Search

The purpose of this study was to examine how practices and attitudes of high school teachers vary when comparing Advanced Placement (AP) courses to regular and honors track courses. The [...]

Many school-improvement efforts include time for teacher collaboration, with the assumption that teachers' collective work supports instructional improvement. However, not all collaboration equally supports learning that would support improvement. As a part of a 5-year study in two urban school districts, we collected video records of more than 100 mathematics teacher workgroup meetings in 16 different middle schools, selected as 'best cases' of teacher collaboration. Building off of earlier discursive analyses of teachers' collegial learning, we developed a taxonomy to describe how conversational processes differentially support teachers' professional learning. We used the taxonomy to code our corpus, with each category signaling different learning opportunities. In this article, we present the taxonomy, illustrate the categories, and report the overall dearth of meetings with rich learning opportunities, even in this purposively sampled data set. This taxonomy provides a coding scheme for other researchers, as well as a map for workgroup facilitators aiming to deepen collaborative conversations. Keywords discourse analysis, inservice education, teacher learning, professional learning communities, conceptual change, Teacher collaboration is at the center of many school-improvement efforts. Because of the frequently observed concurrence of higher than expected student outcomes and strong teacher communities (McLaughlin & Talbert, 2001; [...]

Central in the frameworks proposed to capture the knowledge needed for teaching mathematics is the assumption that teachers need more than pure subject-matter knowledge. Validation studies exploring this assumption by recruiting contrasting populations are relatively scarce. Drawing on a sample of 644 Greek-Cypriots preservice and inservice elementary school teachers and university students with strong mathematical background, this study explored participants' knowledge with respect to four teaching practices: providing and evaluating explanations; selecting and using representations; analyzing student errors, misconceptions, and non-conventional solutions; and selecting tasks. Results emerging from an item response theory (IRT) model and non-parametric tests showed significant differences among these groups, largely in the first two practices. Clinical interviews with a voluntary sub-sample of these participants provided insights into the unexpected findings related to the other two practices. The theoretical, methodological, and practical implications of these findings are discussed, and directions for future studies are offered. Keywords mathematics, item response theory, teacher knowledge, teaching practices, During the last decade, a variety of frameworks have been proposed to capture the knowledge needed for teaching mathematics (e.g., Adler & Davis, 2006; Ball, Thames, & Phelps, 2008; Davis [...]

In this article, the authors report on a study that contributes to a growing body of literature that considers professional development (PD) focused on mathematics and equity. The authors examined how lived experiences provide a foundation for the ways teachers take up equity in their mathematics teaching practice. The constructs of praxis and figured worlds are used to frame the study. In particular, teachers' identities in the figured worlds of standards-based mathematics, multicultural education, and equitable mathematics pedagogy were explored with a focus on how they contributed to where the teachers located praxis for equity in mathematics. The teachers' lived experiences and their participation in the PD were analyzed with an eye toward teachers' evolving identities and how they contribute to where teachers located praxis. Keywords professional development, equity, mathematics education, figured worlds, praxis, Attention to issues of equity and diversity within mathematics education is an area of growing interest. For some, this interest grows out of an effort to understand gaps in achievement [...]

ABSTRACT At times we the math instructors in a classroom are not careful enough to use proper Mathematical wording, e.g. [sin.sup.2] + [cos.sup.2] = 1 without any reference to the [...]

