Mathematical Learning Opportunities Research Articles

Can programming support mathematics learning? An analysis of Swedish lower secondary textbooks

In the wake of the present inclusion of programming in mathematics education, which is a feature of curricular revisions in many countries, we have analysed newly inserted programming activities in mathematics textbooks. The aim was to investigate how such activities relate to and potentially affect students’ opportunities to learn mathematics. Data consist of Swedish textbooks for grades 7–9 (ages 13–15) intended for mathematics classes, where all units labelled as or including programming activities were analysed. Concerning the relation between mathematics and programming, our results show that in the intricate balance between teaching mathematics on the one hand and teaching programming on the other hand, the textbooks seem to lean towards the latter, thus not greatly contributing with mathematical learning opportunities. We see a dominance of mathematics as a context for programming, rather than programming as a tool for learning mathematics. The lack of exploration and rare occurrence of novel mathematics in the programming activities implies a weak relationship between mathematics and programming.

Seeing mathematical learning opportunities in preschool situations: the role of teacher disposition and type of picture book

Pre-school teachers’ competence to see and decide to use learning opportunities in informal play-based situations (i.e. situation-specific skills) is key for high-quality pre-school instruction. Current insights into pre-school teachers’ situation-specific skills and their association with underlying teacher disposition and instructional materials are limited. We aimed to complement existing findings by systematically analysing pre-service and in-service pre-school teachers’ situation-specific skills in association with their underlying disposition and the type of instructional material in the domain of early mathematics. We assessed 274 pre-service and in-service pre-school teachers’ mathematical content and pedagogical content knowledge (MCK, MPCK), beliefs and situation-specific skills, operationalised as the mathematical questions they formulate during simulated shared picture book reading activities. Logistic multilevel regression analyses revealed a complex interplay between pre-service and in-service pre-school teachers’ disposition, the type of instructional material and situation-specific skills, pointing to the need for future studies on the topic.

How do school-related mathematical problems become relevant for prospective teachers in mathematics courses at university? A qualitative interview study

ABSTRACT Prospective mathematics teachers often have to attend courses in academic mathematics. However, many struggle to see the connections between the course content and their future teaching, which is detrimental to learning motivation and success. Many universities try to address this with interventions focusing on the relevance of the mathematical learning opportunities. School-related mathematical problems (SRMPs), which highlight connections between school mathematics and academic mathematics, are a suggested intervention. Since SRMPs focus on the demands of the future profession, one would expect that students attribute high relevance to them. However, empirical results on this remain limited. To evaluate and enhance SRMPs, our study aims to elicit the criteria students use for assessing the relevance of SRMPs. We analysed ten qualitative interviews with prospective teachers. Our results show that similar criteria determine the perceived relevance in all cases. We discuss practical consequences for the design of school-related learning opportunities in teacher education.

Factors associated with classroom participation in preschool through third grade learners on the autism spectrum

BackgroundAccess to mathematics instruction that involves opportunities for critical thinking and procedural fluency promotes mathematics learning. Studies have outlined effective strategies for teaching mathematics to children on the autism spectrum, however, the focus of these interventions often represent a narrow set of mathematical skills and concepts centered on procedural learning without linking ideas to underlying concepts. MethodsThis study utilized classroom video observations to evaluate the variability in and nature of mathematical learning opportunities presented to 76 autistic students within 49 preschool–3rd grade general and special education learning contexts. We examined teacher instructional practices and student participation across 109 mathematical tasks within larger mathematics lessons. ResultsStudents were most often presented with mathematical tasks that required low-level cognitive demand, such as tasks focusing on rote memorization and practicing predetermined steps to solve basic algorithms. Furthermore, the nature of the mathematical task was linked with the language that teachers used, and this in turn, was associated with students’ participation within the learning opportunity. ConclusionsOur findings indicate that features of talk within specific types of mathematical tasks, including math-related talk and responsive language, were associated with increased student active engagement and spontaneous communication. The knowledge gained from this study contributes to the development of optimized instructional practices for school-aged children on the autism spectrum—information that could be used to prepare both preservice and in-service teachers.

