24 research outputs found
Pre-service Teachersâ 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 PSTsâ 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 Teachersâ Professional Noticing and Strategy Evaluation Skills: An Exploratory Study
This study sheds light on three teaching competencies: Pre-service teachersâ (PSTsâ) 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 studentsâ conceptual understanding compared to PSTs with low strategy evaluation skills
Exploring the Relationship between K-8 Prospective Teachersâ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews
In this study, we explored the relationship between prospective teachersâ 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 teachersâ 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 teachersâ 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 Teachersâ 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 teachersâ (PSTsâ) 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 PSTsâ use of different fraction-related NOS skills. The analysis revealed that PSTs did not use all seven fractionrelated NOS skills to the same extent. PSTsâ responses documented their frequent reasoning about the meaning of symbols and formal mathematical language in the context of fractions. To a lesser extent, PSTsâ 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 PSTsâ 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
Feasibility studies of time-like proton electromagnetic form factors at PANDA at FAIR
Simulation results for future measurements of electromagnetic proton form
factors at \PANDA (FAIR) within the PandaRoot software framework are reported.
The statistical precision with which the proton form factors can be determined
is estimated. The signal channel is studied on the basis
of two different but consistent procedures. The suppression of the main
background channel, , is studied.
Furthermore, the background versus signal efficiency, statistical and
systematical uncertainties on the extracted proton form factors are evaluated
using two different procedures. The results are consistent with those of a
previous simulation study using an older, simplified framework. However, a
slightly better precision is achieved in the PandaRoot study in a large range
of momentum transfer, assuming the nominal beam conditions and detector
performance
Study of doubly strange systems using stored antiprotons
Bound nuclear systems with two units of strangeness are still poorly known despite their importance for many strong interaction phenomena. Stored antiprotons beams in the GeV range represent an unparalleled factory for various hyperon-antihyperon pairs. Their outstanding large production probability in antiproton collisions will open the floodgates for a series of new studies of systems which contain two or even more units of strangeness at the PâŸANDA experiment at FAIR. For the first time, high resolution Îł-spectroscopy of doubly strange ÎÎ-hypernuclei will be performed, thus complementing measurements of ground state decays of ÎÎ-hypernuclei at J-PARC or possible decays of particle unstable hypernuclei in heavy ion reactions. High resolution spectroscopy of multistrange Îâ-atoms will be feasible and even the production of Ωâ-atoms will be within reach. The latter might open the door to the |S|=3 world in strangeness nuclear physics, by the study of the hadronic Ωâ-nucleus interaction. For the first time it will be possible to study the behavior of ÎâŸ+ in nuclear systems under well controlled conditions
Prospective K-8 Teachers\u27 Problem Posing: Interpretations of Tasks That Promote Mathematical Argumentation
This study examines pre-service teachersâ (PSTsâ) views of tasks that engage students in mathematical argumentation. Data were collected in two different mathematics courses for elementary school education majors (n = 51 total PSTs). Analyzed were (a) written journals in which PSTs defined tasks that promote student engagement in argumentation, (b) tasks PSTs posed to engage students in mathematical argumentation, and (c) accompanying explanations in which PSTs motivated tasks they posed. The analysis revealed that PSTs interpret tasks that foster argumentation in terms of activities of argumentation that a task elicits and space for argumentation that the task provides. Several features that PSTs associated with each of the two major task characteristics were identified. While posing tasks to engage students in argumentation, PSTs did not place equal emphasis on all of the identified features
Prospective Teachers\u27 Interpretations of Mathematical Reasoning
Calls for teaching school mathematics with a focus on mathematical reasoning (MR) are included in curricular documents across the world, but little is known how prospective teachers (PSTs) understand MR. In this paper, we report on a study in which we engaged 24 PSTs preparing to teach grades 1-8 in analyzing a series of student-generated arguments for evidence of student reasoning with a focus on student-provided justifications. We examined PSTsâ interpretations of MR prior to and after instruction. Our results showed that PSTs interpreted MR broadly in terms of student thinking, validating thinking, problem-solving, connecting ideas, or sense-making. Some PSTs also interpreted MR as evidence of student understanding or described MR in terms of strategies teachers use to support studentsâ reasoning skills. We discuss changes in PSTsâ interpretations of MR after instruction