Explaining mathematics achievement gains in Botswana and South Africa

The purpose of this study is to test empirically whether and how classroom and school factors contribute to student mathematics learning gains in the border region of North West province, South Africa and Southeastern Botswana. Our results suggest that in both regions, improving teaching quality has an important impact on how much mathematics students learn during the year. The amount of effort put into covering the curriculum and teacher mathematics knowledge are also important factors in the learning gains students make in grade 6 classrooms in southern Africa.     

Brokering dialogue between secondary students and teachers to co-construct appropriate pedagogy in reduced-size classes

This study focuses on how two teachers working in reduced-size secondary classes of the same grade adapted their pedagogy as a result of a brokered dialogue between myself as researcher and 43 grade 10 students from the teachers’ classes. Research was carried out over the course of one academic year. First, students’ perspectives on studying in a reduced-size class were elicited before they were invited to suggest ways of improving the teaching and learning. These interviews were transcribed and given to the teachers of these classes. Next, these teachers were interviewed to gauge their opinions on what the students had reported in the earlier interviews. At a later stage, their teaching was observed to determine whether, and to what extent, the two teachers had attempted to incorporate changes based on the feedback from pupils. The study showed that the pupil voice is a very powerful and constructive trigger for enacting teachers’ pedagogical change and developing our understanding of students’ learning processes. Findings demonstrate that teachers responded positively to their students’ perspectives despite initial apprehensions. Implications for professional development and good practices in reduced-size classes are also presented.     

Teaching mathematically talented students: a cross-cultural study about their teachers’ views

The instruction of mathematically talented students (MTS) in heterogeneous classes is an issue of debate. Questions of equity, differential instruction, teacher awareness of their talented students’ needs, and their willingness and competence to face the challenges of nurturing these students are all raised within this context. Our international study compared South Korean, American, and Israeli teachers of mathematics perspectives concerning their (a) perceived competence to teach MTS (b) perceived competence in addressing MTS’ needs through differential instruction, (c) support for separation of MTS into special math classes, and (d) equity views concerning MTS’ needs. Data was collected by means of a questionnaire presented to 80 South Korean, 145 Israeli, and 58 American teachers of mathematics. Findings suggested that most teachers in these countries perceived themselves as competent to teach MTS, while very few of the participants supported the separation of MTS into special classes. South Korean teachers perceived themselves to be less competent in teaching MTS as well as in applying differential instruction and agreed more than their foreign counterparts that the fostering of mathematically weak students is more important than the fostering of MTS. Teachers who had some mathematical background appeared to perceive themselves as more competent to teach MTS than teachers who had no mathematical background. Teachers who predominantly taught large classes felt less competent to teach MTS than teachers who predominantly taught medium-sized classes. Findings were partially interpreted within the perspective of cultural differences. Recommendations for teachers’ professional development are drawn.     

Challenging a Teacher's Perceptions of Mathematical Smartness Through Reflections on Students’ Thinking

Creating equitable opportunities so all students can learn and succeed mathematically has been a key focus of mathematics education across several decades. Central to student achievement are students’ mathematical identity and their feelings of success during instruction. Researchers (e.g., Boaler & Staples, 2008) have shown that teachers can be particularly powerful in shaping students’ beliefs, feelings of success, and achievement, but few studies have investigated how teachers frame what it means to be successful or “smart” in mathematics. Through the social construct of smartness (Hatt, 2012) and the learning perspectives of incremental and entity theories (Blackwell, Trzesnieski, & Dweck, 2007; Yeager & Dweck, 2012), I examine how one teacher, Mrs. Purl, conceptualized what it meant to be smart in mathematics and how this perception changed slowly, over time, through repeated examination and discussion of individual student's thinking. As Mrs. Purl came to know her students at a personal level, she began to see that her perceptions were not always accurate and warranted reexamination.     