Preservice Teachers’ Reflections on the Use of Visual Supports to Improve Mathematics Pedagogy

This case study inspected mathematical learning opportunities that employed the results from the participating preservice teachers’ (n=75) original visual arts creation process. Data obtained during this study provided empirical evidence for the educational viability of employing original Mondrian-style rectangle sets as a context for generating authentic mathematics inquiry opportunities. The participating preservice teachers generally indicated that through the process of creating their Mondrian-style rectangle sets and exploring the mathematical patterns within their works, such as the presence of fractions and ratios, they were able to develop an improved understanding of the pedagogy for teaching these mathematics concepts. The findings from this study suggest that both mathematics teachers and mathematics teacher educators might better serve their students by including more visual supports when teaching mathematics concepts.

Reimagining informal STEM learning opportunities to foster STEM identity development in underserved learners

Informal science, technology, engineering, and mathematics (STEM) learning opportunities offer great potential to position learners as insiders to STEM and to foster their positive STEM identity development. Despite their goal to create equal insights and access to STEM learning for all, however, these informal STEM learning opportunities often fail to reach underserved students, hindering their STEM identity development and perpetuating inequity. To address this issue, out-of-school programs need to be designed with underserved students in mind, and concepts, as well as practical approaches that foster STEM identity development, need to be identified. In this article, we review 13 peer-reviewed publications that investigate informal STEM learning opportunities for underserved learners at a young age. We synthesize concepts such as competence, performance, recognition, supportive relationships, sense of belonging, agency, interest, and attitudes that influence underserved learners’ STEM identity development, and corresponding practical approaches such as personal relationships, role models, authentic settings, hands-on-activities, and non-stereotypical structures fostering agency. We also discuss theoretical frameworks for underserved learners’ STEM identity development. We suggest that recognition, a sense of belonging, supportive relationships, and agency play important roles in fostering STEM identity development in underserved students. The paper concludes with recommendations to change traditional patterns in informal and formal STEM education to empower underserved students to construct their own STEM identity as agentic individuals.

Measuring interaction quality in mathematics instruction: How differences in operationalizations matter methodologically

Quality of interaction can enhance or constrain students’ mathematical learning opportunities. However, quantitative video studies have measured the quality of interaction with very heterogeneous conceptualizations and operationalizations. This project sought to disentangle typical methodological choices to assess interaction quality in six quality dimensions, each of them in task-based, move-based, and practice-based operationalizations. The empirical part of the study compared different conceptualizations with their corresponding operationalizations and used them to code video data from middle school students (n = 210) organized into 49 small groups who worked on the same curriculum materials. The analysis revealed that different conceptualizations and operationalizations led to substantially different findings, so their distinction turned out to be of high methodological relevance. These results highlight the importance of making methodological choices explicit and call for a stronger academic discourse on how to conceptualize and operationalize interaction quality in video studies.

Contextual influences on children's mathematical understandings

In order to maximise children's mathematical learning opportunities in school, we need to take account of what they have already learned about mathematics in their out-of-school contexts. Children's representations provide one such mechanism for gaining insight into their everyday mathematical experiences and understandings. This study utilises an ecological theoretical framework to examine the ways in which children's everyday experiences in a range of contexts influence their early mathematical understandings. Data is presented from a study of 100 four to six-year-old Australian children as they entered and experienced their first year of primary school. Throughout the study, the children completed a series of drawing tasks related to different mathematical concepts, and were invited to provide either verbal or written narratives to accompany their drawings. These data were analysed using an ecological theoretical framework in order to explore the individual components of each context, as well as the relationships between these contexts. Findings demonstrate that children come to school with rich understandings of mathematics which have been shaped by their experiences in a range of contexts. The activities and relationships within children's home settings appear to be the most profound in terms of developing mathematical understandings, with very few children representing mathematics learning within a school context.

