Mathematics Education Research Journal最新文献

This study examined the teacher–child interactions during shared book reading (SBR) in the domain of early mathematics. We investigated preschool teachers’ and children’s talk in terms of (1) communicative acts, mathematical focus, and level of abstraction (literal versus inferential), (2) the sequential relation between teacher’s talk and children’s mathematical inferential talk, and (3) the contribution of the type of picture book (mathematical versus non-mathematical) and teachers’ pedagogical content knowledge (MPCK) to the amount of mathematical inferential talk and the strength of the sequential relation. Twelve preschool teachers read one mathematical and one non-mathematical picture book to their preschoolers, resulting in 24 reading sessions. All 24 sessions were video-recorded, transcribed, and coded. Our analyses revealed that teachers’ mathematical talk was dominated by initiations, follow-ups and comments, and children’s mathematical talk by responses and comments. About 30% of teachers’ mathematical initiations and children’s mathematical responses were inferential; approximately 25% of children’s mathematical comments were inferential. Next, we observed a strong sequential relation between teachers’ mathematical inferential prompts and children’s mathematical inferential responses. Finally, the type of picture book, but not preschool teachers’ MPCK, contributed to the SBR interaction: preschool teachers formulated more inferential elaborative follow-ups when reading a mathematical compared to a non-mathematical picture book, and the sequential relation between teacher’s mathematical inferential prompts and children’s mathematical inferential responses was stronger for mathematical picture books.

Mathematical communication, encompassing writing in, about, and for mathematics, is a critical competency. Defining excellent mathematical writing standards, however, remains challenging. To address this, we conducted a systematic review of 48 scholarly works on quality in mathematical writing. Our findings reveal mathematical writing for different purposes under scrutiny, including general mathematical writing, proof writing, reflective writing, expository writing, and descriptive writing during problem solving. To assess quality, researchers explore a variety of facets, such as syntax and semantics. Progression pathways vary, with both quantitative and qualitative evaluations—analysing text structure, writing style, and the use of different semiotic elements. It seems that in mathematics education, a consensus on quality measurement remains elusive. Proof writing is a notable exception. Among reviewed articles examining proof writing, a common set of standards emerges and provides valuable guidance. We propose that mathematical writing, perhaps especially in the context of reporting solutions in problem solving, can draw from proof writing standards. ‘Good’ mathematical writing would then require students to focus on (1) defining assumptions and assigning variables; (2) producing a coherent narrative, including relevant calculations (semantic issues); (3) using correct language, representations, and mathematical symbols (syntax issues); and (4) attending to what is appropriate in the context.

This study aimed to elicit middle school pre-service mathematics teachers’ personal meanings of realistic mathematics problems. The study presents a portion of a larger design-based study involving teacher training sessions encompassing small-group discussions, writing realistic mathematics problems, and whole-group discussions. The audio records of the pre-service teachers’ discussions and their written artifacts were analyzed in three coding cycles. The findings indicated that the pre-service teachers’ personal meanings of realistic mathematics problems comprised both in-school situations that students themselves could experience and real-life situations that mostly required occupational decisions such as optimization in engineering. Besides, pre-service teachers considered that realistic situations often involve multiple information and could be solved by multiple solution methods that might lead to multiple acceptable answers. This study highlighted the informative role of articulating pre-service mathematics teachers’ personal meanings of realistic mathematics problems in designing teacher education courses and further discussed such implications for mathematics teacher education.

Although absolute value is of interest to mathematics teaching researchers, since many students face problems with it, there does not seem to be an integrated record of students’ errors. The present study attempts to conduct a systematic review to identify and categorize errors and misconceptions of secondary school students aged 12–18 concerning the concept of absolute value. Following the PRISMA method, empirical studies published in English later since 1990 studying the errors and misconceptions of secondary school students with absolute value were looked up through the databases Scopus and Web of Sciences as well as through the Google Scholar search engine. From the 11 empirical studies that were eventually found, a categorization of misconceptions and corresponding errors arose. The first main category concerns the transition from the arithmetic to the algebraic domain while the second main category concerns the definition of absolute value in the form of a piecewise function. It is noteworthy that these two categories sometimes interact and are linked. Based on these findings, practical implications are discussed that strengthen the understanding of mathematical literacy.

In recent years, research on mathematics teachers’ beliefs has increasingly shifted its focus toward understanding their connection with instructional practices. This article introduces a model designed to explore mathematics teachers’ beliefs through a comprehensive analysis of their practices. The contributions of models that study the relationship between beliefs and practices of teachers, such as those from Schoenfeld (Journal of Mathematical Behavior, 18(3), 243–261, 2000) and Cobb and Yackel (Educational Psychologist, 31(3), 175–190, 1996), were reviewed and considered. Additionally, it includes methodological considerations from Leatham and Speer for studying beliefs. These approaches are integrated by utilizing the notions of practice, types of didactic-mathematical practices and norms, derived from the onto-semiotic approach, as the central organizing axis. Furthermore, we demonstrate the application of these stages of analysis for exploring teachers’ beliefs by analyzing the beliefs of a prospective mathematics teacher. The findings enable us to identify the beliefs held by this prospective teacher regarding the use of introductory activities characterized by a high motivational level but a low mathematical level. Additionally, these results provide insights into potential avenues for developing training programs aimed at instigating a shift in these beliefs, thereby fostering an enhancement in teaching practices. These outcomes show the feasibility of the analytical model proposed in this article.