Teachers use of writing to support students’ learning in middle school: A national survey in the United States

A random sample of middle school teachers (grades 6–9) from across the United States was surveyed about their use of writing to support students’ learning. The selection process was stratified so there were an equal number of English language arts, social studies, and science teachers. More than one-half of the teachers reported applying 15 or more writing to learn strategies at least once a month or more often. The most commonly used writing to learn strategies were writing short answers to questions, note taking for reading, note taking while listening, and completing worksheets. While teachers reported using a variety of writing to learn strategies, most of them indicated they received minimal or no formal preparation in college on how to use writing to learn strategies to support student learning, less than one-half of teachers directly taught students how to use the writing to learn strategies commonly assigned, and the most commonly used writing to learn strategies did not require students to think deeply about the material they were learning. We further found that teachers’ reported use of writing to learn strategies was related to their preparedness and the composition of their classroom in terms of above and below average writers, English Language Learners, and students with disabilities.     

In the workplace mathematics does not announce itself: towards overcoming the hiatus between mathematics education and work

After improving enrolment rates significantly, many developing countries such as Peru are facing the challenge to increase learning levels among students. Over the past few years, many researchers have turned to teacher-related variables as a way to better understand classroom processes that may help increase learning levels among students. In this study, we analyze one of these, that falls under what Shulman (Educational Researcher, 15 (2), 4–14, 1986) called pedagogical content knowledge (PCK). Specifically, in this study, we analyze one of the areas of PCK which is knowledge of content and students. This was measured through a test where teachers were asked to explain students’ mistakes and predict responses in similar mathematics exercises. We explore if PCK is associated with the socioeconomic status of children and if it has an effect on children’s achievement. Additionally, we analyze which teacher characteristics are associated with higher scores in PCK. The analysis uses the Young Lives longitudinal survey for Peru. We found that students’ socioeconomic status at age 1 and maternal education were positively associated with their teachers’ PCK by the time students were enrolled in fourth grade, thus depicting a very unequal education system. Furthermore, teachers’ PCK was positively associated with student achievement, but only when a threshold for the PCK test was established. For our sample, male teachers, who were younger, and Spanish speakers had higher PCK scores.     

Mathematics teachers’ learning: a conceptual framework and synthesis of research

How do practicing mathematics teachers continue to develop the knowledge and habits of mind that enable them to teach well and to improve their teaching over time? The question of how (and what) teachers learn lies at the crux of any effort to provide high-quality mathematics teaching for all students. This article reviews 106 articles written between 1985 and 2008 related to the professional learning of practicing teachers of mathematics. We offer a synthesis of this research, guided by Clarke and Hollingsworth’s (Teach Teach Educ 18(8):947–967, 2002) dynamic model of teacher growth. Their model emphasizes the recursive nature of teachers’ learning and suggests that growth in one aspect of teachers’ knowledge and practice may promote subsequent growth in other areas. We report the results in six major areas of teacher learning, identify several crosscutting themes in the literature, and make recommendations for future research aimed at understanding teachers’ professional learning.     

Learning to Learn From Benchmark Assessment Data: How Teachers Analyze Results

Although interim assessments are currently promoted as a mechanism for improving teaching and student learning, we know little about how teachers use this data to modify instruction. This article presents findings from a larger study on teachers’ use of interim assessment information in elementary mathematics. We address the following questions: (a) How do the Philadelphia teachers in our sample analyze benchmark assessment results, (b) how do they plan instruction based on these results, and (c) what are their reported instructional responses to such results? To answer these questions, we interviewed all 3rd- and 5th-grade teachers in five average- and above-average-performing elementary schools three times during the 2006–07 school year. We found that although the teachers in our study used interim assessment results to gain information about students’ learning in mathematics, teachers did not use interim assessments to make sense of students’ conceptual understanding. Furthermore, teachers’ tendency to interpret student errors as procedural missteps was paralleled by a trend toward procedural instructional responses.     

Students’ and teachers’ perceptions of goal structures – Will they ever converge? Exploring changes in student-teacher agreement and reciprocal relations to self-concept and achievement

