Elementary Mathematics Methods 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.

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.

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

Proofs of Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture and Goldbach Conjecture

In this article the elementary mathematical methods are used to prove Beal’s Conjecture, Fermat’s Conjecture, Collatz Conjecture and Goldbach Conjecture.

Design Principles That Support Course Design Innovation for Elementary Mathematics Methods Courses

Learning to teach mathematics is a complex endeavor, requiring sustained focus and time. Yet time is especially scarce in elementary teacher education programs, where preservice teachers (PSTs) learn all content areas. Through a collaborative self-study, five teacher educators identified three time-related tensions in elementary mathematics methods courses: (a) teaching mathematics content and pedagogy; (b) connecting theory and practice; and (c) promoting social contexts in teaching mathematics. To address these tensions, we offer three design principles and illustrative examples: (a) addressing multiple goals for each course component; (b) developing PSTs’ dispositions over time; and (c) building on PSTs’ strengths to develop understanding of mathematics. We present a reflection tool to assist matsshematics teacher educators in designing their courses to maximize their instructional time.

Technology-Immune/Technology-Enabled Problem Solving as Agency of Design-Based Mathematics Education

The paper is written as a reflection on the author’s online teaching of a graduate elementary mathematics content and methods course through the asynchronous modality. The need for developing skills in posing problems that integrate non-technological and technological problem-solving strategies is emphasized. Such problems are considered agency of design-based mathematics education. The importance of revealing hidden mathematical ideas stemming from teacher candidates’ willingness to explore self-posed problems within the forum components of the course is discussed. Using these hidden ideas, the paper demonstrates connectivity among different mathematical concepts including historical connections. Teacher candidates’ reflections on the course have been included and reviewed.

Language Demands Tool: Attuning Prospective Teachers’ Vision to the Role of Language in Mathematics Education

Mathematics standards and practices highlight the vital role that language plays in mathematics education. However, there remains a common misconception that mathematics is somehow language-free or less linguistically demanding than other content areas. This qualitative study describes an intervention implemented in six elementary mathematics methods courses. The intervention was designed to attune prospective teachers’ noticing to the language modalities and supports in mathematics teaching and learning. The intervention began with an observation tool that prospective teachers completed in their field placement classrooms. This article classifies prospective teachers’ noticings and explicates how these noticing became a pedagogical catalyst for further learning and discussion in subsequent mathematics methods classes.

Using Wolfram Alpha with Elementary Teacher Candidates: From More Than One Correct Answer to More Than One Correct Solution

The paper is a reflection on the author’s work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the diversity of mathematical ideas behind a contextual question asked by a second-grade pupil allowing for multiple solution strategies to be used in addressing the question. The second issue deals with the use of Wolfram Alpha in aiding different mathematical features of this demonstration. The paper is congruous with mathematics teaching standards used across six continents and illustrated by reflective comments of the author’s students regarding their mathematics teacher education experiences. Teaching ideas shared in the paper may be of interest to instructors who want to explore elementary mathematics in depth with teacher candidates.

Changes in Pre-service Teachers’ Noticing Through an Elementary Mathematics Methods Course Combining Theory and Practice

The purpose of this study was to analyze the changes in pre-service teachers’ noticing through an elementary mathematics methods course along with a practicum. For this purpose, the comments pre-service teachers made on an entire video-based mathematics lesson were collected three times over the semester. Their comments were analyzed in terms of topic, actor, stance, evidence, and alternative strategy. The results showed that the pre-service teachers’ noticing abilities were slightly changed after learning mathematical content and pedagogy related to teaching elementary mathematics. Substantial changes in their noticing occurred after a four-week practicum and subsequent discussions on their own lesson planning, implementation, and reflections. This study has implications for designing a mathematics methods course to develop teacher expertise and refining a teacher noticing analytic framework.

Connecting engineering design and inquiry cycles: Impact on elementary preservice teachers' engineering efficacy and perspectives toward teaching engineering

AbstractEngineering has become increasingly prominent in science education, with documents such as Next Generation Science Standards detailing the importance of introducing students at all grade levels to science and engineering practices. Yet, many elementary teachers may lack sufficient engineering content and pedagogical knowledge and report feeling unprepared to teach engineering content and processes. To prepare future elementary teachers to teach engineering, two university faculty members in science and mathematics education designed an engineering unit that was incorporated within an elementary science methods course and supported through an elementary mathematics methods course. This unit focused on the engineering design process as well as connections between the work of scientists and engineers; the processes of science, engineering, and mathematics; and the cycles of engineering design and inquiry. The results of the study provide evidence that the unit had a positive influence on the 27 preservice teacher participants’ engineering teaching efficacy, understanding of engineering, and comprehension of the implementation of engineering in the elementary classroom.

