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National Center
for Improving Student Learning and Achievement in Mathematics and Science (NCISLA)

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TEACHER RESOURCES:

K-12 resources

Elementary school resources

Middle school resources

High school resources

Modeling for Understanding in Science Education


Center researchers have collaborated with schools and teachers to create and study instructional approaches that support and improve student understanding of mathematics and science. The instructional resources listed below are informed by our research on how students learn with understanding. See also publications.


K-12 Resources

(CD)Powerful Practices in Mathematics and Science
A multimedia product for educators, professional developers, and leaders

pdfTeaching Culturally Diverse Students Mathematics & Science
This list has a gold mine of rich resources for K-12 educators.

thumbnail of poster section UNIQUE POSTER about student understanding in mathematics and science. Click here to view the poster and get ordering information.

Transforming Teaching in Math and Science: How Schools and Districts can Support Change. Adam Gamoran, Charles W. Anderson, Pamela Anne Quiroz, Walter G. Secada, Tona Williams, Scott Ashman. Publisher:Teachers College Press, 2003.


  Elementary School Resources (articles available in full-text PDF)

pdfChanging the Teaching and Learning of Mathematics, Thomas Romberg. The Australian Mathematics Teacher, 56(4), 2000, pp. 6-9.

pdfGender Equity in Mathematics Education, Linda Levi. Teaching Children Mathematics, Vol. 7, No. 2, October 2000, pp. 101-105.

pdfBuilding a Foundation for Algebra in the Elementary Grades, In Brief, Vol.1, No. 2, Fall 2000.

pdfWhy Are Some Solids Perfect? Conjectures and Experiments by Third Graders, Richard Lehrer and Carmen L. Curtis. Teaching Children Mathematics, Vol. 6, No. 5, January 2000, pp. 324-329.

pdfDeveloping First Graders' Mathematical Reasoning Within the Context of Measurement, Kay McClain, Paul Cobb, Koeno Gravemeijer and Beth Estes. Developing Mathematical Reasoning in Grades K-12, 1999 Yearbook. Stiff, V. Lee and Curcio, R. Frances (Eds.).

pdfA Contextual Investigation of Three-Digit Addition and Subtraction, Kay McClain, Paul Cobb and Janet Bowers. The Teaching and Learning of Algorithms in School Mathematics, 1998 NCTM Yearbook.

pdfChildren's Understanding of Equality: A Foundation for Algebra, Karen Falkner, Linda Levi, and Thomas Carpenter. Teaching Children Mathematics, Vol. 6, No. 4, Dec. 1999, pp. 232-236.

book cover Investigating Real Data in the Classroom - Expanding Children's Understanding of Mathematics and Science. Richard Lehrer and Leona Schauble, editors. A book from: Teachers College Press, 2002.


Building Students' Algebraic Reasoning


Introducing basic forms of algebraic reasoning in elementary school enhances children’s learning of arithmetic and facilitates their transition to learning algebra in high school.
Two NCISLA projects examine (a) children's mathematical and algebraic reasoning and (b) teachers' professional development.

The resources available here were developed through professional development work with elementary school teachers in Massachusetts. The focus of this project is to build teachers’ understanding of how to extend elementary arithmetic tasks (such as computations) to tasks that require algebraic reasoning. Algebraic reasoning refers to a habit of mind by which students regularly and naturally look for patterns and relationships in data, describe their findings through generalizations, and express their generalizations in ways that progress from everyday language to more formal mathematical language.

For more background on this project and research findings, see --

pdf In Brief [2003]

pdf Sample “algebrafied” problems

pdf Tips from teachers

pdf Key ideas about algebraic reasoning and mathematics

For more information about these resources, contact:

Jim Kaput
Professor
Department of Mathematics
University of Massachusetts-Dartmouth

Maria Lynn Blanton
Assistant Professor
Department of Mathematics
University of Massachusetts-Dartmouth

Cognitively Guided Instruction (CGI)

CGI is an approach to elementary mathematics instruction that capitalizes on young children’s intuitive thinking and computational skills. Current research indicates that CGI appears to lay a strong foundation for elementary students' learning of early algebra concepts. CGI also forms a base for transformational teacher professional development. Teachers from around the world are integrating CGI into their classroom instruction. The CGI approach also has become a building block for elementary mathematics instruction in the Phoenix Systemic Initiative and is also a component of teacher professional development supported by the Midwest Comprehensive Regional Assistance Center. To learn more about CGI, see the CGI-focused web site (http://www.wcer.wisc.edu/ccvi/CGISpider/index.html) available through the Comprehensive Center -- Region VI (CC-VI).

