Despite the increasing emphasis on modelling in mathematics curricula, little is known about Chinese Grade 6 students’ performance and error patterns across modelling phases. To identify distinct performance profiles and explore the types of errors students make during the modelling process, we examined 2,078 Chinese Grade 6 students’ mathematical modelling competency through an online assessment. Using latent profile analysis, we identified four groups: Preliminary exploratory modelers, Strategic awakening modelers, Skill-advancing modelers, and Holistically developed modelers, showing differences in observed levels and configurations of mathematical modelling competency. Students in different profiles showed distinct patterns of response duration and response-sequence length. Error analysis revealed systematic differences across students with different profiles. More competent students were prone to select irrelevant information or construct models with missing or extraneous quantitative relations, while less competent students frequently omitted relevant information, made invalid assumptions, or failed to establish any effective relations. These findings underscore the possible diagnostic value of linking performance profiles with error-type analyses and suggest important implications for instructional design, particularly the need for differentiated guidance and targeted feedback to support students’ development of mathematical modelling competency.
This study presents an approach that integrates digital formative assessment tasks with cognitive diagnostic modelling to analyze elementary students’ work characteristics. These characteristics refer to the observable strategies and patterns that students use when working on digital geometry tasks that allow multiple correct student-generated examples and constructions, rather than a single predetermined response. The study focuses on triangle altitudes, a concept that is often challenging for learners and teachers. We designed a sequence of curriculum-aligned tasks and administered them to 73 fifth-grade students in the Arab sector of Northern Israel. Student-generated examples were recorded automatically and coded into seven recurring work characteristics that reflect known perceptual and strategic tendencies. The characteristics were placed within a structured skills-by-task matrix and analyzed with a cognitive diagnostic framework (DINA model). The framework evaluates how consistently individual tasks distinguish recurring patterns in students’ constructions. The analysis identified three patterns in the relationships between work characteristics and correctness. It also highlighted tasks that serve as sensitive indicators of students’ conceptual development. The findings suggest that digital task sequences can support systematic identification and analysis of recurring construction patterns that may inform interpretation of students’ developing geometric understanding.
This study, grounded in the Mathematical Pedagogical Technology Knowledge framework, is an investigation of the relationship between preservice teachers’ cognitive factors (types of fractional reasoning) and affective factors (perceived usefulness and ease of use) and their intentions to integrate FracTopia, a dynamic digital tool that supports comprehension of fractions, into their future teaching. Sixty preservice teachers in South Korea were introduced to FracTopia, used it to solve a fraction multiplication problem, and justified their solutions by explaining their problem-solving process and the quantitative meaning of the operation. They also completed a questionnaire assessing their attitudes toward the tool and their intentions to use it in future classrooms. The findings revealed that while most preservice teachers were able to use FracTopia to solve the problem, they demonstrated three distinct types of reasoning, computational, operational, and quantitative. In addition, many preservice teachers expressed generally positive attitudes toward FracTopia and a strong intention to use the tool in their future teaching. Notably, preservice teachers who demonstrated quantitative reasoning and held positive attitudes toward FracTopia were more likely to consider incorporating it into their teaching. These findings suggest that both cognitive and affective dimensions play meaningful roles in shaping preservice teachers' technology integration intentions. Implications are discussed for the design of teacher education experiences that move beyond tool familiarization to foster conceptually rich, affectively supportive engagement with dynamic digital tools.
In northern Mexico’s border region, some youth navigate structural precariousness shaped by poverty, systemic inequities, criminal violence, and deficit narratives that can individualize academic difficulty and portray young people as destined for failure. This intrinsic case study examines how mathematical errors are framed through instructional interactions in Rafa’s high school mathematics classroom and how students who make errors are positioned as mathematical participants. Drawing on epistemological and positional framing of mistakes and empathetic care, findings show that Rafa framed errors as opportunities to examine and revise mathematical reasoning while positioning students as responsible for making sense of their mistakes. Through the lens of empathetic care, these interactions reflected Rafa’s partnering with students in their mathematical errors, his responsiveness to their frustration, and his efforts to connect mistakes in mathematics with broader challenges in life. By bringing the framing of errors and empathetic care into conversation, this study offers a more relational understanding of classroom interactions around mathematical errors, particularly in contexts where mistakes can become intertwined with broader deficit narratives about students.
