Guiding Teachers in the Use of a Standards‐Based Mathematics Curriculum: Teacher Perceptions and Subsequent Instructional Practices After an Intensive Professional Development Program

Reforms in mathematics education call for K‐12 teachers to employ standards‐based pedagogies, which embody the National Council for Teachers of Mathematics' principles and standards. In order to effectively support teachers' implementation of standards‐based curricula, professional development must be provided that meets teachers' needs. The professional development program in this study focused on the implementation of a standards‐based mathematics curriculum entitled Investigations in Number, Data, and Space (Investigations). This study uses Guskey's framework as a guide to examining teachers' perceptions of the impact of the professional development that they received; their perceptions of mathematics teaching and learning; and how elements of the professional development translated into practice. Twenty‐two participants were randomly selected from the 53 professional development participants to be interviewed and observed during their mathematics teaching. Using a constant comparison method, the data sources in this study highlighted themes surrounding teachers' experiences with professional development and the implementation of the curricula. The analysis of the data sources in this study highlighted themes surrounding teachers' experiences with professional development: teachers as learners, teachers as self‐evaluators, shifting paradigms, enactment of professional development content into practice, and the influence of the state standardized mathematics test. The results of this study have several implications for future professional development and also highlight some of the more general issues that teachers face when attempting to enact new knowledge and skills into their practice.     

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.     

Autobiographical Stories from Preservice Elementary Mathematics and Science Students: Implications for K‐16 Teaching

Autobiographies are an effective tool for assessing students' predispositions toward science and mathematics content and identifying any changes in attitude over time. The purpose of this study was to analyze autobiographies of students enrolled in elementary education methods classes to determine the kinds of K‐12 and college content course experiences affecting their perceptions of mathematics or science. Special attention was given to recollections of events that had positive or negative effects on students' interest in and attitudes toward science or mathematics, their confidence in these areas, and transitions in attitude throughout their experiences. Ninety‐eight autobiographies were collected and analyzed, revealing attitudes that were generally more positive than expected, five major emergent themes, and important information about when and why transitions in attitudes occurred.     

Generation Z goes to math class: How the effective mathematics teaching practices can support a new generation of learners

Middle and high school students are part of Generation Z (birth years 1997–2012), a group that is emerging as very different from their parents and teachers. This article considers ways that generational research about Generation Z learners and NCTM's Effective Mathematics Teaching Practices can be used to inform and innovate practice in the mathematics classroom. Research suggests that while Generation Z learners are digitally engaged, they often display a lack of tech savvy. Generation Z students thrive on personalization and are often uncomfortable with collaborative learning. And the social movements of the early 2000s have shaped their world view. The authors provide resources, such as real-world tasks rooted in social problems, and instructional suggestions for teachers. Teachers who consider the characteristics and preferences of Generation Z in their planning can enact mathematics lessons that better connect to Generation Z learners. With the Effective Mathematics Teaching Practices as a guide, teachers can design and deliver innovative lessons that support Generation Z learners to promote deeper understanding of mathematical content.     

An “inverse” relationship between mathematics identities and classroom practices among early career elementary teachers: The impact of accountability

This qualitative case study guided by portraiture examines the relationships between three early career elementary teachers’ beliefs about themselves in relation to mathematics (mathematics identities) and their classroom practices. Through autobiographical inquiry, reflective practice, classroom observations, interviews, and artifacts, findings show that all three second grade teachers appeared to have an “inverse” relationship between their mathematics identities and their classroom practices. In this relationship, as negative as they felt about themselves with regards to mathematics, they expended that much more effort to ensure that their students would have positive experiences with it and not be stigmatized by it as they had been. Accountability to schools, students, and parents, to increase student achievement appeared to play an important role in this relationship. Implications for preservice teacher education, inservice professional development, and research on beliefs and practices are discussed.     

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM—The International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice.     

Mathematics Anxiety and Learning Styles: What Is the Relationship in Elementary Preservice Teachers?

