Mathematics Methods Course Research Articles

Implementing Equitable Practice-Based Teacher Education to Advance Rural STEM Teacher Candidates’ Pedagogical and Content Knowledge

This longitudinal three-year study explored implementation of practice-based teacher preparation incorporating high-leverage teaching practices to advance PCK. Participants included teacher candidates (n = 45) who completed elementary science and mathematics methods courses at a rural Midwestern university. Students engaged in teaching rehearsals to explore STEM concepts and equitable teaching practices. Data from surveys and student reflections revealed an increase in teacher candidates' perceptions of their knowledge and competence of teaching science and math content equitably.

Implementing Equitable Practice-Based Teacher Education to Advance Rural STEM Teacher Candidates’ Pedagogical and Content Knowledge

This longitudinal three-year study explored implementation of practice-based teacher preparation incorporating high-leverage teaching practices to advance PCK. Participants included teacher candidates (n = 45) who completed elementary science and mathematics methods courses at a rural Midwestern university. Students engaged in teaching rehearsals to explore STEM concepts and equitable teaching practices. Data from surveys and student reflections revealed an increase in teacher candidates' perceptions of their knowledge and competence of teaching science and math content equitably.

An examination of the development of a secondary mathematics preservice teacher's use of effective questioning

AbstractThis case study explores how one secondary mathematics preservice teacher develops his use of questioning for instruction over the course of a year. The article explores how experiences in a secondary mathematics methods course and student teaching provide opportunities for the preservice teacher to use questioning to elicit, interpret, and respond to student thinking. Using classroom activities, plan‐teach‐reflect cycles of instruction, and recordings and transcripts of instructed lessons, the preservice teacher creates, revises, and reflects on his use of questioning over the year. The study shows that preservice teachers can improve their questioning to help elicit, interpret, and respond to student thinking.

Facilitating Productive Struggle in an Online Secondary Education Mathematics Methods Course: Experiences of Pre-Service Teachers

This research investigated preservice teachers’ (PSTs) experiences with productive struggle in an online environment, and how it influenced their pedagogical knowledge. This action research study reports on secondary mathematics pre-service teachers (PSTs) who completed mathematical tasks in weekly synchronous Zoom sessions to develop their understanding of productive struggle. Vygotsky’s (1978) Social Constructivist Theory and the growth mindset framework (Boaler, 2016; Dweck 2006; 2008) provided the lenses through which the research was designed and analyzed. Findings show that presenting opportunities for PSTs to experience productive struggle informs their pedagogical practice, and that providing this experience in an online environment is possible. PSTs gained an increased understanding of the importance of collaborative work, asking purposeful questions, and the alignment between productive struggle and improved mathematical understanding.

Preparing Elementary Preservice Teachers for Antiracist Mathematics Teaching

I describe a unit on antiracist mathematics teaching I developed and implemented in an elementary mathematics methods course. It may serve as an example to other mathematics teacher educators on how to incorporate antiracist mathematics teaching in their courses. I report on the unit's components, its impact on the preservice teachers in my course, my reflections about the unit (including possible modifications), and implications for other mathematics teacher educators.

Demystifying math myths: Examining rules that expire

AbstractIn our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' (Teaching Children Mathematics, 21(1), 18–25) “13 Rules That Expire” article has been a useful resource for us to highlight and challenge students' mathematical misconceptions. In this article, we share the components of an iteratively developed assignment focused on the 13 rules article. We detail how students explored the “lives” of these rules and investigated alternatives to pervasive mathematics shortcuts and tricks. We posit that our intentionally designed assignment provides an opportunity for students to think critically about their views, beliefs, and misconceptions, which encourages a mindset for preservice teachers to consider the kinds of mathematical misconceptions they will encounter in their classroom teaching. We anticipate that sharing this developed assignment with other mathematics teacher educators could provide opportunities for additional adaptations in unique contexts and continued improvements to support future teachers.

An exploratory mixed methods study about teacher candidates’ descriptions of children’s confusion, productive struggle, and mistakes in an elementary mathematics methods course

Recognizing and describing children's mathematical thinking in humanizing ways, especially when students engage in confusion, productive struggle, and mistakes, is a complex and challenging process. This paper describes an exploratory, mixed-methods study about how elementary teacher candidates (TCs) describe children's thinking as a right to exercise and to value their humanity when learning mathematics. The study analyzed transcripts from 64 TCs' summative assessments, which consisted of mock parent-teacher conferences (MPTC). Findings suggest that TCs described children's confusion, productive struggle, and mistakes (RotL 1 and 2) as: a teacher's observation, an opportunity for students to correct or clarify their thinking, an opportunity for teachers to adjust instruction or provide support, and as a normal part of the learning process. More importantly, some TCs reassured children that learners have fundamental rights when learning mathematics, especially when feeling confused and claiming a mistake. Implications for research and teacher education are discussed. Keywords: Elementary, teacher education, mathematics, mixed methods, rehumanizing, Torres’ rights of the learner

