Pre-service Teachers’ Conceptions of Mathematical Argumentation

Drawing on a situated perspective on learning, we analyzed written, open-ended journals of 52 pre-service teachers (PSTs) concurrently enrolled in mathematics and pedagogy with field experience courses for elementary education majors. Our study provides insights into PSTs’ conceptualizations of mathematical argumentation in terms of its meanings. The data reveals how PSTs perceive teacher actions, teaching strategies, classroom expectations, mathematics content, and tasks that facilitate student engagement in mathematical argumentation. It also shows what instructional benefits of enacting mathematical argumentation in the elementary mathematics classroom they perceive

Pre-service K-8 Teachers’ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study

This study sheds light on three teaching competencies: Pre-service teachers’ (PSTs’) professional noticing of student mathematical reasoning and strategies, their ability to assess the validity of student reasoning and strategies, and to select student strategy for class discussion. Our results reveal that PSTs with strong awareness of mathematically significant aspects of student reasoning and strategies (focused noticing) were better positioned to assess the validity of student reasoning and strategies. PSTs with higher strategy evaluation skills were more likely to choose the strategy to engage class in justification or to advance students’ conceptual understanding compared to PSTs with low strategy evaluation skills

Exploring the Relationship between K-8 Prospective Teachers’ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. In contrast, prospective teachers with higher algebraic thinking proficiency were able to pose probing questions to investigate student thinking or help students clarify their thinking. However, less than half of their questions were of this probing type. These results suggest that prospective teachers’ algebraic thinking proficiency is related to the types of questions they ask to explore the algebraic thinking of students. Implications for mathematics teacher education are discussed

K-8 Pre-service Teachers’ Algebraic Thinking: Exploring the Habit of Mind Building Rules to Represent Functions

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers\u27 ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers\u27 ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed

A Proposal for a Problem-Driven Mathematics Curriculum Framework

A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relationship among modeling, conceptual, and procedural knowledge), can be used for programmatic, classroom and individual assessment, and can be easily revised to reflect ongoing changes in disciplinary knowledge development and important applications of mathematics. The discussion prompts ideas and questions for future development of the envisioned software needed to enact such a framework

Exploring Prospective 1-8 Teachers\u27 Number and Operation Sense in the Context of Fractions

This exploratory study examined prospective elementary teachers’ (PSTs’) number and operation sense (NOS) in the context of solving problems with fractions. Drawing on the existing literature, we identified seven skills that characterize fraction-related NOS. We analyzed 230 responses to 23 tasks completed by 10 PSTs for evidence of PSTs’ use of different fraction-related NOS skills. The analysis revealed that PSTs did not use all seven fractionrelated NOS skills to the same extent. PSTs’ responses documented their frequent reasoning about the meaning of symbols and formal mathematical language in the context of fractions. To a lesser extent, PSTs’ responses documented their reasoning about different representations of fractions and operations, about the composition of numbers, and about the effects of operations on pairs of fractions. We also examined possible relationships among the seven fraction-related NOS skills identified across the analyzed responses. The results reveal that some of the fraction-related NOS skills appear to support one another. Given that NOS skills provide a foundation for effective mental computation strategies, our study shows the need for explicit attention in teacher preparation programs to supporting PSTs in developing a strong awareness of and facility with a range of fraction-related NOS skills. Our study also raises questions about the relationship between PSTs’ conceptual understanding of fractions and their fraction-related NOS skills and provides suggestions for future research that explores further connections among the fraction-related NOS skills

Near threshold eta meson production in the d+d->alpha+eta reaction

The d+d->alpha+eta reaction has been investigated near threshold using the ANKE facility at COSY-Juelich. Both total and differential cross sections have been measured at two excess energies, Q=2.6 MeV and 7.7 MeV, with a subthreshold measurement being undertaken at Q=-2.6 MeV to study the physical background. While consistent with isotropy at the lower energy, the angular distribution reveals a pronounced anisotropy at the higher one, indicating the presence of higher partial waves. Options for the decomposition into partial amplitudes and their consequences for determination of the s-wave eta-alpha scattering length are discussed.Comment: 8pp, fig.3 added, normalisation in eq.4.1 correcte