The study investigated the relationship between elementary preservice teachers' mathematics anxiety levels and learning style preferences. Subjects included 72 preservice teachers at a midsized southeastern U.S. university who were at the end of their third year of study. The subjects completed the Mathematics Anxiety Rating Scale and the Style Analysis Survey (SAS). Scores obtained on the two instruments were analyzed using Pearson product‐moment correlations. Eleven of the SAS subscales were examined. The global subscale was the only one related to mathematics anxiety at the p < .05 level of significance. Findings revealed a low (r= .28) but significant (p < .05) positive correlation between mathematics anxiety and a global (right‐brain dominant) learning style. As global orientation scores increased, mathematics anxiety scores increased as well. This study indicated that there is tendency for global learners to possess higher levels of mathematics anxiety.     

Teachers' Considerations of Students' Thinking During Mathematics Lesson Design

Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers notice influences their decision‐making process. This article explores the mathematics lesson planning practices of four 4th‐grade teachers at the same school to understand how their consideration of Students' learning influences planning decisions. Case study methodology was used to gain an in‐depth perspective of the mathematics planning practices of the teachers. Results indicate the teachers took varying approaches in how they considered students. One teacher adapted instruction based on Students' conceptual understanding, two teachers aimed at producing skill‐efficient students, and the final teacher regulated learning with a strict adherence to daily lessons in curriculum materials, with little emphasis on student understanding. These findings highlight the importance of providing professional development support to teachers focused on their noticing and considerations of Students' mathematical understandings as related to learning outcomes. These findings are distinguished from other studies because of the focus on how teachers consider Students' thinking during lesson planning. This article features a Research to Practice Companion Article . Please click on the supporting information link below to access.     

Developing teacher content understanding by integrating pH and logarithms concepts

Logarithms are notorious for being a difficult concept to understand and teach. Research suggests that learners can be supported in understanding logarithms by making connections between mathematics and science concepts such as pH. This study investigated how an integrated chemistry and mathematics lesson impacted 29 teachers’ understanding of the logarithmic relationship and pH. Pre- and post-test data indicated 23 teachers improved their understanding of logarithms and 28 improved their understanding of pH, suggesting that teacher educators in both science and mathematics context can use this approach to foster better understanding with their teachers and ultimately school students. Our analysis also identified professional development components and teacher characteristics associated with gains in understanding of pH and logarithms, which mathematics and science teacher educators can use to strategically adapt and implement the lesson within other teacher education settings.     

Professional Development Strategically Connecting Mathematics and Science: The Impact on Teachers' Confidence and Practice

The press to integrate mathematics and science comes from researchers, business leaders, and educators, yet research that examines ways to support teachers in relating these disciplines is scant. Using research on science and mathematics professional development, we designed a professional development project to help elementary teachers improve their teaching of mathematics and science by strategically connecting these disciplines. The purposes of this study are: (a) to identify changes in teachers' confidence and practice after participating in the professional development and (b) to identify different ways to connect mathematics and science during the professional development. We use a Likert‐scale survey to assess changes in teachers' confidence related to teaching mathematics and science. In addition, we report on a thematic analysis of teachers' written responses to open‐ended questions that probed teachers' perceived changes in practice. We analyze field notes from observations of project workshops to document different types of opportunities for connecting mathematics and science. We conclude with implications for future professional development that connects mathematics and science in meaningful ways, as well as suggestions for future research.     

Constructing confidence and identities of belonging in mathematics at the transition to secondary school

This case study investigates students' perspectives on their mathematics learning experiences and identity constructions, in the context of transition to secondary school. In-depth, semi-structured interviews were conducted with six girls, halfway through their first year at their new school. Thematic analysis and discourse analysis were used to interpret and deconstruct their narratives. The girls' stories contribute to our understandings of how confidence in mathematics is discursively constructed. The stories also clarify the importance of gaining a sense of belonging in the transition from primary to secondary school mathematics. Through promoting this belonging within the mathematics classroom, teachers may engender confident performances in class and, through this, contribute to the construction of positive mathematical identities.     

Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective

This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.     