Enacting multilingual learner core practices: a PST’s approximations of practice of mathematics language routines

AbstractThis study considered a preservice teacher’s (PST’s) attention to multilingual learner core practices within her approximations of practice of mathematics language routines during a secondary mathematics methods course. We used a framework of approximations of practice to understand how a PST enacted and developed an understanding of multilingual learner core practices. To provide a vision for what multilingual learner core practices can look like in nontraditional instructional contexts, we qualitatively analyzed four approximations of practice of mathematics language routines from a single PST during a single semester of a methods course. We share how she navigated the remote teaching context and engaged sample students in all of the multilingual learner core practices despite the challenges of the COVID-19 pandemic, providing an example of what these practices may look like in remote instruction. We also discuss how these multilingual learner core practices interact and complement one another. We consider possible implications, limitations, and future research directions.

Grades or No Grades? Promoting Deeper Learning in a Middle Level Mathematics Methods Course

This action research investigated pre-service teachers (PSTs) experiences with ungrading practices in a mathematics methods course designed for middle level PSTs (grades 4-8). This study analyzed archival data through the lenses of pedagogical content knowledge, growth mindset, and self-efficacy to investigate how PSTs’ experiences with the process of ungrading supported their development of pedagogical content knowledge. Throughout the course, verbal feedback was provided during class discourse and the interactive lectures and written feedback was provided for all submitted assignments. The feedback provided was both positive and constructive in nature. Based on the assignment or activity, constructive feedback was either provided to improve future work submissions or for a revise and resubmit of the current assignment. The findings provide evidence that the process of ungrading can be beneficial to learning. Ungrading supported PSTs by teaching them how to grow from the feedback provided and to reflect on their learning throughout the semester. The PSTs developed and improved their pedagogical content knowledge through the processes of revision and reflection. Ungrading is a process that takes more planning, support, and time, but the outcome is well worth the effort.

The landscape of US elementary mathematics teacher education: course requirements for mathematics content and methods

AbstractThe adequate preparation of future teachers of mathematics is critical, requiring sufficient opportunities to develop both pedagogical skill and content knowledge. Yet, despite new recommendations for mathematics teacher preparation, we know little about the landscape of course-based learning opportunities in US elementary teacher education programs. To what extent do US elementary teacher education programs meet the Standards for Preparing Teachers of Mathematics outlined by the Association of Mathematics Teacher Educators (AMTE) for mathematics content and methods courses? Based on an a priori power analysis, we gathered a random sample of 291 higher education institutions. Within these institutions, we analyzed 736 programs, including Bachelor’s, Master’s, and Credential programs. We found that overwhelmingly US elementary teacher education programs do not meet the aspirations outlined in the AMTE standards, with Master’s and Credential programs and those covering all elementary grades particularly falling short. Potential explanations for these challenges and implications for teacher education program design are discussed.

Engaging Preservice Teachers with Equity-Related Cases to Make Visible the Inequities in Mathematics Teaching

ABSTRACT Reform in teacher education seeks to engage preservice teachers (PSTs) in authentic classroom situations that explore equitable practices by connecting theory to professional practice. One way for PSTs to examine how equity and inequity operate in schools is with the aid of equity-related case-based instruction. This study reports on mathematics teacher educators using equity-related cases in their mathematics methods courses to encourage critical reflection on the various ways inequitable practices can create invisible barriers that have disenfranchised marginalized students from learning mathematics. Two cases are reviewed that were designed to prompt PSTs to examine implicit biases and school policies that reaffirm systemic inequities in mathematics education. Findings detail how mathematics teacher educators and PSTs used the cases to prompt PSTs to recognize and respond to inequitable practices in mathematics teaching. Particular attention is drawn to how PSTs made educational inequities visible, critiquing teachers’ assumptions and examining how such assumptions impact instructional decision-making. This study offers recommendations and a planning tool for designing and using similar equity-related cases in teacher education to strengthen professional practice that challenges and disrupts unjust beliefs that sustain educational inequities.

