Math Classroom Research Articles

Which is more predictive: Domain- or task-specific self-efficacy in teaching and outcomes?

Students' academic performance and learning experiences are crucial in school education, yet their relationships with instructional characteristics remain an open question. The present study examined how cognitive activation and teacher support were associated with students' academic emotions and achievement in math classrooms via domain- and task-specific self-efficacy. In total, 5388 eighth graders from central China participated in this study. Cognitive activation, teacher support, math-related enjoyment and anxiety, and domain- and task-specific self-efficacy were measured with self-reported student questionnaires. The math achievement was measured with a standardized test. Our findings showed that the two instructional characteristics were positively related to math achievement and enjoyment but negatively related to math anxiety, with the mediation effects of task- and domain-specific self-efficacy. In detail, cognitive activation had a stronger relationship with math anxiety through task-specific self-efficacy than domain-specific self-efficacy. Whereas, cognitive activation had a greater linkage with math enjoyment through domain-specific self-efficacy than task-specific self-efficacy. In addition, teacher support had a greater association with learning outcomes through domain-specific self-efficacy than task-specific self-efficacy. The relational mechanism of cognitive activation and teacher support on math achievement and academic emotions were differentially mediated by task- and domain-specific self-efficacy in Chinese math classrooms.

Specially Designed Instruction of Early Numeracy in the Inclusive Elementary Classroom for Students With Extensive Support Needs

Abstract Inclusive opportunities for students with extensive support needs are a predictor of both in school and post-school outcomes; however, successful inclusion must consider how student learning needs and evidence-based practices are incorporated. Potential exists to align evidence-based instruction for students with extensive support needs utilizing the Multi-tiered System of Support (MTSS) framework for all students within the inclusive math classroom across tier 2 and tier 3. Findings of this single-case, multiple probe, across student research study suggest that embedded instruction is an effective and feasible instructional practice to support specially designed instruction in early numeracy within a tiered support model for students with extensive support needs in the inclusive math classroom. Based upon our findings, we sought to develop a model of practice for specially designed instruction (SDI) within tiered systems of support for students with extensive support needs that educational teams, school administrators, and policymakers can use to design math instruction within inclusive settings.

Integrative Supports, Resources, and Opportunities—Exploring and Expanding Urban High School Students’ Science Identity: A Longitudinal Qualitative Study

Using a case study approach, we explored the science and math classroom experiences of urban high school students. Our purposeful sample included 11 high-achieving students (mostly minoritized students) who graduated from the same school and participated in an out-of-school science and medicine/health program. Using 35 semistructured interviews collected over 3 years, we focused on understanding the multiple contextual factors that contributed to the restructuring of students’ science experiences and reshaping of their science identity formation during high school. We expanded on Carlone and Johnson’s (2007) science identity model to propose an updated model for understanding students’ experiences within science, technology, engineering, mathematics, and medicine/health contexts. Our findings suggested that an integration of supports, resources, and opportunities lies at the core of what influences students’ science identities, which they revealed are inclusive of their science interest/passion, knowledge, participation, and achievements. Our study’s contribution is a unique perspective of the cultivation and sustainability of students’ science identities at the secondary level.

수학교실에서 인공지능(AI)을 활용한 교수학습 방안 탐색

The purpose of this study is to explore the teaching and learning method using artificial intelligence (AI) in the mathematics classroom. To this end, to predict the direction of mathematics education using AI in the mathematics classroom, this study investigates the fields where AI is applied to education, and discuss issues to consider when introducing AI through scenario development using AI in middle school statistics. This study is meaningful in that it specifically considered how artificial intelligence can be grafted into the mathematics classroom through the development of scenarios that integrate and apply artificial intelligence that has been developed and used segmentally in the current middle school statistics. Afterwards, based on the contents of this study, implications for using AI in the math classroom were derived.

Math in Arabic and other languages: exploring the possibilities of translanguaging practices in the classroom

ABSTRACT This article presents the findings from a study on lower secondary math teaching (year 7 and 9) in a Danish school. The study is part of a larger action research project aiming at developing new ways of teaching and learning in culturally and linguistically diverse classrooms. The math teachers hypothesised that their students would be able to benefit more from math instruction if they were able to draw on their full linguistic repertoire in class. As a response to this, a series of teaching activities addressing mathematical discourse in Danish, Arabic, and the other languages present in the classrooms were developed and delivered to the two classes. A group of Arabic-speaking students worked with math assignments and mathematical discourse using learning materials in both Danish and Arabic, but other languages present in the linguistically heterogenetic classes were also involved in the teaching and learning activities, integrating translanguaging practices in math teaching activities. Findings indicate that translanguaging practices in the math classroom have the potentials to elicit linguistic awareness about the nature of mathematical discourse in students, but also raise awareness about the role of languages in the classroom as such.

