Comparing the Mathematical Practices Pre-Service Teachers and Mathematics Teacher Educators Identified as Relevant to Problems and Tasks

Abstract

In the U.S., state adopted or developed college- and career-ready mathematics standards, including the Common Core State Standards for Mathematics, not only impact districts, students, and their teachers, but also university teacher preparation programs. In order to attain and sustain Common Core’s vision of developing mathematically competent citizens, teacher preparation programs must support pre-service teachers’ development of practical conceptions of the Standards for Mathematical Practice. In this article, we examine the mathematical practices middle grades pre-service teachers (grades 4-9 licensure) and mathematics teacher educators identified as playing a role in attempts to make sense of and work toward solutions to mathematics problems. In addition, we compare the mathematical practices indicated both within and across pre-service teachers and mathematics teacher educators. Results identify pre-service teachers’ potential difficulties operationalizing six specific mathematical habits of mind. Finally, we describe how such comparisons can guide the design of future teacher education and professional learning by describing a process for identifying problems and tasks with the greatest potential to support pre-service teachers’ development of practical conceptions of mathematics or other content-specific habits of mind.

Mathematics teachers’ awareness of effective teaching practices: A comparative study

“…For example, Diletti (2017) pointed out that an effective teacher must possess many teaching practices, namely, facilitating dialog and discussion among students so that they have multiple opportunities to express their ideas, enhancing students' expression in solving mathematical problems, teaching students to appreciate the ideas of their colleagues, and helping students think and infer through realistic learning. Courtney and Caniglia's (2021) study recommended the importance of training mathematics teachers before and during service on effective teaching practices in practical, applied ways to improve their students' mathematical concepts, skills, and thinking habits.…”

“…It was also suggested to rethink the partnership between teaching staff and the school to select cooperative teachers and develop them professionally. Courtney and Caniglia (2021) also highlight the importance of giving mathematics teachers training in effective teaching practices both pre-and during service in a practical way to enable them to develop and enhance their students' mathematics skills and habits of mind.…”