Sociocultural perspectives in research on and with mathematics teachers: a zone theory approach

Sociocultural theories view teacher learning as changing participation in social practices that develop their professional identities rather than as acquisition of new knowledge or beliefs that are internal to the individual. Although sociocultural research on mathematics teacher education has tended to focus on understanding teachers’ learning, this article argues that sociocultural perspectives can also guide more interventionist research involving changing classroom practice. The approach illustrated here uses an adaptation of Valsiner’s zone theory to analyse teacher learning and development in two separate research studies. In one study the aim was to understand how teachers incorporated digital technologies into their practice, while the other study helped teachers implement an investigative approach to working mathematically consistent with a new syllabus. In both studies, productive tensions between teachers’ beliefs, contexts, and goals were a trigger for learning and development.     

Rural teacher leadership in science and mathematics

This study adds to our understanding of science and mathematics teacher leadership in rural schools. Through In Vivo and Concept coding of teacher interviews, we investigated 20 secondary science and mathematics teachers' perceptions of rural teacher leadership during their participation in a three-year professional development program. As the teachers developed as teacher leaders, they broadened their focus from improving their own students' learning to sharing new knowledge learned through the program with other teachers both informally and formally. We compared our program components to the Teacher Leader Model Standards and added an emphasis on the importance of disciplinary content knowledge. We also identified patterns in science and mathematics teacher leadership that are contextually connected to teachers' instruction in rural high poverty schools. Rural teacher leadership included the importance of building strong teacher–student relationships, providing new academic opportunities for students, encouraging students' success, and building community connections.     

Knowing students as mathematics learners and teaching numbers 10–100: A case study of four 1st grade teachers from Romania

Researchers have increasingly linked teacher effectiveness with teacher knowledge of subject matter, curriculum, and teaching. Moreover, teacher knowledge of students has been regarded as another very significant component of teacher knowledge, influencing the classroom practice and student performance. Knowing students as mathematics learners means being aware of the ways students learn certain topics. This study examined the knowledge of students as mathematics learners displayed by four 1st grade teachers from Romania when designing and implementing a lesson on numbers 10–100. Findings show that knowledge of students as mathematics learners influenced the ways teachers planned and implemented their lesson. Teachers learned about students as mathematics learners from one series to another, and they tailored their use of manipulatives and classroom activities to meet the needs of their current students.     

Teachers learning the registers of mathematics and mathematics education in another language: an exploratory study

Many mathematics teachers around the world teach in a language different from the one in which they studied or completed their teacher education. Often these teachers must learn both the registers of mathematics and of mathematics education to teach in the additional language. This paper examines the factors that help teachers to learn these registers in Māori, the Indigenous language of New Zealand. Many of these teachers are second-language learners of the Māori language and attended English-medium schools and teacher-education programmes. After a brief discussion about the key role of language in teaching mathematics, this paper examines data from teachers at two Māori-immersion schools and a professional development facilitator. The analysis provides initial understanding of the factors that support or hinder their learning of the mathematics registers. Finally, a research agenda is suggested for further investigation of this issue.     

PANEL DISCUSSIONS

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics.     

The Road to Reform: A Grounded Theory Study of Parents' and Teachers' Influence on Elementary School Science and Mathematics

Though elementary teacher educators introduce new, reform‐based strategies in science and mathematics methods courses, researchers wondered how novices negotiate reform strategies once they enter the elementary school culture. Given that the extent of parents' and veteran teachers' influence on novice teachers is largely unknown, this grounded theory study explored parents' and teachers' expectations of children's optimal science and mathematics learning in the current era of reform. Data consisted of semi‐structured, open‐ended interviews with novice teachers (n = 20), veteran teachers (n = 9), and parents (n = 28). Researchers followed three stages of coding procedures to develop a logic model connecting participants' discrete designations of the landscape, regulating phenomena, contextual orientation, and desired outcomes. This logic model helped researchers develop propositions for future research on the interactive nature of parents' and teachers' influential role in elementary science and mathematics education. Implications encourage science and mathematics teacher educators—as well as school administrators—to explicitly develop and support novice teachers' ability to initiate and sustain parent/family engagement in order to create a school climate where teachers and parents are synergistically motivated to change.