Background, Process & Outcomes

Vision Statement

Leveraging Funding Streams Matrix

Criteria to Assess Promising Practices

Promising Practices

Research and Resources

Tool Participants

Research, Resources, & Case Studies

This section provides research, resources, and case studies that highlight projects and/or initiatives that effectively integrate technology into mathematics.

• Research
• Resources
• Case Studies

Research

Bransford, John D., Ann L. Brown, and Rodney R. Cocking. (Eds). (2000). How People Learn Brain, Mind, and School. National Academy Press: Washington, D.C.

Learning is a basic, adaptive function of humans. People are designed to be flexible learners and active agents in acquiring knowledge and skills. This research provides a deep understanding of complex reasoning and performance on problem-solving tasks and skill development and understanding in key subjects.

This book presents a 21st century account of the principles of learning. Five themes are addressed that change conceptions of learning and shift instructional emphasis form diligent drill and practice to developing student understanding and application of knowledge.

Graphing Calculators

A growing body of research shows that graphing calculator use improves students’ math skills as well as their attitudes toward math. Specific research studies show that use of graphing calculators:

• Improves student skills and achievement in high school and middle school math.
• Positively impacts student performance in algebra.
• Improves math test scores – with and without student calculator use during testing.
• Leads to significantly better student attitudes toward math.
• Promotes higher student achievement when incorporated into the curriculum.
  

Hiebert, James, Thomas P. Carpenter, Elizabeth Fennema, Karen C. Fuson, Diana Wearne, Hanlie Murray, Alwyn Olivier, and Piet Human. (1997). Making Sense: Teaching and Learning Mathematics with Understanding. Heinemann: Portsmouth, NH.

James Hebert and his colleagues provide teachers with the best current research-based ideas for designing classrooms that support students’ mathematical understanding. This work is based upon the authors’ research in four separate programs, all of which investigated the effects of specific instructional approaches. Making Sense provides glimpses into the authors’ work and the essential features of K- 8 classrooms that exhibit these features.

Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. (Eds). (2001). Adding It Up: Helping Children Learn Mathematics. National Academy Press: Washington, D.C.

Adding It Up explores how students in PK through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.

The authors discuss what is known from research about teaching and mathematics proficiency, about focusing on the interactions between teachers and students around educational materials and about how teachers develop proficiency in teaching mathematics.

Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, probability and statistics is included.

SimCalc- the Mathematics of Change

SimCalc materials are designed to teach higher level mathematics by integrating technology, curriculum, and professional development. A recent study conducted by SRI International reported that students in Texas showed significant learning gains when using SimCalc materials.

Sowder, Judith, and Bonnie Schappelle. (2002). Lessons Learned from Research. National Council of Teachers of Mathematics. Reston, VA.

This volume is a compilation of research articles from NCTM’s Journal for Research in Mathematics Education. These articles have been specifically recast to reach the classroom teacher audience and to provide commentary that highlights the values of each article.

Each segment provides the original article with a commentary that highlights its value within the classroom and assists classroom teachers to appreciate what research offers for their day-to-day instruction. The goal is to give teachers confidence in applying strategies purported in original research and to assist them in appreciation of the benefits that research has to offer the classroom teacher.

Sutton, John, and Alice Krueger. (Eds). (2002). EDThoughts What We Know About Mathematics Teaching and Learning. Mid-Continent Research for Education and Learning (McREL). Aurora, CO

This publication summarizes education research and surveys best practices for teaching mathematics and it offers implications for improved teaching and learning. EDThoughts is a tool for professional development on the following topics: Mathematics for All, Mathematics Teaching, Mathematics Assessment, Mathematics Curriculum, Mathematics Instructional Technology, and Mathematics Learning

TI-Navigator™ System

A growing body of research states that the use of the TI-NavigatorTM system and graphing calculators improves student engagement, understanding and performance:
Specific research studies show that the use of the TI-Navigator system:

• Improves student performance in algebra.
• Enhances conceptual understanding by students.
• Keeps students on task and more focused on completing assignments.
• Fosters classroom interaction, group learning and student discussions.
• Sparks greater student engagement and immediate attention in solving problems.
• Strengthens the teacher’s ability to assess and guide student performance and understanding.

