Fostering a “head start” in math: observing teachers in early childhood mathematics engagement

ABSTRACT

Studies show that early engagement with mathematics leads to increased math achievement later in life. Yet, early childhood teachers do not regard mathematics as critical to young learners’ development and lack confidence with helping children learn mathematics. Early childhood teacher comfort and engagement with mathematics is a critical element to promoting intentional math instruction. Research was conducted to examine the effects of an innovative professional development program for Head Start preschool teachers with the goal of increasing pedagogical content knowledge and confidence in teaching mathematics. The findings in this article focus on classroom observations that concentrated on teacher engagement with mathematics.     

Elementary mathematics teachers’ judgment accuracy and calibration accuracy: Do they predict students’ mathematics achievement outcomes?

In this study we investigated whether elementary mathematics teachers’ knowledge of their students, as reflected in both the accuracy and confidence with which they are able to estimate their students’ task-specific performance on sets of mathematics problems, predicted students’ overall mathematics achievement. Thirty-nine teachers made predictions about the performance of a random sample of target students (n = 150) in their classrooms on sets of “easy” and “difficult” multiplication and division problems. Teachers also provided confidence ratings for those judgments. From these data, indicators of teachers’ judgment accuracy, judgment confidence and calibration accuracy (a measure of metacognitive monitoring) were then related to all of their students’ (n = 834) performance on year-end standardized mathematics achievement tests. Multilevel analyses indicate that teachers’ calibration accuracy, but not their task-specific judgment accuracy, significantly predicted students’ mathematics achievement. Implications for future research on teacher knowledge as well as professional development programs are discussed.     

ICT use in the teaching of mathematics: Implications for professional development of pre-service teachers in Ghana

Included in the contemporary mathematics curricula in Ghana is the expectation that mathematics teachers will integrate technology in their teaching. However, importance has not been placed on preparing teachers to use ICT in their instruction. This paper reports on a study conducted to explore the feasibility of ICT use in mathematics teaching at senior high school levels in Ghana. Interviews and survey data were used for data collection. Preliminary results showed that mathematics teachers in Ghana do not integrate ICT in their mathematics instruction. Among the major perceived barriers identified were: Lack of knowledge about ways to integrate ICT in lesson and Lack of training opportunities for ICT integration knowledge acquisition. To overcome some of these barriers, opportunities of a professional development arrangement for pre-service mathematics teachers were explored. Findings from the study revealed specific features of a professional development scenario that matters for ICT integration in mathematics teaching in the context of Ghana.     

Less experienced mathematics teachers report what is wrong with their professional support system

Teachers with seven years of teaching experience or less (n = 10) participating in a large‐scale mathematics professional development program in the United States were interviewed. The goal of this qualitative study was to better understand less experienced teachers' reactions to professional development and professional support in the teaching profession. The interview data ­indicate that these less experienced mathematics teachers are not satisfied with their mentors orcollaboration in their department and would welcome opportunities for classroom observations. In addition, these teachers were disappointed and surprised at their more experienced peers' lack of mathematics content knowledge. The results of this study have direct implications for the structure and philosophy for professional development to better serve incoming and less experienced teachers.     

Professional development on fostering students’ academic language proficiency across the curriculum—A meta-analysis of its impact on teachers’ cognition and teaching practices

This meta-analysis aggregates effects from 10 studies evaluating professional development interventions aimed at qualifying in-service teachers to support their students in mastering academic language skills while teaching their respective subject areas. The analysis of a subset of studies revealed a small non-significant weighted training effect on teachers’ cognition (g’ = 0.21, SE = 0.14). An effect aggregation including all studies (with 650 teachers) revealed a medium to large weighted overall effect on teachers’ classroom practices (g’ = 0.71, SE = 0.16). Methodological variables moderated the effect magnitude. Nevertheless, the results suggest professional development is beneficial for improving teachers’ practice.     