Previous studies have shown that alignment between teachers’ and students’ perceptions of goal structures (i.e., student-teacher agreement) ranges from non-existent to, at most, moderate. However, existing work is limited in that it all relies on cross-sectional data, meaning that we lack an understanding of changes in student-teacher agreement on goal structures over time. The present study therefore (a) attempts to shed light on changes over one semester in student-teacher agreement on six dimensions of goal structures (task, autonomy, recognition, grouping, evaluation, and time) in mathematics classes. In addition, we address the question (b) whether differentiated developmental trajectories of student-teacher agreement emerge for the period before vs. after the first mathematics test in the semester. Furthermore, the study (c) examines whether and how students’ self-concept and indicators of students’ initial and actual achievement are (reciprocally) related to agreement and changes in agreement. Data for this study was collected at five measurement points in newly assembled classes (Grade 9) after a transition within secondary education. The sample contained 130 students and their mathematics teachers, resulting in 130 student-teacher dyads. Applying piecewise growth curve modeling indicated changes in agreement regarding recognition, evaluation, and time. Higher increases in self-concept before the test forecasted declines in agreement regarding autonomy after the test. Moreover, we found effects of achievement on changes in agreement for the dimensions of autonomy, evaluation and time. To conclude, the study’s findings support a dynamic view of student-teacher agreement on several dimensions and provide insights into the interplay between changes in agreement, self-concept, and achievement.     

Understanding the low mathematics achievement of Chilean students: A cross-national analysis using TIMSS data

The low performance of Chile in the TIMSS 1998/99 international study of mathematics and science achievement was a great disappointment for that country. To investigate the likely causes for low performance in mathematics, this study (1) compared Chile to three countries and one large school system that had similar economic conditions but superior mathematics performance, and (2) examined how important characteristics of the Chilean educational system could account for poor student achievement in mathematics. The study finds that, compared to South Korea, Malaysia, the Slovak Republic, and Miami-Dade County Public Schools: (a) Chilean 8th graders had parents with fewer years of schooling and with fewer educational resources at home; (b) the Chilean mathematics curriculum covered less content and fewer cognitive skills; and (c) the meager official curriculum translated into a weaker curricular implementation. Hierarchical linear models found that, in Chile, school assets were unequally distributed across social classes, with schools in socially advantaged areas more likely to have their own mathematics curriculum and better prepared teachers who emphasized more advanced mathematics content. Schools with their own mathematics curriculum and whose teachers covered more advanced content had significantly higher student achievement in mathematics.     

Instructional practice in algebra: Building from existing practices to inform an incremental improvement approach

Algebra is considered key to success in secondary mathematics, yet instruction remains mostly teacher-centered and procedurally oriented, with limited opportunities for students to develop algebraic understanding. This study draws on a large sample of video-recorded ninth grade U.S. algebra lessons to explore the nature of learning opportunities that may help deepen students’ algebraic understanding. I highlight aspects of opportunities to learn algebraic procedures and describe instruction that can enrich these opportunities. I posit that this holds promise as an incremental improvement approach—relatively small adjustments in teachers’ current practices that can serve as a bridge to more ambitious teaching.     

EXPLORING TEACHERS’ KNOWLEDGE AND PERCEPTIONS ACROSS MATHEMATICS AND SCIENCE THROUGH CONTENT-RICH LEARNING EXPERIENCES IN A PROFESSIONAL DEVELOPMENT SETTING

This paper examines upper elementary and middle school teachers’ learning of mathematics and science content, how their perceptions of their disciplines and learning of that discipline developed through content-rich learning experiences, and the differences and commonalities of the teachers’ learning experiences relative to content domain. This work was situated within a larger professional development (PD) program that had multiple, long-term components. Participants’ growth occurred in 4 primary areas: knowledge of content, perceptions of the discipline, perceptions about the learning of the discipline, and perceptions regarding how students learn content. Findings suggest that when embedded within an effective professional development context, content can be a critical vehicle through which change can be made in teachers’ understandings and perceptions of mathematics and science. When participants in our study were able to move beyond their internal conflicts and misunderstandings, they could expand their knowledge and perceptions of content and finally bridge to re-conceptualize how to teach that content. These findings further indicate that although teachers involved in both mathematics and science can benefit from similar overall PD structures, there are some unique challenges that need to be addressed for each particular discipline group. This study contributes to what we understand about teacher learning and change, as well as commonalities and differences between teachers’ learning of mathematics and science.     

A Conceptual Approach to Teaching Mathematics to Students With Intellectual Disability

Swedish compulsory school for students with intellectual disability (ID) has been criticized for focusing on care and not presenting the students with enough knowledge-related challenges. The purpose of this study is to investigate how a conceptually-based mathematics curriculum can be interpreted and constructed for students with ID. A total of 18 mathematics lessons in 6 classes for students with ID were filmed, and the teachers were interviewed in connection with the lessons. A qualitative content analysis approach was used to identify aspects of mathematical competency content and to analyze the teaching. Three major groups of teaching strategies are identified: pedagogical mathematics activities, focusing on students’ perceptions of mathematical content, and encouraging dialogue between students.     

