THE PLANNING OF MANIPULATIVE MATERIALS IN THE CONTEXT OF LESSON STUDY IN CONTINUOUS TEACHER TRAINING FOR INCLUSIVE MATHEMATICAL LITERACY (original) (raw)

Preparing Middle School Mathematics Teachers: Rethinking Engagment and Learning

2012

In this theoretical research paper we describe a collaborative effort between researchers and university faculty to improve how teachers are prepared to teach middle school mathematics. Two powerful instructional frameworks, UDL and TPACK are dovetailed within in a web-based dynamic textbook, "Proportional Dynabook" that focuses on proportional reasoning concepts related to ratio, similarity, and linear function. Theoretical tensions between special and general education teacher preparation programs influence the ongoing design of Proportional Dynabook. Pre-service and in-service special education teachers used Proportional Dynabook in a graduate level methods class to design a ratio lesson for a student who struggled with the concept. Teachers developed deeper understanding of ratio and related pedagogical strategies that make the content of mathematics accessible to diverse learners. Classrooms are more diverse than ever due to recent legislation such as No Child Left Behind and the Individuals with Disabilities Education Improvement Act that require all students to have access to the general education curriculum and to be included in the same assessments (Van Garderen, Scheuermann, Jackson, & Hampton, 2009).To meet the increasingly diverse needs of students with learning differences who are being educated in the general education classroom, special education services are being brought to the general education classroom. The lines between general and special education are blurred and teachers are being asked to collaborate to meet the educational needs of an extremely diverse group of learners. These collaborative efforts are based on the idea that each teacher has specific knowledge and expertise that address the instructional needs of the class (Van Garderen et al., 2009). However, collaboration in theory does not address the friction that exists in practice. Philosophical differences in pedagogy and learning theory create tension in the design of instruction. While this tension can be an obstacle to the design of effective instruction, it can also be the vehicle that brings together special and general education researchers to conceive and design innovative instructional tools and practices to meet the needs of all students. Students with high achievement, with learning disabilities and English Language learners are all receiving mathematics instruction from teachers who have been trained as math teachers or special education teachers but not usually both. Special education teachers tend to focus on pedagogy and interventions while general education teachers focus more on the content and structure of mathematics (Van Garderen et al., 2009). Now both teachers are given the formidable task of "raising the floor by expanding achievement for all, and lifting the ceiling of

Effective Choices and Practices: .QRZOHGJHDEOHDQG((SHULHQFHG7HDFKHUV∂ Uses of Manipulatives to Teach Mathematics

2013

This study was a comprehensive examination of the use of mathematics manipulative materials by a group of K-8 teachers identified as knowledgeable and experienced mathematics manipulative users. Because the teachers in this study were knowledgeable and experienced, the inquiry focused what mathematics materials the teachers chose to use. Analysis of over 500 lesson summaries from 116 K-8 teachers indicated that there were three common mathematics materials used by K-8 teachers who are knowledgeable and experienced manipulative users (dice, pattern blocks and snap cubes). The results support previous research showing that frequency of manipulative use declines from grades K through 8. In addition, the results revealed that the variety of manipulative used by teachers in this project also decreased across grades K through 8. An additional difference among the grade-specific groups was the way that teachers used the mathematics materials in their lessons, with Grades K-2 and 3-4 teache...

Effective Choices and Practices : Uses of Manipulatives to Teach Mathematics

2013

This study was a comprehensive examination of the use of mathematics manipulative materials by a group of K-8 teachers identified as knowledgeable and experienced mathematics manipulative users. Because the teachers in this study were knowledgeable and experienced, the inquiry focused what mathematics materials the teachers chose to use. Analysis of over 500 lesson summaries from 116 K-8 teachers indicated that there were three common mathematics materials used by K-8 teachers who are knowledgeable and experienced manipulative users (dice, pattern blocks and snap cubes). The results support previous research showing that frequency of manipulative use declines from grades K through 8. In addition, the results revealed that the variety of manipulative used by teachers in this project also decreased across grades K through 8. An additional difference among the grade-specific groups was the way that teachers used the mathematics materials in their lessons, with Grades K-2 and 3-4 teache...

Examining the Role Lesson Plans Play in Mathematics Education

International Group for the Psychology of Mathematics Education, 2015

Scott A. Courtney Kent State University scourtn5@kent.edu Esra Eliustaoglu Kent State University eeliusta@kent.edu Amy Crawford Kent State University crawf18@kent.edu Formal lesson plans have long been touted as a best practice in mathematics teacher preparation. Experienced teachers frequently view formal lesson plans as nonessential to the planning, implementation, and evaluation of instruction. We discuss results from an online survey designed to make the perspectives of 60 prospective and practicing mathematics and special education teachers regarding lesson plans explicit. Practicing teachers identified their use of formal lesson plans as a reflective tool and for organization purposes, whereas for prospective teachers lesson plans served as a guide and for accountability reasons. Finally, we describe future mathematics teacher education engagements designed to promote productive yet practical perspectives of formal lesson plans.

Making Manipulatives for Mathematics Education

6th FabLearn Europe / MakeEd Conference 2022

This paper describes the efforts of an interdisciplinary team of researchers as they collaborated to create a digital fabrication curriculum module for mathematics teacher education. The initial four-day workshop design was piloted with five pre-service teachers. The design objective was to introduce digital fabrication techniques joint with mathematical concepts and the design of classroom activities to develop pre-service teachers' technological, pedagogical, and content knowledge. The workshops included activities to find, adapt, create, and share mathematical manipulatives using digital fabrication tools, techniques, and platforms. Manipulatives are tangible objects reifying mathematical concepts and one type of representation used in mathematics teaching. The paper reports on the design process and our design motivations to address contextual constraints and varying levels of exposure to digital fabrication for both pre-service teachers and teacher educators. The developed "find-adapt-create-share" framework for introducing digital fabrication was evaluated through researchers' self-reflection and pre-service teachers' feedback during concluding interviews. CCS CONCEPTS • Applied computing → Education.

Lesson Study with Mathematical Resources: A Sustainable Model for Locally-Led Teacher Professional Learning

Mathematics Teacher Education and Development, 2014

Teams of educators conducted lesson study independently, supported by a resource kit that included mathematical tasks, curriculum materials, lesson videos and plans, and research articles, as well as protocols to support lesson study. The mathematical resources focused on linear measurement interpretation of fractions. This report examines the resource kit content, the changes in teachers' fractions knowledge, and the lesson study processes that enabled changes in teachers' knowledge. Quantitative findings show that teachers in the experimental condition (lesson study supported by resource kits) significantly improved three of the four facets of fractions knowledge studied, including understanding the whole, unit fractions, and fractions as numbers; whereas control group teachers did not. Qualitative data, including video and written reflections, illuminate activities that supported teachers' knowledge development, including solving and discussing mathematical tasks, studying curriculum and research, and observing students during research lessons.

What’s Going on Backstage? Revealing the Work of Lesson Study with Mathematics Teachers

2000

In this project twelve mathematics teachers in four Canadian schools, ranging in experience levels from novice to over twenty years, engaged in Japanese Lesson Study cycles. Their focus was on the use of interactive whiteboards and manipulatives as supports to student learning in mathematics. These teachers identified a variety of ‘backstage activities’ during the formal Lesson Study cycle, including, for

“How I Want to Teach the Lesson”: Framing Children’s Multiple Mathematical Knowledge Bases in the Analysis and Adaptation of Existing Curriculum Materials

2018

We consider how prospective elementary teachers think about multiple mathematical knowledge bases as they consider adapting existing mathematics curriculum materials to meet the needs of culturally, linguistically, and socioeconomically diverse students. Multiple mathematical knowledge bases include both children’s mathematical thinking and the cultural-, home-, and community-based funds of knowledge that children inevitably bring into the classroom. We explored how prospective elementary teachers attended to multiple mathematical knowledge bases as they used a lesson analysis tool, the Curriculum Spaces Table, to evaluate existing curriculum materials and identify spaces for adapting these curriculum materials to more efficiently meet the needs of all students. Our analysis examined 47 written reflections on the analysis of and adaptations for a Grade 3 lesson. Findings showed that prospective teachers paid considerable attention to children’s mathematical thinking and gave some at...

Introduction to Mathematics Manipulatives: Preservice Teachers Create Digital Stories Illustrating Types and Application of Manipulatives

2013

Math concepts can be difficult for students to understand due to their abstract nature. Because of this, the National Council of Teachers of Mathematics (NCTM) has urged teachers to focus on the facilitation of students’ understanding and conceptualization rather than on drill and practice of rote procedures (NCTM, 2000). The use of manipulative materials in mathematics classrooms supports this attempt to provide students with a more thorough understanding of mathematics by allowing students to discover and apply concepts presented in class (Canny, 1984; Clements & Battista, 1990; Dienes, 1960; Driscoll, 1981; Fennema, 1972, 1973; Skemp, 1987; Sugiyama, 1987; Suydam, 1984). Manipulative materials are concrete models that can be touched and moved around by the students, thereby providing tangible investigative experiences for abstract mathematics concepts as well as how concepts are related. Incorporating the use of manipulative materials with an emphasis upon the thought process of ...