This article draws on interviews with a recent graduate of an inquiry-based initial teacher education program, and on video data collected in his Grade 6 classroom, to explore the extent to which he was able to enact inquiry-based teaching approaches in his teaching of mathematics and to consider the kinds of resources (administrative and curricular) necessary to sustain and enhance such practices in today's schools. The findings support existing literature noting the importance of a supportive and knowledgeable school principal and extend that literature to detail the kinds of support that make a difference in sustaining, in particular, inquiry-oriented teaching practices. The study also draws attention to the need for further research concerning the kinds of curricular support materials necessary to help new teachers who are attempting to enact such practices to thrive in schools. Keywords: Inquiry-based teaching and learning, mathematics teaching, novice teachers Cet article s'appuie sur des entretiens avec un jeune diplome d'un programme de formation initiale des enseignants base sur l'investigation, et sur les donnees video enregistrees dans sa classe de 6e annee, le but etant d'etudier dans quelle mesure il etait capable d'adopter des approches pedagogiques basees sur l'investigation dans son enseignement des mathematiques et de prendre en compte les types de ressources (administratives et curriculaires) necessaires au maintien et a l'amelioration de ces pratiques dans les ecoles d'aujourd'hui. Les resultats soutiennent la documentation actuelle constatant l'importance d'un directeur d'ecole qualifie et sur lequel on peut compter, en allant meme plus loin et en detaillant les types de soutien pour ameliorer, soutenir et mantenir, en particulier, les pratiques pedagogiques axees sur l'investigation. L'etude attire egalement l'attention sur la necessite de poursuivre les recherches concernant les types de supports pedagogiques necessaires pour aider et encourager les nouveaux enseignants qui tentent d'adopter de telles pratiques dans les ecoles. Mots-cles: Enseignement et apprentissage bases sur l'investigation, l'enseignement des mathematiques, enseignants debutants, Introduction Within the literature on newly-graduated teachers' experiences of beginning to teach (e.g., Grossman & Thompson, 2008; Scherff, 2008), studies show that conditions in schools are often challenging for new [...]

Teacher: What do you think the equal sign means? Student 1: I think it means like what's the next number of the addition problem. Student 2: It means the sum. [...]

Algebra students may often demonstrate a certain degree of proficiency when manipulating algebraic expressions and verbalizing their behaviors. Do these abilities imply conceptual understanding? What is a reliable indicator that would provide educators with a relatively trustworthy and consistent measure to identify whether students learn algebraic concepts beyond procedures? How might teachers know when the transition from 'operational' or 'process conception' to 'structural' or 'object conception' takes place? Assessing mathematics students' conceptual understanding is critical for educators to make informed decisions when selecting curriculum, planning instruction and developing an assessment program. These decisions should be supported by strong educational foundations and be rooted in theory that provides sustained basis for understanding how mathematics students construct knowledge and how mathematics can be taught. The multiyear research study described in this article attempts to answer these questions. The article introduces a framework for assessing middle school algebra students' levels of understanding of linear equations with one unknown. The framework is rooted in Orit Hazzan and Rina Zazkis's ideas of reducing level of abstraction, Uri Wilensky's and Victor Cifarelli's ideas of the degree of abstraction, Anna Sfard's theory of operational and structural conception, Ed Dubinsky and Michael McDonald's APOS theory, and the concept of representation in mathematics and mathematics education. THE KEY WORDS: conceptual understanding in algebra, reducing level of abstraction, multiple representations of mathematical relationship., Introduction The concept of unknown and operations with unknowns are central to teaching and learning middle school algebra. Learning about linear relationship with one unknown, students may often demonstrate a [...]

The issue of rigor is examined through two demonstration lessons aimed at integrating literature and mathematics. Rigor is seen by students from the realm of teaching and learning, while teachers see it from the realm of curriculum.

The Reggio Emilia lesson-planning framework, which takes into account both math content and student context, includes formative and summative assessment. As a result, the mathematical needs of students can be emphasized since ongoing feedback about teaching and learning can be provided. Repercussions of applying this framework to U.S. classrooms are explored.

The Mathematics Scan (M-Scan) is an observation tool intended to help teachers in assessing the quality of mathematics instruction. The eight dimensions of classroom instruction in the M-Scan framework encompass a high-quality mathematics lesson and characterize a model lesson. Recommendations on integrating these dimensions into daily practice are also provided.

Mathematical knowledge for teaching requires not only mathematical understanding but also skill, fluency, and sensibility to effectively help others learn mathematics. Suggestions on determining mathematical downsides of mathematics teaching, on applying mathematical knowledge, and on boosting mathematical capacity in practice are also provided.

This study draws on the theoretical underpinnings of the research literature in identity and investigates the transition from experienced teacher to novice mathematics coach. The 4 components of a math coach's identity (coach as supporter of teachers, coach as supporter of students, coach as learner, and coach as supporter of the school-at-large) that this study highlights were enacted by the beginning coaches on their school stage and negotiated with their audience (i.e., teachers, principals) as they attempted to fulfill these roles within the school environment. By examining the roles, expectations, and interactions of first-year mathematics coaches, we deepen our understanding of the demands placed on novice mathematics coaches as they assume new roles and identities.

