Introduction
Math Out of the Box is a standards-based K-5 Mathematics curriculum under development in the College of Engineering and Science at Clemson University. The first of four curriculum strands was published in 2005.
Each curriculum strand consists of an instructional module for each grade level. Each module includes all the instructional materials needed to teach a class of 30 students. The curriculum program is designed to be released in four independent, fully developed, yet interrelated strands. Each strand can serve as a supplement to address "content gaps" in existing curriculum programs. The four strands may be used collectively to provide a comprehensive mathematics curriculum program that is designed to support the mathematical development of all students, the professional development of teachers, and the development of the larger school community, both within and external to the school.
In parallel development with each curriculum strand, is a facilitator module designed to provide instructional leaders with materials for supporting the implementation of the curriculum strand in the school, district, and larger community through a program of professional development. In addition to professional development materials to support implementation of individual strands, the Math Out of the Box professional development program also includes a component which utilizes assessment as a vehicle for building connections among the strands, and a component for educating stakeholders in the school community.
This product is unique in that the K-5 mathematics curriculum program serves as the impetus for a program of professional development within a school or district. An iterative cycle occurs so that the professional development of the teachers facilitates the implementation of the curriculum, and conversely, the implementation of the curriculum facilitates the professional development of the teachers. Using a K-5 mathematics curriculum to support professional development has been suggested by a number of researchers and educational leaders throughout the past decade, (Ball & Cohen, 1996; Davis & Krajcik, 2005; Diaz, 2004; Guskey, 2003; Lloyd, 2002; Loucks-Horsley, 2003; Remillard, 2000; Reyes, Tarr & Chavez, 2004; Russell, 1997; Schmidt, Houang, & Cogan, 2002; Spencer, Chiappinelli & Mark, 2004).
Research Base
Math Out of the Box is designed based on knowledge about teaching and learning mathematics, and knowledge about curriculum design and development. A number of recent reports and publications have informed the curriculum content and design of Math Out of the Box&; both in terms of K-5 mathematics development and in terms of K-5 professional development. Among these are How People Learn: Brain, Mind, Experience, and School (NRC, 2000); Handbook of Research Design in Mathematics and Science Education (Erlbaum, 2000); The Influence of Instructional Processes on Student Cognitive Development (Department of Education, 2000); Adding It Up: Helping Children Learn Mathematics (NRC, 2001); Brain Matters: Translating Research into Classroom Practice (Wolfe, 2001); Practice-Based Professional Development for Teachers of Mathematics (Smith, 2001); Understanding By Design (Wiggins & McTighe, 2001); Handbook of International Research in Mathematics Education (Erlbaum, 2002); Mathematical Proficiency for All Students (RAND Mathematics Study Panel, U.S. Department of Education, 2003); Designing Professional Development for Teachers of Science and Mathematics (Loucks-Horsley et al, 2003); and How Students Learn: Mathematics in the Classroom (NRC, 2005).
Content Base
To meet the challenge of improving education at a national scale, a number of educational agencies have released documents which outline standards of content that should be learned by all students. Because the developers of Math Out of the Box recognize that mathematics is not an isolated discipline, but impacts and is impacted by other disciplines, national standards from a variety of disciplines inform the development of the content of the Math Out of the Box; curriculum program. Standards from the following documents inform the content found in Math Out of the Box: National Council of Teachers of Mathematics, Principles and Standards of School Mathematics, (2000); American Association for the Advancement of Science (AAAS) National Science Education Standards (2001); International Society for Technology in Education (ISTE) National Educational Technology Standards (2000); National Council of Teachers of English (NCTE) Standards for the English Language Arts (1996). By integrating mathematics, science, technology, and English language arts standards in meaningful ways, it is expected that the curriculum will support students and teachers in developing mathematical understanding in a real world context and in relationship to other disciplines, particularly to STEM disciplines. While the focus of the Math Out of the Box curriculum program is mathematics, the approach is holistic in terms of how mathematical ideas connect to each other, to other disciplines, and to the world. Integrating national standards from other disciplines in appropriate ways is one of the ways in which the developers accomplish this holistic design.
