Mathematical Content Areas Research Articles

Mathematical practices are everywhere: The intersections of pre‐service teacher claims, non‐mathematics‐education faculty claims, and observable actions

AbstractMathematics traditionally has been taught in a way that reifies the cultural belief that it is discrete in nature and, therefore, irrelevant to other content areas and the real world. National Council of Teachers of Mathematics, inclusive of mathematics teacher educators, views this belief as unproductive to learning and has stressed the need for students to make connections between mathematical content areas, to other disciplines, and to the real world. Unfortunately, many teacher‐preparation programs (TPPs) structurally are organized with overt divisions between content areas, which likely perpetuates the belief that mathematics is disconnected and irrelevant. Nonetheless, this project was motivated by the hope that at the individual classroom level within such TPPs, non‐mathematics teacher educators (TEs) were integrating mathematical practices and, thus, assisting in changing this unproductive belief. An analysis was completed of a three‐part, data‐collection process of (a) 180 pre‐service teachers' assignments requiring that they align activities from non‐mathematics education courses with mathematical practices; (b) 16 TEs' questionnaire data on how they use mathematical practices in their instruction; and (c) 11 full‐class, video‐taped observations of TEs teaching. Findings revealed that TEs do implement mathematical practices but do not claim always that this is what they are doing.

A Quantitative Systematic Literature Review of Self-Monitoring Components Within Mathematics Instruction and Intervention

The purpose of this quantitative systematic literature review was to identify and describe published mathematics studies from 1980 to 2021 that incorporated a self-monitoring component ( k = 22 studies; N = 1,787 students). We examined specific self-monitoring procedures, instructional contexts, implementation variables, and methodological quality. For inclusion, studies needed to (a) include self-monitoring (defined as students observing, evaluating, and/or recording their behaviors), (b) include co-occurring mathematics instruction, (c) include at least one mathematics outcome measure, (d) occur in a school setting, (e) include students in Grades K–12, and (f) utilize a single-case, experimental, or quasiexperimental design. Variables of interest were coded and methodological quality was assessed using What Works Clearinghouse standards. Our findings suggest that students with and without disabilities generally benefit from embedded self-monitoring procedures across mathematical content areas and tiers of instructional support. Future research should further unpack definitions of self-monitoring and related constructs.

Non-Digital Games That Promote Mathematical Learning in Primary Years Students: A Systematic Review

Despite primary school teachers demonstrating strong preferences for using non-digital games over digital games to support mathematics instruction, much of the research review literature has focused on learning outcomes associated with digital mathematical games. To address this gap, the current systematic literature review focuses on non-digital, games-based, empirical studies in the primary mathematics classroom over the past two decades from 2003 to 2022. The Preferred Reporting Items for Systematic Reviews (PRISMA) statement was employed as a guideline for the data-collection process. The review presents an analysis and synthesis of 34 manuscripts, representing 32 distinct studies. Over three-quarters of manuscripts employed quantitative methodologies and around half qualitative methodologies, whilst studies focused exclusively on student, as opposed to teacher, outcomes. Despite Australia and Indonesia being comparatively overrepresented, the studies in scope were notable for both their geographic diversity and the eclectic range of game types and structures incorporated; although they did tend to disproportionately focus on number and operations, as opposed to other mathematical content areas. Moreover, the impact of mathematical games was generally positive across the broad range of outcomes considered, suggesting that mathematical games are potentially effective for both developing mathematical proficiencies, as well as improving dispositions towards mathematics. Future research directions are discussed.

Topic-specific characteristics of proof-related reasoning

Students’ difficulties with proofs are well documented. To remedy this, it is often recommended that reasoning and proving be focused on in all grades and content areas of school mathematics. However, proofs continue to have a marginal place in many classrooms, or are only given explicit attention in courses in Euclidean geometry. Geometry is also the most common topic for educational research on reasoning and proving. This paper compares what four other topics in secondary school mathematics – logarithms, primitive functions, definite integrals, and combinatorics – can offer in terms of opportunities to learn proof. The types and natures of reasoning in expository sections and students’ tasks in 11 Swedish and Finnish textbooks are analysed in search of similarities and differences between these topics. The results are accounted for with special focus on opportunities for reasoning about general cases. Finally, the findings are discussed in relation to mathematical aspects of the four analysed topics.

