Promoting teacher learning: a framework for evaluating the educative features of mathematics curriculum materials

Educative curricula, curriculum materials that intentionally foster teacher professional development, can serve as a site for teacher learning through their use in daily instructional practices. The present article introduces a framework, Teacher Learning Opportunities in Mathematics Curriculum Materials (TLO-Math), for designing and evaluating mathematics curriculum materials’ educative features according to seven theoretically based variables: (1) mathematics content knowledge for teaching, (2) teacher knowledge of student thinking in mathematics, (3) teacher knowledge of disciplinary discourse in mathematics, (4) teacher knowledge of assessment in mathematics, (5) teacher knowledge of differentiated instruction in mathematics, (6) teacher knowledge of technology use in mathematics, and (7) teacher knowledge of mathematical community. Each variable is illustrated with a definition, guiding questions, discipline-specific literature, and examples from two sets of elementary mathematics curriculum materials. The development of the TLO-Math framework is a critical first step for further study of the use of mathematics curriculum materials as sites for teacher learning.     

Special Education Teacher Education: A Perspective on Content Knowledge

The passage of No Child Left Behind and the Individuals with Disabilities Education Act has strengthened the conditions for instructional accountability for all learners. The standards‐based approach promulgated by curriculum and state assessments is central to the accountability of conditions in today's schools; however, national and state data continue to document a performance gap between students with learning disabilities (LD) and their nondisabled peers. Building on 5 years of experience in developing and testing the Blending Assessment with Instruction Program in mathematics, we present three basic principles that are essential to ensuring that students with LD achieve curriculum standards: (1) instruction must be aligned with curriculum standards, (2) teachers' content knowledge is essential to translating curriculum standards into aligned instruction, and (3) instructional methodology should receive greater attention during teacher preparation.     

Relationship between perceived and observed student-centred learning environments in Qatari elementary mathematics and science classrooms

Recently, Qatar established educational reform in charter (independent) schools focusing on curriculum standards, student-centred teaching, standards-based assessment, English as the language of instruction, and extensive professional development. A primary area of emphasis was the creation of student-centred mathematics and science classrooms characterised by inquiry and active student participation. The purpose of this study was to investigate differences in the learning environments of Qatari mathematics and science classrooms at two levels: in higher- and lower-performing Qatari schools implementing the recent Education for a New Era reform elements; and in classes of teachers who experienced professional development focused on student-centred teaching strategies and those who did not. Participants included teachers and students in 47 grade 3 and 4 mathematics and science classrooms. Classroom observations were conducted and student learning environment surveys were administered at the beginning and end of the semester. Results indicated low levels of student-centred instruction, despite significant improvement over time. Few differences by level of school performance or professional development participation existed. However, Personalisation emerged as a key learning environment variable related to teachers’ implementation of student-centred instruction.     

Is It DAP? American Preschool Teachers’ Views on the Developmental Appropriateness of a Preschool Math Lesson from China

Planned instruction is an important teaching form in early childhood mathematics education, but some educators are concerned about its developmental appropriateness. The present study was undertaken to address this issue. One hundred and seven American preschool teachers participated in the study: They watched a video-taped math lesson that was conducted in a 4-year-olds’ classroom in China and answered video-cued questions in a questionnaire. A mix of qualitative and quantitative methods was used in analyzing the data. Research Findings: Results show that on average, participants rated the quality and developmental appropriateness of the lesson as high. They acknowledged children’s active learning, teacher’s careful preparation, and use of different learning methods. But, they also identified inadequate elements such as lack of peer interactions and lesson differentiation. Practice or Policy: A relief of American preschool teachers’ current beliefs regarding the developmental appropriateness of math lessons provides critical reference for professional preparation/development programs. American preschool teachers’ high value of children’s active learning in a planned math lesson and their appreciation of teacher’s skillful guidance imply an imperative need to promote American preschool teachers’ pedagogical knowledge and skills in teaching mathematics to young children.     

Developing Practical Knowledge of the <Emphasis Type="Italic">Next Generation Science Standards</Emphasis> in Elementary Science Teacher Education

Just as the Next Generation Science Standards (NGSSs) call for change in what students learn and how they are taught, teacher education programs must reconsider courses and curriculum in order to prepare teacher candidates to understand and implement new standards. In this study, we examine the development of prospective elementary teachers’ practical knowledge of the NGSS in the context of a science methods course and innovative field experience. We present three themes related to how prospective teachers viewed and utilized the standards: (a) as a useful guide for planning and designing instruction, (b) as a benchmark for student and self-evaluation, and (c) as an achievable vision for teaching and learning. Our findings emphasize the importance of collaborative opportunities for repeated teaching of the same lessons, but question what is achievable in the context of a semester-long experience.     

Characterizing pivotal teaching moments in beginning mathematics teachers’ practice

Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding.     

