Toward Improving the Mathematics Preparation of Elementary Preservice Teachers

Research suggests the importance of mathematics knowledge for teaching (MKT) for enabling elementary school teachers to effectively teach mathematics. MKT involves both mathematical content knowledge (M‐CK) and mathematical pedagogical content knowledge (M‐PCK). However, there is no consensus on how best to prepare elementary preservice teachers (PSTs) to achieve M‐CK and M‐PCK. This study builds on research related to MKT by investigating influences of mathematics content courses designed specifically for elementary PSTs (IMPACT courses—Impact of Mathematics Pedagogy and Content on Teaching) on their attitudes (i.e., confidence and motivation) toward M‐CK and M‐PCK. Results suggest that the PSTs who participated in these IMPACT courses not only acquired high levels of confidence and motivation toward M‐CK, but also showed significant and greater gains in attitudes toward M‐PCK, after taking the required mathematics methods course, than their counterparts. Further, the findings suggest that these IMPACT courses provided a mathematical foundation that allowed the PSTs to engage in mathematics teaching methods better than those PSTs who did not have such a foundation. These results suggest potential course experiences that may enhance M‐CK and M‐PCK for elementary PSTs.     

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.     

Promoting Preservice Elementary Teachers' Awareness of Learning and Teaching Mathematics Conceptually Through KTEM

In this article, we describe preservice elementary teachers' reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers' memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually.     

Linking Preservice Teachers' Mathematics Self‐Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

This study examined preservice teachers' mathematics self‐efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self‐Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and the Illinois Certification Testing System (ICTS) Basic Skills Test. The results indicate that preservice teachers' mathematics self‐efficacy is positively correlated to their personal mathematics teaching efficacy. In addition, their mathematical performance is related to their mathematics self‐efficacy and mathematics teaching efficacy. In regard to affecting student outcomes, only those preservice teachers who are very confident in their ability to teach believe they can have an effect on their students. Implications on teacher education programs are discussed.     

A Problem-Solving Based Mathematics Course and Elementary Teachers' Beliefs

This study examined the impact a problem-solving based mathematics content course for preservice elementary education teachers (PSTs) had on challenging the beliefs they held with respect to mathematics and themselves as doers of mathematics. Nine PSTs were interviewed to gain insight into changes that occurred to their belief systems and what aspect(s) of the course were instrumental in producing those changes. Surveys to measure how strongly PSTs subscribed to five mathematical beliefs were administered to 137 PSTs who were enrolled in the course. Significant positive changes (p < .01) were observed for four of the five beliefs. When changes were studied by achievement level, students with final grades of A or B showed statistically significant changes (p < .005) in three of the five beliefs. Students who were interviewed consistently reported increased confidence in their mathematical abilities as a result of the course.     

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.     

Preservice mathematics teachers' conceptions and enactments of modeling standards

Mathematical modeling has been highlighted recently as Common Core State Standards for Mathematics (CCSSM) included Model with Mathematics as one of the Standards for Mathematical Practices (SMP) and a modeling strand in the high school standards. This common aspect of standards across most states in the United States intended by CCSSM authors and policy makers seems to mitigate the diverse notions of mathematical modeling. When we observed secondary mathematics preservice teachers (M‐PSTs) who learned about the SMP and used CCSSM modeling standards to plan and enact lessons, however, we noted differences in their interpretations and enactments of the standards, despite their attendance in the same course sections during a teacher preparation program. This result led us to investigate the ways the M‐PSTs understood modeling standards, which could provide insights into better preparing teachers to teach mathematical modeling. We present the contrasting ways in which M‐PSTs presented modeling related to their conceptions of mathematical modeling, choices of problems, and enactments over an academic year, connecting their practices to extant research. We consider this teaching and research experience as an opportunity to make significant changes in our instruction that may result in our students enhanced implementation of mathematical modeling.     