Learning opportunities in mathematics: the role of first language in bilingual settings

Learning opportunities in mathematics: the role of first language in bilingual settings

Konzeptualisierung und Messung der Qualität der adaptiven Lernunterstützung in Lernsituationen mit mathematischen Regelspielen im Kindergarten. Eine Studie in Deutschland und der Schweiz

ZusammenfassungDie Qualität der adaptiven Lernunterstützung ist wichtig für die Förderung des mathematischen Lernens von Kindergartenkindern. Entsprechend bedarf es geeigneter Instrumente zur Bewertung der Planung, Durchführung und Reflexion von mathematischen Lernangeboten im Kindergarten. Bestehende Instrumente berücksichtigen vor allem die mikro-adaptive (mathematische) Lernunterstützung, die den Fokus auf die Interaktion zwischen der Fachkraft und den Kindern legt. Die Qualität der makro-adaptiven (mathematischen) Lernunterstützung (Planung und Reflexion von Lernsituationen) wurde im Kindergarten bis jetzt noch nicht umfassend untersucht. Sie gewinnt jedoch im Hinblick auf die zunehmende Bedeutung von Bildungsplänen im Kindergarten und der damit verbundenen Förderung von fachbezogenen Kompetenzen an Bedeutung.Im Artikel wird erstens die Qualität von (mathematischer) Lernunterstützung in Regelspielsituationen im Kindergarten konzeptualisiert. Dabei wird die Qualität der makro-adaptiven von der mikro-adaptiven Lernunterstützung unterschieden. Letztere wird getrennt in fachunabhängige Unterstützungsqualität (Gruppenmanagement, emotionale Wärme) und in instruktionale, mathematikbezogene Unterstützungsqualität (Lernanregung, Verwendung Fachsprache). Zweitens wird ein Messinstrument (Rating) zur Analyse der Qualität der Lernunterstützung in mathematischen Lernsituationen vorgestellt. Dieses wurde zur Analyse von videografierten Regelspielsituationen und anschließenden Leitfadeninterviews von 145 pädagogischen Fachkräften aus Deutschland und der Schweiz eingesetzt. Pro Fachkraft standen zwei Videosequenzen und zwei Interviews zur Verfügung. Auf der Basis dieser Daten wird das Messinstrument hinsichtlich verschiedener Gütekriterien sowie des Einflusses der Ausbildung der Fachkräfte (akademisch, nicht akademisch) und des Bildungskontextes (Deutschland, Schweiz) analysiert. Die theoretisch angenommene Unterscheidung von Gruppenmanagement, emotionaler Wärme und instruktionaler Unterstützungsqualität lässt sich durch eine konfirmatorische Faktorenanalyse stützen. Die Ergebnisse bestätigen die Bedeutung des Einbezugs von Planung und Reflexion als Dimensionen von adaptiver Lernunterstützungsqualität.

Facilitating Preschool Children’s Mathematics Development in China, Japan, and the United States: Is the Classroom Library Considered?

The two studies examined in this paper compare the different mathematical opportunities provided in preschool classrooms in China, Japan, and the United States, with an emphasis on mathematical-themed books in classroom libraries. Study one presents the results of an online survey to examining the content of preschool classroom libraries in China (N = 134), Japan (N = 168), and the United States (N = 291). Study two presents data obtained from semi-structured interviews of teachers in China (N = 8), Japan (N = 8), and the United States (N = 8). The interviews examined teacher perceptions of how they teach mathematics, the importance of teaching mathematics, and the use of the classroom library as a venue for mathematics. Study one results indicated that teachers from all three countries encourage classroom library use; however, teachers from China reported more mathematics storybooks than their Japanese or United States counterparts. Study two results indicated that teachers from all three countries viewed mathematics as important and provided various mathematics learning opportunities to children throughout the school day. Chinese teachers reported providing the most mathematics learning opportunities using whole group instruction, mathematics centers, and free play. Japanese teachers reported few whole group forms of instruction other than circle time but reported providing opportunities for using mathematics during free play and other embedded activities. United States teachers indicated that mathematics learning occurred using whole group instruction and mathematics centers.

‘몇 시 몇 분 전’으로 시각 읽기에 얽힌 수학적 활동의 탐색

This article arose from the question ‘how can the relative time reading be regarded as doing mathematics?’ To answer the question, I explored the interplay of time words relative time reading and mediation of tools which reflect two different time representational systems from a sociocultural description on learning that includes explicit treatments of word meaning and use. I conducted the clock reading test with 126 3rd graders and interviews with students who proved their ability for reading time in a relative way. The findings were as follows: (1) Participating students were approaching the relative time reading in a different manner as absolute time reading. The differences in performance upon tools were also identified. (2) Students were endorsing various mathematical narratives to read time in a relative way. (3) Errors in the relative time reading were related to the structural properties of time tools. Draw on the finding, the word 전(jeon) in relative time reading is dynamically interwoven with doing mathematics and interacting with tools reflect representational systems. The fact that the use and meaning of words become doing mathematics indicates that words themselves are dynamically interwoven with activity. The meaning of doing mathematics mediated by tool properties which are possible only in time learning and implications for the chance to increase mathematical learning opportunities in time contents in elementary mathematics were discussed.