Mathematical Modeling Through the Eyes of Elementary and Middle Preservice Teachers

Mathematical modeling is a useful pedagogy in mathematics education, but preservice teachers (PSTs) conceptualization of the teaching and learning of modeling practices is an ongoing concern. This research study examined 31 elementary and middle grades PSTs’ conceptualization of mathematical modeling and their experiences with such modeling. The study participants were recruited from two, four-year university mathematics methods courses located in northeastern and midwestern United States. Data for this study was collected through a questionnaire and analyzed using qualitative and quantitative methods. Results indicated that most of the PSTs had little understanding of the intersection of mathematical modeling, and the teaching and learning of mathematics. As such, many perceived mathematical modeling as an exclusive action reserved for teachers. Additionally, the results revealed that most participants had minimal, if any, experience with mathematical modeling. These limited experiences portrayed mathematical modeling as a show and tell method or step-by-step explanation. Our results expand the inadequate research into elementary and middle grades PSTs’ knowledge of and experiences in mathematical modeling and warrant the exigency for the inclusion of extensive mathematical modeling practices into methods and content courses for PSTs. The directions for future research and implications for researchers and teacher education programs are also discussed.

Developing preservice teachers intuitions about computational thinking in a mathematics and science methods course

Developing preservice teachers intuitions about computational thinking in a mathematics and science methods course

When Only White Students Talk: EQUIP-ing Prospective Teachers to Notice Inequitable Participation

We introduce a teacher learning practice called EQUIP-ing, which aims to foster sociopolitical noticing by leveraging EQUIP, an equity-oriented classroom observation tool. We detail our iterations of EQUIP-ing to a field-based Number Talk experience in a secondary mathematics methods course with 25 White prospective teachers (PTs). We offer empirical accounts of how EQUIP-ing empowered PTs to connect their teaching practices with racialized and gendered patterns of student participation; as a result, PTs began to reconsider taken-for-granted practices. However, we also found that PTs demonstrated potentially detrimental ways of attributing marginalizing patterns to minoritized students without actionable plans to redress the inequity. We conclude by inviting mathematics teacher educators to apply EQUIP-ing while emphasizing purposeful support for asset-based noticing.

Exploring how writing-to-learn in a mathematics methods course influences preservice teachers’ beliefs

Despite research demonstrating positive effects of writing on student achievement, writing-to-learn remains under-utilised in mathematics and mathematics teacher education. In this paper, we explore how writing-to-learn tasks in a mathematics methods course influenced elementary preservice teachers’ beliefs about teaching in two domains: mathematics and writing. Preservice teachers engaged in weekly writing-to-learn tasks designed to support their understanding of mathematics content and mathematics pedagogy over the course of a semester. Using survey data, we found no significant difference in their beliefs from pre to post. Such null findings led us to ask new qualitative questions, resulting in a concurrent mixed methods design. Through qualitative analyses of student writing, we found several meaningful and non-meaningful practices for engaging in writing-to-learn tasks. This research supports teacher educators, teachers, and researchers to understand how to implement writing-to-learn tasks and to support students towards meaningful engagement in the tasks.

Investigating the Effects of Integration on the Development of Mathematical Knowledge for Teaching: A Case of Pre-Service Teachers in the Colleges of Education in Ghana amidst Curriculum Changes

The study examined the effects of integration on the development of Mathematical Knowledge for Teaching (MKT) among pre-service teachers while enrolled in a math program at the colleges of education in Ghana in the face of the new curriculum. In all, two hundred and forty-seven (247) pre-service teachers (PSTs) were sampled for the study. The experimental group comprised one hundred and thirty (130) PSTs who were taught both Mathematics content and method courses in an integrated manner, while the control group, comprised of one hundred and seventeen (117) PSTs, was taught Mathematics content and method courses separately. The non-equivalent static-group comparison design was used for the study. Both groups of PSTs were post-tested after they had received instruction in mathematics courses up to the point where they were ready to go for their macro teaching (Off Campus Teaching Practice) to compare their achievements in terms of their mathematical knowledge for teaching. Analysis of data using the independent sample t-test revealed that the control group had a mean score lower than the experimental group, and the standard deviation showed that the scores of the control group were far from their mean score. That is, the scores of the control group were more heterogeneous than that of the experimental group. The experimental group scored higher than the control group on the post-test, and their scores were more homogeneous than the control group. At a significant level of 0.05, there was a statistically significant difference between the means of the two groups on the post-test. With a mean difference of 5.042, the experimental group performed better than the control group on the post-test. Hence, the students in the experimental group turned out to achieve better on MKT components than the students in the control group. It was recommended, among others, that the use of the integrated approach in the teaching and learning of Mathematics should be encouraged, monitored, and supported throughout the Colleges of Education in Ghana.