Preparation for Practice: Elementary Preservice Teachers Learning and Using Scientific Classroom Discourse Community Instructional Strategies

Despite historical national efforts to improve elementary science education, science instruction continues to be marginalized, varying by state. This study was designed to address the ongoing challenge of educating elementary preservice teachers (PSTs) to teach science. Elementary PSTs are one of the science education community's major links to schools and science education reform. However, they often lack a strong background in science, knowledge of effective science teaching strategies, and consequently have low confidence and self‐efficacy. This investigation explored the initial learning of elementary PSTs using an interdisciplinary model of a scientific classroom discourse community during a science methods course. Findings post‐methods course suggested that the PSTs gained confidence in how to teach inquiry‐based elementary science and recognized inquiry‐based science as an effective means for engaging student learning. Additionally, PSTs embraced the interdisciplinary model as one that benefits students' learning and effectively uses limited time in a school day.     

Non‐Traditional Preservice Teachers and Their Mathematics Efficacy Beliefs

In Florida, recent legislative changes have granted community colleges the ability to offer baccalaureate degrees in education, frequently to non‐traditional students. Based on information obtained from the literature covering preservice teachers' math knowledge, teachers' efficacy beliefs about math, and high‐stakes mathematics testing, a study examined a population of preservice teachers in a new Florida teacher preparation program. The research investigated relationships surrounding non‐traditional preservice teachers' characteristics such as: ages, high‐stakes math failures, lower division mathematics history, and math methods course performance, in relation to their efficacy beliefs about mathematics. Results revealed that preservice teachers' ages, lower division mathematics history, and math methods course performance, did have a significant relationship with their math efficacy beliefs, as measured by the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI); the variable of high‐stakes math failures did not. Additionally, a multiple regression model including the aforementioned variables did predict preservice teachers' MTEBI scores, but did not generalize to the greater population. The findings from this study can assist new teacher preparation programs in isolating variables that identify preservice teachers who are at risk for poor mathematical attitudes; can posit avenues for fostering positive math beliefs in preservice teachers; and can recommend further research in this area.     

Using Video‐Based Pedagogy in an Elementary Mathematics Methods Course

The study explored the impact of using video‐based pedagogy on preservice teachers' cognitions about teaching mathematics. The use of video‐based pedagogy was integrated into the course, Methods for Teaching Elementary School Mathematics. A variety of written and interview data were collected during the course and, in the following semester, during student teaching. Evidence from case studies of three preservice teachers indicates that they engaged in reflection and reconstruction of their beliefs about how children learn mathematics and moved from a more didactic perspective of teaching mathematics toward a student‐centered perspective. Such movement appears to have been influenced by the use of video‐based pedagogy.     

Development of the Environmental Education Teaching Efficacy Belief Instrument

The increasing popularity of including environmental topics and issues in school curricula has created a need for effective environmental education teachers. One way to evaluate teacher effectiveness is through teacher efficacy, a belief measure that evaluates a teacher's perception that he/she can teach effectively. Research suggests that teachers’ instructional decisions are influenced by their beliefs, which are framed by their personal experiences. Because teacher efficacy is content specific, the purpose of this study was to develop a survey, the Environmental Education Teacher Efficacy Belief Instrument (EETEBI), to measure the teacher efficacy beliefs of preservice teachers as they relate to environmental education teaching strategies and outcomes.     

Examining preservice teachers’ noticing of equity-based teaching practices to empower students engaging in productive struggle

Our study examined ways preservice teachers (PSTs) make connections between teaching practices and use of student resources that support productive struggle and promote equity. Our research questions are: (1) How do PSTs notice and describe the equity-based mathematics teaching practice of leveraging student resources to support student struggles? and (2) In what ways do PSTs make connections to and interpret the role student resources play in the resolution of students’ mathematical struggles? The qualitative study examined 39 PSTs in a mathematics content course for PSTs. Data come from a video analysis assignment where PSTs described their mathematical interpretations of the student struggle(s) and teacher’s use of student resources to support the struggle resolution. Findings show that PSTs noticed teacher moves that leveraged student’s mathematical thinking and linguistic funds of knowledge and based the productive level of the struggle on actions built upon peers, linguistic knowledge and prior mathematical knowledge.     