Teachers’ Mathematics Learning Opportunities During One-on-One Coaching Conversations

Coaching is a popular, yet costly, professional development structure. Therefore, understanding the learning opportunities coaching provides is essential. Following a framework by Campbell and Griffin (2017), we explore five elementary school teachers’ learning opportunities during 15 meetings and 23 lessons with two instructional coaches in two schools. Using Greeno’s (2005) situative perspective, we focus on coach–teacher dyads, examining the substance and depth (Coburn, 2003) of their conversations. Results indicate that most coach–teacher talk centered on logistics, whereas mathematics conversations were rare. We consider institutional contexts that shaped the dyads’ discussions, ultimately viewing the coaches and teachers as “sensible beings" (Leatham, 2006) with valid reasons for focusing discussions as they did. Coaching implications and directions for research are discussed.

Learning to Lead: an Approach to Mathematics Teacher Leader Development

This paper describes a partnership between a university and an urban school district, formed with a goal of preparing mathematics teacher leaders to conduct professional development (PD) at their schools. The university and district partners worked together to achieve the district’s mission of providing every student with high-quality instruction and equitable learning opportunities in mathematics by building the district’s capacity to conduct school-based PD for mathematics teachers. Given the power of school-based subject-specific PD for improving instructional quality, we worked with Teacher Leaders from participating schools to prepare and support them to lead PD workshops at their schools. In this paper, we examine how Teacher Leaders learn and adapt key elements of a PD model over three school years through the lenses of Prediger et al.’s Three-Tetrahedron-Model (2019) and the university’s Learning to Lead model. Over 3 years, we see that Teacher Leaders use the key structures of the PD model; make adaptations in response to school goals, interests, and priorities; and gain confidence in their work with colleagues. By viewing the adaptations through the lens of pedagogies of practice as well as the relationships illustrated by the 3-T model, this work offers insights into the complexities of teacher leadership development.

Supporting parents to co-produce differentiated learning opportunities in mathematics

ABSTRACT The complex relationship between schools, parents and children surrounding mathematics homework is one that is yet to be fully resolved. In a contribution to reconfiguring mathematics homework, a take-home mathematics games kit focusing on multiplication was trialled with primary school children and their parents. Diary and interview data from nine parent participants showed evidence of parents co-producing meaningful engagement experiences that were differentiated by mathematical complexity, their children’s dispositions and interests, and family routine. The findings suggest that flexible offerings of homework tasks underpinned by a core idea can support parents’ opportunities to engage deeply with their children’s learning.

Mathematical Modeling Projects Oriented towards Social Impact as Generators of Learning Opportunities: A Case Study

This paper presents a case study carried out at an elementary school that led to a characterization of mathematical modeling projects aimed at generating social impact. It shows their potential as generators of mathematical learning opportunities. In the school project, upper-grade students (sixth grade, 11-year-olds) studied the way in which the rest of the students at the institution traveled from their homes to school. Its purpose was to identify risk points from the standpoint of road safety and to develop a set of recommendations so that all the children could walk safely to school. In our study, we identified, on the one hand, the mathematical learning opportunities that emerged during the development of the project and, on the other, the mathematical models created by the students. We discuss the impact of the project on the different groups in the school community (other students, parents, and teachers). We conclude with a characterization of the mathematical modeling projects oriented towards social impact and affirm that they can be generators of mathematical learning opportunities.

