References
of the

Mathematics Framework
for California Public Schools:
Kindergarten Through Grade Twelve

Adopted by the California State Board of Education, November 2013
Published by the California Department of Education
Sacramento, 2015


References
Abrams, Joshua. 2001. Mathematical Modeling: Teaching the Open-ended Application of Mathematics.
Roslindale, MA: Joshua Paul Abrams. (accessed
March 18, 2014).
. 2012. “Teaching Mathematical Modeling at the High School Level.” From Proceedings of the
2012 Asia-Pacific Economic Cooperation (APEC) Workshop, Indonesia, 34–51. Singapore: APEC.
Achieve, Inc. 2013. Implementing the Common Core Standards: The Role of the Elementary School Leader.
Washington, DC: Achieve, Inc. (accessed March 18, 2014).
Achieve the Core. 2012. Where to Focus in K–8 Math, Grades K–2. />where-to-focus-in-k-8-math (accessed March 26, 2014).
Adams, Gary, and Douglas W. Carnine. 2003. “Direct Instruction.” In Handbook of Learning Disabilities,
edited by H. Lee Swanson, Karen R. Harris, and Steve Graham, 403–16. New York: Guilford Press.
American Speech–Language–Hearing Association (ASHA). 2015. Augmentative and Alternative
Communication. Rockville, MD: ASHA. />(accessed July 17, 2015).
Anstrom, Kristina, Patricia DiCerbo, Frances Butler, Anne Katz, Julie Millet, and Charlene Rivera. 2010.
A Review of the Literature on Academic English: Implications for K–12 English Language Learners.
Arlington, VA: The George Washington University Center for Equity and Excellence in Education. http://
www.ceee.gwu.edu/Academic%20Lit%20Review_FINAL.pdf [Link no longer valid](accessed March 18, 2014).

Arizona Department of Education (ADE). 2010. Arizona’s College and Career Ready Standards—

Journal of Mathematical Modelling and Application 1 (1): 45–58.
Bosse, Michael J., and Johna Faulconer. 2008. “Learning and Assessing Mathematics Through Reading
and Writing.” School Science and Mathematics 108 (1): 8–19.
Bourdieu, Pierre. 1977. “Cultural Reproduction and Social Reproduction.” In Power and Ideology in
Education, edited by Jerome Karabel and A. H. Halsey, 485–511. New York: Oxford University Press.
———. 1986. “The Forms of Capital.” In Handbook of Theory and Research for the Sociology of Education,
edited by John Richardson. New York: Greenwood Press.
Browder, Diane M., Fred Spooner, Lynn Ahlgrim-Delzell, Amber A. Harris, and Shawnee Wakeman.
2008. “A Meta-Analysis on Teaching Mathematics to Students with Significant Cognitive Disabilities.”
Exceptional Children 74 (4): 407–32.
Bruner, Jerome, Jacqueline Jarrett Goodnow, and George Austin. 1956. A Study of Thinking. New York:
Wiley.
Burden, Paul R., and David M. Byrd. 2009. Methods for Effective Teaching: Meeting the Needs of All
Students. 5th ed. Boston: Allyn & Bacon.
Burkhardt, Hugh. 2006. “Modelling in Mathematics Classrooms: Reflections on Past Developments and
the Future.” ZDM: The International Journal on Mathematics Education 38 (2): 178–95.
California County Superintendents Educational Services Association (CCSESA). 2011a. K–8 California’s
Common Core Standards: Parent Handbook. Sacramento, CA: CCSESA. />special-projects/common-core-standards-communication-tools/ (accessed March 26, 2014).
. 2011b. Transitional Kindergarten (TK) Planning Guide: A Resource for Administrators of California
Public School Districts. Sacramento, CA: CCSESA. />TKGuide_11311_Web.pdf (accessed March 26, 2014).
California Department of Education (CDE). 2006. Mathematics Framework for California Public Schools:
Kindergarten Through Grade Twelve. Sacramento, CA: California Department of Education.
. 2008. California Preschool Learning Foundations, Volume 1. Sacramento, CA:
California Department of Education. />(accessed March 18, 2014).
. 2010a. California Preschool Curriculum Framework, Volume 1. Sacramento, CA: California
Department of Education. />(accessed March 18, 2014).
864

