissions: closed (1 March 2025) | Viewed by 20404

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Special Issue Editors

Dr. Christopher R. Rakes

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Guest Editor

Associate Professor, Department of Education, University of Maryland Baltimore County, Baltimore, MD 21250, USA
Interests: mathematics education; teacher knowledge; teacher preparation and professional development; education technology
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Robert N. Ronau

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Guest Editor

Emeritus: College of Education and Human Development, University of Louisville, Louisville, KY 40292, USA
Interests: mathematics education; education technology; STEM evaluation; professional development

Dr. Jon Saderholm

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Guest Editor

Associate Professor, Education Studies Department, Berea College, Berea, KY 40404, USA
Interests: STEM education; teacher preparation; program evaluation; STEM outreach

Special Issue Information

Dear Colleagues,

Professional practice in mathematics education demands explicit attention to equity (National Council of Teachers of Mathematics (NCTM), 2018). Professional development discussions about equity might include systemic issues such as tracking. In classroom practice, the focus is on developing robust mathematics lessons that open the conceptual space for all students (e.g., increased student communication, multiple representations, climate of respect; Sawada et al., 2002) and providing instructional supports to ensure the success of all students (e.g., additional time; NCTM, 2018). Equitable, meaningful assessment is an indispensable component of classroom practice, for example, aligning expectations with assessments, providing multiple forms of assessment, giving high-quality and consistent feedback, consciously attending to the influence of biases and assumptions about student ability, and distinction of assessment from grades (Copur-Gencturk et al., 2020; Porter et al., 2007; Webb, 1997).

Teachers regularly carry out research in their classrooms (Anderson and Shattuck, 2012) and seek out research that is directly applicable to the classroom (Drill et al., 2012). Teachers may at the same time think of “research” as a hands-off activity with little connection to the classroom (Drill et al., 2012). Methods such as design-based research are especially useful to support partnerships between researchers and practitioners with a goal of generating outcomes that are both practical and contribute to theory (Anderson and Shattuck, 2012). Viewing research as a seamless component of professional practice adds access, richness and complexity to the process and has been shown to improve professional learning outcomes for teachers (e.g., Atay, 2008; Elliot, 1990; Savoie‐Zajc and Descamps‐Bednarz, 2007; Zeichner, 2003).

This Special Issue provides the opportunity to present original research and evaluation of mathematics education innovation. Research-to-practice articles are also highly valued. Potential themes for papers include (but are not limited to) some of the following:

Effective mathematics teaching through theoretical and conceptual framework foundations
Culturally relevant pedagogy in mathematics education
Student leadership in mathematics learning
Portraying mathematics phenomena through non-linguistic representations
Supporting special populations in mathematics
Building authentic mathematics connections
Engaging students through collaborative mathematics learning
Strengthening meta-cognition in mathematics
Promoting mathematical thinking and reasoning
Teaching mathematics through inquiry, discovery, experimentation, and simulation
Engaging students in technology explorations in mathematics
Assessment in mathematics education
Research and evaluation in mathematics education
Future directions in teacher research partnerships

We look forward to receiving your contributions.

Dr. Christopher R. Rakes
Prof. Dr. Robert N. Ronau
Dr. Jon Saderholm
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a double-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Education Sciences is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

mathematics education
professionalism
research
evaluation
research-to-practice

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Published Papers (8 papers)

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Research

11 pages, 183 KiB

Open AccessArticle

Exploratory Study on Geometric Learning of Students with Blindness in Mainstream Classrooms: Teachers’ Perspectives Using the Van Hiele Theory

by Hisae Miyauchi and Robinson Thamburaj

Educ. Sci. 2025, 15(4), 475; https://doi.org/10.3390/educsci15040475 - 11 Apr 2025

Viewed by 322

Abstract

Ensuring mathematics education for all learners, including students with blindness learning in mainstream classrooms, is crucial. This exploratory research aims to clarify the characteristics of geometric learning among students with blindness and to identify the factors contributing to the challenges faced by this population. The Van Hiele theory of geometric thought served as a reference framework. Qualitative data were gathered through group interviews with specialists in the field of education for students with blindness and analyzed using inductive analysis. Participants affirmed that students with blindness progress through Van Hiele levels of geometric thought in a manner similar to sighted students, suggesting that much of the learning can take place alongside sighted peers in mainstream classrooms. However, they also highlighted the unique challenges these students face in reaching level 0, a level where students recognize shapes without a formal understanding of their properties or attributes. Among the reasons for these challenges were that for these particular students, subskills, such as bimanual exploration, hand coordination, and cognitive integration, are required to reach level 0. The study also identified the necessity for specialists in visual impairment education to guide students using appropriate tasks and learning materials that reflect the characteristics of haptic perception. Since level 0 serves as a gateway to both basic and advanced geometry, the findings underscore the importance of providing differentiated support that targets these subskills early in students’ schooling. To ensure meaningful geometry instruction, mainstream teachers are encouraged to collaborate with specialists in visual impairment education, who can guide the selection of appropriate learning tools and support the development of the subskills. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

20 pages, 1322 KiB

Open AccessArticle

The Impact of the COVID-19 Pandemic upon Mathematics Assessment in Higher Education

by Eabhnat Ní Fhloinn and Olivia Fitzmaurice

Educ. Sci. 2025, 15(4), 449; https://doi.org/10.3390/educsci15040449 - 3 Apr 2025

Viewed by 446

Abstract

Historically, the assessment of mathematics in higher education comprised closed-book, summative, proctored examinations. Related disciplines and subjects like statistics, mathematics education, and the history of mathematics lend themselves to a broader range of assessment techniques that have been reported to provide a more balanced picture of students’ abilities. In 2020, an online environment for the teaching and learning of mathematics was imposed on the academic world globally as a result of the COVID-19 pandemic. In an effort to teach and assess remotely while maintaining institutional academic standards, the majority of lecturers were in a situation where closed-book, proctored assessments were not an option. As a result, other methods were adopted. This paper reports on an investigation into how mathematics lecturers worldwide assessed mathematics before the pandemic, during the initial lockdown restrictions, and in the immediate aftermath, while some restrictions were still in place, to see if any changes were sustained. There was a statistically significant difference in the proportion of respondents who used many of the assessment types investigated across the three time periods, including open-book timed, open-book untimed, closed-book, multiple-choice questions, online proctored, in-person proctored, presentations, projects, and assignments. The majority of those who favoured closed-book proctored examinations prior to the pandemic moved to timed open-book assessments. Differences between the weightings of final examinations versus continuous assessments were also statistically significant, with greater weight given to continuous assessment once the pandemic began. Respondents’ satisfaction levels with their assessments were significantly different also, with the highest satisfaction levels prior to the pandemic and the lowest during the initial lockdown restrictions. Academic integrity was a key concern of the majority of respondents when assessing the learning outcomes of their modules and played a role in the vehicle of assessment they chose. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

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25 pages, 395 KiB

Open AccessArticle

The Use of Guided Reflections in Learning Proof Writing

by Kathleen Hoffman, Tory H. Williams and Kerrie Kephart

Educ. Sci. 2024, 14(10), 1084; https://doi.org/10.3390/educsci14101084 - 4 Oct 2024

Cited by 1 | Viewed by 1235

Abstract

We investigated written self-reflections in an undergraduate proof-writing course designed to mitigate the difficulty of a subsequent introductory analysis course. Students wrote weekly self-reflections guided by mechanical, structural, creative, and critical thinking modalities. Our research was guided by three research questions focused on the impact of student self-reflections on student metacognition and performance in the interventional and follow-up class. To address these questions, we categorized the quality of the students’ reflections and calculated their average course grades within each category in the proof-writing, the prerequisite, and the introductory analysis courses. The results demonstrated that writing high-quality self-reflections was a statistically significant predictor of earning higher average course grades in the proof-writing course and the analysis course, but not in the prerequisite course. Convergence over the semester of the students’ self-evaluations toward an experts’ scorings on a modality rubric indicates that students improve in their understanding of the modalities. The repeated writing of guided self-reflections using the framework of the modalities seems to support growth in the students’ awareness of their proof-writing abilities. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

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20 pages, 2497 KiB

Open AccessArticle

Developing a Novel Model for ICT Integration in South African Education: Insights from TIMSS

by Marien Alet Graham, Guillaume Matthys Kruger and Linda van Ryneveld

Educ. Sci. 2024, 14(8), 865; https://doi.org/10.3390/educsci14080865 - 9 Aug 2024

Viewed by 3828

Abstract

ICT integration in the classroom is viewed as a panacea towards resolving education challenges. A quantitative approach using South African Trends in International Mathematics and Science Studies (TIMSS) 2019 Grades 5&9 data with a positivist philosophical stance was used to explore ICT use. For a long time, most school research took the form of small-scale qualitative studies, such as case studies or critical policy studies; however, research in education has witnessed an increasing demand for high-quality, large-scale quantitative studies such as the current study. TIMSS utilised a two-stage stratified cluster sampling design, sampling schools by size and selecting intact classes. This study focusses on South Africa where 297 schools, 294 mathematics teachers, and 11,903 students were sampled at Grade 5 level, and, at Grade 9 level, the sample consisted of 519 schools, 543 mathematics teachers and 20,829 students. More than 50% of students attend schools lacking computers/tablets, a figure that rises to nearly 90% concerning their availability in classrooms. Less than half of students attend schools utilising online learning systems or providing digital resources. Principals in approximately half the schools indicated shortages/inadequacies in technologically competent staff, and audio-visual and computer technology/software resources. Approximately 80% of teachers expressed interest in future technology integration training for both grades when surveyed. Over half of the students lacked home internet access; however, the majority had access to cell phones and computers/tablets at home. In tailoring this study to the South African context, a novel model for ICT integration emerged which draws upon the Dynamic Model of Educational Effectiveness and the TIMSS curriculum model. Recommendations for improving policy and practice in ICT implementation in schools are structured around the new model. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

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12 pages, 392 KiB

Open AccessArticle

(Up)Grading: A (Re)Humanizing Assessment Process with a Focus on Feedback

by Stefanie D. Livers, Kristin E. Harbour and Patrick L. Sullivan

Educ. Sci. 2024, 14(6), 646; https://doi.org/10.3390/educsci14060646 - 15 Jun 2024

Viewed by 1499

Abstract

Researchers across two universities and three different mathematics education courses implemented their vision of a novel grading approach called (Up)grading. (Up)grading shifts the focus of assessment from grades to growth. Key features of implementing (Up)grading included (a) providing students with opportunities to reflect upon and grow from their learning experiences, and (b) giving them a voice in determining their course grade. The findings suggest that most students perceived (Up)grading as a positive experience in their learning and as an assessment approach. The features of (Up)grading students believed contributed to the positive experience included giving them opportunities to reflect on their work and learn from their mistakes, as well as targeted feedback, enabling them to independently move their thinking forward. Tensions in the process did arise, including students’ initial anxiety with the norm shift from grades to growth and instructors’ management of the flow of assignments. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

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21 pages, 2402 KiB

Open AccessArticle

Interactive Homework: A Tool for Parent Engagement

by Laura Moore and Robert N. Ronau

Educ. Sci. 2024, 14(1), 103; https://doi.org/10.3390/educsci14010103 - 17 Jan 2024

Cited by 1 | Viewed by 1986

Abstract

Families have largely been excluded from the implementation of the Common Core State Standards in Mathematics (CCSSM), reducing their ability to extend their child’s mathematics learning. CCSSM emphasizes different instructional elements (e.g., pictorial representations, problem solving, multiple strategies for solving) that may differ greatly from how parents learned mathematics. In addition, many school officials have ineffectively engaged parents in the changes, further diminishing their capacity to participate in their child’s learning. This case study examined parent mathematics self-efficacy and parent mathematics knowledge for teaching, factors that influence the effectiveness of their engagement in their child’s mathematics learning. This study was also implemented to identify elements that the parent participant found helpful for their child’s mathematics learning. A thematic analysis was performed on the data sources, the interactive homework assignments, a survey, observations, a researcher’s journal, and an interview to conclude that the interactive homework assignments improved parent mathematics self-efficacy and parent mathematics knowledge for teaching. The parent participant also identified the assignments’ side-by-side examples, additional practice, and the easy access of the assignments as features of the intervention that enhanced her ability to support her child. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

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13 pages, 891 KiB

Open AccessArticle

Concrete–Representational–Abstract (CRA) Instructional Approach in an Algebra I Inclusion Class: Knowledge Retention Versus Students’ Perception

by Sherri K. Prosser and Stephen F. Bismarck

Educ. Sci. 2023, 13(10), 1061; https://doi.org/10.3390/educsci13101061 - 22 Oct 2023

Cited by 1 | Viewed by 6563

Abstract

Mathematical manipulatives and the concrete–representational–abstract (CRA) instructional approach are common in elementary classrooms, but their use declines significantly by high school. This paper describes a mixed methods study focused on knowledge retention and perceptions of students in a high school Algebra I inclusion class after a lesson on square roots using a novel algebra manipulative. Twenty-five students in a high school Algebra I inclusion class engaged in an interactive lesson on square roots paired with the manipulative to support their conceptual understanding. Participants completed a pretest, a post-treatment questionnaire, and a delayed post-test. The two-sample t test showed a significant difference in students’ pretest–post-test scores. However, conventional content analysis of the questionnaires showed that most students did not believe the CRA instructional approach supported their learning. Implications include increased use of manipulatives to teach abstract algebraic topics to support students’ conceptual understanding and destigmatizing the use of manipulatives in secondary mathematics classrooms. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

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20 pages, 2531 KiB

Open AccessArticle

Building Mathematics Learning through Inquiry Using Student-Generated Data: Lessons Learned from Plan-Do-Study-Act Cycles

by Christopher R. Rakes, Angela Wesneski and Rebecca Laws

Educ. Sci. 2023, 13(9), 919; https://doi.org/10.3390/educsci13090919 - 9 Sep 2023

Cited by 2 | Viewed by 2584

Abstract

This paper describes how plan-do-study-act cycles engaged a classroom mentor teacher and student teacher in a professional collaboration that resulted in two inquiry activities for high-school geometry classes. The PDSA cycles were carried out in four high school geometry classes, each with 30 to 35 students, in a mid-Atlantic urban school district in the U.S. The four geometry classes were co-taught by the second and third authors of this paper. The data consisted of classroom documents (e.g., activity prompts, tasks), classroom observations, student feedback about activities, and monthly PDSA reports. The PDSA cycles had a direct effect on the professional learning of the teachers. The resultant classroom activities used a data collection approach to engaging students in inquiry to learn about trigonometry functions and density. Student learning behaviors were noticeably improved during these activities compared with traditional mathematics instruction. We concluded that the data collection sequence provided an accessible entry point for students to begin scientific inquiry in mathematics. The process opened the conceptual space for students to develop curiosity about mathematical phenomena and to explore their own research questions. The use of culturally relevant topics was especially compelling to students, and the open-ended nature of these exploratory activities allowed students to see mathematics through their own cultural lenses. Full article

(This article belongs to the Special Issue Innovations in Mathematics Education: Evaluation, Research and Practice)

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