Methods of improving the ability to formulate and evaluate mathematical arguments by using logical necessity are discussed. Understanding logical necessity is an important skill for prospective elementary school mathematics teachers.

The design and implementation of math trails can promote meaningful mathematical learning outside the classroom walls. They also help develop children into flexible and creative mathematical thinkers and problem solvers.

Culturally relevant pedagogy is not well understood as an instructional strategy in the mathematics classroom. This study reveals the challenges two teachers faced when they implemented a pilot project with [...]

Elementary school mathematics teachers have found the topic of elections as a good context in exploring fractions, probability, and combination. The activity was also found to have touched on the students' interest in the subjects of fairness, ballots, and election processes.

How a teacher used her experiences in developing a curriculum program that allowed her to enact a coherent mathematics course which continually assesses and builds on the students' mathematical thinking is discussed. While teachers deal with continually changing factors like teaching standards, they are expected to use curriculum materials to do what is best for their students.

How and why teachers transition conventional elementary textbook lessons into Standards-based teaching is discussed. Teachers are encouraged to study, and draw on research and best practices to design lessons. Teachers should also consider the mathematical content and on ways that will support students' understanding.

How the mathematician's chair strategy can be implemented in second-grade classrooms is described. It was found that teachers should provide additional time, support, and strategies to address the frustrations associated with how students solve mathematical problems.

How an elementary mathematics teacher developed a strong mathematical environment is presented. The teacher developed the environment along with the fifth-graders who were left out when an oversized class was split into two. The improvement of the environment involved the physical design of a classroom, as well as the discussion of class expectations.

A lesson that is designed by a professional learning team for second-graders in studying areas is presented. The lesson involves partitioning a region with a two-dimensional unit of measure, as well as iterating a unit to cover the region without overlap, and exploring the conservation of area.

Teachers and families are encouraged to work together to ensure that mathematical experiences are relevant and meaningful, while encouraging strong connections between home and school. Good relationships between teachers and families also empower children to explore and build a mathematical understanding of the world.

Mathematics teachers should allow their students to generate their own data representations to help them understand their data better. This also allows students to recognize different methods of data representation and problem solving.

Mathematics teachers aiming for specific responses from their students should use more focused and explicit questions than more open ones. This method can elicit responses even from students who do not participate much in discussions.

Mathematics teachers can help improve each other's practices through engaging in dialogue about the implications of mathematics demonstration classrooms. They can also learn about other aspects of mathematics teaching not seen in demonstration videos.

The processes involved in a lesson study experience implemented with preservice secondary mathematics teachers are described. The utility of the lesson study program in enabling collaborative reflection among preservice teachers, and improving instruction of in-service teachers is discussed.

The process of inquiring into students' mathematical understandings, developing their inner voices to make sense of students understandings of mathematics and provide sample instructional activities are discussed. Hermeneutic listening though dialogue or written responses is a vital tool to guide instruction.

The article discusses two studies in which maths talk in U.S. and Chinese classrooms is examined to see if any differences exist between the teaching methodologies between the two. It is seen that teachers should not speak much but instead should allow the students to do math talk to arrive at a better mathematical knowledge.

Videotaped interview-based assessment or (VIBA) is described and its benefits as an intensive assessment tool as well as a major source for teachers' professional learning are discussed. VIBA is a very beneficial tool that is very relevant to classroom teaching and also intensive intervention.

The article discusses how mathematics teachers and students can solve mathematical problems by investigating some interesting architecture and using it to relate to various geometric shapes. One project is a visit to the Lincoln Memorial to try and work out different shapes.

The article discusses a preassessment student self-evaluation diagnostic instrument and a postassessment student self-evaluation instrument, developed by a mathematics teacher. The aims of these preassessments are to help students recognize what knowledge they have actually mastered and the concepts they are still struggling with.

A common technique used by mathematics teachers to teach students place value by decomposing numbers is counting the days of school. It helps provide a much-needed basis and foundation for children's work with algorithms for addition and subtraction.