References


California Mathematics Project. 2012. Exploring World Maps. (accessed March 19, 2014).
Carr, John, and Catherine Caroll. 2009. “Making Mathematics Accessible to English Learners.” Webinar.
(accessed October 21, 2012).
California Mathematics Framework

References

865


Carr, John, Catherine Caroll, Sarah Cremer, Mardi Gale, and Rachel Lagunoff. 2009. Making Mathematics
Accessible to English Learners: A Guidebook for Teachers. San Francisco, CA: WestEd.
Celedón-Pattichis, Sylvia. 2004. “Rethinking Policies and Procedures for Placing English Language
Learners in Mathematics.” NABE Journal of Research and Practice 2 (1): 176–92.
Celedón-Pattichis, Sylvia, and Nora G. Ramirez. 2012. Beyond Good Teaching: Advancing Mathematics
Education for ELLs. Reston, VA: National Council of Teachers of Mathematics.
Center for Applied Special Technology (CAST). 2011. Universal Design for Learning (UDL) Guidelines—
Version 2.0. Wakefield, MA: CAST. />(accessed March 19, 2014).
Center for the Collaborative Classroom. 2015. Lesson Study. Emeryville, CA: Center for the Collaborative
Classroom. (accessed July 8, 2015).
Centers for Disease Control and Prevention (CDC). 2002. National Health and Nutrition Examination Survey,
2002. Atlanta, GA: CDC. [Link no longer valid] (accessed July 28, 2014).

Challenge Success. 2012. Cheat or Be Cheated? What We Know About Academic Integrity in Middle & High
Schools & What We Can Do About It. Stanford, CA: Challenge Success, Stanford University. http://
www.challengesuccess.org/wp-content/uploads/2015/07/ChallengeSuccess-AcademicIntegrityWhitePaper. pdf (accessed September 29, 2015).
The Charles A. Dana Center at the University of Texas at Austin. 2012. The Mathematics Common Core
Toolbox, Sequenced Units, First Through Eighth Grades. />resources_samples.html (accessed March 19, 2014).
Charles, C. M., and Gail W. Senter. 2012. Elementary Classroom Management. 6th ed. Boston: Pearson.
Cheung, Alan C. K., and Robert E. Slavin. 2011. The Effectiveness of Educational Technology Applications

March 19, 2014).

Cooper, James M., ed. 2006. Classroom Teaching Skills. 8th ed. Boston: Houghton Mifflin.
Council for Economic Education. 2013. National Standards for Financial Literacy. New York: Council for
Economic Education. />national-standards-for-financial-literacy.pdf (accessed March 19, 2014).
Cummins, Jim. 2000. Language, Power, and Pedagogy: Bilingual Children in the Crossfire. Clevedon,
England: Multilingual Matter.
Darling-Hammond, Linda, Ruth Chung Wei, Alethea Andree, Nikole Richardson, and Stelios Orphanos.
2009. Professional Learning in the Learning Profession: A Status Report on Teacher Development in the
U.S. and Abroad. Oxford, OH, and Stanford, CA: National Staff Development Council (now Learning
Forward) and the School Redesign Network at Stanford University.
Dauber, Susan L., Karl L. Alexander, and Doris R. Entwisle. 1996. “Tracking and Transitions Through the
Middle Grades: Channeling Educational Trajectories.” Sociology of Education 69 (4): 290–307.
Davis, Trina, Mila Fuller, Sharnell Jackson, Joyce Pittman, and James Sweet. 2007. A National
Consideration of Digital Equity. Washington, DC: International Society for Technology in Education.
(accessed March 19,
2014).
Devaney, Elizabeth, and Nichole Yohalem. 2012. The Common Core Standards: What Do They Mean for
Out-of-School Time? Out-of-School Time Policy Commentary #17. Washington, DC: The Forum
for Youth Investment. (accessed March 27, 2014).
Diamond, Linda. 2004. “Universal Access: When All Means A-L-L and Not S-O-M-E.” Oakland, CA:
The Consortium on Reading Excellence, Inc. (CORE). />CORE-BriefingPaperUniversalAccess.pdf (accessed July 17, 2015).
DO-IT. 2012. “A Smart Board in the Classroom: A Promising Practice for Engaging Students.” Seattle, WA:
University of Washington. (accessed March 19,
2014).
Duncan, Greg J., Chantelle J. Dowsett, Jeanne Brooks-Gunn, Amy Claessens, Kathryn Duckworth, Mimi
Engel, Leon Feinstein, Aletha C. Huston, Crista Japel, Pamela Klebanov, Katherine Magnuson, Linda
Pagani, and Holly Sexton. 2007. “School Readiness and Later Achievement.” Developmental Psychology
43 (6): 1428–46. />[Link no longer valid] (accessed December 3, 2012}.