Analysis of Research Trends on General Mathematics at Universities : Focusing on Papers Published in Korean Journals Over the Past 10 Years

In this study, in order to provide a developmental discussion on general mathematics in universities and the direction for follow-up research, research trends were examined for papers published in Korean domestic academic journals over the past 10 years. The results of the research are as follows: First, among studies related to mathematics education and general education, research on general mathematics in universities is severely lacking. Considering that nearly all universities offer courses related to general mathematics, professors and researchers responsible for general mathematics should dedicate more attention to research on general college mathematics. Second, concerning the subjects and content areas of mathematics, research on general mathematics shows a bias towards basic general mathematics for science and engineering students. Therefore, there is a need for research on basic general mathematics for students in the humanities and social sciences, as well as research on pure general mathematics applicable to all students. Third, there is a lack of research on evaluation and educational technology in the field of general mathematics. Evaluation plays a crucial role in education, and it is important to conduct research on the evaluation of general mathematics and the utilization of educational technology, especially considering the increasing emphasis on the use of various technological tools in mathematics education. Fourth, in terms of research methods, the majority of studies focus on quantitative research. Therefore, it is necessary to employ diverse research methods that are suitable for the teaching and learning environment of general mathematics. Fifth, concerning the research topic on teaching and learning, while there have been numerous studies targeting science and engineering students, there is a need for a variety of studies on teaching and learning that encompass all students, including those in the humanities and social sciences, as well as the professors themselves.

A Critical Exploration of Mathematics Learning Trajectories Research in the Korean Context: A Systematic Literature Review

This paper conducts a systematic literature review of research on mathematics learning trajectories within the Korean context and suggests directions for future learning trajectory research. Specifically, the aim of this review is to illuminate the trends of existing and emerging research on learning trajectories in the Korean context, ultimately guiding future research directions in the international research and practice field. This review critically examines 32 articles published in Korea Citation Index journals and reports on national research projects, focusing on the necessities, purposes, and types of research categorized by mathematical content area, as well as the theoretical frameworks used. The results reveal that the types of learning trajectory research conducted in Korea are diverse, encompassing exploration, development, and application of learning trajectories. We suggest that the learning trajectories research warrants further investigation, including discussion on different perspectives in the international contexts. We also posit that these types of research have the potential to create synergy when conducted in a connected series, rather than as disconnected studies.

Strengthening STEM Teaching in Rural, Indigenous-Serving Schools through Long-Term, Culturally Responsive Professional Development

This paper describes a particular teacher professional development model offered in schools on and bordering the Navajo Nation in the southwestern United States. The Diné Institute for Navajo Nation Educators (DINÉ) offers professional development across all content areas and grade levels, but here we focus specifically on our work in science, technology, engineering, and mathematics (STEM) content areas. Our work is situated explicitly within the literatures on Indigenous education, Native Nation Building, and culturally responsive schooling, but we also draw broadly on research in STEM education and teacher professional development. The research question explored in this paper is: To what extent and in what ways do teachers in the DINÉ develop STEM curriculum units that evidence culturally responsive principles and STEM education best practices? We share findings from three cohorts of teachers in the DINÉ’s STEM-focused professional development seminars. Teacher-authored curriculum units developed in the DINÉ were analyzed with two specific protocols: the CRAIS Tool, and the SCOOP notebook. Finally, we look closely at the curriculum units written by a single teacher in the DINÉ across the three years in order to get a clearer understanding of the nuances and richness of the findings and themes reported from the aggregate data.