TIMSS 2019数学评价的框架、结果与启示

TIMSS 2019数学评价发现,中小学生的数学学习成绩正在逐渐提高,达到国际基准的比例也在提高,并存在区域、性别、领域和认识差异。同时,家庭与学校环境、师生教学准备、学生数学学习态度和数学课程与教学等背景因素都影响数学学习。为了促进我国数学教育的健康发展,我们要继承中华优秀教育传统,吸收先进教育理念,更新数学课程内容,优化教育教学评价,培养积极学习态度。     

Use of comics to enhance students’ learning for the development of the twenty-first century competencies in the mathematics classroom

Abstract

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (1) several sets of comic strips expounding all related mathematical concepts in a lively way; (2) tiered practice questions for learning reinforcement; and (3) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and 11 students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.     

The role of lesson analysis in pre-service teacher education: an empirical investigation of teacher learning from a virtual video-based field experience

A video-based program on lesson analysis for pre-service mathematics teachers was implemented for two consecutive years as part of a teacher education program at the University of Lazio, Italy. Two questions were addressed: What can preservice teachers learn from the analysis of videotaped lessons? How can preservice teachers’ analysis ability, and its improvement, be measured? Two groups of preservice teachers (approximately 140 in total) participated in the program. A three-step lesson analysis framework was applied to three lesson videos: (1) goal(s) and parts of the lesson; (2) student learning; and, (3) teaching alternatives. Preservice teachers’ ability to analyze lessons was measured through an open-ended pre- and post-assessment. In the assessment, preservice teachers were asked to mark and comment on events (in a lesson not included in the program) that they found interesting for: teachers’ actions/decisions; students’ behavior/learning; and, mathematical content. A coding system was developed based on five criteria: elaboration, mathematics content, student learning, critical approach, and alternative strategies. In both studies, the ability to analyze instruction improved significantly on all five criteria. These data suggest promising directions for the development of both an instrument to measure lesson analysis abilities and a model for teacher learning.     

INSTRUCTIONAL COHERENCE IN CHINESE MATHEMATICS CLASSROOM—A CASE STUDY OF LESSONS ON FRACTION DIVISION

In this study, we examined the instructional coherence in a Chinese mathematics classroom by analyzing a sequence of four videotaped lessons on the topic of fraction division. Our analysis focused on the characteristics of instructional coherence both within and across individual lessons. A framework was developed to focus on lesson instruction in terms of its content and process and the teacher's use of classroom discourse. The analyses of lesson instruction were further supplemented with the analyses of teaching materials and interviews with the teacher. The findings go beyond previous studies that mainly focused on a single lesson to provide further evidence about Chinese teachers' instructional practices and their possible impact on students' learning. In particular, the teacher tried to help students build knowledge connections and coherence through lesson instruction. Results also suggest that coherent curriculum and the teacher's perception of the knowledge coherence facilitated the teacher's construction of coherent classroom instruction.     

Opportunities for learning given to prospective mathematics teachers: between ritual and explorative instruction

The mathematics education field, including prospective teacher education program, has seen a continuous effort to change teaching practices to be more cognitively demanding, conceptually oriented and student centred. Our goal in this study was to examine how certain underlying assumptions about mathematical learning, as reflected in a skilled instructor’s discourse, align with opportunities to learn. The data included a set of fully transcribed 11 lessons from an introductory algebra course. The method of analysis was built upon the communicational (commognitive) framework and included discerning between the instructor’s mathematizing and identifying talk. This framework was extended to quantify the instructor’s identifying talk over the whole set of lessons. Our findings showed that at the surface level, the instruction in the class seemed to align with “explorative” goals. On a deeper level, however, it was more aligned with “ritual” goals that are concerned with producing narratives about people, not about mathematics.     

Addressing the Sociopolitical Realities of Teaching through Standards-Based Reform to Post-Licensure Master’s Degree Programs

ABSTRACT

Physical education teacher education programs have a responsibility to prepare preservice teachers in the technical aspects of teaching while also preparing them for the sociopolitical realities of teaching a marginalized subject. There is also a need for inservice teachers to engage in continuing professional development related to socialization and school sociopolitics to build upon lessons learned during initial teacher education. In the United States, one such professional development opportunity is reflected in master’s degree programs. These programs are typically guided by the National Association for Sport and Physical Education advanced standards for physical education teacher education. However, these standards do not currently have any reference to socialization or sociopolitical learning. The purpose of this article is to propose that an additional standard focusing on sociopolitical skills and teacher socialization be added to the National Association for Sport and Physical Education advanced standards for U.S.-based post-licensure master’s degree programs.     

Elementary school teachers’ uses of mathematics curricular resources

With the adoption of new content standards, teachers are often left without adequate curriculum resources. This study examined how educators used their curricular resources to teach new mathematics standards in the USA. Analyses of open-ended survey responses from 257 teachers and teacher–leaders in Grades 3 through Grade 5 indicated that every educator reported supplementing their districts’ or schools’ primary curricular resources with other materials. These supplements primarily included resources found for free on websites and resources that claimed to be aligned to the new standards, but varied in terms of alignment to national standards for effective mathematics curriculum. Implications for this study include further research on how teachers make decisions regarding curriculum resources as well as increasing teachers’ access to quality curriculum materials that can support students’ mathematical learning.     