Excellence. Sacramento, CA: California Department of Education. />(accessed April 8, 2014).
Ellington, Aimee J. 2003. “A Meta-Analysis of the Effects of Calculators on Students’ Achievement and
Attitude Levels in Precollege Mathematics Classes.” Journal for Research in Mathematics Education 34
(5): 433–63.
Emmer, Edmund T., and Carolyn M. Evertson. 2009. Classroom Management for Middle and High School
Teachers. Upper Saddle River, NJ: Pearson.
Encyclopedia of Language and Literacy Development. 2012. London, Ontario, Canada: Western
University. [Link no longer valid] (accessed March 19, 2014).
EngageNY. 2012. Common Core Exemplar for Middle School Math. Albany, NY: New York State Education
Department. />(accessed March 19, 2014).
English, Lyn D. 2007. “Complex Systems in the Elementary and Middle School Mathematics Curriculum:
A Focus on Modeling.” The Montana Mathematics Enthusiast (TMME) 3: 139–56. http://
www.math.umt.edu/tmme/monograph3/english_monograph3_pp.139_156.pdf [Link no longer
valid] (accessed March 27, 2014).
868

References

California Mathematics Framework


Federal Reserve Bank of Cleveland. 2007. Great Minds Think: A Kid’s Guide to Money. Cleveland, OH:

Federal Reserve Bank of Cleveland. />great_minds_think/Great_Minds_Think.pdf [Link no longer valid](accessed March 19, 2014).
Finkelstein, Neal, and Anthony Fong. 2008. Course-Taking Patterns and Preparation for Postsecondary
Education in California’s Public University Systems Among Minority Youth. (Issues & Answers Report,
REL 2008–No. 035). Washington, DC: U.S. De-partment of Education, Institute of Education Sciences,
National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory
West. (accessed March 19, 2014).
Finkelstein, Neal, Anthony Fong, Juliet Tiffany-Morales, Patrick Shields, and Min Huang. 2012. “College



Gersten, Russell, Sybilla Beckmann, Benjamin Clarke, Anne Foegen, Laurel Marsh, Jon R. Star, and
Bradley Witzel. 2009. Assisting Students Struggling with Mathematics: Response to Intervention (RtI)
for Elementary and Middle Schools. Washington, DC: National Center for Education Evaluation and
Regional Assistance, Institute of Education Sciences, U.S. Department of Education. />ncee/wwc/publications_reviews.aspx (accessed March 19, 2014).
Gersten, Russell, David J. Chard, Madhavi Jayanthi, Scott K. Baker, Paul Morphy, and Jonathan
Flojo. 2008. Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning
Mathematics: A Synthesis of the Intervention Research. Portsmouth, NH: RMC Research Corporation,
Center on Instruction. />(accessed March 19, 2014).
Gibbons, Pauline. 2009. English Learners, Academic Literacy and Thinking. Portsmouth, NH: Heineman.
Goos, Merrilyn, and Anne Bennison. 2007. “Technology-Enriched Teaching of Secondary Mathematics:
Factors Influencing Innovative Practice.” Mathematics: Essential Research, Essential Practice,
Proceedings of 30th Annual Conference of Mathematics Education Research Group of Australasia
1:315–24.
The Great Schools Partnership. 2014. The Glossary of Education Reform. Portland, ME: The Great Schools
Partnership. (accessed July 17, 2015).
Griffith, Linda K. 2012. “Common Core State Standards Mathematics 5: Purposeful Pedagogy and
Discourse.” />5-Handout.pdf [Link no longer valid] (accessed March 19, 2014).
Grotzer, Tina. 1999. “Understanding Counts: Teaching for Depth in Math and Science.” In Math/Science
Matters: Resource Booklets on Research in Math and Science Learning—Booklet 1: Cognitive Issues
That Affect Math and Science Learning. Cambridge, MA: Project Zero, Harvard Graduate School of
Education.
Guerrero, Shannon, Norman Walker, and Sharon Dugdale. 2004. “Technology in Support of Middle Grade
Mathematics: What Have We Learned?” Journal of Computers in Mathematics and Science Teaching 23
(1): 5–20.
Hadwin, Allyson Fiona, Lori Wozney, and Oonag Pontin. 2005. “Scaffolding the Appropriation of SelfRegulatory Activity: A Socio-Cultural Analysis of Changes in Teacher–Student Discourse about a
Graduate Research Portfolio.” Instructional Science: An International Journal of Learning and Cognition
33 (5–6): 413–50.
Hallinan, Maureen T. 1994. “Tracking: From Theory to Practice.” Sociology of Education 67:79–84.