高中数学教师专业知识研究--基于吉林省数学教师的调查

教师专业发展必然需要教师专业知识的有力支撑。对高中数学教师专业知识进行的问卷调查和访谈发现：目前高中数学教师基本上较好地掌握了常用的教师专业知识,但也存在一些问题：对数学学科知识的关注范围过于狭窄;运用数学教学知识进行教学时偏向于被动;对数学课程标准的理解存在偏差。另外,研究还发现：数学教学知识的增长并非是持续的;不同层级的教师之间、不同类别学校中的教师之间,其差异主要体现在数学学科知识与数学教学知识。进而对数学教师教育提出相应建议：数学教师应适当拓展数学学科知识的关注范围;应依据调查数据加强数学教师教育培养计划的针对性;关于教师一般教育学知识的评价方式亟需改进等。     

Book Reviews

ABSTRACT

Student foundational knowledge of science, technology, engineering, and mathematics (STEM) is formed in their elementary education. Paradoxically, many elementary teachers have constrained background knowledge, confidence, and efficacy for teaching STEM that may hamper student STEM learning. The association between teacher preparation to teach STEM and student achievement in STEM motivated the authors' professional development program. The authors created and implemented a professional development program to address K–5 teacher confidence for, attitudes toward, knowledge of, and efficacy for teaching inquiry-based STEM. Using data from 2 independent cohorts the authors found significant and consistent increases in pre- to postinstitute assessments of teacher confidence, efficacy, and perceptions of STEM. Further, they found increased participant attention toward linking STEM curriculum and instruction to learning standards. Implications and suggestions for future research are discussed.     

Prospective teachers' conceptions of teaching and learning revealed through metaphor analysis

This study investigated the metaphors that prospective teachers in Turkey (N = 1,142) formulated to describe the concept of “teacher”. Participants completed the prompt “A teacher is like… because…” by focusing on only one metaphor to indicate their conceptualization of teaching and learning. Altogether 64 valid personal metaphors were analyzed and 10 main conceptual themes were identified. Significant associations were detected between participants' gender and study program type and six of the conceptual themes. Metaphors seem to provide a powerful cognitive tool in gaining insight into prospective teachers' professional thinking.     

The relationship among elementary teachers’ content knowledge,attitudes, beliefs,and practices

This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.

An evaluation of a professional learning network for computer science teachers

This paper describes and evaluates aspects of a professional development programme for existing CS teachers in secondary schools (PLAN C) which was designed to support teachers at a time of substantial curricular change. The paper’s particular focus is on the formation of a teacher professional development network across several hundred teachers and a wide geographical area. Evidence from a series of observations and teacher surveys over a two-year period is analysed with respect to the project’s programme theory in order to illustrate not only whether it worked as intended, by why. Results indicate that the PLAN C design has been successful in increasing teachers’ professional confidence and appears to have catalysed powerful change in attitudes to learning. Presentation of challenging pedagogical content knowledge and conceptual frameworks, high-quality teacher-led professional dialogue, along with the space for reflection and classroom trials, triggered examination of the teachers’ own current practices.     

Developing a deeper understanding of <Emphasis Type="Italic">mathematics teaching expertise</Emphasis>: an examination of three Chinese mathematics teachers’ resource systems as windows into their work and expertise

In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics “expert” teachers. Exploiting the Western and Eastern literature we examine the notion of “mathematics teaching expertise”, as it is perceived in the East and the West. The data consist of two rounds of in-depth interviews, observations and teachers’ representations of their resource systems, where teachers describe their resources connected to their practice, their perceptions of mathematics teaching expertise, and how to develop it. Subsequently, the data are analyzed with respect to the different facets of the notion of teaching expertise and related to the teachers’ views and practices, in order to deepen our understandings of what proficiency in mathematics teaching might mean and how to develop it, seen through the lens of ‘resources’. The significance of the study relates to the enhancement of mathematics teachers’ expertise and capacity building when working in collectives (e.g., in teacher professional development), in order to develop a strong workforce for supporting and helping to improve pupil learning.     

Designing Curriculum-Based Mathematics Professional Development for Kindergarten Teachers

This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement.     