Opportunities to learn: Mathematics textbooks and students’ achievements

This study explores how textbooks function in education. It asked whether opportunities provided in math textbooks to engage in tasks demanding different levels of understanding correlate with students’ achievements on tasks demanding equivalent levels of understanding on a standardized exam. The textbooks evaluated were two 8^th grade mathematics textbooks used by students in the Arab community in Israel, showing that Textbook A makes more cognitive demands than Textbook B. The study correlated textbooks’ cognitive demand with the scores of all 8^th grade students in the Arab community who completed the national math test in 2015 and studied in schools using either Textbook A or B (N = 4040), while attending to mediating variables. The findings show that if a textbook provides the opportunity to engage in tasks demanding higher levels of understanding, students using this book will have higher scores. The study shows that gender and SES play an important role in how opportunities provided in textbooks interact with students’ scores. Many factors influence variations in mathematics achievements within and between nations. The findings illuminate textbooks’ ability to provide opportunities to learn mathematics. As a result, they raise new questions about how teachers use textbooks and about the role of textbooks in promoting access and equity in mathematics education. Although the work explored specific textbooks, its findings shed light on how learning opportunities relate to achievements more generally.     

Teaching mathematics after hours

The quantum of instruction time allocated to curriculum subjects such as mathematics facilitates greater exposure to knowledge and skill development, leading to higher levels of achievement. There are a number of manifestations of time to consider when investigating the quantum of time in mathematics education. The OECD have investigated the time allocated to mathematics by schools internationally, while also reporting on the prevalence of private tuition and time spent on homework. However, to date, no attention has been afforded to the provision of ‘hidden curriculum time’ for mathematics. This study seeks to advance the work of the OECD and describes a case study that sought to ascertain if teachers in Ireland provide additional mathematics lessons outside of school hours. The authors examined how prevalent this practice is, how many additional minutes some students receive as a result of this practice and ascertained teachers’ reasons for providing/not providing these additional mathematics classes. The results from this case study show that the majority of teachers at Senior Cycle provide these classes while a large proportion of Junior Cycle teachers also do. In extreme cases, these additional classes expose students to an additional 88.3 h of mathematics over the two-year Senior Cycle programme.     

数学课堂规范的讨论和分析

数学课堂规范包括支配课堂的一般社会规范和围绕特定数学交互的数学规范.数学课堂规范的特征有:数学课堂规范是"预成性"和"生成性"统一的结果;学生数学观念影响数学课堂规范的发展;社会规范和数学课堂规范之间有差异;创生数学课堂规范就是创造一种信任和尊重的学习气氛.做数学的新规范和标准也需面对传统教学方式的桎梏,学生数学观的局限性,以及数学参与公正性等的挑战性和复杂性。     

初中数学教学如何建立民主、平等、和谐的师生关系

近年来,中学数学教学倡导以生为本的思想,重视建立新型的师生关系。为此,需要创建一个民主、和谐、平等的师生关系,这样才能让中学生的学习主动性和创造性真正体现出来,学生才能更好的学会生活和发展。本文以初中数学教学为例,从树立争取的学生观、要平等的对待学生、培训学生的民主意识和加强师生之间的沟通四个方面对如何建立民主、平等、和谐的师生关系进行了探讨,拟对做好初中数学教学工作提供一点借鉴。     

Teacher perceptions of the mathematical potential of students in special education in the Netherlands

Research has shown that high expectations of teachers about their students’ academic development have a positive influence on how these students actually develop. Therefore, when aiming to improve students’ learning results it is essential to know how teachers think about their students’ abilities. The present study was meant to investigate what perceptions primary school teachers in special education have of their students’ potential in mathematics and what possibilities they see to reveal this potential. Data were collected through an online questionnaire. Surprisingly, the responses showed that, although the teachers teach students with low achievement scores in mathematics, most of the teachers were positive about the mathematical potential of their students. The teachers often attributed unused potential to causes outside the student and they underpinned this view with observations from school practice. The article concludes with discussing the consequences of these findings for the professional development of teachers.