Pedagogical Strategies
In addition to its standards-based design, the Math Out of the Box curriculum program has been deliberately designed to support the attainment of mathematical proficiency based on the most current and reliable knowledge about teaching and learning mathematics. The study of the mind that has taken place in the last fifty years has led to many of the currently held views of intelligence and cognitive learning styles which highlight ways to increase educational effectiveness by improving instructional methods (Baumgartner, Lee, Birden, & Flowers, 2003; Doyle, Edison, & Pascarella, 2000; Grouws & Cebulla, 2000; MacRae-Campbell, 1989; Wolfe, 2001). This new knowledge about teaching and learning, coming primarily from the fields of cognitive science and brain research, is a fundamental consideration in the curriculum design of Math Out of the Box&;, whether for student materials or for professional development materials.
Development Plan
Each Math Out of the Box curriculum strand is developed through a rigorous cycle of research, lesson development, lesson testing, and lesson revision. The development team consists of K-12 classroom teachers, K-16 specialists in teacher development (in-service and pre-service), mathematicians, statisticians, university mathematics faculty, mathematics educators, instructional leaders, and corporate consultants. Different individuals are involved at various stages of development, and a core group of developers are involved throughout the complete development cycle. Parallel to the development of each K-5 student curriculum strand is the development of a K-5 facilitator module designed to provide professional development support and guidance for instructional leaders in schools and districts that implement the strand.
The first curriculum strand, Developing Algebraic Thinking, was published in 2005 by Carolina Biological Supply Company. This curriculum strand is focused in the content areas of algebra and data analysis. In 2003 the RAND Mathematics Study Panel recommended that "improvement of proficiency in algebra" be the "initial domain" of focus for supporting improvement in mathematical proficiency (p. xix). The content domain of algebra was not included for grades K-4 in the 1989 NCTM Curriculum and Educational Standards for School Mathematics, the national standards on which the majority of currently available curricula have been based. Consequently, a content gap in the domain of algebra exists in many of the currently available mathematics curricula. The decision to begin the Math Out of the Box curriculum project with the algebra strand was influenced by this void.
The four phase development cycle of research, lesson development, lesson testing, and lesson revision, is applied to each of the four curriculum strands and is carried out in such a way that each of the previous phases inform the upcoming phase, and what is learned during the develop of each curriculum strand informs the development of future strands. Formative and summative assessments of the program are built directly into the development cycle. Existing research concerning national standards, best instructional practices, and cognitive development of particular mathematical ideas informs what and how lessons are developed. The dynamic research and development of lessons then informs the professional development aspects of this program. During field testing, both formative and summative assessments are made and used to direct the final revision of the lessons and professional development materials. In the final revision phase, the publishing layout and editorial team provide feedback to the developers, and once all parties are satisfied with the results, the strand is submitted for publication.
When citing this document, please use the following
Moss, D.A., Diaz, D.P., & Moss, W.F. (2005). About Math Out of the Box. Center of Excellence in Science and Mathematics Education, Clemson University. Retrieved month day, year, from http://www.mathoutofthebox.org/research/about.shtml.
References
American Association for the Advancement of Science. (2001). Atlas of science literacy: Project 2061. Washington, DC: AAAS & NSTA.
American Association for the Advancement of Science (2001). National Science Education Standards. Washington, DC: AAAS.
Ball, D.L. (1996). Teacher learning and the mathematics reforms: What we think we know and what we need to learn. Phi Delta Kappan, 77, 500-508.
Ball, D.L., & Cohen, D.K. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6-8,14.
Baumgartner, L.M., Lee, M., Birden, S., Flowers, D. (2003). Adult learning theory: A primer. Office of Educational Research and Improvement. Washington D.C.: Department of Education.
Clements, D. (2002). Linking research and curriculum development. In L.D. English (Ed.) Handbook of international research in mathematics education (pp.599-630). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
Davis, E. A. & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational researcher, 34 (3), 3-14.
Diaz, D. P. (2004). The role of standards-based curricula in teacher learning and instructional reform. Unpublished doctoral dissertation. Clemson University.
Doyle, S.K., Edison, M.I., Pascarella, E.T. (2000). The influence of instructional processes on student cognitive development. National Center on Postsecondary Teaching, Learning, and Assessment. Washington D.C.: Department of Education.
Handbook of International Research in Mathematics Education. (2002). English, L.D. (Ed.) Mahweh, NJ: Lawrence Erlbaum Associates.
Handbook of Research Design in Mathematics and Science Education. (2000). Kelly, A.E. & Lesh, R.A. Lesh (Eds.) Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
Grouws, D. and Cebulla, K. (2000). Improving Student Achievement in Mathematics. Brussels: International Academy of Education. Retrieved February 14, 2005, from http://www.ibe.unesco.org/International/Publications/EducationalPractices/EducationalPracticesSeriesPdf/prac04e.pdf.
