Search

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.

Recent reform efforts state the importance of providing students with opportunities to persevere with challenging mathematics to make meaning. We posit translanguaging practice as a vital option by which Latinx bilingual students can sustain collective perseverance during problem solving. In this paper, we employ a constant-comparative overlay analysis to simultaneously study the discursive translanguaging and perseverance practices of Latinx bilingual students and the corresponding classroom supports. We observed collaborative problem solving in two classrooms of 12th-grade Latinx bilinguals working to make sense of an exponential function and the involvement of the same monolingual English-speaking teacher. Working within similar, supportive classroom environments, we describe how one group of students spontaneously and dialogically leveraged communicative resources to help persevere with in-the-moment obstacles, while another group of students worked together across languages but did not engage in a translanguaging mathematical practice to persevere. We suggest that only establishing a classroom environment conducive for translanguaging and perseverance practice is insufficient and that teachers should not solely rely on students spontaneously engaging in these practices. To complement this environment, we recommend specific teacher moves and scaffolds that could help Latinx bilingual students initiate collaborative translanguaging and support their ongoing perseverance to make meaning of mathematics.

We investigated how the time elementary preservice teachers (PSTs) spent studying certain mathematics topics during teacher education coursework was related to performance on teaching-related tasks administered after graduation. In two studies, participants completed tasks assessing their specialized content knowledge (SCK) for teaching 12 mathematical topics addressed to varying degrees in the preparation program. We found that instructional time was positively associated with SCK demonstrated both immediately postgraduation and 2years later. Several possible confounding factors were assessed; one, entering PSTs' average SCK for topics, appeared to influence the relationship. Accounting for professional learning postgraduation, such as attending professional development, did not change the underlying relationship. Considering these findings, we identify policy implications for the mathematics curriculum of PST education.

Perseverance is vital for the process of learning mathematics with understanding. To do so, students must wrestle with obstacles and amend their problem-solving plan when necessary. I collected qualitative data to investigate the nature of perseverance for 11 ninth-grade algebra students working on a challenging task for which they affirmed interest. Employing analytical frameworks of achievement goal perceptions and subsequent perseverant actions, the findings inform three distinct profiles of in-the-moment perseverance states. These profiles suggest that perseverant actions are not always aligned with students' goals of meaning-making. Although students may report being motivated by building conceptual understanding, they may not fully grasp what it means to achieve such mastery goals. I provide suggestions for teachers to further encourage the development of more perseverant learners.

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.

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-themoment 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.

In the United States, teacher preparation programs are under increased pressure to demonstrate their effectiveness in producing graduates with knowledge, abilities, and competencies to be quality teachers. However, very little research shows this kind of evidence. In a rare exception, Hiebert, Miller, and Berk (2017) found significant positive results of the influences of an elementary teacher education program on graduates' knowledge. Due to the rarity of these kinds of findings, we replicated their analyses with a different cohort of graduates from the same preparation program. Graduates completed a video analysis task correlated with high quality mathematics teaching for topics taught during their program and topics not taught during their program. Our results corroborate theirs, showing that graduates performed better on topics taught during their program versus topics not taught. These findings suggest that teacher education programs can have a significant positive and lasting effect on graduates' knowledge several years after graduation.

This article describes the implementation of a collaborative--competative pedagogy in a Year 10 class and the productive motivational outcomes that followed.

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.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Perseverance, or initiating and sustaining productive struggle in the face of obstacles, promotes making sense of mathematics. Yet, engaging in struggle can be grueling and is avoided by some students, and little is known about if and how student perseverance can improve over time. The purpose of this study was to investigate the effect of scaffolding mathematics tasks on student perseverance over the course of six weeks. The results showed that prompting secondary students to conceptualize a mathematical situation prior to problem-solving can encourage re-initiating and re-sustaining mathematically productive effort upon reaching an impasse. Further, encouraging such conceptualization work often improved students' selection of problem-solving strategies and affect regulation over time, suggesting the malleability of perseverance. For learning mathematics with understanding, these findings suggest supportive learning environments that provide consistent opportunities for students to practice (and improve) their perseverance in problem-solving. • Conceptual thinking scaffolding can help students' perseverance in problem-solving. • Conceptual thinking scaffolding can help improve students' perseverance over time. • Student perseverance in problem-solving is malleable. [ABSTRACT FROM AUTHOR]