The Perspective of the Mathematics Teacher Educator on the Design of Mathematics Teaching Method Courses for Elementary Teacher Candidates

This study examines the perspective of a mathematics teacher educator (MTE) regarding the design and structuring of mathematics teaching method course in the elementary teaching education program. The research was designed as a single case study. The case was a teacher educator who has been delivering mathematics methods course for elementary teacher candidates for 10 years. The data were collected through an in-depth interview on items placed in a questionnaire. The thematic analysis method was used for data analysis. The focus of our analysis is on MTE's perspective as a course designer and practitioner for the mathematics teaching method course. Our findings show that this course has a nature in design and structuring and that the teacher trainer builds on these four arguments, namely value judgments, resources, big ideas, and professed practices while supporting the mathematics teaching development of prospective elementary teachers. Based on the findings, we discuss the interactions among these four arguments. In addition, it is examined whether there is a perspective in the design and structuring of the mathematics teaching course among teacher educators who deliver this course.

Pre-Service Teachers' Discourse Moves During Whole Class Mathematical Discussions: An Analysis and Proposed Framework

Learning to facilitate whole-class mathematical discussions is a complex task. Teachers must become adept at using discourse moves to elicit and extend student thinking and move discussions towards a mathematical point. Practice-based mathematics methods courses give pre-service teachers opportunities to rehearse these moves in a controlled setting. Providing opportunities for practice, often called rehearsals or approximations of practice, have been shown to be effective at developing pre-service teachers' abilities to use discourse moves, but we still do not have a clear understanding of the types of discourse moves pre-service teachers use during discussions or how these moves change over the course of a discussion. In this article, we analyze. whole-class discussions facilitated by pre-service teachers to determine the types of discourse moves used as the discussion progresses. Based on this data and relevant literature, we propose a framework for the structure of whole-class mathematical discussions.

Using virtual classroom simulations in a mathematics methods course to develop pre‐service primary mathematics teachers' noticing skills

AbstractThis study proposed a low‐cost, easy to set up and easy to modify virtual classroom simulation environment, CartoonClass, and tested its impact on 27 pre‐service primary school teachers' noticing development during a semester‐long mathematics methods course. The participants' perceptions of using CartoonClass were also examined. A Wilcoxon signed‐rank test of the pre‐test and post‐test results showed that the participants (1) significantly developed their noticing skills, with regard to both general classroom events and attending‐to skills; and (2) significantly changed their focus on ‘mathematics thinking,’ an accepted indicator of better noticing skills. (3) However, a novel video‐summarising task aimed at detecting the participants' skills to quickly notice and grasp a complex teaching situation found no significant change in such ability over the course of the experiment. On the other hand, the qualitative data analysis showed the participants had positive perceptions of the virtual environment regarding realism, enjoyment and effectiveness. Practitioner notesWhat is already known about this topic Using virtual classroom simulations can improve pre‐service teachers' expertise, but teacher educators need a low‐cost virtual environment that can be easily used in their own classrooms. Our understanding of using classroom simulations to improve teacher noticing is still limited. Using animation‐based assessment in teacher noticing is meaningful. Examining teacher noticing relies much on written reflections of watching videos but developing different types of tasks is critical. What this paper adds This study provided an economical and easy way to build a virtual classroom environment. Compared with previous classroom simulation studies, this study used a more structured instrument to examine pre‐service teachers' noticing performance. A novel task (write a full‐video outline with a short time watching) was created to examine teachers' noticing skills in quickly recognising a classroom situation. Implications for practice and/or policy The two types of questions (general and specific) in assessing teacher noticing yielded different results that may provide valuable insights for future research on this topic. As our pre‐service teachers developed only basic noticing skills (ie, attending‐to), we suggest that teacher educators should be provided with more intensive training in teacher noticing. Developing only attending‐to skills may be not sufficient for quickly recognising a classroom situation.

How Preservice Teachers Learn through a Pedagogy of Enactment in a Middle School Mathematics Methods Course

Concerns about the disconnect between what goes on in teacher preparation programs and school classrooms have led to a greater emphasis on opportunities for preservice teachers to engage in the practice of teaching during their teacher education programs. Pedagogies of enactment have been shown to provide opportunities for preservice teachers to enact teaching practices and to learn from that enactment. However, little is known about how preservice teachers learn from pedagogies of enactment. This study examines how preservice teachers learn through the implementation of a pedagogy of enactment, the Bellringer Sequence, in the context of a middle school mathematics methods course. The results of the study show that preservice teacher learning takes place through rich generative conversation centered on preservice teachers’ contributions and collaboratively negotiated interactions with those contributions. The study identified communication that prompted learning (learning prompts), 16 speech events that characterized conversation in the learning prompts, and three stages of learning in the learning prompts—Initiation, Precisification, and Equilibration. The study provides insight into how preservice teacher learning can be supported through intentional use of pedagogies of enactment.