Assessing Preservice Teachers' Beliefs about the Teaching and Learning of Mathematics and Science

With increased study of teachers' beliefs about science and mathematics teaching in recent years, there is a need for instruments that assess beliefs in both content areas. Moreover, early field experiences in schools and professional development efforts may influence the beliefs that preservice and in‐service teachers develop, and instruments for this purpose are limited. This article describes the development and validation of the Confidence, Commitment, Collaboration, and Student thinking in Mathematics and Science (CCCSMS) beliefs scales, a set of 10 six‐item scales. Collectively, these scales measure teachers' self‐confidence in doing and teaching science and mathematics, confidence in understanding children's thinking and building models of that thinking, commitment to teaching science and mathematics from a standards‐based perspective, and commitment to collaborating with peers. The scales represent an efficient and effective way of assessing beliefs of large groups. Although this article focuses predominantly on development of the scales, results from initial use indicate that there are positive correlations between beliefs related to mathematics and beliefs related to science, but the correlations are low enough to show that many teachers think differently about the two subjects.     

Turkish Preservice Primary School Teachers' Science Teaching Efficacy Beliefs and Attitudes Toward Science: The Effect of a Primary Teacher Education Program

The main purpose of this study was to investigate the effectiveness of a primary teacher education program in improving science teaching efficacy beliefs (personal science teaching efficacy beliefs and outcome expectancy beliefs) of preservice primary school teachers. The study also investigated whether the program has an effect on student teachers' attitudes toward science. Data were collected by administering the “Science Teaching Efficacy Beliefs Instrument” and “Attitudes toward Science Scale” to 282 preservice primary teachers (147 freshmen, 135 seniors). Statistical techniques such as means and t‐test were used to analyze the data. Results of the study showed that the primary teacher education program has a medium positive effect on science teaching efficacy beliefs of the primary preservice teachers (t = 4.791, p = .000) and that there were no gender differences in terms of efficacy beliefs. Results also indicated that preservice primary teachers' attitudes toward science were moderately positive and differ by class level. Fourth‐year preservice teachers' attitudes toward science were found to be significantly more positive than the first years (t = 5.494, p = .000). There were no gender differences in attitudes toward science.     

Computational estimation skill of preservice teachers: operation type and teacher view

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers’ estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the meaning of estimation and the importance of teaching it. Three sets of instruments were used: an estimation task, a computational task, and a belief survey. Results indicated that PSTs performed differently depending on the types of operations on the estimation test. It was also found that different types of problems elicited different strategies. Furthermore, the intervention of the study, along with five other factors were found to significantly correlate with estimation skills. The five factors include PSTs’ mathematical knowledge, their reported confidence about estimation skills, their self-reported knowledge about calculator use in instruction, their views of estimation in teaching mathematics, and their definition of estimation. A negative correlation was documented for the knowledge of calculator use in instruction, and positive correlations were present for other factors. Implications are discussed in accordance with these findings.     

Book Vignettes

Bell , Frederick H., Teaching Elementary School Mathematics: Methods and Content for Grades K-8 Tomera , Audrey N., Understanding Basic Ecological Concepts. British Museum (Natural History), Dinosaurs and Their Living Relatives.     

A Longitudinal Look at Attitudes and Perceptions Related to the Integration of Mathematics,Science, and Technology Education

The purpose of this study is to provide an in‐depth analysis of attitudes and perceptions related to the integration of mathematics, science, and technology education of preservice teachers preparing to teach STEM disciplines. Longitudinal data by individual cohort and across 7 years of the Integrated Mathematics, Science, and Technology (MSAT) Program are reported, analyzed, and interpreted to help design and improve preservice teacher education programs and improve teaching and learning in STEM classrooms. Results of quantitative analyses indicate that there was generally no change in preservice teacher attitudes and perceptions related to the value of the integration of mathematics, science, and technology education—they clearly valued integration at the onset and at the completion of the program. However, there was a significant change in preservice teacher attitudes and perceptions related to integration feasibility in terms of inefficiency and difficulty. Implications for teacher education programs include: (a) more exposure to concepts, processes, and skills in STEM that are similar, analogous, complementary, or synergistic; (b) familiarity with instructional strategies and access to resources; (c) deeper understanding of content across STEM; and (d) strategies for collaboration and team work to make integrated instruction time more efficient and less difficult to manage.