skip to main content

This content will become publicly available on January 1, 2023

Title: Systemic coherence through a shared vision of mathematics instruction. Proceedings of the 49th Annual Meeting of the Research Council on Mathematics Learning, 2-11.
Recent research on instructional vision offers new insights into the challenges of systemic coherence when implementing educational innovations at scale. In this paper, we retrospectively examine the work of our statewide partnership of mathematics education leaders for implementing new state mathematics standards. we identify three categories of designs that improved coherence during implementation and highlight the role of instructional vision in each.
Authors:
; ; ; ;
Editors:
Bateiha, S.; Cobbs, G.
Award ID(s):
2100895
Publication Date:
NSF-PAR ID:
10336162
Journal Name:
Proceedings of the 49th Annual Meeting of the Research Council on Mathematics Learning
Page Range or eLocation-ID:
2-11
Sponsoring Org:
National Science Foundation
More Like this
  1. Undergraduate research is increasingly prevalent in many fields of study, but it is not yet widespread in mathematics education. We argue that expanding undergraduate research opportunities in mathematics education would be beneficial to the field. Such opportunities can be impactful as either extracurricular or course-embedded experiences. To help readers envision directions for undergraduate research experiences in mathematics education with prospective teachers, we describe a model built on a design-based research paradigm. The model engages pairs of prospective teachers in working with faculty mentors to design instructional sequences and test the extent to which they support children’s learning. Undergraduates learn about the nature of systematic mathematics education research and how careful analyses of classroom data can guide practice. Mentors gain opportunities to pursue their personal research interests while guiding undergraduate pairs. We explain how implementing the core cycle of the model, whether on a small or large scale, can help teachers make instructional decisions that are based on rich, qualitative classroom data.
  2. This research paper studies the challenges that mathematics faculty and graduate teaching assistants (GTAs) faced when moving active and collaborative calculus courses from in-person to virtual instruction. As part of a larger pedagogical change project (described below), the math department at a public Research-1 university began transitioning pre-calculus and calculus courses to an active and collaborative learning (ACL) format in Fall 2019. The change began with the introduction of collaborative worksheets in recitations which were led by GTAs and supported by undergraduate learning assistants (LAs). Students recitation periods collaboratively solving the worksheet problems on whiteboards. When COVID-19 forced the rapid transition to online teaching, these ACL efforts faced an array of challenges. Faculty and GTA reflections on the changes to teaching and learning provide insight into how instructional staff can be supported in implementing ACL across various modes of instruction. The calculus teaching change efforts discussed in this paper are part of an NSF-supported project that aims to make ACL the default method of instruction in highly enrolled gateway STEM courses across the institution. The theoretical framework for the project builds on existing work on grassroots change in higher education (Kezar and Lester, 2011) to study the effect of communitiesmore »of practice on changing teaching culture. The project uses course-based communities of practice (Wenger, 1999) that include instructors, GTAs, and LAs working together to design and enact teaching change in the targeted courses alongside ongoing professional development for GTAs and LAs. Six faculty and five GTAs involved in the teaching change effort in mathematics were interviewed after the Spring 2020 semester ended. Interview questions focused on faculty and GTA experiences implementing active learning after the rapid transition to online teaching. A grounded coding scheme was used to identify common themes in the challenges faced by instructors and GTAs as they moved online and in the impacts of technology, LA support, and the department community of practice on the move to online teaching. Technology, including both access and capabilities, emerged as a common barrier to student engagement. A particular barrier was students’ reluctance to share video or participate orally in sessions that were being recorded, making group work more difficult than it had been in a physical classroom. In addition, most students lacked access to a tablet for freehand writing, presenting a significant hurdle for sharing mathematical notation when physical whiteboards were no longer an option. These challenges point to the importance of incorporating flexibility in active learning implementation and in the professional development that supports teaching changes toward active learning, since what is conceived for a collaborative physical classroom may be implemented in a much different environment. The full paper will present a detailed analysis of the data to better understand how faculty and GTA experiences in the transition to online delivery can inform planning and professional development as the larger institutional change effort moves forward both in mathematics and in other STEM fields.« less
  3. Graziana, K. (Ed.)
    In the current climate of a technology-centered world and standards-based educational system, the vision of including computer science and computational thinking at the elementary level has gained momentum in recent years. This paper examines the similarities between elementary mathematics and computer science content standards and practices, and describes a hands-on, visual coding curriculum that allows teachers to integrate the two into mathematics instruction that meets the requirements of the standards using research based instructional strategies.
  4. The purpose of this report is to share a conceptual model useful in the design of professional learning about teaching for university mathematics faculty. The model is illustrated by examples from a particular design effort: the development of an online shortcourse for faculty new to teaching mathematics courses for prospective primary school teachers. How novice mathematics teacher educators grow as instructors is an emerging area of research and development in the United States. At the same time, it is well established that effective instructional design of any course, including a course for faculty, requires breadth first: understanding and anticipating the needs of the learner. Therefore, given the sparse knowledge base in the new arena of mathematics teacher educator professional growth, effective design requires leveraging the scant existing research while also exploring and iteratively refining broad goals and objectives for faculty learning. Only after a conceptual foundation is articulated for what is to be learned and what will constitute evidence of learning, can cycles of design productively examine and test-bed particular course features such as lesson content, structures (like scope and sequence), and processes (like communication and evaluation). In the example used in this report, several researchbased perspectives on learning in/for/aboutmore »teaching guided design goals and short-course objectives. These valued perspectives informed creation and prioritization of principles for short-course design which, in turn, informed evaluation of faculty learning. With these conceptual foundations in place, design of lessons to realize the goals, principles, and objectives rapidly followed. The work reported here contributes to the knowledge base in two ways: (1) it addresses faculty professional development directly by describing and illustrating a model for supporting instructional improvement and (2) it provides metanarrative to scaffold the professional growth of those who design professional learning opportunities for post-secondary mathematics faculty.« less
  5. Recent studies have shown that US high school students are not as prolific as other countries in terms of their performance in mathematics. One of the most effective solutions can be a change in the way mathematics subjects is taught in high school. The NSF-funded “Understanding How Integrated Computational Thinking, Engineering Design, and Mathematics Can Help Students Solve Scientific and Technical Problems in Career Technical Education (INITIATE) project is a collaboration of The University of Toledo and high schools in Toledo that aims to improve mathematics teaching. Project-based learning (PBL) and integrating math with career technology education (CTE) have been established as efficient ways to improve high school students’ understanding of mathematics. Nevertheless, implementation of new ways of teaching is not always easy for the teachers, and many factors may inhibit the teachers from implementing PBL methods. This research analyzes common concerns teachers experienced regarding enacting new teaching methodologies in their classroom. The Stages of Concern Questionnaire (SoCQ) was used to measure the teachers’ perceptions of and comfort with implementing computational thinking (CT) concepts PBL lessons. Possible relationships between teachers’ SoCQ CBAM score and other variables such as their understanding of PBL and CTE are examined and discussed.