Preservice teachers’ mathematics task modification for emergent bilinguals

Implementing mathematically challenging tasks is difficult for teachers when working with emergent bilinguals because cognitively demanding tasks in mathematics commonly have high language demand. Currently, inadequate teacher preparation for teaching emergent bilinguals is becoming a significant concern in the United States as this population of students is rapidly growing. This study investigated how two mathematics preservice teachers (PSTs) support middle school emergent bilinguals to understand cognitively demanding mathematical problems through task modification. Fieldwork with a concurrent intervention was designed for the PSTs to work with emergent bilinguals in a one‐on‐one setting. The PSTs modified cognitively demanding mathematics tasks and designed a lesson for the emergent bilinguals based on the modified tasks. The results revealed that the task modification made by the PSTs tended to shift from reducing cognitive demands in mathematics and language to maintaining the demands through learning strategies of contextual support.     

A study of factors impacting elementary mathematics preservice teachers: Improving mindfulness,anxiety, self-efficacy,and mindset

Innovation is more imperative now than ever before given the upcoming shortage in prepared teachers and the need to produce students with a strong knowledge of mathematics. A sense of urgency is impacting teacher education/preparation programs as instructional practices need to discover how to arm teachers to increase the number of students to be not only college-ready but also desiring to pursue Science, Technology, Engineering, and Mathematics majors. As such, the purpose of this study, was to determine how the four variables (mindfulness, mathematics anxiety, self-efficacy, and mindset) are interconnected within preservice elementary teachers (PSETs), and how we as teacher educators can better address these variables within our own PSETs. Each semester included three seminars with similar overall foci including the four variables. Participants in this study were recruited from Elementary Education students at an east south central regional university enrolled in a mathematics methods course. Thirty-seven participants were divided into control (N = 20) and treatment (N = 17). In this article, we present both qualitative and quantitative results from our mixed-methods study that considered these questions. With the results of this study revealing an inter-connectedness among the four variables, this research further informs the teacher educator community.     

From numbers to narratives: Preservice teachers experiences’ with mathematics anxiety and mathematics teaching anxiety

This paper presents qualitative and quantitative approaches to exploring teachers’ experiences of mathematics anxiety (for learning and doing mathematics) and mathematics teaching anxiety (for instructing others in mathematics), the relationship between these types of anxiety and test/evaluation anxiety, and the impacts of anxiety on experiences in teacher education. Findings indicate that mathematics anxiety and mathematics teaching anxiety may be similar (i.e., that preservice teachers perceive a logical continuity and cumulative effect of their experiences of mathematics anxiety as learners in K–12 classrooms that impacts their work as teachers in future K–12 classrooms). Further, anxiety is not limited to occurring in evaluative settings, but when anxiety is triggered by thoughts of evaluation, preservice teachers may be affected by worrying about their own as well as their students' performances. The implications for preservice experiences within a teacher education program and for impacting future students are discussed.     

Students' gendered perceptions of mathematics in middle grades single‐sex and coeducational classrooms

With the introduction of single‐sex classroom settings in coeducational public schools, there is an ongoing debate as to whether single‐sex education may reduce or reinforce traditional stereotypes and gender roles. In this article we present findings from a study that investigated the extent to which mathematics is perceived as a gendered domain among adolescent students enrolled in single‐sex classes and coeducational classes. Further we analyzed the relationships between student characteristics, class‐type, and teacher variables on students' perceptions of gender in mathematics. Findings from this study challenge the traditional view of mathematics as a male domain. Female participants more frequently considered mathematics to be a female domain than the male participants. Male participants, on the other hand, typically did not stereotype the mathematics as a gendered domain. Results from this study do not indicate, for girls at least, that participation in single‐sex classes results in a greater propensity to stereotype mathematics as a gendered domain than would be the case in coeducational classes. This study contributes to the evolving discourse and understanding of adolescents' gendered attitudes and beliefs towards mathematics—especially in light of stereotyped assertions that have a bearing on efforts to promote the learning of mathematics and science.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