Illustrative Mathematics. 2013a. (accessed March 19, 2014).
. 2013b. Illustrations, 4.OA Double Plus One. />illustrations/487 (accessed March 19, 2014).
. 2013c. Illustrations, 6.EE Chocolate Bar Sales. />illustrations/806 (accessed March 19, 2014).
. 2013d. Illustrations, 7.G.4 The Circumference of a Circle and the Area of the Region it
Encloses. (accessed March 19, 2014).
. 2013e. Illustrations, 7.SP.3,4—Offensive Linemen. />illustrations/1341 (accessed March 19, 2014).
. 2013f. Illustrations, 8.EE Ant and Elephant. />illustrations/476 (accessed March 19, 2014).
. 2013g. Illustrations, A-CED Growing Coffee. />illustrations/611 (accessed March 19, 2014).
. 2013h. Illustrations, A-CED Throwing a Ball. />illustrations/437 (accessed March 19, 2014).
. 2013i. Illustrations, F-BF Lake Algae. />(accessed March 19, 2014).
. 2013j. Illustrations, F-BF Skeleton Tower. />illustrations/75 (accessed March 19, 2014).
. 2013k. Fractions Progression Module. />progression (accessed March 19, 2014).
California Mathematics Framework

References

871


. 2013l. Illustrations, G-MG Ice Cream Cone. />illustrations/414 (accessed March 19, 2014).
. 2013m. Content Standards: High School. />(accessed March 19, 2014).
. 2013n. Content Standards: Kindergarten Through Grade Eight. http://
www.illustrativemathematics.org/standards/k8# (accessed March 19, 2014).
. 2013o. Illustrations, N-Q Felicia’s Drive. />(accessed March 19, 2014).
. 2013p. Illustrations, N-Q Runners’ World. />illustrations/19 (accessed March 19, 2014).
. 2013q. Illustrations, S-CP The Titanic 2. />illustrations/950 (accessed March 19, 2014).
Ingersoll, Richard, and David Perda. 2010. “Is the Supply of Mathematics and Science Teachers
Sufficient?” American Educational Research Journal 43 (3): 563–94.
Inside Mathematics. 2015. “Problems of the Month.” (accessed July 17, 2015).
Institute for Mathematics and Education, University of Arizona; Center for Science, Mathematics, and