The Intersection of Culturally Responsive Pedagogy and Engineering Design in Secondary STEM

The instructional practices of the engineering design process and culturally responsive pedagogy have each garnered national attention and multiple decades of research. Findings from the respective literature bases call for educators and policymakers to integrate these two pedagogical approaches into K-12 classroom instruction. Scholars have argued that this integration would improve student engagement and academic achievement. There is a significant amount of research that supports the positive student outcomes associated with each approach, yet there remains a dearth of literature that addresses the integration of these two practices into the science and mathematics content areas. The movement around educational reform is rooted in teachers serving as learners; however, understanding how teachers learn and respond to reform is largely overlooked. The present research sought to examine the way in which teachers perceive and define integrated pedagogical approaches upon implementation. The authors utilized a comparative case study design to represent experiences of five secondary math and science teachers enrolled in graduate-level coursework and professional development on culturally responsive pedagogy and the engineering design process. Findings suggest that teachers’ self-reported pedagogical beliefs acted synergistically between the two pedagogical approaches. Subsequently, participating teachers expressed a strong preference towards the enactment of an integrated pedagogy of a culturally responsive engineering design process. The present research offers valuable recommendations for teacher educators, professional development providers, policymakers, and researchers who wish to integrate culturally responsive pedagogy and the engineering design process in math or science K-12 classrooms. The significance of this research underscores the importance of empowering teachers with professional development, around implementation of novel pedagogical approaches, to both shape and inform their beliefs and practices.

Fermi problems as a hub for task design in mathematics and stem education

Abstract In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi problems. In addition, we discuss a framework (called the Fermi problem activity template [FPAT] framework) for supporting the design and use of Fermi problems to facilitate students' learning within particular mathematics content areas and/or aimed at particular concepts or higher-order thinking skills. We also illustrate how the FPAT framework can be used to (i) facilitate interdisciplinary collaborations with other subjects such as the social sciences, but in particular with the other STEM subjects; and (ii) support teachers in adapting and implementing Fermi problems in their classrooms.

How grade levels shape underperforming elementary student preferences about learning mathematics in the classroom

There is evidence that student attitudes towards mathematics become more negative as students move through their schooling. However, less is known about the different factors that shape student attitudes at various stages. This qualitative study sought to shed light on this issue and consider how stage of schooling influenced self-perceived supports for what helped underperforming students to learn mathematics. One hundred and seventy-nine students in Grades 2/3 and 5/6 completed a questionnaire before they participated in a mathematics intervention program, targeting students who had fallen behind in mathematics. Participating students were asked to complete the sentence stem. The best thing about learning mathematics in my classroom is … and answered the question: What helps you learn mathematics in the classroom? Thematic analysis revealed that the majority of younger students emphasized specific tasks (e.g. games) and mathematical content areas (e.g. counting) when describing the best thing about learning mathematics at school and were twice as likely to highlight such aspects compared with older students. By contrast, older students were far more likely to indicate the importance of being supported directly by their teacher or peers when learning mathematics, compared with younger students.

GEOGEBRA INTERVENTION: HOW HAVE STUDENTS’ PERFORMANCE AND CONFIDENCE IN ALGEBRA ADVANCED?

The study’s goal was to provide an educational intervention in Algebra through GeoGebra that would boost students’ confidence, improve their learning, and correct their most minor mastered skills, allowing them to improve their Algebra performance. The research design was quasi-experimental, with 40 nonrandomly chosen participants comprising the GeoGebra and control groups. Mean and standard deviation was employed to describe the algebra performance and confidence of the respondents, while independent and dependent t-tests to determine the students’ significant difference in algebra performance and confidence in the pre-and post-test between the control and GeoGebra groups. GeoGebra effectively improved algebra confidence, enhanced learning, and remedied the students’ least mastered skills. GeoGebra is recommended as an instructional material in teaching and learning Algebra and can be extended to other mathematics content areas.

