skip to main content

This content will become publicly available on February 1, 2023

Title: Teaching Mathematics with Technology: TPACK and Effective Teaching Practices
This paper examines how 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face to face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, TCs, classroom mentor teachers, field experience supervisors, and university faculty formed a Networked Improvement Community (NIC) to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the NIC at the subsequent monthly meeting. The Technology Pedagogical Content Knowledge framework (TPACK) and the TPACK levels rubric were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP2) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs. MCOP2 results indicated that TCs increased their use of effective mathematics teaching practices. However, growth in TPACK was not significant. A relationship between TPACK and MCOP2 was not evident, indicating a potential need for explicit focus on using technology for mathematics conceptual understanding.
Authors:
; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
2013250 2013266 2013256 2013397
Publication Date:
NSF-PAR ID:
10330729
Journal Name:
Education Sciences
Volume:
12
Issue:
2
Page Range or eLocation-ID:
133
ISSN:
2227-7102
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract
    These data are for 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs, who implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face-to-face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, a Networked Improvement Community (NIC) was formed by teacher candidates, classroom mentor teachers, field experience supervisors, and university faculty to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the NIC at the subsequent monthly meeting. The Technology Pedagogical Content Knowledge framework (TPACK) and the TPACK levels rubric (Lyublinskaya & Tournaki, 2011) were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP^2; Gleason, Livers, & Zelkowski, 2015) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs.
  2. 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
  3. Security is a critical aspect in the design, development, and testing of software systems. Due to the increasing need for security-related skills within software systems and engineering, there is a growing demand for these skills to be taught at the university level. A series of 41 security modules was developed to assess the impact of these modules on teaching critical cyber security topics to students. This paper presents the implementation and outcomes of the first set of six security modules in a Freshman level course. This set consists of five modules presented in lectures as well as a sixth module emphasizing encryption and decryption used as the semester project for the course. Each module is a collection of concepts related to cyber security. The individual cyber security concepts are presented with a general description of a security issue to avoid, sample code with the security issue written in the Java programming language, and a second version of the code with an effective solution. The set of these modules was implemented in Computer Science I during the Fall 2019 semester. Incorporating each of the concepts in these modules into lectures depends on both the topic covered and the approach to resolvingmore »the related security issue. Students were introduced to computing concepts related to both the security issue and the appropriate solution to fully grasp the overall concept. After presenting the materials to students, continual review with students is also essential. This reviewal process requires exploring use-cases for the programming mechanisms presented as solutions to the security issues discussed. In addition to the security modules presented in lectures, students were given a hands-on approach to understanding the concepts through Model-Eliciting Activities (MEAs). MEAs are open-ended, problem-solving activities in which groups of three to four students work to solve realistic complex problems in a classroom setting. The semester project related to encryption and decryption was implemented into the course as an MEA. To assess the effectiveness of incorporating security modules with the MEA project into the curriculum of Computer Science I, two sections of the course were used as a control group and a treatment group. The treatment group included the security modules in lectures and the MEA project while the control group did not. To measure the overall effectiveness of incorporating security modules with the MEA project, both the instructor’s effectiveness as well as the student’s attitudes and interest were measured. For instructors, the primary question to address was to what extent do instructors change their attitudes towards student learning and their teaching practices because of the implementation of cyber security modules through MEAs. For students, the primary question to address was how the inclusion of security modules with the MEA project improved their understanding of the course materials and their interests in computer science. After implementing security modules with the MEA project, students showed a better understanding of cyber security concepts and a greater interest in broader computer science concepts. The instructor’s beliefs about teaching, learning, and assessment shifted from teacher-centered to student-centered, during his experience with the security modules and MEA.« less
  4. 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
  5. In 2016, 10 universities launched a Networked Improvement Community (NIC) aimed at increasing the number of scholars from Alliances for Graduate Education and the Professoriate (AGEP) populations entering science, technology, engineering, and mathematics (STEM) faculty careers. NICs bring together stakeholders focused on a common goal to accelerate innovation through structured, ongoing intervention development, implementation, and refinement. We theorized a NIC organizational structure would aid understandings of a complex problem in different contexts and accelerate opportunities to develop and improve interventions to address the problem. A distinctive feature of this NIC is its diverse institutional composition of public and private, predominantly white institutions, a historically Black university, a Hispanic-serving institution, and land grant institutions located across eight states and Washington, DC, United States. NIC members hold different positions within their institutions and have access to varied levers of change. Among the many lessons learned through this community case study, analyzing and addressing failed strategies is as equally important to a healthy NIC as is sharing learning from successful interventions. We initially relied on pre-existing relationships and assumptions about how we would work together, rather than making explicit how the NIC would develop, establish norms, understand common processes, and manage changing relationships.more »We had varied understandings of the depth of campus differences, sometimes resulting in frustrations about the disparate progress on goals. NIC structures require significant engagement with the group, often more intensive than traditional multi-institution organizational structures. They require time to develop and ongoing maintenance in order to advance the work. We continue to reevaluate our model for leadership, climate, diversity, conflict resolution, engagement, decision-making, roles, and data, leading to increased investment in the success of all NIC institutions. Our NIC has evolved from the traditional NIC model to become the Center for the Integration of Research, Teaching and Learning (CIRTL) AGEP NIC model with five key characteristics: (1) A well-specified aim, (2) An understanding of systems, including a variety of contexts and different organizations, (3) A culture and practice of shared leadership and inclusivity, (4) The use of data reflecting different institutional contexts, and (5) The ability to accelerate infrastructure and interventions. We conclude with recommendations for those considering developing a NIC to promote diversity, equity, and inclusion efforts.« less