Unitedstreaming™ Dicsovery Education. Silver Spring, MD.

Unitedstreaming™ is a digital video-on-demand service from Discovery Education. Districts subscribe to the video library and teachers can access on demand individualizes streamed clips for their class instruction.

In 2004 Frank J. Boster replicated a research study evaluating the effects of using Unitedstreaming™ resources in grades 6 and 8 mathematics in the Los Angeles Unified School District. Both at the 6th grade and the 8th grade the experimental groups that used judiciously selected video clips as learning tools in mathematics scored at statistically significant higher number than and control groups.

The sixth-grade students whose teachers showed them video clips during instruction improved an average of 5 percentage points more than student in the control group during post-testing. Eight-grade students improved an average of 3 percentage points more that students in the control group. When the results are averaged across the two experiments the experimental group performance exceeds that of the control group by 3.8%.

Wagner, Sigrid. (2000). Research Ideas for the Classroom: Middle Grades Mathematics. National Council of Teachers of Mathematics: Reston, VA.

This is a three volume series that presents a comprehensive compilation of research implications in mathematics education from early childhood through the middle grades and high school. Classroom teachers can use Research Ideas for the Classroom as a handy reference for mathematics education research or as supplementary textbooks for pre service, mentoring, and in-service teacher education.

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Resources

Burns, Marilyn (2005). About Teaching Mathematics. 2nd Edition. Marilyn Burns Education Associates.

About Teaching Mathematics provides an introduction to teaching mathematics through problem solving translating the NCTM Standards into classroom practice. The purposes include helping teachers examine how children learn mathematics, helping them understand the elements of a comprehensive mathematics curriculum; and assisting them in establishing a classroom environment that supports children’s learning of mathematics. The second edition includes of the first edition plus a fourth section that provides in-depth discussions around the mathematics of many of the specific activities in the book.

Bush, William S. and Anja S. Greer. (2006). Mathematics Assessment: a Practical Handbook for Grades 9-12. National Council of Mathematics: Reston, VA.

Both practical and inspirational, the Classroom Assessment for School Mathematics, K-12 Series of handbooks and casebooks foster insights into what students know, what they can do, and how they think mathematically.

Carpenter, Thomas P., Maria Lynn Blanton, Paul Cobb, Megan Loef Franke, James Kaput and Kay McClain. (2004). Scaling Up Innovative Practices in Mathematics and Science. National Center for Improving Student learning and Achievement in Mathematics and Science.

This research study calls for fundamental changes both in mathematics and science content taught in schools and in the approaches to teaching that content. This reform process is based on learning with understanding. For students new ideas take on meaning by the ways they are related to other ideas. When students or teachers acquire knowledge with understanding they apply that knowledge to learn new topics and solve unfamiliar problems.

Community Learning Network

Community Learning Network is designed to help K-12 teachers integrate technology into the classroom. Here you'll find over 5,800 annotated links to educational sites with free resources, all organized by theme pages and keyword search. Over 160 theme pages supply two kinds of links: curricular links with information on a topic and instructional materials links with teaching support including lesson plans.

“The Learning Lab” is a place for teachers to increase their competence with technology and explore effective models of technology use in their teaching, learning, and personal/professional growth within the context of their content area.

“The Resource Scrapbook” links to professional e-Learning opportunities and research studies, such as the United States Open e-Learning Consortium.

“For Kids Only” is an activity center for numerous learning games and activities for students of all ages. The mathematics instructor will find links to curricular resources, and online courseware of instructional materials on a specific topic for a specific audience; plus there are pages covering careers in math, fractals, math history and tessellations.

Congnitive Tutor®. Carnegie Learning. Pittsburg, PA.

The Cognitive Tutor®, mathematics curriculum from Carnegie Learning, is based on extensive scientific research from Carnegie Mellon University. This curricular program represents an innovative application of technology, artificial intelligence and cognitive science. The programs give students the opportunity to receive individualized attention, maximizing the amount of time spent actively learning and mastering fundamental thinking skills. The software monitors the status of each student’s knowledge on a moment-by-moment basis and tailors course material for each student based on these continual assessments

Donovan, M. Suzanne, and John D. Bransford. (Eds). (2005). How Students Learn Mathematics in the Classroom. 2nd edition, National Academy Sciences: Washington, D.C.

