Trena L. Wilkerson

Lesson Study: The Impact on Teachers' Knowledge for Teaching Mathematics

This qualitative study examined whether or not participation in lesson study provided educators the opportunities to improve their knowledge for teaching mathematics. Participants for the study consisted of 24 middle school mathematics teachers from seven urban schools who formed five lesson study groups. Analysis of the data consisted of both a within and across case comparison. Analysis showed that particular factors in the lesson study cycle provided greater opportunity for teachers to increase their knowledge for teaching mathematics. These factors are referred to as “windows of opportunity.” Findings showed participants in three of the five lesson study groups showed an increase in their knowledge for teaching mathematics as a result of how teachers reacted to the “opportunities.”

A Triad Model for Preparing Preservice Teachers for the Integration of Technology in Teaching and Learning.

Abstract This article provides a model for preparing preservice teachers for the integration and implementation of technology in teaching and learning. The technology integration approach implemented focuses on a triad model that identifies three areas of technology infusion: communication, productivity, and research/instruction. This triad model demonstrates one approach for designing curriculum and appropriate experiences in a teacher preparation program that provides hands-on experience with technology as supported by the vision of the National Educational Technology Standards (ISTE, 2000). Descriptions are given of specific assignments, projects, and learning experiences designed to engage preservice teachers in enriching technological experiences to enhance their own learning while at the same time serving as a model for teaching.

Unifying the Algebra for All Movement.

There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the Algebra for All movement. In light of this movement, there must be a clear consensus about what is taught in the name of algebra. Yet, researchers documented this is not the case. The present research proposes to unify the leading algebra standards and assessment framework documents to identify the key ideas of algebra. The analysis resulted in six key ideas: (a) Variables, (b) Functions, (c) Patterns, (d) Modeling, (e) Technology, and (f) Multiple Representations. Outlined is the research process and resulting unification of existing algebra framework documents, and consideration is given for its uses in educational policy regarding algebra and potential directions for future research.

Walking the Talk: Lessons Learned by University Mathematics Methods Instructors Implementing Lesson Study for Their Own Professional Development

Seven university professors participated in lesson study of their own mathematics methods teaching. They presented a research lesson four times in elementary mathematics methods classes and a fifth time as a public research lesson at a national mathematics education conference. The lesson focused on the use of invented strategies in elementary mathematics instruction. The project demonstrated that lesson study is a powerful tool for mathematics teacher educator professional development, supporting the premise that mathematics instruction is a problem to solve rather than a set of teaching techniques to implement.

An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach.

This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in teacher-led classroom instruction with a series of six research-based lessons, and then were given a posttest. The purpose was to examine the use of discrete and continuous models and the impact on student understanding of fractions. A mixed-methods approach was utilized, with descriptive statistics discussed relative to quantitative pre/post data. Qualitative data were collected in the form of observer notes, teacher reflections, and anecdotal assessment. A case study approach was taken to examine findings within and across grade levels. Major findings include (1) students demonstrated growth in understanding of fractions with both models; (2) students generally understood fraction concepts better using discrete models, but results were mixed; (3) students were not necessarily able to express fractional ideas at a rigorous level; and (4) 3rd-graders were able to use partitioning effectively but were able to recognize equivalence more easily within the discrete model.

Preservice Teachers’ Critical Connections to Effective Mathematical Teaching Practices: An Instructional Approach Using Vignettes

ABSTRACT Preservice teachers (PSTs) must be able to link content, effective teaching practices, and student learning; thus, it is critical for teacher educators to emphasize connections between research and practice in methods courses. Reflection plays an important role in this process. In this article, the authors discuss and illustrate a vignette activity sequence used in a secondary mathematics methods course focused on the Common Core State Standards Mathematical Practices and the National Council of Teachers of Mathematics Mathematical Teaching Practices. This activity sequence includes a mathematical task with authentic student work, a targeted vignette, and a reflection exercise connected to the PSTs’ ongoing fieldwork. The authors include a guide to implementing the activity sequence with an accompanying example used in a methods course. In addition, implications for research and practice are discussed including utilization in other content areas.

Contributing to the Development of Grand Challenges in Maths Education

David Barnes, Associate Executive Director for Research, Learning and Development, National Council of Teachers of Mathematics Trena Wilkerson, Professor, Curriculum and Instruction Graduate Program Director, Department of Curriculum & Instruction, Baylor University & NCTM Board of Directors Michelle Stephan, Assistant Professor, Department of Middle, Secondary, and K-12 Education. University of North Carolina – Charlotte.