Educational Studies in Mathematics最新文献

This study assessed the effectiveness of a spatialized mathematics intervention on the mathematical performance and spatial visualization skills of students from an underprivileged Indonesian community. Grade 8 students (N = 407) were assigned to one of twelve experimental classes, receiving the spatial mathematics intervention, or one of seven control classes, continuing with the standard mathematics curriculum. Prior to and following the intervention, a pre-test and post-test design was administered. The data were analyzed using Analysis of Covariance to ascertain the effect of the intervention. Results revealed that the students in the experimental group exhibited significant improvements in spatial visualization skills and mathematics performance (including both spatial and non-spatial competencies), compared to the control group. Importantly, the findings provide evidence that the transfer effects of the spatialized curriculum occur differentially for students of varying ability levels. The findings highlight the importance of spatial intervention in enhancing mathematics performance and spatial visualization skills. The study suggests potential avenues for a paradigm shift in mathematics education that recognizes and embraces the profound influence of spatial thinking.

Repeating patterning proficiency predicts students’ later mathematical proficiency. A comparative multi-case design enabled the present study to compare patterning success and strategy use for repeating patterns of 75 Norwegian 6-year-old grade 1 students. We provided the students with duplicate, extend, transfer, and unit isolation activities in a semi-structured, task-based interview that was video-recorded. The students’ number sense was also measured using a digital assessment. In-depth analysis of 52 students (divided evenly into two groups based on their number sense scores, lowest and highest) was performed. A statistically significant group difference was found for extend activities. Multimodal video analysis of strategies employed revealed that both student groups used recursive and different strategies and only students with high number sense used relational strategies. The students with low number sense used more variants of recursive patterning strategies. Our findings also demonstrated that attention to pattern features may both hinder identification of a pattern’s underlying structure and reflect advanced strategy use rather than not showing pattern awareness. We discuss group differences in terms of decomposition and awareness of mathematical pattern and structure and emphasise the need for scaffolding awareness of mathematical pattern and structure through communication.

Mathematical language (or the content-specific words in mathematics) has repeatedly shown to be related to mathematical abilities in preschool and in the early grades of primary education. Research in this field has predominantly focused on young children’s quantitative and spatial language. At the same time, recent research has discovered that children in the early years of primary education already possess advanced mathematical skills such as reasoning about patterns, proportions and probabilities. In this study we developed an advanced mathematical language task to measure children’s understanding of mathematical language proper of the domains of patterning, proportionality, and probability, specifically aimed at first, second, and third graders (ages 5 -8). To develop a valid test instrument, our task was substantiated by a review of relevant literature and previously conducted studies. Further, the task was optimized based on the feedback received from expert professionals and a pilot study with 36 children. After administering the advanced mathematical language task to 236 first, second, and third graders, the results suggest that the task provides reliable scores in these grades. The internal consistency is excellent (α = .993). In addition, the test–retest reliability was checked in 49 children (r = .704; p < .001), and shows that the test also produces stable results over time.

School reform efforts are situated within social and political contexts and, as such, are susceptible to the commonsense discourses circulating through, and shaping, society. Two discourses prevalent in US education reform are those perpetuating the ideologies of neoliberalism and neoconservatism. These ideologies are inherently contradictory—with the former promoting a small state and the latter a strong state—but converge to promote their agendas, shaping school reform efforts. How this occurs is not always clear, especially in rural contexts, where there has been limited attention to ideological discourses’ relation to schooling. In this analysis, we describe how dominant, yet contradictory, discourses of neoliberalism and neoconservatism are resolved in a rural context. We find that the leaders of one rural, public school district identified fifth-grade number sense as a problem of practice needing improvement—framing the cause of their problem as misalignment and the solution as consistency within and across grade levels. In doing so, district leaders’ conversations were limited to those of standardization (e.g., state-mandated mathematics standards, approaches to timed-fact tests, and curriculum between grade levels). Alignment as a frame excluded conversations related to deeper considerations, such as students’ experiences in mathematics or issues of equity. We find that dominant discourses constrain the ways district leaders frame their mathematics-related problem and work through the frame (in this case, one of alignment) to resolve inherent contradictions and advance their agendas. We suggest that these discourses serve to distract from potentially more pressing issues in education.