Graphics Out Loud: Perceptions and Strategic Actions of Students With Visual Impairments When Engaging With Graphics

Introduction: Facility in graphics use is critical to accessing data visualizations in science, technology, engineering, the arts, and mathematics (STEAM) content areas. Efforts to understand the cognitive processes underlying strategic action by students with visual impairments must consider both metacognition and self-regulated learning. Methods: Think-aloud transcripts were analyzed using a priori level one coding based on the Model of Graphic Interpretation (MoGI) followed by second-level coding to analyze nuanced commonalities and differences based on performance, medium, and level. Results: Differences in each component of the MoGI were found for print graphic and tactile graphic users, particularly based on performance and level. Higher performers were better able to articulate strategy use and reasons for selecting strategies. Discussion: Findings coincide with quantitative findings of the participants (see Zebehazy & Wilton, 2021 ). Transcripts provided additional confirming evidence of the interdependence of MoGI components. Implications for Practitioners: Use of think aloud can support assessment and instruction of students with visual impairments to build strategic action and metacognition when engaging with graphics.

Gender Perspectives on Mathematical Content Preferences at Secondary Level

This study was conducted to examinestudent’spreferences on mathematical content area and contents within each content area at secondary level. The respondent were 60 students, including 33 girls and 27 boys, who were selected using stratified random sampling method. Descriptive survey design was used with the help of survey questionnaire. Data were analyzed using descriptive statistics (Mean and Std.) and inferential statistics (t-test). The result of the study revealed that Set was the most preferable content area in mathematics in compare to other area for both boys and girls. Whereas, boys least preferableand difficult area was Geometry, while girls was Probability. Most important contents for their future life were Arithmetic related contents in comparison to other contents within content area. Likewise, the study found that the mean difference between boys and girls was not statistically significant with preferences in overall mathematical content area and overall contents within content area. Similarly, there was not significant differences exist between boys and girls with preferences in each content area and every contents within each content area except one content of Arithmetic.

The Effects of a Multicomponent Motivational System Intervention Using Peer-Tutoring for Implementation on the Automation of Single-Digit Addition Tasks of Four Struggling Elementary Students

Derived math fact fluency becomes more imperative across all mathematical content areas during a students’ mathematics development. However, many of them struggle to automate the most basic math facts sufficiently and therefore are not able to deal with more complex mathematical problems. This leads to the fact that many of them are already left behind in the early years of their school careers whether they have diagnosed learning disabilities or not. In this single-case research project, we evaluated a peer-tutoring approach designed to extend the number of automated single-digit addition tasks for four struggling elementary students through a multicomponent motivational system including immediate correction of errors, graphical feedback on performance, positive reinforcement, direct instruction flashcards, and a racetrack game. A multiple-baseline design (ABE) across subjects was applied to assess the effects of the treatment. The results indicate significant and large effects of the intervention on the number of automated math facts for the participants. This substantiates the assumption that the math-fact recall performance of struggling students can be improved through the method of peer tutoring even with the limited resources available in everyday school life.

Whose Research Counts? Teacher Research and the Practitioner-Academic Divide

Scholars have theorized about the growing movement of teacher research, where school-based practitioners engage in systematic examinations of their own work. They have argued that teacher research challenges relationships of knowledge and practice, as teacher-researchers are likely to ask different questions and offer different perspectives compared to university-based researchers. Synthesizing teacher research studies published in peer-reviewed journals across the content areas of mathematics, science, social studies, and literacy/language arts, this review compares the questions asked and the results reported on content area studies done by PreK–12 teacher- and university-based researchers. This review provides a critical examination of our understanding of classroom instruction and student learning, revealing the important potential of practitioner research to inform educational change.

The nature and prevalence of diagnostic testing in mathematics at tertiary-level in Ireland

Abstract In this study, we conducted a survey of all tertiary level institutions in Ireland to find out how many of them use diagnostic tests, and what kind of mathematical content areas and topics appear on these tests. The information gathered provides an insight into what instructors expect students to know on entry to university and what they expect students to have difficulty with. In total, 12 diagnostic tests from 11 Irish institutions were collected during the study. An item-by-item analysis was carried out on each diagnostic test to determine the content areas and topics that are assessed on the diagnostic tests and to identify any additional knowledge required for successful completion. We compare the tests administered in the university sector and the Institute of Technology (IT) sector of the Irish tertiary level education system. In addition, current diagnostic tests are compared with two tests from the 1980s to see if the level of mathematical preparedness expected of first-year students has changed over time. Our analysis is situated in a discussion of previous research on diagnostic testing both nationally and internationally.