Formative assessment and the role of teachers' content area

Professional development (PD) programs focused on increasing teachers' use of formative assessment generally provide a framework designed to help teachers understand the breadth and complexity of formative assessment, while advocating for teacher choice with respect to the specific implementation. This study examined the implementation patterns of 82 high school mathematics and science teachers to understand whether implementation approaches differed by content area. Results suggested that mathematics and science teachers significantly increased their self‐reported practice of formative assessment, in similar ways; however, the specific approaches that mathematics and science teachers chose to operationalize on a daily basis differed. These findings have implications for the design of PD and future research efforts.     

Models are a “metaphor in your brain”: How potential and preservice teachers understand the science and engineering practice of modeling

We investigated beginning secondary science teachers’ understandings of the science and engineering practice of developing and using models. Our study was situated in a scholarship program that served two groups: undergraduate STEM majors interested in teaching, or potential teachers, and graduate students enrolled in a teacher education program to earn their credentials, or preservice teachers. The two groups completed intensive practicum experiences in STEM‐focused academies within two public high schools. We conducted a series of interviews with each participant and used grade‐level competencies outlined in the Next Generation Science Standards to analyze their understanding of the practice of developing and using models. We found that potential and preservice teachers understood this practice in ways that both aligned and did not align with the NGSS and that their understandings varied across the two groups and the two practicum contexts. In our implications, we recommend that teacher educators recognize and build from the various ways potential and preservice teachers understand this complex practice to improve its implementation in science classrooms. Further, we recommend that a variety of practicum contexts may help beginning teachers develop a greater breadth of understanding about the practice of developing and using models.     

The long term impact of a coherence based model for mathematics intervention

This article presents a large-scale longitudinal study of hundreds of students across the state of Kentucky that participated in a dual-focus mathematics intervention initiative when they were in the third grade. Rather than an exclusive focus on intervention, this initiative focused on both (i) high quality pull-out intervention and (ii) coherence between pull-out intervention and classroom instruction. The study found that over half of the third grade intervention students that participated in this initiative were classified as “novice” (the lowest possible performance category) on state standardized mathematics assessments at the end of the third grade. However, over the course of the following four years, the novice reduction rate of these students was significantly (p < .01) greater than other novices in Kentucky that did not participate in the initiative. These findings indicate that when implementing intervention initiatives to help students that are struggling with mathematics, it may be important to establish coherence between pull-out intervention and classroom instruction. The long term impact of this approach among traditionally underrepresented minorities suggest that this publication may provide insight into important equity issues where long-term analyses may sometimes be needed to capture the full impact of intervention initiatives.     

Teacher Mentoring as a Community Effort

This article presents the findings from a study of a mentoring program for novice mathematics and science teachers, which was provided by their teacher education program. This study reports the findings of interviews with novice math and science teachers, their mentors, and the mentoring program administrators to explore stakeholder perceptions of mentoring support. Findings suggest the importance of using multiple mentoring strategies to develop, support, and retain high‐quality math and science teachers in the teaching profession. This study contributes to what is known about the role that teacher education programs may play in mentoring novice math and science teachers who have graduated from their programs.     

The impact of metacognitive practice and teacher feedback on academic achievement in mathematics

The purpose of this study is to determine the effects of metacognitive strategies and content‐specific feedback on student achievement in high school mathematics. Participants consisted of a convenience sample of students in honors geometry. An analysis of variance with repeated measures was employed to address the research questions. For both the posttest and retention test, students in the experimental group significantly outperformed the students in the comparison group. However, students scored lower in the retention test than the posttest. The findings of this study offer a modest contribution to the body of empirical research on the impact of metacognitive practice and content‐specific feedback on academic achievement at the high school level.     

Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms

This paper examines the implementation of an instructional module on preservice elementary teachers’ professional noticing of children’s mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic elementary mathematics classrooms. Findings indicated that two of the three components of professional noticing (attending and interpreting) showed statistically significant increases in a treatment group that did not occur in a comparison group. The deciding component remains a challenge that warrants further research.     