Racism against Asians is often ignored worldwide, and the field of mathematics education is no exception. The anti-Asian racism unveiled during the COVID-19 pandemic necessitates that we rethink the current discussions of equity and social justice in mathematics education regarding how the needs of many Asian students have been forgotten and often excluded from these discussions. When Asian students are mentioned, it is often for the purpose of reifying a racial hierarchy of mathematical ability (Martin, Teachers College Record 111(2):295–338, 2009; Martin et al., 2017). Based on an analysis of the particularities of the U.S. context, this essay argues that the model minority myth and other covert forms of anti-Asian racism, such as yellow peril and forever foreigner myths, racialize Asian Americans and create a monolithic view of diverse groups of people with different histories and needs, including within mathematics education. While incorporating current race and racism concepts from Asian Critical Theory (Iftikar & Museus, International Journal of Qualitative Studies in Education 31(10):935–949, 2018), we aim to conceptualize the racialization that Asian-American students experience in mathematics classrooms and how it affects their well-being, and propose implications to (re)construct Asian-American students’ counterstories and identities in mathematics education. We also scrutinize mathematics education researchers’ and educators’ roles in advancing equity for all students by countering the hidden racism toward Asian Americans.

Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers’ learning of these rules when being taught them explicitly. Our data come from academically motivated high-school students who took a special course in undergraduate mathematics. The course teacher dedicated three academic hours to introducing and explaining selected rules of proof to support students’ shift to the new discourse. The homework assignment consisted of typical proof-requiring problems and a scriptwriting task, asking students to compose a dialogue between fictional characters about a proof-related mistake of their choice. We analyzed the differences and similarities between the rules discussed in the classroom and those that students addressed and implemented in their proofs. The analysis showed that while students’ solutions to proof-requiring problems required rule implementation, fictitious dialogues opened the space for rule formulation and substantiation. In many cases, the students discussed the rules presented in the classroom, extending, elaborating, and specifying the teacher’s formulations. Furthermore, while the students’ proofs were mainly consistent with the teacher’s expectations, some of their rule formulations were more radical and overgeneralized than expected. These findings suggest that newcomers’ communication about the rules of proof may lag behind their capability to implement those rules to prove mathematical statements.

Preparing prospective mathematics teachers to become teachers who recognize and respond to students’ mathematical needs is challenging. In this study, we use the construct of critical incident as a tool to support prospective mathematics teachers’ reflection on their authentic fieldwork activities, notice students’ thinking, and link it to the complexity of mathematics teaching. Particularly, we aim to explore the characteristics and evolution of prospective mathematics teachers’ noticing of students’ mathematical thinking when critical incidents trigger reflective discussions. Critical incidents are moments in which students’ mathematical thinking becomes apparent and can provide teachers with opportunities to delve more deeply into the mathematics discussed in the lesson. In the study, twenty-two prospective mathematics teachers participated in fieldwork activities that included observing and teaching secondary school classrooms. The prospective teachers identified critical incidents from their observations and teaching, which were the foci for reflective discussion in university sessions. By characterizing the prospective teachers’ reflective talk in these discussions, we demonstrate the discussion’s evolution. In it, participants questioned learning and teaching mathematics and suggested alternate explanations. This characterization also shows that using critical incidents in the university discussions enabled the prospective teachers to link students’ thinking with the teacher’s teaching practices while supporting their reflection using classroom evidence. We emphasize the importance of descriptive talk in the discussion, which allows for deepening the prospective teachers’ reflections. Further, we explore the teacher educator’s contributions in those discussions, showing that the teacher educator mainly maintained the reflective talk by contextualizing the critical incidents and pressing the participants to explain further issues they raised in the discussions. Implications for mathematics teacher education are discussed.

Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade classes. One goal was that by the end of first grade, students would be able to solve tasks such as subtracting 8 from 15 by using part-whole number relations. In this paper, we report on learning outcomes from task-based interviews with intervention and control groups before, immediately after, and one year after the intervention, in order to investigate long-term effects and whether students used a structural approach when solving tasks in a higher number range in the second grade. In comparison to controls, students in the intervention group showed higher increases in their learning outcomes. Moreover, the intervention group used a structural approach to a larger extent when solving tasks in higher number ranges, whereas students in the control group more commonly used single-unit counting to solve such tasks. These findings have implications both for teaching and for research on students’ development of arithmetic skills.