Effectiveness of educational technology in early mathematics education: A systematic literature review

Abstract Despite the general agreement regarding the importance of stimulating young children’s early mathematical skills, mathematical learning opportunities in preschool are limited. Educational technology (ET) may be an effective tool to address this problem. Taking into account the weaknesses of previous reviews, we conducted a systematic and comprehensive review of the research literature on the effectiveness of ET in early mathematics education, critically analyzing the findings of studies adhering to a media comparison approach (comparing an ET condition to a non-ET condition or another ET condition) versus studies following a value-added approach (comparing at least two ET conditions which only differ with respect to one feature in the ET or in its implementation). Reviewing 54 studies, we systematically analyzed (1) the effectiveness of ET, (2) the features of the ET and ET implementation associated with ET effectiveness, and (3) child characteristics associated with ET effectiveness. Our analyses indicated that media comparison studies comparing an ET to a non-ET condition provide evidence for the effectiveness of ET for enhancing young children’s mathematical competencies. Second, value-added studies pointed to ET implementation features associated with ET effectiveness, namely teacher support during ET use and an individual grouping structure. Finally, both media comparison and value-added studies revealed that ET effectiveness is associated with children’s performance in the ET and with their prior knowledge. To further advance the field, value-added studies on features of the ET and its implementation are required, as well as studies focusing on important child characteristics that are associated with ET effectiveness.

Students’ desires for high-level teaching and learning opportunities: Views of Namibian Grade 11 students observed to have difficulties in learning mathematics

This study focusses on the views of students in learning grade 11 mathematics in terms of their needs and aspirations regarding access to high-level mathematics teaching and learning opportunities. Students who participated in this study (88 grade 11 Namibian students) were identified as having learning difficulties by their mathematics teachers, but these students did not (themselves)consider that they had difficulties. The author attempts to understand why students believed they do not have difficulties in learning mathematics. A qualitative method was employed, and the students were investigated via semi-structured interviews. The transcripts were analysed using an interpretational analysis. This study revealed that students display interest in learning mathematics and that they tend to feel comfortable with the subject despite certain influencing factors. The students’ perceptions are that their learning processes were negatively affected by aspects of systemic factors, teachers’ and students’ own factors, and access to learning resources. The students feel that they lack high-level access to teaching and learning, and this limits their potential for achieving the level at which they are expected to perform and be academically successful. In addition to the implications that emerged, this study makes recommendations on what should be done to address the negative factors perceived by the students.

Early Sources of Children’s Math Achievement in Chile: The Role of Parental Beliefs and Feelings about Math

ABSTRACT Research Findings: Two hundred and sixty-seven Chilean children from grades 1–3, their fathers and their mothers completed measures of implicit and explicit math-related beliefs (math–gender stereotypes, math self-concepts) and feelings (math anxiety), as well as tests of mathematical achievement. Children, fathers, and mothers exhibited stereotypes that link math with males. More specifically, mothers identified more with language than with math, while fathers and children identified more with math than with language. Path analyses models revealed that children’s explicit math self-concepts significantly predicted their actual math achievement. Children’s explicit self-concept was, in turn, explained marginally by the mathematical anxiety of their mothers. Practice or Policy: These results contribute to our understanding of the relation between parental and children’s beliefs and children’s math achievement during early elementary school years. In countries such as Chile, with a significant gender gap in math achievement, these findings may highlight relevant aspects to consider when designing interventions aimed at educational equity and providing equal mathematical learning opportunities to boys and girls.

The Effect of Peer-Assisted Mathematics Learning Opportunities in First Grade Classrooms: What Works for Whom?

To investigate whether child × instruction effects contribute to mathematics gains in first grade, we conducted a cluster randomized controlled trial with 454 (205 treatment; 249 control) students in 28 classrooms. Classrooms were randomly assigned to implement Math Peer Assisted Learning Strategies (Math PALS) to supplement Saxon Math or Saxon Math alone. Teachers received professional development on either Math PALS (treatment) or individualized reading instruction (control). Intent-to-treat and treatment-on-the-treated results revealed no significant difference between the Math PALS and control groups in student mathematics gains. However, Math PALS effectiveness varied with initial math skills. Based on modeled results of the continuous fall math score, students who scored at the 75th percentile of the sample demonstrated significantly stronger mathematics outcomes compared with the treated control group; there was no significant treatment effect for students at the 50th percentile. For students with lower initial math skills (modeled at the 25th percentile of the sample), the effect of the treatment was negative. Students with lower initial mathematics skills made greater gains in the control group (Saxon Math alone) versus the Math PALS group.