Preservice teachers learning to teach proof through classroom implementation: Successes and challenges

Proof and reasoning are central to learning mathematics with understanding. Yet proof is seen as challenging to teach and to learn. In a capstone course for preservice teachers, we developed instructional modules that guided prospective secondary mathematics teachers (PSTs) through a cycle of learning about the logical aspects of proof, then planning and implementing lessons in secondary classrooms that integrate these aspects with traditional mathematics curriculum in the United States. In this paper we highlight our framework on mathematical knowledge for teaching proof and focus on some of the logical aspects of proof that are seen as particularly challenging (four proof themes). We analyze 60 lesson plans, video recordings of a subset of 13 enacted lessons, and the PSTs’ self- reported data to shed light on how the PSTs planned and enacted lessons that integrate these proof themes. The results provide insights into successes and challenges the PSTs encountered in this process and illustrate potential pathways for preparing PSTs to enact reasoning and proof in secondary classrooms. We also highlight the design principles for supporting the development of PSTs’ mathematical knowledge for teaching proof.     

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

The 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.     

A review of research on affect of elementary prospective teachers in university mathematics content courses 1990–2016

The purpose of this study was to review the existing research on affect (beliefs, attitudes, and emotions) of elementary prospective teachers (EPTs) in university mathematics content courses. We use as our time period from publication in the United States of the Curriculum and Evaluation Standards for Schools Mathematics through 2016. A search of a combination of electronic databases and targeted international journals resulted in a total of 11 studies that looked at some aspect of affect with EPTs in all or some part of a university mathematics course over the 27‐year time period. Nine of the 11 studies occurred in the context of a course or courses categorized as involving an alternative pedagogy that was student‐centered. Overall we found that a student‐centered approach to instruction supported changes in EPTs’ affect that align with pedagogical recommendations in reform documents such as the NCTM Standards. However, shifts were sometimes difficult to come by and encountered resistance from EPTs. Implications for course learning experiences are offered and conflicting results between studies suggest directions for future research.     

Influence of mentoring and professional communities on the professional development of a cohort of early career secondary mathematics and science teachers

A challenge for public schools is to successfully support and professionally develop early career teachers (ECTs) and thereby prepare them for long and successful careers in education. The purpose of this qualitative research study was to describe how the professional practices of early career science and mathematics teachers, some of whom are career changers, were influenced by their interactions with mentors and professional communities. Topics examined included the contextual elements that influenced the ECTs’ interactions with mentors and professional communities, how teachers positioned themselves within multiple professional communities, and how they perceived these experiences had influenced the development of their teaching practice. An extensive semi-structured interview of the ECTs generated data that were analyzed to identify emergent themes and patterns. The findings of this study indicated that navigating professional communities and interacting with mentors had influenced the ECTs’ decisions to adopt important components of a learner-centered approach to teaching that included engaging students in active learning processes, utilizing formative assessment, and responding to students' individual needs. These findings have implications for school policies and approaches related to supporting and professionally developing unique cohorts of ECTs.     

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.     

The DESTIN: Preservice Teachers' Drawings of the Ideal Elementary Science Teacher

The aim of this study is to report findings from the Drawing‐Elementary‐Science‐Teacher‐Ideal‐Not, or the DESTIN procedure. The study utilizes a simple drawing procedure accompanied by a narrative and discussion for understanding preservice teachers' images of science, science teaching, and the science teacher. Ninety drawings from two sections of an elementary science methods course were analyzed. Looking at the pre‐drawings from the beginning of the semester and post‐drawings done at the end of the semester, the findings relate the value of using drawings in teacher education and the usefulness of this procedure to promote discussions about science teaching, the construction of new images and practices for teaching elementary science, and teacher identity. The DESTIN procedure has potential as a productive activity for teacher education and long‐term professional development by making more explicit teachers' views of science teaching and learning and their past experiences as science learners.