Latinx Bilingual Students' Perseverance on a Mathematical Task: A Rehumanizing Perspective

We draw on a rehumanizing perspective that covets a student-centered viewpoint around the discipline of mathematics. For Latinx bilinguals, we posit that a translanguaging practice is a vital option by which collective perseverance during problem solving can be sustained and leveraged for meaningful learning. This study explores and examines the collaborative efforts of a group of Latinx twelfth-grade students persevering to make meaning of an exponential relationship. We employed a discursive thematic analysis of this groups’ ongoing engagement with a challenging mathematical task, paying specific attention to the ways in which these bilingual students encountered and overcame mathematical obstacles and setbacks. Our findings suggest that Latinx bilingual students can spontaneously and dialogically leverage communicative resources to help persevere with in-the-moment obstacles and build mathematical understandings. We argue for the development of more explicit translanguaging support systems in mathematics classrooms to privilege the viewpoint and experiences of the student, and the ways in which they develop mathematical understandings

Supporting novice mathematics teacher educators teaching elementary mathematics content courses for the first time

In order to be effectively prepared by a teacher education program, prospective elementary teachers (PTs) need to experience high quality mathematics instruction in their mathematics content courses. The instructors of these courses typically consist of individuals (mathematicians and mathematics educators) with ranging experiences, from tenured faculty members to first-year assistant professors or graduate students. This paper explores how to support novice mathematics teacher educators (MTEs) who are teaching elementary content coursework for PTs for the first time. We detail and describe how to implement three systems for supporting novice MTEs: working with a mentor, being provided with educative curriculum materials, and working in a collaborative teaching environment. We close by discussing specific challenges associated with these supports, and call for more institutions to share how they have successfully implemented systems to support novice MTEs

Distinguishing between Grit, Persistence, and Perseverance for Learning Mathematics with Understanding

Learning mathematics with understanding involves productively struggling to make connections between different mathematical ideas. Such productive struggle is associated with three primary constructs: grit, persistence, and perseverance. Each of these constructs has a distinct definition, background, and implied utility in mathematics education research. However, these constructs are often colloquially conceptualized as synonyms, leading to a misconception of what can be learned through the lens of each construct. The purpose of this paper is to carefully examine the literature on grit, persistence, and perseverance and to review and distinguish the ways in which these constructs offer insights into learning mathematics with understanding

Supporting secondary students' perseverance for solving challenging mathematics tasks

Jansen, Amanda M.Perseverance is a key process through which mathematics can be learned with understanding. However, withstanding such uncertainty can be difficult for students to endure and necessitates support. In this study, I investigated ways in which embedded scaffolds encouraged 10 ninth-grade students’ perseverance for solving a series of analogous challenging mathematics tasks. I designed a Three-Phase Perseverance Framework to capture the student perspective of how they persevered, both before and after reaching a perceived impasse. I conducted think-aloud interviews, video-reflection interviews, and an exit interview with each student as he or she engaged with one task per week for five weeks. Three tasks were embedded with conceptualization scaffolds prompting students to record their initial conceptual thinking prior to engagement; two tasks had no scaffolds. Results showed that students persevered significantly more on scaffolded tasks than on non-scaffolded tasks, with the most notable difference occurring after students encountered an impasse. Also, the quality of students’ perseverance improved over time, more so when working on scaffolded tasks than on non-scaffolded tasks. Students attributed much of their perseverance success to their preliminary conceptualization work prompted by the scaffolds. The findings suggest these scaffolds supported perseverance in problem solving in a cyclical manner, as students were encouraged to revisit their initial conceptual thinking upon impasse and re-initiate and re-sustain their productive struggle by exploring a different set of mathematical ideas. Furthermore, the data show malleability of perseverance, suggesting students can improve their perseverance in problem solving over time through carefully designed deliberate practice.University of Delaware, School of EducationPh.D

Instructional Perseverance in Early-Childhood Classrooms: Supporting Children’s Development of STEM Reasoning in a Social Justice Context