初中数学“章起始课”的探索与思考

在数学课程标准研制与修订中,一个重要的改进是强调整体把握课程,掌握课程的知识、方法、思想体系,促进学生核心素养、数学核心素养的发展。在数学教学中,如何上好数学“章起始课”的探索和实践是一个重要的抓手。围绕章起始课的教学要遵循六条基本原则:统领性、整体性、逻辑性、发展性、温故性、激趣性。     

中学数学教学的资源

课程资源是实现数学教学目标的基础和保障,是课程设计、课程实施不可缺少的要素。教师要了解获取数学课程资源的途径,以及对数学课程资源进行分析、评价和加工。     

Defining the Difference: Comparing Integrated and Traditional Single-Subject Lessons

Early childhood curricula should be authentic and child-centered, however, many teachers still rely on direct instruction lessons. To better define how an integrated curriculum meets the needs of students, this study examined teacher talk and actions during instructional activities with first and second graders under two conditions: (1) subject-integrated social studies lessons of an integrated curriculum unit (experimental condition); and (2) single subject-focused mathematics lessons of a traditional separate subject curriculum (control condition). The mixed-methods study sought to define and compare characteristics of both curriculum approaches. Fourteen hours of observations were collected in each setting. In the integrated curriculum setting, the teacher was a facilitator of teamwork, offering choices, and giving praise; students made choices, decisions, and worked collaboratively. In the traditional setting, the teacher delivered direct instruction and controlled behavior; students followed directions, recalled knowledge, and worked individually. Less teacher energy was expended for behavior management in the integrated curriculum setting, indicating intrinsic motivation of students. Implementation of integrated curricula is recommended because of the student-centered focus that results in greater motivation, ownership, and teamwork, along with deeper knowledge connections. Because many factors hinder implementation, teachers need support when first teaching with this approach.     

The role of pupil voice as a trigger for teacher learning in Lesson Study professional groups

This paper focuses on the role of pupil voice as a trigger for teacher learning and for improving teaching quality. This is investigated in the context of Lesson Study (LS), a professional development model that can incorporate pupil voice into teachers’ collaborative reflections on lessons. Data are from two LS groups of mathematics teachers in London (one primary and one secondary school). Video-recorded pupil interviews and teacher discussions were transcribed. Episodes of teacher discussions were coded for reference to pupil input and subsequent impact on future plans. Qualitative analysis of discussions examined whether some pupils’ input was favoured over others’. Results are significant in pointing to LS as a mechanism for attending to pupil voice. In so doing, it is suggested that pupil input provided a challenge for teachers in their interpretations of pupil learning, evaluating lessons and planning, and in contributing to teacher learning from LS.     

What textbooks offer and what teachers teach: an analysis of the Dutch reading comprehension curriculum

In the Netherlands, the quality of the reading curriculum is currently under debate because of disappointing results on national and international assessments of students’ reading skills and motivation. In a mixed-method study, we analyzed the content of Dutch textbooks for reading comprehension instruction (i.e., the implemented curriculum) and teachers’ evaluation and use of these books (i.e., the enacted curriculum). A materials analysis of reading comprehension lessons (N?=?80) in eight textbooks for grades 4 and 5 was complemented with semi-structured teacher interviews (N?=?29) and lesson observations (N?=?11), with a focus on the quality of reading strategy and text structure instruction in the curriculum. Main findings are (1) a lack of alignment between lesson goals, theory, and assignments, (2) a strong focus on practicing strategies, (3) limited declarative knowledge about strategies and text structure, (4) little opportunities for self-regulated strategy application. The teachers that were interviewed mention similar problems, but still hardly deviate from the textbook’s content and pedagogical guidelines. We make recommendations to improve the quality of the curriculum.

     

STRUCTURE OF PRIMARY MATHEMATICS TEACHER EDUCATION PROGRAMS IN SPAIN

Spain was 1 of the 17 countries that participated in the International Association for the Evaluation of Educational Achievement’s Teacher Education and Development Study in Mathematics (TEDS-M 2008). In this paper, we explore and describe the structure of Spanish primary mathematics teacher education programs. We analyzed the documents collected from the 48 sampled Spanish institutions that participated in TEDS-M. Our approach to the syllabus analysis focused on the established content dimension of curriculum in educators’ syllabi. These contents are structured into 4 knowledge domains—school mathematics, advanced mathematics, general pedagogy, and mathematics pedagogy—and categorized into subjects and topics. The results show that Spanish teacher education programs are diverse across institutions, but follow a basic structure that emphasizes the teaching of general pedagogy subjects.     

论信息技术与初中数学课程的有效整合

运用信息技术能够有效地解决中学数学课程中的重点、难点讲解,提高教学效率,体现出科学的教学模式。信息技术与数学课程的有效整合,能够实现课堂教学的最优化。因此,在初中数学教学中,教师要根据教学目标、教材内容,以及学生的实际状况,设计好在不同的知识点、教学环节上计算机对学习活动所应达到的支持水平。这样才能有效地运用信息技术,提高课堂教学效率。