Klibanoff, Raquel S., Susan C. Levine, Janellen Huttenlocher, Marina Vasilyeva, and Larry V. Hedges. 2006.
“Preschool Children’s Mathematical Knowledge: The Effect of Teacher ‘Math Talk.’” Developmental
Psychology 42 (1): 59–69.
Kroesbergen, Evelyn H., and Johannes E. H. Van Luit. 2003. “Mathematics Interventions for Children with
Special Needs.” Remedial and Special Education 24 (2): 97–114.
Kurlaender, Michal, Sean F. Reardon, and Jacob Jackson. 2008. “Middle School Predictors of High School
Achievement in Three California School Districts: California Dropout Research Project Report #13,
June 2008.” Santa Barbara, CA: University of California, Santa Barbara.
Lamon, Susan J. 2012. Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and
Instructional Strategies for Teachers. 3rd ed. New York: Routledge.
Li, Qing, and Xin Ma. 2010. “A Meta-Analysis of the Effects of Computer Technology on School Students’
Mathematics Learning.” Educational Psychology Review 22 (3): 215–43.
Liang, Jian-Hua, Paul E. Heckman, and Jamal Abedi. 2012. “What Do the California Standards Test Results
Reveal About the Movement Toward Eighth-Grade Algebra for All?” Educational Evaluation and
Policy Analysis 34 (3): 328–43. (accessed March 19,
2014).
Lopez, Omar S. 2010. “The Digital Learning Classroom: Improving English Language Learners’ Academic
Success in Mathematics and Reading Using Interactive Whiteboard Technology.” Computers and
Education 54 (4): 901–15.
Los Angeles Unified School District (LAUSD). 2012. English Learner Master Plan. />(accessed March 19, 2014).
Loveless, Tom. 2004. “Computational Skills, Calculators, and Achievement Gaps: An Analysis of NAEP
Items.” Presentation given at the American Educational Research Association, San Diego, CA,
April 2004.
Ma, Liping. 2010. Knowing and Teaching Elementary Mathematics. New York: Taylor and Francis
Routledge.
MacSwan, Jeff, and Kellie Rolstad. 2003. “Linguistic Diversity, Schooling, and Social Class: Rethinking our
Conception of Language Proficiency in Language Minority Education.” In Sociolinguistics: The Essential
Readings, edited by Christina Bratt Paulston and G. Richard Tucker. Oxford, United Kingdom:
Blackwell Publishing Ltd.
Martinez, Michael E. 2010. Learning and Cognition: The Design of the Mind. Columbus, OH: Merrill.

Moschkovich, Judit. 2012a. “ELLs and the Common Core in Mathematics.” Webinar. Stanford, CA:
Graduate School of Education, Stanford University. (accessed March 20, 2014).
. 2012b. “Mathematics, the Common Core, and Language: Recommendations for Mathematics
Instruction for ELs Aligned with the Common Core.” Understanding Language: Commissioned Papers
on Language and Literacy Issues in the Common Core State Standards and Next Generation Science
Standards, April 5, 2012.
Moss, Connie M., and Susan M. Brookhart. 2009. Advancing Formative Assessment in Every Classroom.
Alexandria, VA: Association for Supervision and Curriculum Development.
National Center for Education Statistics.1995. Pursuing Excellence: A Study of U.S. Fourth-Grade
Mathematics and Science Achievement in International Context. Washington, DC: National Center for
Education Statistics, U.S. Department of Education. />(accessed April 16, 2014).
. 2013. Kids’ Zone. (accessed March 20, 2014).
National Center for Improving Student Learning and Achievement in Mathematics and Science. 2000.
“Cognitively Guided Instruction: A Research-Based Teacher Professional Development Program for
Elementary School Mathematics.” Madison, WI: University of Wisconsin–Madison.
874

References

California Mathematics Framework


National Center on Accessible Information Technology in Education (AccessIT). 2015. About AccessIT.
Seattle, WA: University of Washington. (accessed July 17, 2015).
National Council of Teachers of Mathematics (NCTM). 1995. Assessment Standards for School Mathematics.
Reston, VA: National Council of Teachers of Mathematics.
. 2000. Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers
of Mathematics.
. 2007. Mathematics in Early Childhood Learning. />aspx?id=12590 [Link no longer valid] (accessed March 20, 2014).
. 2011a. Technology in Teaching and Learning Mathematics. />aspx?id=31734 [Link no longer valid] (accessed March 20, 2014).

(accessed March 20, 2014).
. 2010g. Mathematics, Notes on Courses and Transitions. />Content/note-on-courses-transitions/courses-transitions (accessed March 20, 2014).
. 2010h. Mathematics Standards, Grade 1, Introduction. />Content/1/introduction (accessed March 20, 2014).
. 2010i. Mathematics Standards, Grade 2, Introduction. />Content/2/introduction (accessed March 20, 2014).
. 2010j. Mathematics Standards, Grade 3, Introduction. />Content/3/introduction (accessed March 20, 2014).
. 2010k. Mathematics Standards, Grade 4, Introduction. />Content/4/introduction (accessed March 20, 2014).
. 2010l. Mathematics Standards, Grade 5, Introduction. />Content/5/introduction (accessed March 20, 2014).
. 2010m. Mathematics Standards, Grade 6, Introduction. />Content/6/introduction (accessed March 20, 2014).
. 2010n. Mathematics Standards, Grade 7, Introduction. />Content/7/introduction (accessed March 20, 2014).
. 2010o. Mathematics Standards, Grade 8, Introduction. />Content/8/introduction (accessed March 20, 2014).
. 2010p. Mathematics Standards, Kindergarten, Introduction. />Math/Content/K/introduction (accessed March 20, 2014).
. 2010q. Mathematics, Standards for Mathematical Practice. />Practice (accessed March 20, 2014).
. 2012. K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics. Washington,
DC: National Governor’s Association Center for Best Practices, Council of Chief State School Officers.
/>(accessed March 20, 2014).
. 2013. High School Publishers’ Criteria for the Common Core State Standards for Mathematics.
Washington, DC: National Governor’s Association Center for Best Practices, Council of Chief State
School Officers. />FINAL.pdf (accessed March 20, 2014).
National Mathematics Advisory Panel. 2008. Foundations for Success: The Final Report of the National
Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. http://
bdscomm/list/mathpanel/report/final-report.pdf [Link no longer valid] (accessed March 31, 2014).