Culturally Sustaining Practices in Content Area Instruction for CLD Students with Learning Disabilities

AbstractCulturally and linguistically diverse (CLD) students comprise a substantial population of students with learning disabilities, and are historically disproportionately represented in special education. To effectively teach CLD students with learning disabilities, teachers should integrate evidence‐based practices and culturally sustaining pedagogy in their practice. This article highlights several practical examples of culturally sustaining evidence‐based practices across the content areas of mathematics, reading, and writing. Suggestions for practice and future research are presented in the article.

How context specific is teachers\u2019 analysis of how representations are dealt with in classroom situations? Approaching a context-aware measure for teacher noticing

Although raised in the early days of research on teacher noticing, the question of context specificity has remained largely unanswered to this day. In this study, we build on our prior research on a specific aspect of noticing, namely teachers’ analysis of how representations are dealt with in mathematics classroom situations. For the purpose of such analysis, we examined the role of context on the levels of mathematical content area and classroom situation. Using a vignette-based test instrument with 12 classroom situations from the content areas of fractions and functions, we investigated how teachers’ analyses regarding the use of representations are related concerning these two mathematical content areas. Beyond content areas, we were interested in the question of whether an overarching unidimensional competence construct can be inferred from the participants’ analyses of the different individual classroom situations. The 12 vignettes were analysed by N = 175 secondary mathematics teachers with different degrees of teaching experience and their written answers provided the data for this study. Our findings show that the data fit the Rasch model and that all classroom situations contributed in a meaningful way to the competence under investigation. There was no significant effect of the mathematical content area on the participants’ analyses regarding the use of multiple representations. The results of the study indicate that explicitly considering questions of context can strengthen research into teacher noticing.

프랑스 중학교 수학 교육과정 분석

In this study, I have investigated the middle school mathematics curriculum in France, which was reformed according to the change of ‘Socle commun’ in 2015. I have analyzed the area of ‘algorithms and programming' that was newly introduced into the curriculum. The result shows that the area of ‘algorithms and programming' is effectively connected with all the other mathematical content areas rather than simply being added to the list of existing mathematics content areas. In this process, scratch plays a crucial role. In other words, scratch interweaves traditional mathematical contents with the area of ‘algorithms and programming' and thus creates a new type of mathematics curriculum. The curricular reform in France was made by pursuing algorithmic thinking rather than CT(Computational Thinking). In the age of artificial intelligence, the reform in the curriculum of middle school mathematics in France raises the necessity of introducing this area and scratch into the middle school mathematics curriculum in Korea.

English learners' achievement in mathematics and science: Examining the role of self-efficacy

The goals of the current study were twofold. The first goal was to describe levels of mathematics and science self-efficacy and achievement among a sample of students with varying levels of English language proficiency. The second goal was to examine the extent to which students' self-efficacy explains the relation between their English proficiency level and mathematics and science achievement. The sample consisted of 332 fifth graders (mean age = 10.46 years, SD = 0.38) and their 63 teachers in 20 schools. The student sample was linguistically diverse with parents reporting 22 different home languages. Based on district classification procedures, each student was coded into one of three English language proficiency level categories: English proficient-speaking students (English proficient), English Learner (EL) students who are reaching proficiency, yet are still being monitored (reaching proficiency), and EL students who are receiving English for Speakers of Other Languages services (ESOL; limited English proficient). Regression analyses indicated that students identified as limited English proficient consistently demonstrated lower achievement and self-efficacy across the content areas of mathematics and science as compared to their peers who were English proficient and reaching proficiency. In addition, students' self-efficacy partially explained the relation between limited English proficiency level and achievement for science, but not for mathematics. Results indicate that educators should consider variability in students' English proficiency levels as they select supports to promote both science achievement and self-efficacy. Findings also suggest promise for practices and programs that foster self-efficacy in addition to language and content skills.