Integrating Mathematics Education with Technology

Technology, as well as the educational system, has evolved fast in recent decades. Today's demand is for practical as well as modern-oriented mathematics education. In today's world, modern and realistic mathematics education is critical in every country. The value of technology-based mathematics education has increased, signifying a fundamental shift in how mathematics education is seen today. Mathematics education will be simplified if students can access a virtual math classroom over the internet. As a result of the development of computer media, educators, students, and scientists are presented with a challenge: Theoretical frameworks are used in innovation studies in the field of teaching mathematics, but this research focuses on what such theoretical perspectives have to offer. The author's mathematical team's main goal is to create exercises that will enable communication. In addition, they should use technology to improve and broaden their pupils' math skills. This article discusses the approach for generating and employing chemicals for such an objective.

Connecting the “Real-World” to the Math Classroom: Implementing Professional Development for Mathematical Modeling

This qualitative research study focused on the changes in classroom pedagogy and content of rural mathematics teachers who engaged in a year-long professional development project focused on mathematical modeling. During a 2-week summer institute, teachers solved mathematical modeling problems as learners and then went through an iterative design process of creating, testing and refining lessons for classroom implementation. The lessons were implemented during the academic year. Results of this study indicate that teachers developed a willingness to move from traditional lecture and replication as the main form of pedagogy. Instead they incorporated more group tasks, alternate assessments, and created their own mathematical modeling problems that were relevant to their students’ lives.

A Reflection on Growth Mindset and Meritocracy

As mathematicians working in higher education we reflect on meritocracy and growth mindset with a focus on the relationship between the two. We also note the subtle differences between growth mindset and grit. Our reflection ends with suggestions for how to move forward in the math classroom and throughout the collegiate level.

A Bibliometric Study of the Research on Instructional Uses for Nonfiction Graphic Novels

The intention of this bibliometric study is to examine the research on the use of graphic novels in classrooms and libraries during the past two decades to highlight how this topic has changed and developed over time. The focus of the research is on the use of nonfiction graphic novels in the English Language Arts, Writing, Social Studies, History, Science, and Math classrooms. This study notes similarities in the research on uses for graphic novels and identifies the prevailing journals which have published articles on this topic. The authors who have written about this topic the most frequently are identified. This study also provides a list of some highly recommended nonfiction graphic novels cited in the research by authors for classroom use.

A multidimensional examination of math anxiety and engagement on math achievement.

Math anxiety (MA) and math achievement are generally negatively associated. This study investigated whether and how classroom engagement behaviors mediate the negative association between MA and math achievement. Data were drawn from an ongoing longitudinal study that examines the roles of affective factors in math learning. Participants consisted of 207 students from 4th through 6th grade (50% female). Math anxiety was measured by self-report using the Mathematics Anxiety Scale for Children (Chiu & Henry, 1990, Measurement and valuation in Counseling and Development, 23, 121). Students self-reported their engagement in math classrooms using a modified version of the Math and Science Engagement Scale (Wang et al., 2016, Learning and Instruction, 43, 16). Math achievement was assessed using the Applied Problem, Calculations, and Number Matrices subtests from the Woodcock-Johnson IV Tests of Achievement (Schrank et al., 2014, Woodcock-Johnson IV Tests of Achievement. Riverside). Mediation analyses were conducted to examine the mediating role of classroom engagement in the association between MA and math achievement. Students with higher MA demonstrated less cognitive-behavioral and emotional engagement compared to students with lower MA. Achievement differences among students with various levels of MA were partly accounted for by their cognitive-behavioral engagement in the math classroom. Overall, students with high MA exhibit avoidance patterns in everyday learning, which may act as a potential mechanism for explaining why high MA students underperform their low MA peers.

Growth mindset in the maths classroom: a key to teachers’ well-being and effectiveness

ABSTRACT The present study evaluated the effects of a programdesigned to promote a growth mindset in maths teachers (i.e., the belief that maths ability can improve through experience and learning) to enhance teaching and learning outcomes in their maths classes. The sample was composed of 155 Israeli high-school maths teachers who were randomly assigned to a one-year intervention or control condition. Growth mindset, professional well-being and emotional teaching efficacy improved significantly in the intervention group over time but did not change in the control group. Teachers’ professional well-being, was associated with an increase in student grades and a decrease in class dropout rates. These findings reinforce the need to promote a growth mindset in teachers to maximise their students’ potential for maths success.

The potential of relevance interventions for scaling up: A cluster-randomized trial testing the effectiveness of a relevance intervention in math classrooms.