National Research Council. 2001. Adding it Up: Helping Children Learn Mathematics. Washington, DC:
National Academies Press.
876

References

California Mathematics Framework


Kindergarten–8th Grade. (accessed March 31, 2014).
NYU Steinhardt. 2009. “ELLs and Mathematics.” Online educational module. New York: New York
University, Steinhardt School of Culture, Education, and Human Development. .
edu/scmsAdmin/uploads/004/738/NYU_PTE_Math_Module_For_ELLS_Oct_8_2009.pdf
(accessed March 19, 2014).
California Mathematics Framework

References

877


Oakes, Jeannie, Adam Gamoran, and Reba N. Page. 1992. “Curriculum Differentiation: Opportunities,
Outcomes, and Meanings.” In Handbook of Research on Curriculum, edited by Phillip Jackson. New
York: Macmillan.
Oakes, Jeannie, Kate Muir, and Rebecca Joseph. 2000. Coursetaking and Achievement in Mathematics and
Sciences: Inequalities that Endure and Change. Madison, WI: University of Wisconsin, WCER, National
Institute of Science Education.
O’Connor, Ken. 2007. “The Last Frontier: Tackling the Grading Dilemma.” In Ahead of the Curve: The Power
of Assessment to Transform Teaching and Learning, edited by Douglas Reeves, 127–45. Bloomington,
IN: Solution Tree Press.
Ohio Department of Education (ODE). 2011. Ohio’s New Learning Standards: K–12 Mathematics, Model
Curricula, Grades 1 and 3. Columbus, OH: Ohio Department of Education.cation.
ohio.gov/GD/Templates/Pages/ODE/ODEDetailaspx?page=3&TopicRelationID=1704&ContentID=
126041&Content=141858 (accessed March 20, 2014).

Oxford Dictionaries. 2013. (accessed March 20, 2014).
Park City Mathematics Institute. 2013. Cabri 3D—Steve Phelps. Princeton, NJ: School of Mathematics
at the Institute for Advanced Study. />shortfiles/phelps.html (accessed March 20, 2014).
Parrish, Sherry. 2010. Number Talks: Helping Children Build Mental Math and Computation Strategies—

Learning. Bloomington, IN: Solution Tree Press.
Ruthven, Kenneth, Rosemary Deaney, and Sara Hennessy. 2009. “Using Graphing Software to Teach
about Algebraic Forms: A Study of Technology-Supported Practice in Secondary-School Mathematics.”
Educational Studies in Mathematics 71 (3): 279–97.
Saunders, William, and Claude Goldenberg. 2010. “Research to Guide English Language Development
Instruction.” In Improving Education for English Learners: Research-Based Approaches. Sacramento, CA:
California Department of Education.
Schleppegrell, Mary J. 2007. “The Linguistic Challenges of Mathematics Teaching and Learning:
A Research Review.” Reading & Writing Quarterly 23 (2): 139–59.
Science NetLinks. 2013. Marble Mania! Washington, DC: American Association for the Advancement of
Science. (accessed March 20,
2014).
Serido, Joyce, and Soyeon Shim. 2011. Young Adults’ Financial Capability. Tucson, AZ: The University of
Arizona. (accessed March 20, 2014).
Shodor Education Foundation, Inc. 2015. (accessed February 26, 2015). Durham,
NC: Shodor.
Smarter Balanced Assessment Consortium (Smarter Balanced). 2011. Content Specifications for the
Summative Assessment of the Common Core State Standards for Mathematics (Revised Draft, June
2013). [Link no longer valid] (accessed October 22, 2014).
. 2012a. (accessed March 20, 2014).
. 2012b. Mathematics Item Specifications, Grades 6–8. rterbalanced. org/
wordpress/wp-content/uploads/2012/05/TaskItemSpecifications/Mathematics/
MathematicsGeneralItemandTaskSpecificationsGrades6-8.pdf [Link no longer valid]
(accessed March 20, 2014).
. 2012c. Smarter Balanced Assessment Consortium General Item Specifications. http://www.
smarterbalanced.org/wordpress/wp-content/uploads/2012/05/TaskItemSpecifications/
ItemSpecifications/GeneralItemSpecifications.pdf [Link no longer valid] (accessed March 20,
2014).