The current study examined how prospective first- and second-grade mathematics teachers define the polygon diagonals concept, how they reconstruct their definition during and following an intervention, and how their concept images develop over time. Twenty-three prospective teachers participated in the study, during which they were asked to analyze mathematical events involving a conflict that could be resolved using a precise mathematical definition of a polygon diagonal. Data were collected from prequestionnaires, postquestionnaires, and observations of class discussions. The study findings indicate that before the intervention, all participants provided incorrect definitions and struggled to identify nonprototypical examples of polygon diagonals in the prequestionnaire. However, the process of analyzing mathematical events helped the participants reconstruct their definitions of polygon diagonals and identify the critical attributes of this concept, which improved their ability to extend the concept’s image to include nonprototypical examples. The participants’ improved understanding was evident in the significant improvements in the postquestionnaire.

In this study, we explored elementary school teachers’ experiences working on open-ended mathematics tasks during a 10-day professional development (PD) workshop. Teachers engaged with the tasks daily in a session call Morning Math (MM). Thirty-two elementary teachers from three school districts in the USA participated in a 2-year professional development (PD) program. Analysis of videos of teacher engagement in the tasks and interviews shows that the use of open-ended mathematics tasks embedded within problem-solving focused PD could shape elementary school teachers’ personal meanings about learning mathematics through problem-solving. The findings indicate that the teachers’ take-aways from the PD were not limited to the mathematical content of the MM problems (i.e., mathematical residue), instead teachers’ experiences with open-ended mathematics tasks engendered personal meanings reflecting pedagogical residue with cognitive, affective, and social components. This result shows the crucial role of PD in shaping teachers’ mathematics-related personal meanings which research suggests that it will subsequently influence their beliefs and instruction.

The use of manipulatives to develop conceptual understanding is a prevalent practice in many mathematical learning experiences, particularly in the early years of schooling. From primary student perspectives, our understanding of the impact of manipulatives in mathematics education on students’ attitudes is limited. This study evaluates the impact of mathematical manipulatives on Young Children’s Attitudes Towards Mathematics (YCATM) by examining children’s drawings, as well as their written and verbal descriptions of their drawings from 106 year 2 and year 3 students. Classroom observations were conducted to investigate how attitudes towards mathematics are enacted during mathematical learning experiences. The modified three-dimensional model of attitude (MTMA) and Bruner’s experiential stages were used to investigate how manipulatives influence YCATM. Data analyses used systematic, numerical coding, and thematic and comparative approaches, employing inductive, deductive, and anticipatory coding for data from both lesson and non-lesson contexts. The findings suggest that young children enjoyed using manipulatives, contributing to their vision of mathematics and perceived competence. However, the transition between enactive, iconic, and symbolic experiences can contribute to the formation of negative attitudes. The present study also emphasizes the importance of context, content, and familiarity with the use of manipulatives.

Numeracy is important for everyday life. Being numerate has a positive impact on the quality of life of individuals, with positive economic, health, and social outcomes. Despite this, little is known about the role of numeracy in the lives of adults with intellectual disability (ID). Design research has been used to develop ways to support mathematical learning for typically developing students. This study investigates the use of design research to develop context-specific, physical tools to support adults with intellectual disability to improve their numeracy capabilities and engagement in daily tasks. Using observation and interview data, findings demonstrate increased engagement and participation in the numeracy demands of these tasks. Participants reported positive perceptions of improved competence and independence. This study demonstrates the application of design research to the field of numeracy for adults with intellectual disability, and the usefulness of designing context-specific tools to support their numeracy development and independence.

This study explores variations in prospective teachers’ (PTs’) noticing of students’ mathematical thinking based on narrative writing within the context of a practicum course. The research involved eight PTs, each of whom produced ten weekly narratives throughout the course duration. Most PTs displayed noticing abilities within the average range, with a tendency towards moderate levels, particularly in mixed and focused noticing, as per van Es’s (2011) framework. At the mixed noticing level, PTs predominantly focused on their instructional approaches while also considering learners’ reasoning, albeit with a general perspective. They often made evaluative comments without delving deeply into the specifics that would strengthen their analyses. In contrast, at the focused level of noticing, they dedicated more attention to the specifics of learners’ mathematical reasoning and offered interpretive insights. They cited specific instances and interactions to support their evaluations, demonstrating a more detailed and nuanced engagement with the classroom dynamics. The findings also reveal three distinct profiles of variation in noticing among PTs underscoring the complexity of enhancing noticing skills over time. While profile 1 (average to high levels of noticing) and profile 2 (low to moderate levels of noticing) showed more variation, profile 3 demonstrated a more stable pattern at the moderate levels. These variations might be a result of the bidirectional relationships that exist between the skills of noticing. It could also stem from the events that PTs based their narratives on, affirming that enhancement in noticing is an iterative, context-sensitive process influenced by classroom context and situation awareness.