Exploring White Preservice Mathematics Teachers' Racial Identity and Culturally Relevant Teaching Practices

The purpose of this study was to examine what factors affect the construction of preservice white mathematics teachers’ racial identities and the relationship between their racial identities and Culturally Relevant Teaching (CRT) practices. We examined five white female preservice teachers who enrolled in an elementary mathematics methods course at a private university in the US. We collected data consisting of lesson plans, semi-structured interviews, and reflection of a taught lesson in the 2018 fall term and examined them using qualitative research methods. We found that preservice teachers’ racial identities were affected by their backgrounds, K-12 school experiences, and practicum school environment. We also found a relationship between teachers’ sensitivity to racial issues and their endorsement of CRT strategies. The findings also revealed that the relationships were mediated by practicum school contexts. Based on the findings, we provided practical implications for the teacher education programs.

One university’s story on teacher preparation in elementary mathematics: examining opportunities to learn

This multi-case study examines how three elementary mathematics methods instructors, in the same teacher education program, provide their prospective teachers with learning opportunities. Qualitative data were collected through interviews, classroom observations, and artifacts. The findings suggest that the instructors’ beliefs associated with teaching philosophies influence both the content that prospective teachers have the opportunity to learn (what) and the nature of the prospective teachers’ opportunities to learn (how). Through analytic induction, three assertions were developed to understand and explicate: similarities in opportunities to learn, differences in opportunities to learn, and perceptions about the purpose of the methods courses across the three cases. Specifically, the first assertion examines how all three methods instructors focused on developing conceptual understanding and combating mathematical misconceptions for which prospective teachers most often experience opportunities to learn through representations and approximations. The second and third assertions place more emphasis on differences across the cases based upon observed instructor actions and their beliefs. This study is significant because it helps us gain a deeper understanding about prospective teachers’ opportunities to learn within one teacher education program, and therefore, may point toward what can be done in the future to better prepare teachers in elementary mathematics education and the development of ambitious instruction. Additionally, this study unpacks how prospective teachers in the same teacher education program may have varying experiences and thus varied access to opportunities to learn.

The impact of integrated STEM modeling on elementary preservice teachers’ self‐efficacy for integrated STEM instruction: A co‐teaching approach

AbstractThe purpose of the current study was to evaluate the impact of co‐taught integrated STEM methods instruction on preservice elementary teachers’ self‐efficacy for teaching science and mathematics within an integrated STEM framework. Two instructional methods courses (Elementary Mathematics Methods and Elementary Science Methods) were redesigned to include STEM integration components, including STEM model lessons co‐taught by a mathematics and science educator, as well as a special education colleague. Quantitative data were gathered at three time points in the semester (beginning, middle, and end) from 55 preservice teachers examining teacher self‐efficacy for integrated STEM teaching. Qualitative data were gathered from a purposeful sample of seven preservice teachers to further understand preservice teachers’ perceptions on delivering integrated STEM instruction in an elementary setting. Quantitative results showed a significant increase in teacher self‐efficacy across all three time points. Item‐level analysis revealed that self‐efficacy for tasks involving engineering and assessment (both formative and summative) were low across time points, while self‐efficacy for tasks involving technology and flexibility were consistently high. Qualitative results revealed that the preservice teachers did not feel adequately prepared by university‐level science and mathematics courses, in terms of content knowledge and integration of science and mathematics for elementary students.

Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom

This study highlighted the characteristics and patterns of preservice teachers’ informal formative assessment conversations woven into mathematics classrooms. Participants were four preservice teachers from an elementary mathematics methods course whose videotaped lessons were analyzed using an analytic framework based on Initiation, Response and Follow-up (IRF) sequences. Findings indicated that the patterns of IRF sequence were varied across the preservice teachers, although they taught the same topic. We also found common patterns in their IRF sequences in that preservice teachers mainly initiated and drove classroom conversations of mathematics, while students’ roles were passive. In addition, they used frequent follow-up questions; however, most of them were closed questions intended to guide students to quickly give correct responses. Regarding feedback, their feedback were mostly made to affirm or elaborate on what students said or to clarify meanings of statements, not to explore students’ initial ideas or reasoning processes.

Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes

Teaching geometry at the elementary level is challenging. This study examines the impact of van Hiele theory-based instructional activities embedded into an elementary mathematics methods course on preservice teachers’ geometry knowledge for teaching. Pre- and post-assessment data from 111 elementary preservice teachers revealed that van Hiele theory-based instruction can be effective in improving three strands of participants’ geometry knowledge for teaching: geometry content knowledge, knowledge of students’ van Hiele levels, and knowledge of geometry instructional activities. As a result, this paper offers implications for teacher educators and policy makers to better prepare elementary preservice teachers with geometry knowledge for teaching.

Reflecting on Action: Implications from the Child Mathematics Inquiry Portfolio

This article examines how the Child Mathematics Inquiry Portfolio (CMIP), a semester-long field experience project attached to an elementary mathematics methods course, can impact preservice teachers’ understanding about teaching and learning mathematics and set them on more positive mathematics teaching journeys as they prepare to enter the field. This action research study, grounded in reflective practice, was contextualized in undergraduate and graduate elementary mathematics methods courses with 92 participants over two academic years. Data came from preservice teachers’ written reflections on the child mathematics inquiry process. Findings reveal that the CMIP impacted the preservice teachers’ mathematics teaching and learning in four major areas: bridge between mathematics methods course, textbook, and actual classroom experience; mathematical confidence; greater understanding of how teachers shape students’ mathematics dispositions; and personal. Implications for mathematics teacher education are discussed.

A tale of two researchers: Commonalities, complementarities, and contrasts in an examination of mental computation and relational thinking

This paper describes a research collaboration between an educational psychologist and a mathematics education researcher, namely a didacticien des mathématiques. Our joint project aimed to explore the mental computation strategies of preservice teachers in an elementary mathematics methods course and to investigate the relationship between mental computation and relational thinking. The primary objective of the paper, however, is to go beyond the data and their interpretation. We describe the commonalities, complementarities, and points of contrast that emerged between us as researchers who hail from different disciplines, but who have the same overarching interests in mathematical thinking. In particular, we untangle issues we encountered during our collaboration related to our research questions, methodologies, and epistemological stances. We detail the ways in which we navigated these issues in the context of the research and describe what we learned about our own disciplinary perspectives and each other’s. We conclude by discussing what our story offers as a means of reflecting on our individual fields and potential interactions between them.

Tinkering with Logo in an Elementary Mathematics Methods Course

With an increased push to integrate coding and computational literacy in K–12 learning environments, teacher educators will need to consider ways they might support preservice teachers (PSTs). This paper details a tinkering approach used to engage PSTs in thinking computationally as they worked with geometric concepts they will be expected to teach in K–5. Experiences programming in Logo to construct authentic artifacts in the form of two-dimensional geometric graphics not only supported PSTs’ understanding of core geometric and spatial concepts, but also helped them to make connections between mathematics and computational literacy. Artifacts and discourse are discussed as they relate to three core considerations: engaging learners to construct authentic artifacts, supporting a communitarian ethos, and supporting various types of rapid feedback.

The Emphasis of Inquiry Instructional Strategies: Impact on Preservice Teachers’ Mathematics Efficacy

Using a Mixed Methods approach, this study investigated changes in levels of self-efficacy among elementary preservice teachers following a semester course on teaching elementary students’ mathematics. Participants in this study included 347 preservice elementary teachers at a mid-size regional university who had just completed an elementary mathematics methods course. The data were collected from several semester groups. The instruments used were the Mathematics Teaching Efficacy Beliefs Instrument, interview data, and observation data collected during the clinical experience. The focus of this study was to compare the changes in teacher self-efficacy following a methods course that emphasized hands-on mathematics instruction with manipulatives by means of the 5E instructional format. The results of the paired-samples t-test indicated that there was a significant difference in the preservice elementary teachers’ self-efficacy for teaching mathematics after engaging in the elementary methods course. Preservice teachers reported that their understanding of various instructional practices changed significantly from a “tell, show, and do” model to an approach utilizing interactive and engaging activities. They also reported that their attitude toward mathematics had improved significantly and that there had been a direct impact on their confidence for teaching mathematics as a result of the structure of the elementary math methods course.