In early childhood education (ECE) classrooms, teachers navigate practices about how to allow space for students to make sense of new STEM-based ideas. We posit that such pedagogical moves require ample in-the-moment perseverance by the instructor. In this paper, we seek to explore the nature of such instructional perseverance in ECE classrooms and how it manifests when ECE educators are supporting young children to develop their STEM reasoning, with a primary focus on the mathematics discipline in a social justice context. Working with a dataset consisting of four ECE classroom episodes, we employed an analytical framework that captured evidence of instructional perseverance. We found that the instructional perseverance of the ECE teacher was integral to the development of STEM reasoning of her young students. We present an illustrative case that details the instructional perseverance of the ECE teacher and the related STEM reasoning of her students in the context of exploring income variance by race. We argue that teacher education development must address how ECE teachers can plan for and navigate in-the-moment instructional obstacles in order to support young students’ STEM reasoning development, which positions students for productive STEM-based outcomes

Documenting professional learning focused on implementing high-quality instructional materials in mathematics: the AIM–TRU learning cycle

Abstract Background To increase teachers’ capacity to implement high-quality instructional materials with fidelity in their classrooms through a video-based professional learning cycle, the Analyzing Instruction in Mathematics Using the Teaching for Robust Understanding framework (AIM–TRU) research–practice partnership was formed. Drawing upon the design-based research paradigm, AIM–TRU created the initial design for the professional learning cycle and wanted to engage in continued iterative redesign as the year progressed. This necessitated a method, common among those who adjust their designs when applying them in context, by which to document and justify changes made over time to our model. The research contained in this article used qualitative methods to articulate and test the design underlying our professional learning cycle by advancing conjecture mapping, a device by which the embodiments of the design are made transparent to be analyzed in practice. Results The initial design conjectures and activity structures teachers engaged in through our model of professional learning were refined to address three themes that emerged. Firstly, it was found that the ways participants engaged with the mathematics of the lesson were underwhelming, in large part, because our own definition of what rich talk around mathematics should entail was lacking in details such as the mathematical objects in the lesson, the presence of multiple solution pathways, or the various representations that students could use. Second, talk structures did not always allow for equitable exchanges among all teachers. Finally, activity structures did not encourage teachers to delve deeply into the mathematics so they could perceive the lesson as a coherent piece of their own classroom curriculum. Our design conjectures and activity structures were revised over the course of the year. Conclusions Our use of conjecture mapping allowed us to address the concern with research–practice partnerships that they should develop and utilize tools that make the systemic inquiry they engage in transparent, allowing for other researchers, practitioners, and stakeholders to see the complete design process and make use of the findings for their local context. Implications for this process as a tool for those who pilot and scale professional development are raised and addressed

Supporting Novice Mathematics Teacher Educators Teaching Elementary Mathematics Content Courses for the First Time

In order to be effectively prepared by a teacher education program, prospective elementary teachers (PTs) need to experience high quality mathematics instruction in their mathematics content courses. The instructors of these courses typically consist of individuals (mathematicians and mathematics educators) with ranging experiences, from tenured faculty members to first-year assistant professors or graduate students. This paper explores how to support novice mathematics teacher educators (MTEs) who are teaching elementary content coursework for PTs for the first time. We detail and describe how to implement three systems for supporting novice MTEs: working with a mentor, being provided with educative curriculum materials, and working in a collaborative teaching environment. We close by discussing specific challenges associated with these supports, and call for more institutions to share how they have successfully implemented systems to support novice MTEs

Use of words and visuals in modelling context of annual plant

<p>This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual representations such as flowcharts are used not only in the process to symbolization, but also used in the justification of symbols, (2) some of the visual representations serve as a bridge between the words in the problem context and the symbols that represent the mathematical equations of the number of annual plants and (3) words and context help to introduce visual representations and symbols. Also, once students come up with the visual representations and symbols, they show better understanding about words used in the problem context. These observations imply that the modelling and mathematization process is not just one-directional and linear from words describing real-life situations to the symbols in mathematical equations and expressions. Rather, the mathematization can be promoted through using other visuals that help make this transition smooth by organizing the given information in a way that can be used towards mathematization.</p

Simulating Remote Support for Mathematical Perseverance Through a Digital Sketching Application

This exploratory study showed how a digital sketching application helped keep 4th-grade students engaged with challenging mathematics tasks and support their perseverance to learn mathematics conceptually. The application is currently being developed as a tool based on digital assignments for which students freehand sketch visual representations to solve conceptual fractions tasks. Participants engaged with a simulation of the application and received personalized and conceptual feedback based on their sketching mistakes. Our findings showed that participants were able to leverage such feedback to persevere with the task and make mathematical progress, even at moments when they were most challenged and frustrated