Guskey, T.R. (2003). What makes professional development effective? Phi Delta Kappan, 84 (10), 748-749.
Horizon Research, Inc. (2002). Status of elementary school mathematics teaching. 2000 National Survey of Science and Mathematics Education. Chapel Hill, NC.
International Society for Technology in Education (ISTE). (2000). National Educational Technology Standards for Students-Connecting Curriculum and Technology. Eugene, OR: International Society for Technology in Education.
Lloyd, G. (2002). Mathematics teachers’ beliefs and experiences with innovative curriculum materials: The role of curriculum in teacher development. In G. Leder, E. Pehkonen, and G. Törner (Eds.), Beliefs: A Hidden Variable in Mathematics Education? (pp. 149-160). Netherlands: Kluwer Academic Publishers.
Loucks-Horsley, S., Love, N., Stiles, K.E., Mundry, S., & Hewson, P.W. (2003). Designing Professional Development for Teachers of Science and Mathematics. Thousands Oaks, CA: Corwin Press, Inc.
MacRae-Campbell, L. (1989). The importance of neurological and cognitive research for reading instruction. Office of Educational Research and Improvement: U.S. Department of Education.
National Commission of Excellence in Education. (1983). A nation at risk: The imperative for educational reform. Washington, DC: U.S. Government Printing Office.
National Commission on Mathematics and Science Teaching for the 21st Century. (2000). Before it’s too late: A report to the nation from the National Commission on Mathematics and Science Teaching for the 21st Century. Washington, DC: U.S. Department of Education.
National Council of Teachers of English & International Reading Association. (1996). Standards for the English language arts. Urbana, IL: NCTE.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards of School Mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (2000). Principals and Standards of School Mathematics. Reston, VA: NCTM.
National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
National Research Council (2000). How people learn: Brain, mind, experience, and school. Bransford, J.D., A.L. Brown, and R. Cocking (Eds.) Washington, DC: National Academy Press.
National Research Council (2005). How students learn: Mathematics in the classroom. Donovan & Bransford (Eds.). Committee on How People Learn: A targeted report for teachers.
Princeton Review (2003). Testing the Testers 2003: An Annual Ranking of State Accountability Systems Executive Summary. Available online: http://www.princetonreview.com/footer/testingTesters.asp
Remillard, J. (2000). Can curriculum materials support teachers’ learning? Two fourth-grade teachers’ use of a new mathematics text. The Elementary School Journal, 100 (4), 331-350.
Reyes, R., Tarr, J., & Chavez, O. (2004). Do textbooks matter? Findings from a study of NSF and non-NSF mathematics curricular materials. Paper presented at the 36th Annual Conference of the National Council of Supervisors of Mathematics, Philadelphia.
Russell, S.J. (1997). The role of curriculum in teacher development. In S.N. Friel & G.W. Bright (Eds.), Reflecting on our work: NSF teacher enhancement in K-6 mathematics (pp. 247-254). Lanham, MD: University Press of America.
RAND Mathematics Study Panel. (2003). Mathematical Proficiency of all students: toward a strategic research and development program in mathematics education. Office of Educational Research and Improvement: U.S. Department of Education.
Secretary’s Commission on Achieving Necessary Skills (SCANS). (1990). Identifying and describing the skills required by work. Employment and Training Administration: U.S. Department of Labor.
Schmidt, W., Houang, R., Cogan, L. (2002). A coherent curriculum: A case of mathematics. American Educator, 26 (2), 10-26, 47-48.
Schoenfeld, A. H., (2002). Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity. Educational Researcher. 31. Number 1, pp. 13-25.
Smith, M.S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: NCTM.
Spencer, D., Chiappinelli, K., & Mark, J. (2004). The textbook matters: Why instructional materials are a powerful lever for improvement. Paper presented at the 36th Annual Conference of the National Council of Supervisors of Mathematics, Philadelphia.
Whitehurst, G. (2003). Presentation for Mathematics and Science Initiative: Mathematics Summit. Institute of Educational Sciences: U.S. Department of Education.
Wiggins, G., and J. McTighe. (2001). Understanding by Design. Upper Saddle River, NJ: Merrill/Prentice Hall.
Wolfe, P. (2001). Brain matters: Translating research into classroom practice. Alexandria, VA: Association for Supervision and Curriculum Development.