Research Report #54

Developing Preservice Teachers’ Noticing of Knowledge Bases and Productive Struggle

Shawnda Smith, Texas Woman's University

Abstract

This study examines the development of preservice teachers’ (PSTs) understanding of the connections between teacher actions and use of resources that support productive struggle in a semester-long mathematics content course through video analysis. Our qualitative case study examines 6 PSTs in two sections of a mathematical content course for prospective elementary teachers. The PSTs completed writing assignments analyzing student struggles in video episodes using the Productive Struggle Framework (Author, 2015). The assignments were analyzed, focusing on connections PSTs described between the student struggle(s), interpretation of student thinking, teacher actions, and the teacher’s use of multiple student resources. Findings show that PSTs made frequent connections between student struggles and the teacher actions, but fewer connections between the resources and student struggles or teacher actions. PSTs also viewed the productive level of the struggle episode through a progress-focused or answer-focused lens, and some incorporated teacher actions and resource use into their justifications.

What do AP Calculus teachers believe leads students to be successful in their course?

Veronica Faraci, St. John's University

Abstract

In this case study the opinions of two Advanced Placement (AP) Calculus teachers are being cross examined. After a review of literature and analysis of the interviews in this study, there were many areas of convergence and divergence which leads to an introduction of a non-linear framework; peer support and discourse in the classroom, increased motivation, and ability to apply content to real world situations. In our current educational climate, Science, Technology, Engineering, and Mathematics (STEM) is the buzz term. The STEM pipeline is referenced by my many politicians in order to develop citizens with educational and career qualities to solve the problems that our global world faces. It is essential to research the opinions of practitioners who are positioned in the field in order to understand the data that is manifesting in current research and data collection.
Keywords: AP Calculus, success, STEM career, teacher opinions

Pedagogical Content Knowledge of Statistics: It’s Not Just for Teacher Preparation Programs Anymore

Randall Groth, Salisbury University

Abstract

Pedagogical content knowledge (PCK) is an important part of teacher preparation. PCK helps teachers make subject matter comprehensible to others. However, teachers are not the only ones with this responsibility. During the COVID-19 pandemic, the public needed to understand certain core statistical principles underlying the fight against the pandemic. Those in government, social media, medicine, and the news were given public platforms that could be used to foster such understanding. Unfortunately, there were several missed opportunities to help the public develop and act on this understanding. Three specific missed opportunities are analyzed. They deal with the statistics subject matter of experimental study design, univariate distributions, and big data analysis algorithms. Collectively, the examples suggest that PCK in statistics should not be considered solely a component of teacher preparation. Those responsible for communicating public health messages need to be able to make statistical principles comprehensible to a broad audience as well.

Jan 27, 2022 07:00 PM : Becoming a Teacher of Mathematical Modeling, Grades 6–12

As we think about our role in education, we take to heart our responsibility to use education to leave the world better than we found it. In our work, we have come to realize that mathematical modeling inherently provides opportunities for access, equity, and empowerment for every student, and we see in teaching mathematical modeling the opportunity to teach empathetic critical thinking skills. Modeling is a way for students—human beings—to use their mathematical skills in examining different solutions to authentic problems based on different perspectives. Because students bring their own knowledge and perspectives to a modeling problem, it is likely that the modeling process will unfold in different ways for different problems. To help navigate this complexity, we ground our conceptualization of modeling in four big ideas that underpin the classroom practice of mathematical modeling. In this session, we will discuss these four big ideas and explore examples of how they play out in grade 6-12 classroom settings, focusing on how empathy, as a practice, can and should be cultivated in students’ mathematical modeling.