How Students Learn Mathematics in the Classroom builds on the discoveries detailed in How People Learn and it takes the work of the previous volume to the next step of specificity. This volume provides examples of how the principals and findings of the original research and findings might be incorporated in the teaching of a set of topics that frequently appear in the K-12 curriculum. The goal is to provide for teachers what is critical effective learning by moving the abstract thought to concrete contexts that provide deeper meaning for the classroom teacher.

Eduhound Weekly Focuses on Measurement

EduHound is a highly specialized educational directory with built-in resource links for a broad range of over 55 educational subjects. It is offered free to educators, students and parents as a teaching and learning tool. This collection of resources focuses on measurement.

ENC Online

ENC Online, formally the Eisenhower National clearing house for Mathematics and Science Education (ENC) offers a wealth of curriculum resources and professional development materials, including ENC Focus. Over twelve years, resources were developed through the Eisenhower National Clearinghouse. (www.goenc.com – formerly www.enc.org).

It is a K-12 math and science teacher center with information divided into four sections: Web Links, Curriculum Resources, Education Topics, and Professional Development. At Web Links educators explore thousands of online lesson plans, student activities, and teacher learning tools that can be accessed by subject area or through special features: Digital Dozen, Lessons & Activities, Professional Resources, Student/Classroom, Reference Sources, and Math Topics.

Explorations™Series

Explorations™ is a series of activity books and professional development documents for middle and high school mathematics teachers published by Texas Instruments. The middle school series includes: General Math, Algebra I, General Science and Data Collection. The high school series includes: Algebra, Geometry, Pre-Calculus, Calculus, Statistics, Programming, Data Collection, and Biology. The goal of T3 Professional Development is to provide quality training that enables the mathematics educator to be successful in the classroom through the appropriate use of technology. This training is available in various formats: Teacher Leader Cadre, T3 Outreach Workshops, and Teachers Teaching with Technology, a college short course.

Johnnie's Math Page

A collection of K-8 interactive math activities gathered by an elementary math teacher; great for individual practice or whole-group interactive whiteboard use

Interactive School Mathematics. MathResources. Halifax, Nova Scotia, Canada.

This interactive curriculum fully integrates technology into teaching and learning middle school mathematics through interactive software and online content. The three courses cover all of the material typically taught in middle school math programs, including algebra. The curriculum ranges from decimals and percents to quadratic equations and polynomials.

Math Forum

The Math Forum is an online community of teachers, students, researchers, parents, educators, and citizens at all levels who have an interest in mathematics and math education. The Math Forum has been consistently recognized as the leader in its field, and continues to provide high quality content and useful features.

This site contains the best resources for teaching math at all levels as reviewed by Drexel University staff. This space is not only for teachers but has been built in part by teachers. The features include: The Student Center, Teachers Place, Problems of the Week, Internet Mathematics Library, Ask Dr. Math, Teacher2 Teacher, Math Forum Searches, Teacher Exchange, Math Forum Internet Newsletter, Forum Showcase and Special Projects, and Discussion Groups.

Mumme, Judy, Nanette Seago, and Nicholas Branca. (2004) Learning and Teaching Linear Functions: Video Cases for Mathematics Professional Development, 6-10. Heinemann. United Kingdom.

Developed under a National Science foundation grant, these video-based resources help math teachers in grades 5-10 address some of the pedagogical problems in teaching algebra. The modules equip teachers with the skills to prepare and enact lessons that will help students develop conceptual understandings. These models employ a case-based methodology to investigate mathematics, teaching, and learning that arise in real classroom situations and they deepen teachers’ understanding of algebraic functions. The five modules are in CD-ROM format. Each of the modules focuses on one of the following:

• Conceptualizing and representing linear relationships,
• Using records of mathematical reasoning to help generalize,
• Making use of student ideas during discussion;
• Interpreting students methods and ideas, and
• Launching lessons.

National Library of Virtual Manipulatives for Interactive Mathematics

Developed at Utah State University and funded by the National Science Foundation, a library of web-based interactive virtual manipulatives and concept tutorials. Manipulatives are sorted by grade level and math content area, and each manipulative includes instructions, suggested activities, lesson plans, and connection to relevant NCTM standards. The manipulatives include some that are commonly used in teaching (base 10 blocks, pattern blocks, and algebra blocks).

Seeing Math™. Concord Consortium. Concord, MA.

Seeing Math™ has developed interactive software tools to clarify key mathematical ideas for middle and high school mathematics. Each interactive provides a real-time connection between multiple representations of the mathematics (symbolic, graphical, etc.) so that changes in one representation instantly cause changes in the other. These interactives and the secondary courses illustrate and reinforce key mathematical ideas for teachers and students of algebra. They accelerate learning and enhance comprehension of difficult concepts and allow users to save images of the interactive and share them with other participants. The interactives can be downloaded free for instructional activities.

Strong, Richard W., Harvey F. Silver, and Matthew J. Perini. (2001). Teaching What Matters Most: Standards and Strategies for Raising Student Achievement. Association for Supervision and Curriculum Development: Alexandria, VA.

Based on 10 years of research, the authors lay out a blueprint for curriculum, instruction and assessment for cutting through the confusion of standards and accountability. Lessons plans, teaching practices, and assessment tools show how to ensure that standards stay meaningful in daily teaching and learning.

NCTM Math Resources: Technology Tips

This links to resources developed or released over the past several years.

NCTM Position Statement on Technology in Math Instruction

NCTM states that technology is an essential tool for teaching and learning mathematics effectively; it extends the mathematics that can be taught and enhances students' learning. NCTM presents the rationale for this statement and recommendations.

Tuttle, H (2007). Making Math Work. Tech Learning.

The article discusses the different technologies used in the classroom, and how it helps students to see concepts and move from abstract ideas to hands-on applications.

Case Studies
SETDA collected case studies from states with programs that effectively integrate technology into mathematics.

The case studies include the following information about the model programs:

• General Information
• Initial Planning and Implementation Phase
• Program Successes
• Sharing the Benefits
• Leadership Documents

Case Study Template [Word document]

Case Studies that Effectively Integrate Technology into Mathematics

CO - Help with English Language Proficiency program “HELP Math”
Download Case Study [Word Document]

HELP Math is a research-based, digital supplemental curriculum which addresses the specific issues of teaching mathematics to English language learners (ELLs) by removing language barriers from the learning of math skills and math content. The program is comprised of 44 lessons (over 100 hours of self-paced instruction) that comprehensively align to NCTM (National Council for Teachers of Mathematics) and key ELL state math standards for grades 6-8. HELP engages students through interactive multimedia lessons that break down mathematical terms and concepts, so that students can easily understand and retain the content. Unlike many curricula currently used with students receiving special services, HELP moves beyond basic skills to thoroughly engage students in advanced mathematical thinking and problem solving.

NJ - Math Achievement To Realize Individual eXcellence (MATRIX) Grant Program – The Bridge Project at MacKinnon Middle School
Download Case Study [Word document]

Wharton MATRIX site
MATRIX Bridges Project
NJ Department of Education MATRIX site

For the past three years, Wharton Borough Public Schools has participated in a Title II, Part D discretionary grant program entitled Math Achievement To Realize Individual eXcellence (MATRIX). The grant has focused on integrating technology into the middle grades math curriculum (grades 6-8).

The Bridge Project is a lesson plan developed as part of MATRIX. In the Bridge Project, students plan for the construction of a new bridge over the Hudson River to meet the needs of an expected future increase in traffic. As bridge designers, students plan, design and construct models of their bridges to connect New York and New Jersey. Seventh grade special education students involved in the MATRIX grant program took first place for their bridge designs and models at the middle school level during the National Council of Teachers of Mathematics (NCTM’s) National Conference in Atlantic City on October 19, 2006. The teaching team and district administrators were especially proud of this achievement because the students competed without the judges’ knowledge of their special math needs.

GA – eMath
Download Case Study. [Word document]

eMath is a four-year grant designed to increase student achievement in mathematics, improve classroom access to modern learning technologies, and enhance educators’ understanding of scientifically-based research and evaluation. The grant serves 46 districts across the state and should impact approximately 900 teachers and 25,000 students.

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