Smith, Aaron. 2010. Home Broadband 2010. Washington, DC: Pew Research Internet Project. http://

Levels of Cognitive Demand. Portsmouth, NH: Heinemann.
. 2013. Differentiating Mathematics Instruction So EVERYONE Learns. STEM White Paper,
McGraw-Hill Education. />diffentiating_math.pdf [Link no longer valid] (accessed March 20, 2014).
Thompson, Ian. 2010. “The Principal Counting Principles.” United Kingdom: National Centre for
Excellence in the Teaching of Mathematics. />The+principal+counting+principles.pdf (accessed March 31, 2014).
Thompson, Sandra J., Amanda B. Morse, Michael Sharpe, and Sharon Hall. 2005. Accommodations
Manual: How to Select, Administer, and Evaluate Use of Accommodations for Instruction and
Assessment of Students with Disabilities. 2nd ed. Washington, DC: Council of Chief State
School Officers. />(accessed March 20, 2014).
Thompson, Virginia, and Karen Mayfield-Ingram. 1998. Family Math: The Middle School Years, Algebraic
Reasoning and Number Sense. Berkeley, CA: University of California, Lawrence Hall of Science.
TK California. 2013. (accessed March 20, 2014).
Tomlinson, Carol Ann. 2001. How to Differentiate Instruction in Mixed-Ability Classrooms. 2nd ed.
Alexandria, VA: Association for Supervision and Curriculum Development (ASCD).
880

References

California Mathematics Framework


Tomlinson, Carol Ann, and Marcia B. Imbeau. 2010. Leading and Managing a Differentiated Classroom.
Alexandria, VA: ASCD.
Trotter, Andrew. 2007. “Digital Divide 2.0.” Bethesda, MD: Editorial Projects in Education. http://www.
edweek.org/dd/articles/2007/09/12/02divide.h01.html (accessed March 20, 2014).
Understanding Language. 2012. “The Common Core for English Language Learners: Challenges and
Opportunities.” Webinar. Stanford, CA: Stanford University, Graduate School of Education.
/>2005-18-12.pdf (accessed March 24, 2014).
United States Census Bureau. 2009. Computer and Internet Use. Washington, DC: U.S. Census Bureau.
(accessed March 20, 2014).

California Mathematics Framework

References

881


. 2013a. Draft 3–5 Progression on Number and Operations—Fractions. http://commoncoretools.
me/wp-content/uploads/2011/08/ccss_progression_nf_35_2013_09_19.pdf (accessed April 2, 2014).
. 2013b. Draft High School Progression on Algebra. (accessed April 2, 2014).
. 2013c. Draft High School Progression on Functions. (accessed April 2, 2014).
Usiskin, Zalman. 2011. “Mathematical Modeling in the School Curriculum.” Presentation given at
Teachers College, Columbia University, September 26, 2011.
Van de Walle, John A. 2007. Elementary and Middle School Mathematics: Teaching Developmentally.
6th ed. Boston: Pearson/Allyn and Bacon.
Van de Walle, John A., and Sandra Folk. 2005. Elementary and Middle School Mathematics: Teaching
Developmentally. Toronto: Pearson Education Canada.
Vaughn, Sharon, and Candace S. Bos. 2012. Strategies for Teaching Students with Learning and Behavior
Problems. 8th ed. Boston: Pearson.
Vaughn, