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Critical Issues in Mathematics Education

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A special issue of Education Sciences (ISSN 2227-7102).

Deadline for manuscript submissions: closed (15 January 2017) | Viewed by 107429

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Prof. Dr. Patricia S. Moyer-Packenham

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Professor, Mathematics Education; Director, Mathematics Education and Leadership Programs, School of Teacher Education and Leadership, 318 EEJ Early Childhood Education and Research Center; Emma Eccles Jones College of Education and Human Services, Utah State University, 2605 Old Main Hill, Logan, UT 84322-2605, USA
Interests: mathematics representations; physical manipulatives; pictorial images; symbolic systems; virtual manipulatives; mathematics teacher development

Special Issue Information

Dear Colleagues,

This Special Issue of Education Sciences focuses on critical issues in mathematics education. There are a variety of critical issues that currently face mathematics educators and researchers today. In this Special Issue, we invite educators and researchers to identify some of the most compelling critical issues in mathematics education today and submit a research manuscript based on their topic.

One example of a critical issue might be the use of technologies for mathematics teaching and learning. This includes the use of a variety of mobile technologies (e.g., iPads, iPods, phones, tablets) and other instructional devices and software. Some of the most compelling questions about the use of technologies for teaching mathematics might include: How do mobile technologies provide access to 21st Century mathematics learning? What affordances of the technology support learning? and What are effective practices for using technologies for mathematics instruction?

Another example of a critical issue might be equitable access to mathematics for all students that meets their specific needs. This includes access to mathematics for special needs and gifted students. Some of the most compelling questions around this issue might include: What are the most important issues to address in the mathematics education of special needs and gifted students? How do teachers, researchers, specialists, and others advocate for change in math education for gifted students or students with special needs? and What technologies support mathematical learning for special needs and gifted students?

Another example of a critical issue is that life in our global society removes boundaries across countries and opens channels of communication. This provides mathematics educators with the opportunity to share ideas across countries and cultures to support mathematics teaching and learning all over the world. Some of the most compelling questions around this issue might include: What can we learn from other countries to support mathematics teaching and learning in our own context? What models of instruction and assessment are shown to be effective across different cultures and contexts? and What innovations and collaborations exist in mathematics education that cross country boundaries? These are just a few examples of critical issues, and there are many more.

In this issue we are particularly interested in authors identifying and reporting research on a critical issue in mathematics education. For this Special Issue to be published in 2017, we invite manuscripts to be submitted for review on or before January 15, 2017. Manuscripts will be subject to the process of blind peer review coordinated by the Special Issue Guest Editor.

Patricia S. Moyer-Packenham
Guest Editor

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 papers will be 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. 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

technologies for mathematics teaching and learning;
mobile technologies;
mathematics for special needs students;
mathematics for gifted students;
learning about mathematics from other countries;
instruction and assessment in different cultures and contexts;
collaborations in mathematics that cross country boundaries

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Published Papers (11 papers)

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2699 KiB

Open AccessArticle

Engaging Elementary Students in the Creative Process of Mathematizing Their World through Mathematical Modeling

by Jennifer M. Suh, Kathleen Matson and Padmanabhan Seshaiyer

Educ. Sci. 2017, 7(2), 62; https://doi.org/10.3390/educsci7020062 - 8 Jun 2017

Cited by 20 | Viewed by 11577

Abstract

This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1) How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2) What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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893 KiB

Open AccessArticle

Using Grounded Theory to Extend Existing PCK Framework at the Secondary Level

by Dragana Martinovic and Agida G. Manizade

Educ. Sci. 2017, 7(2), 60; https://doi.org/10.3390/educsci7020060 - 6 Jun 2017

Cited by 8 | Viewed by 7085

Abstract

This paper addresses two critical issues in mathematics education, the need: (a) to understand the nature of educator’s subject matter knowledge and pedagogical content knowledge; and (b) to find ways to measure them. It stems from a mixed-methods study designed to inspect the secondary mathematics teachers’ pedagogical content knowledge (PCK) related to the area of a trapezoid, a common topic in intermediate/secondary school classes. Based on the provided exemplars of student work, in-service teachers were invited to propose possible ways for addressing perceived difficulties of students and provide extensions. Using a Grounded Theory approach, we identified themes in our data and incorporated them with existing conceptualizations of knowledge for teaching secondary level mathematics, and developed rubrics that allow discriminating different levels of teachers’ PCK. In this paper, we describe the process of developing the rubrics, and propose ways to: (a) extend the existing frameworks for PCK in/for teaching mathematics at the secondary level; and (b) measure multiple facets of PCK in order to design technology-based professional development for mathematics teachers. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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1043 KiB

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Mathematics Intervention Supporting Allen, a Latino EL: A Case Study

by Marialuisa Di Stefano, Kristy Litster and Beth L. MacDonald

Educ. Sci. 2017, 7(2), 57; https://doi.org/10.3390/educsci7020057 - 31 May 2017

Cited by 1 | Viewed by 7116

Abstract

This research discusses a single case study of a first-grade Latino English Learner (EL) student, Allen (pseudonym), from a larger inquiry-based intervention on inversion and mental reversibility development. The purpose of this case study was to develop a better understanding of the relationship between Allen’s English language proficiency and his ability to solve inversion and compensation mathematics tasks. The integration of multiple paradigms confronting radical constructivism and sociocultural theory of learning via culturally relevant pedagogy provided us with a multi-faceted set of perspectives in understanding the interconnection between Allen’s cultural and linguistic background and his development of algebraic reasoning. Through conceptual and retrospective analyses, we found that Allen’s language features are highly correlated with the development of his thinking strategies and his ability to solve mathematics tasks. Implications of this study include the development of teaching strategies that address critical issues in mathematics, such as the individual differences of learners, specifically ELs from Latino background. We suggest further research is needed in the field of language acquisition and access to STEM related concepts. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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Open AccessArticle

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

by Helena P. Osana, Emmanuelle Adrien and Nathalie Duponsel

Educ. Sci. 2017, 7(2), 52; https://doi.org/10.3390/educsci7020052 - 3 May 2017

Cited by 7 | Viewed by 8506

Abstract

Concrete objects used to illustrate mathematical ideas are commonly known as manipulatives. Manipulatives are ubiquitous in North American elementary classrooms in the early years, and although they can be beneficial, they do not guarantee learning. In the present study, the authors examined two factors hypothesized to impact second-graders’ learning of place value and regrouping with manipulatives: (a) the sequencing of concrete (base-ten blocks) and abstract (written symbols) representations of the standard addition algorithm; and (b) the level of instructional guidance on the structural relations between the representations. Results from a classroom experiment with second-grade students (N = 87) indicated that place value knowledge increased from pre-test to post-test when the base-ten blocks were presented before the symbols, but only when no instructional guidance was offered. When guidance was given, only students in the symbols-first condition improved their place value knowledge. Students who received instruction increased their understanding of regrouping, irrespective of representational sequence. No effects were found for iterative sequencing of concrete and abstract representations. Practical implications for teaching mathematics with manipulatives are considered. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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I Thought This Was a Study on Math Games: Attribute Modification in Children’s Interactions with Mathematics Apps

by Stephen I. Tucker and Teri N. Johnson

Educ. Sci. 2017, 7(2), 50; https://doi.org/10.3390/educsci7020050 - 1 May 2017

Cited by 8 | Viewed by 7753

Abstract

Technology is an increasingly important component of education. Children’s mathematical interactions with technology have become a focus of mathematics education research, but less research has investigated constructs that contribute to these mathematical interactions. Attributes of children and technology play a key role in mathematical interactions and both children and technology can modify attributes during these interactions. Grounded in the Artifact-Centric Activity Theory and linked to recent developments in research on technology in mathematics education, this qualitative study extended an earlier exploratory study to investigate attribute modification. In particular, this study examined patterns of attribute modification evident during fifth grade students’ mathematical interactions with two mathematics virtual manipulative touchscreen tablet apps. Results included three categories related to attribute modification: (1) reactive attribute modification (linear progression or repeated repetition); (2) unperceived attributes and opportunities for proactive modification; and (3) proactive modification (seeking equilibrium, seeking disequilibrium, or seeking equilibrium and disequilibrium). Findings have implications for designers, teachers, and researchers of educational technology. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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Making Mathematics Learning More Engaging for Students in Health Schools through the Use of Apps

by Helen Willacy and Nigel Calder

Educ. Sci. 2017, 7(2), 48; https://doi.org/10.3390/educsci7020048 - 19 Apr 2017

Cited by 9 | Viewed by 8142

Abstract

This paper reports on an aspect of a case study of four 11-to-13-year-old students of a Regional Health School (RHS) in New Zealand, using apps on their own mobile devices as part of their mathematics programs. It considers the issue of engaging students in mathematical learning when they are recovering from significant health issues. The paper examines the influence of apps on these students’ engagement with mathematical learning through the facilitation of differentiated learning programs. The research design was a case study with semi-structured interviews, questionnaires and observation used to generate the data. A number of themes arose from the data including both the positive and negative influences of apps on student engagement and the influence of apps on facilitating differentiated learning programs. The results indicated that using apps for mathematics had a positive influence on student engagement for most students. The positive student engagement seemed to be partly due to the apps’ ability to support differentiated learning. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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Examining Pinterest as a Curriculum Resource for Negative Integers: An Initial Investigation

by Joshua T. Hertel and Nicole M. Wessman-Enzinger

Educ. Sci. 2017, 7(2), 45; https://doi.org/10.3390/educsci7020045 - 1 Apr 2017

Cited by 27 | Viewed by 8026

Abstract

This paper reports an investigation of mathematical resources available on the social media site Pinterest. Pinterest is an online bulletin board where users create visual bookmarks called pins in order to share digital content (e.g., webpages, images, videos). Although recent surveys have shown that Pinterest is a popular reference for teachers, understanding of the mathematical resources available on the site is lacking. To take initial steps in investigating the curriculum resources provided by Pinterest, we used keyword searches to gather a database of pins related to the topic of negative integers. A content analysis was conducted on the pins with a focus on several characteristics including mathematical operations, mathematical models, use of real-world context, and whether mathematical errors were present in source material. Results show a dominance of addition and subtraction over other operations, use of mathematical models in half of pins, infrequent use of real-world context, and mathematical errors in roughly one-third of pins. We provide a breakdown of these results and discuss implications of the findings for mathematics teacher education and professional development. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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Variations of Reasoning in Equal Sharing of Children Who Experience Low Achievement in Mathematics: Competence in Context

by Jessica Hunt, Arla Westenskow and Patricia S. Moyer-Packenham

Educ. Sci. 2017, 7(1), 37; https://doi.org/10.3390/educsci7010037 - 3 Mar 2017

Cited by 2 | Viewed by 5650

Abstract

For children with persistent mathematics difficulties, research and practice espouses that an altered kind of mathematics instruction is necessary due to sustained performance differences. Yet, a critical issue in mathematics education rests in the question of why research locates the problem within these children. In this paper, we challenge a longstanding assumption about the type of mathematics children with low achievement in mathematics “need” along with how these children are positioned in terms of mathematical thinking and reasoning. Our aim in this work is to identify ways of reasoning evident in the partitioning activity of 43 fifth-grade children as they solved equal sharing situations independent of instruction over ten sessions. Results reveal three themes of reasoning that show a resemblance between these children’s reasoning and existing frameworks of reasoning in equal sharing problems found in prior research among children who did not show low achievement in mathematics. We discuss the results in terms of the problem of a continued conceptualization of low achieving students’ need for specific kinds of teaching and learning experiences and/or detached instructional experiences in school. We advocate for an increase in research that examines how teachers can support participation of these children in mathematics classrooms such that children might develop powerful mathematics conceptions. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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1004 KiB

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Conceptualizations of Students with and without Disabilities as Mathematical Problem Solvers in Educational Research: A Critical Review

by Rachel Lambert and Paulo Tan

Educ. Sci. 2017, 7(2), 51; https://doi.org/10.3390/educsci7020051 - 1 May 2017

Cited by 47 | Viewed by 17696

Abstract

Students with disabilities are often framed as “the problem” and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. Fifty percent of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with little analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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The Use of Learning Map Systems to Support the Formative Assessment in Mathematics

by Neal M. Kingston and Angela Broaddus

Educ. Sci. 2017, 7(1), 41; https://doi.org/10.3390/educsci7010041 - 16 Mar 2017

Cited by 8 | Viewed by 9722

Abstract

Despite much theoretical support, meta-analysis of the efficacy of formative assessment does not provided empirical evidence commensurate with expectations. This theoretical study suggests that teachers need a better organizing structure to allow a formative assessment process to live up to its promise. We propose that the use of learning map systems can provide that structure, and we describe aspects of using learning map systems to support mathematics instruction in two projects: the Dynamic Learning Maps^® alternate assessment (DLM) and the Use of Learning Maps as an Organizing Structure for Formative Assessment (also referred to as Enhanced Learning Maps, or ELM). Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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Techno-Mathematical Discourse: A Conceptual Framework for Analyzing Classroom Discussions

by Katie L. Anderson-Pence

Educ. Sci. 2017, 7(1), 40; https://doi.org/10.3390/educsci7010040 - 10 Mar 2017

Cited by 6 | Viewed by 11047

Abstract

Extensive research has been published on the nature of classroom mathematical discourse and on the impact of technology tools, such as virtual manipulatives (VM), on students’ learning, while less research has focused on how technology tools facilitate that mathematical discourse. This paper presents an emerging construct, the Techno-Mathematical Discourse (TMD) framework, as a means for analyzing and interpreting aspects of learning when students use technological representations to mediate mathematical discussions. The framework focuses on three main components: classroom discourse, technology tools, and mathematical tasks. This paper examines each of these components, and then illustrates the framework using examples of students’ exchanges while interacting with virtual manipulatives. The TMD Framework has applications relevant to teachers, teacher educators, and researchers concerning how technology tools contribute to discourse in mathematics classrooms. The TMD framework addresses a critical issue in mathematics education, in that classroom teachers and researchers need to understand how technology facilitates classroom interactions and how to best leverage technology tools to enhance students’ learning of mathematics. Full article

(This article belongs to the Special Issue Critical Issues in Mathematics Education)

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