Self-regulated learning microanalysis as a tool to inform professional development delivery in real-time

Elementary teachers in the United States are tasked with teaching all core subject matter and have training that involves many topics, which may limit the depth of their subject matter knowledge. Since they have low content knowledge, they often feel less confident about teaching technical subject matter, such as science (Bleicher Journal of Science Teacher Education 17:165–187, 2006). The problem of low confidence of elementary teachers for science instruction is exacerbated when they are expected to teach science using inquiry (Hanuscin et al. Science Education 95:145–167, 2010). Self-regulated learning microanalysis, which supports both instruction and assessment, can help teachers reflect on their learning processes. This technique may provide clues for teachers to improve strategies for learning and give information to professional development instructors to inform teacher professional development experiences. The purpose of this study was to examine self-regulatory learning cycles that fourteen elementary teachers experienced while engaged in learning about inquiry during a professional development. Results of this study showed that before the professional development, teachers reported low self-efficacy but high task value and perceived instrumentality for learning about inquiry. As the professional development progressed, teachers improved their goal setting skills, self-monitoring performance, and learning tactics. The self-regulated learning microanalysis revealed information not communicated in the professional development experience, which led to adaptation of the activities in real-time to meet the needs indicated on the self-regulated learning microanalysis reports. Measuring teacher learning processes allowed the professional development instructors to pinpoint difficulties and successes during the learning tasks, which aided in precise adaptation of experiences for teacher needs.     

Investigating the Influence of a Mixed Face-to-Face and Website Professional Development Course on the Inquiry-Based Conceptions of High School Science and Mathematics Teachers

The purposes of this study are to report the influences of a mixed delivery professional development [PD] course involving face-to-face classes and the mentoring assisted inquiry-based teaching [MAIT] website that addressed the conceptual change and self-efficacy of high school mathematics and science teachers’ conceptions of inquiry-based teaching. Twenty-five in-service high school science and mathematics teachers participated in a 9 weeks, 4 h per week PD course. Data collection included the pre-post Inquiry Teaching Efficacy Questionnaire [ITEQ], teachers’ reflective journals posted on the MAIT website, teachers’ assignments requested by the course instructor, and follow-up teachers’ interviews. Findings revealed that both mathematics and science teachers’ conceptions of inquiry teaching show significant improvements after the course. The mixed delivery PD course had the same influence on science and mathematics teachers. The authentic video clips and lesson plans provided on the MAIT website and the specific feedback toward teachers’ performance are the main factors that shaped teachers’ inquiry-based teaching conceptions.     

Professional development for practicing mathematics teachers: a critical connection to English language learner students in mainstream USA classrooms

This article examines the effects of changing teacher self-efficacy on student achievement. Results from a quantitative study of mathematics teachers in a USA mid-Atlantic state showed that teachers experienced reduced self-efficacy when working with English language learner students (ELLs) relative to non-ELLs. Further, the article explores professional development opportunities for strengthening teachers’ effectiveness with ELLs. The study utilized a four-part survey instrument based on the Teacher Sense of Efficacy Scale (TSES). All participants (n = 181) were mathematics educators from the highlighted state, and 94 % of them were preK-12 public school practicing classroom teachers. Study results indicate that teachers’ participation in professional development on ELL instruction is positively correlated to their heightened sense of self-efficacy. This finding points to continuing education as a potentially viable approach to reducing academic challenges for ELL students in mainstream mathematics classrooms by developing ever more effective practicing teachers.     

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.

     

Can teachers and mathematicians communicate productively? The case of division with remainder

Is it possible that a meeting of mathematicians and primary school teachers will be productive? This question became intriguing when one professor of mathematics initiated a professional development course for practicing primary school teachers, which he taught alongside a group of mathematics Ph.D. students. This report scrutinizes the uncommon meeting of these two communities, who have very different perspectives on mathematics and its teaching. The instructors had no experience in primary school teaching, and their professed goal was to deepen the teachers’ understanding of the mathematics they teach, while teachers were expecting the course to be pedagogically relevant for their teaching. Surprisingly, despite this mismatch in expectations, the course was considered a success by teachers and instructors alike. In our study, we analyzed a lesson on division with remainder for teachers of grades 3–6, taught by the professor. The framework used for the data analysis was mathematical discourse for teaching, a discursive adaptation of the well-known mathematical knowledge for teaching framework. Our analysis focuses on the nature of the interactions between the parties and the learning opportunities they afforded. We show how different concerns, which might have hindered communication, in fact fueled discussions, leading to understandings of the topic and its teaching that were new to all the parties involved. The findings point to a feasible model for professional development where mathematicians may contribute to the education of practicing teachers, while they are gaining new insights themselves.