Also, teachers and professional developers will find the following useful:

book cover Children’s Mathematics: Cognitively Guided Instruction (with two multimedia CDs), Thomas P. Carpenter, Elizabeth Fennema, Megan Loef Franke, Linda Levi and Susan B. Empson. Published through Heinemann. To find this book, go to Heinemann site and search for Children’s Mathematics.

CGI videotapes and summative log book complement the above publication. To order, contact Cheryle Wampole at the Wisconsin Center for Education Research, 1025 W. Johnson Street, Room 242, Madison, WI 53706, TEL: (608) 265-9698 FAX: (608)263-6448. CGI Logs & Videotapes — Elizabeth Fennema, Thomas Carpenter, Linda Levi, Megan Loef Franke, Susan Empson. $100.00 single set.


Middle School Resources


pdf
Improving Data Analysis Through Discourse, Kay McClain, Maggie McGatha, and Lynn Hodge. Mathematics Teaching in the Middle School, Vol. 5, No. 8, April 2000, pp. 548-553.

pdf Supporting Students' Ways of Reasoning about Data, Kay McClain, Paul Cobb and Keono Gravemeijer. Learning Mathematics for a New Century, 2000 NCTM Yearbook.

web siteModeling for Understanding in Science Education. The Modeling for Understanding in Science Education (MUSE) web site features science curricula consistent with the goals set forth in the National Science Education Standards and the Benchmarks for Scientific Literacy. The curricula and teacher's guides focus on astronomy (earth-moon-sun dynamics), evolutionary biology (natural selection) and classical genetics, with each unit unfolding over nine weeks. The product of a teacher-student-researcher collaboration and long-term research, the in-depth curricula provide teachers access to scientific modeling strategies that can enable students to engage in inquiry and learn key concepts and ideas with understanding.

web siteMathematics in Context (MiC) curriculum (available through the Encyclopedia Britannica and the Show Me Center sites). MiC is a comprehensive mathematics curriculum for grades 5-8. The complete program contains 40 units, ten at each grade level. The intent of MiC is to engage students in learning and applying mathematics in the context of interesting, real-life problems. MiC has been highly rated by Project 2061 of the American Association for the Advancement of Science (AAAS). MiC content emerged from research conducted through NCRMSE, and the curriculum was funded by the National Science Foundation.

web siteModeling Middle School Mathematics. Modeling Middle School Mathematics (MMM) teacher professional development program, funded by the National Science Foundation, features on-line video clips, interviews, and teacher reflections focusing on teachers' efforts to improve mathematics instruction in grades 5-8. Teachers and students use the Mathematics in Context curricula to develop in-depth understanding of geometry and algebra. The MMM project, affiliated with the Show-Me Project at the University of Missouri, provides glimpses into students' learning, classrooms, and collaborating teachers' practices. MMM also shows ways that teachers have sought to implement state and NCTM standards. (Special note: The featured classrooms and teachers have been a focus of the national center research program.)

web siteDigital Library of Mathematics & Science Activities. Teachers can access several thought-revealing activities that focus on "big ideas" in mathematics and science through a digital library located at Purdue University. Developed by Center researcher Richard Lesh and colleagues, the activities are grounded in the NCTM (1989) Curriculum and Evaluation Standards. They are intended to help teachers recognize and reward a broader range of abilities than those emphasized in traditional textbooks and tests. Teachers should also check out the creative Rational Inquirer.

web siteClassroom Assessment as a Basis of Teacher Change (CATCH) a project of NCISLA, with a subcontract to the Freudenthal Institute (Fi) at the University of Utrecht in The Netherlands. CATCH is a project based on the belief that teachers are the key to reform in the teaching and learning of mathematics, and changing assessment practices is a means of helping teachers make such changes. A resource for teachers involved in the CATCH research and professional development project, the CATCH website is based at -- and maintained by staff of -- the Freudenthal Institute in the Netherlands. The Great Assessment Picture Book, one of CATCH's products, is available online at: http://www.fi.uu.nl/catch/products/GAP_book/intro.html


High School Resources

pdf file High School Students "Do" and Learn Through Scientific Modeling, In Brief, Vol. 1, No. 1, Winter 2000.


web siteModeling for Understanding in Science Education. The Modeling for Understanding in Science Education (MUSE) web site features science curricula consistent with the goals set forth in the National Science Education Standards and the Benchmarks for Scientific Literacy. The curricula and teacher's guides focus on astronomy (earth-moon-sun dynamics), evolutionary biology (natural selection) and classical genetics, with each unit unfolding over nine weeks. The product of a teacher-student-researcher collaboration and long-term research, the in-depth curricula provide teachers access to scientific modeling strategies that can enable students to engage in inquiry and learn key concepts and ideas with understanding.