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In this article, the authors present a framework for guiding elementary preservice teachers in adapting mathematics word problems to better meet English language learners' (ELLs) needs. They analyze preservice teachers' ELL adaptations implemented in a one-on-one setting. Through qualitative methods, four themes regarding implemented adaptations are identified: language adaptations, mathematical adaptations, tool/visual adaptations, and structural adaptations. The authors conclude that the framework was successful in helping preservice teachers learn about adapting curriculum by interacting with ELLs. Implications for teacher education are discussed.

Preservice elementary teachers often struggle with prime decomposition and other mathematical topics that correlate with number theory. This paper provides a framework for integrating prime factor tiles into their curriculum with a particular emphasis on prime decomposition. Using this framework, preservice teachers explored and evaluated numbers using prime factor tiles. The results of the exploratory inquiry showed that preservice teachers made some progress in their understanding of prime decomposition after exploring with the tools. However, they struggled with problems requiring the application of prime decomposition. More time to delve into this topic is probably needed in order to observe further gains.

As there has recently been an onslaught of video cases being developed and implemented with preservice teachers, it is important to evaluate how we should use these cases. This research investigates the features elementary preservice teachers consider valuable when using video cases in mathematics education. The researchers used hierarchical cluster analysis to create a dendrogram that displayed statistically significant features. The study revealed two primary clusters--(a) cross-subject lessons emphasizing adaptations and techniques to reach a variety of learners and (b) problem-based lessons with students in groups supported by lesson analysis--as well as (c) a small third cluster of collection and distribution of materials. Ultimately, such findings can be used to guide the design and incorporation of tools for using mathematics-based video cases. (Contains 2 tables and 1 figure.)

Family math night can easily be implemented into mathematics methodology courses providing an opportunity for field-based learning. Preservice teachers were asked to develop and implement an inquiry-based activity at a family math night event held at a local school with personnel, elementary children and their parents in attendance. This action research examines what preservice teachers discovered about how children learn mathematics during their interactions with parents and children. Preservice teachers' individual reflections focusing on children's learning were qualitatively analyzed and clustered. In addition, data from teacher educator's observation notes was used to triangulate findings. Four themes were identified in relation to children's needs for promoting learning in mathematics: (1) activity adjustment (2) engagement through guiding and questioning (3) motivational issues and (4) the use of manipulatives and visuals. The event appeared to offer preservice teachers insight into the elements of activities needed to guide children's learning in mathematics.

This study examined the structure of two preservice teachers' understandings of educational software in mathematics using repertory grid techniques. Specifically, the study focused on how teacher educators can enable preservice teachers to discern the features of mathematics software, and develop pedagogical goals that reflect the affordances and constraints of available tools. Results showed a deepening of knowledge and a differentiation of knowledge following experiences of exploration, evaluation, and comparison of different types of software. Results imply that directing preservice teachers' attention to utilizing the functional characteristics of software for developing plans and for the design of instruction may be fruitful for more effective integration of software in their future teaching. However, participants' preexisting content knowledge and their pedagogical worldview tempered this effect. (Contains 8 figures and 2 tables.)

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern‐based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze linear, geometric, and quadratic integer patterns using color tiles. Then they created, extended, described, and analyzed their own patterns while working in groups (n = 8). The research question was: What algebraic errors do PSTs demonstrate in the process of constructing, explaining, and analyzing their own linear, geometric, and quadratic patterns using color tiles? The analysis, which focused on errors and misunderstandings preservice teachers demonstrated in their final unit, revealed three specific areas of difficulties: figural errors, explanation challenges, and improper use of algebraic language. Participants failed to connect their algebraic images in a coherent manner, there was confusion in articulating their algebraic thought processes, and algebraic terminology was improperly used. Implications for teaching and further research are described. [ABSTRACT FROM AUTHOR]

With the ever-changing dynamics of society, teachers are often faced with a classroom of students who have diverse linguistic and academic needs. Research has shown that schools are becoming more linguistically diverse throughout the United States and that English language learners (ELLs) are posing their own sets of challenges for teachers. Teaching mathematics to ELLs can be particularly challenging. Mathematics contains many of the same challenges as other subjects and can be perceived as being less difficult because it is based on the language of numbers. By using deliberate strategies to adjust the phrasing of word problems, teachers can provide a richer mathematics experience for ELLs. The author presents two examples of word problems written in a traditional format and rewritten in an adjusted format reducing linguistic demands while maintaining rigor. The framework can be used by teachers to support their ELLs by modifying word problems to focus more on the mathematics. (Contains 2 figures.)

Video cases are becoming more and more prevalent throughout the United States to assist in the development and growth of preservice teachers' instruction. This research investigates the perspectives of preservice teachers and their naive understandings of the kinds of learning and assistance video cases can provide in their methodology courses. Personal Construct Theory was used to uncover participants' perceptions of their needs in terms of curriculum content of video cases. Hierarchical cluster analysis revealed six distinct clusters which serve as themes for discussing the early needs of preservice teachers and how video cases might be configured to address these perceived needs. Results reveal that preservice teachers' beliefs, though naive, do reflect the research on the actual needs of teachers in their first years of induction and support. Perhaps if preservice teachers' predilections are examined, this data can help guide the future implementation of video cases in their university courses.

This article describes a structure to help preservice teachers get invaluable field experience by aligning theory with practice supported by the integration of elementary school children into their university mathematics methodology course. This course structure allowed preservice teachers to learn about teaching mathematics in a nonthreatening environment without the formal observations and evaluations common in student teaching situations. It also allowed teachers to view lessons and to teach using appropriate framework to produce optimum problem-based learning. In addition, teachers experienced the proper use of manipulatives and discovered how manipulatives support student learning. (Contains 1 figure.)

The potential to use mathematics software to enhance student thinking and development is discussed and a taxonomy of software categories is outlined in this paper. Briefly, there are five categories of tool-based mathematics software that can be used fruitfully in a mathematics curriculum: (a) review and practice, (b) general, (c) specific, (d) environment, and (e) communication. A description of the affordances and constraints of the five types of software and how each facilitates different aspects of student learning clarifies the ways in which diverse off-the-shelf offerings can be used to address the goals of mathematics instruction, from building basic skills to exploring mathematical applications in the real world.

The article focuses on the utilization of deliberate strategies to adjust the phrasing of word problems to offer a deeper mathematical experiences for English language learners (ELLs) in the U.S. It mentions the basic principles for adjusting word problems for ELLs such as writing shorter sentences, adding additional language for clarification, and simplifying the grammar. It notes that the strategy must be regarded as a temporary action until students have developed proficiency in mathematics.