The potential of relevance interventions for scaling up: A cluster-randomized trial testing the effectiveness of a relevance intervention in math classrooms.

‘Schreibzeit’ (marking time): an exploration of the permutational art and calendar calculations of Hanne Darboven

Mathematical aspects of the work of the German conceptual artist, Hanne Darboven, are discussed, including the role of permutation, number representation and symmetry in her early works, and the use of a checksum calculation to record calendar dates in her later works. We analyse the multiple ways she represents the checksum calculations and explore the similarities and differences of her work with mathematics. We also suggest several mathematical questions arising from her work that would be interesting to explore in a discrete mathematics, number theory or liberal arts math classroom.

An example of functional integration and application of diversity, inequities, and social determinants of health in an applied physiology course.

Increasing diversity, including diverse perspectives in science, technology, engineering, and math (STEM) classrooms and teaching practices, is recognized as a current higher education priority. Resources to assist institutions and instructors are growing; however, many STEM instructors still hesitate to implement diverse teaching practices and discussions of diversity issues in their courses for a variety of reasons. This paper describes an example of the incorporation and discussion of diversity and social justice issues as part of an upper level physiology of aging course. The general approach was to examine the functional intersection of the sociology and physiology using social determinants of health as mechanistic influencers of physiology and examining how they affect healthy aging and etiology of age-associated diseases. Activities included in-class and virtual discussion, collaboration with the university diversity department, and a written assignment where the students explored in depth how a social determinant of health affected molecular physiology of aging. Students were also provided with strategies they can use in careers as health practitioners to be more inclusive in their practices. Student participation and feedback indicated that this approach and activities were engaging, enlightening and useful and should be continued. They specifically appreciated the social issues discussed in their sociology courses being included in their physiology major course and thinking about how those issues are mechanistically linked to physiology. This was the first attempt at this approach, and strategies for future activity improvement and tips for successful implementation are also addressed.

On the Mathematical Narration by Trans-Spectrum University Students

More than 80 years of literature support the idea that math attitudes and experiences differ by gender. However, such research treats gender as a simple and dichotomous variable, which it is not. As such, our understandings of math affective variables are completely dominated by a cisgender narrative and a false gender binary. In particular, I argue that it is important to research the lived experiences in the math classroom and the sense of belonging felt by trans-spectrum students. This qualitative study has employed a narrative methodology to analyze the semi-structured interviews of 6 participants who identify as trans-spectrum university students in order to explore the tactile lived experiences in the math classroom as it relates to gender, when gender is considered holistically. Overall, the participants indicated that while mathematics as a discipline is not gender-specific, the participants face discrimination and microaggressions around mathematics that help create a chilly atmosphere. The participants, then, narrate their sense of belonging in regard to a separation between mathematics as a discipline and mathematical activities. Collectively, all participants presented stories that highlight conflicts within various social binaries, such as male/female or private/public school.

Look Who's Talking: Teaching and Discourse Practices across Discipline, Position, Experience, and Class Size in STEM College Classrooms.

Students are more likely to learn in college science, technology, engineering, and math (STEM) classrooms when instructors use teacher discourse moves (TDMs) that encourage student engagement and learning. However, although teaching practices are well studied, TDMs are not well understood in college STEM classrooms. In STEM courses at a minority-serving institution (MSI; n = 74), we used two classroom observation protocols to investigate teaching practices and TDMs across disciplines, instructor types, years of teaching experience, and class size. We found that instructors guide students in active learning activities, but they use authoritative discourse approaches. In addition, chemistry instructors presented more than biology instructors. Also, teaching faculty had relatively high dialogic, interactive discourse, and neither years of faculty teaching experience nor class size had an impact on teaching practices or TDMs. Our results have implications for targeted teaching professional development efforts across instructor and course characteristics to improve STEM education at MSIs.

Examining the Acute Effects of Classroom-Based Physical Activity Breaks on Executive Functioning in 11- to 14-Year-Old Children: Single and Additive Moderation Effects of Physical Fitness.

Objective: Research supports the efficacy of acute, classroom-based, physical activity breaks on executive functioning in children. However, research pertaining to the effect of physical fitness on the acute physical activity—executive functioning relationship remains limited. The primary purpose of this study was to investigate the acute effects of classroom-based, teacher-delivered, physical activity breaks on executive functioning in 11–14-year-old children. We also investigated the potential moderating effects of both aerobic and musculoskeletal fitness on the acute physical activity—executive functioning relationship.Method: Participants (N = 116) completed pre- and post-test assessments of executive functioning (i.e., inhibition, switching, and updating) separated by a classroom-based physical activity break or sedentary classroom work. We manipulated the dose (i.e., length) and type of physical activity breaks. With regards to dose, participants in the experimental conditions engaged in 5-, 10-, or 20-min of physical activity whereas controls completed sedentary classroom math work at their desk. With regards to type, one experimental condition completed traditional physical activity breaks whereas the other experimental condition completed academic physical activity breaks (i.e., performed mental math and physical activity). Participants' mood, motivation, and self-efficacy were also assessed following the experimental manipulations.Results: Overall, executive function scores improved across each assessment following the physical activity breaks when compared to sedentary classroom work regardless of dose and type. Participants also reported more positive mood states, higher motivation to complete the executive function tests, and higher self-efficacy to perform the executive functions tests following the physical activity breaks. Single moderation analyses showed that low-moderate levels of aerobic fitness moderated the acute physical activity—executive functioning relationship. Additive moderation analysis showed, collectively, that both aerobic and musculoskeletal fitness moderated the acute physical activity—executive functioning relationship.Conclusion: Findings from the present study provide evidence for the acute effects of short (i.e., 5–20 min) classroom-based physical activity breaks on executive functioning and psychological states in children. Results also suggest levels of both aerobic and musculoskeletal fitness moderate these effects, however future research is needed to further elucidate this complex relationship.

How to engender learning in the learning process? Mathematics, events and the invention of a mathematical education

This article proposes an exercise of problematization and denaturalization of a math classroom that is born from research carried out with a cartographic approach, in which, when occupying the elementary school math classroom, questions are asked: what happens in a math classroom? Which mathematics happens in a classroom? The event is here in affinity with the philosophy of the event of Gilles Deleuze, in which event is that which cuts time off, drags it, breaks it. Events are possible worlds that erupt in the things that happen. To do so, the writing of this paper takes place in relation to an episode in a classroom, evoking events that involve mathematical production, "mistakes" and learning, experiencing engendering of learning in the learning process. This writing involves two problematizing movements: the first one unfolds the problem of connection between learning and teaching in mathematical education; the second one in which, by the force of the event in the math classroom, the connection between learning and teaching as something necessary is under suspicion since it suffers an inflection in tradition in and of a mathematical education.

COVID-19: A MOTIVATOR FOR CHANGE IN ENGINEERING EDUCATION?

Despite recent research and initiatives, learner-centered instructional practices have not made their way into post-secondary Science, Technology,Engineering and Math (STEM) classrooms, even though there is clear evidence showing the benefits include increased grades, higher student engagement, and deeper learning. STEM educators rank the barriers associated with active learning higher than their colleagues in other disciplines, and identify the inability to cover all the content as a key factor in their decision to adhere to didactic practices. Insights and instructional strategies and methods garnered from teaching-related faculty development opportunities are often tried, but their use is not generally sustained unless a personal experiencedrives that change in practice. Unquestionably, COVID-19 has had an immediate, global impact on higher education. Educators have been forced to alter their teaching practices to accommodate the switch to remote learning. Most Teaching and Learning Centers offered myriad workshops to facilitate this change. This quantitative study set out to determine if COVID-19 precautions created the personal experience necessary to initiate a change in STEM teaching practices. Using educator-related threshold concepts as a framework, it analyzed institutional registration records to determine the type of faculty development opportunitieschosen by engineering educators, and the extent to which they participated in those related to learner-centered instructional practices for remote delivery.Analysis shows that engineering educators participated proportionally less than their colleagues in other disciplines, and there is an indication that the pandemic may facilitate an ongoing change in the teaching practices of engineering educators. Opportunities for enhancing faculty development practices for engineering educators are proposed.

The impact of alternative authentic assessment outcomes in Palestinian fourth grade math classrooms

Focusing on evaluating students’ performance in basic math classrooms, the researchers in this study examined the impact of alternative assessments on learning outcomes in fourth grade Palestinian classrooms. Representing a large sector of education in the Palestinian territories, fourth grade students were randomly selected to participate in the study in which they participated in various math instructional and assessment activities throughout multiple lessons and cycles. Alternative assessment approaches were used including student self- assessment, peer assessment, and teacher assessment in terms of three main achievement levels to measure the extent to which students learned the math concepts by recall and remembrance, ability to apply, and making inferences. Mixed Design ANOVA measures were used to analyze and interpret the results which showed significant trends and correlations across the four cycles of math instruction and indicated that alternative authentic assessment methods have had a positive impact on students’ learning and application of math. Implications for integrating authentic assessment measures as well as peer and self- assessments were drawn in light of the promising outcomes of augmenting student motivation and developing critical life-long skills.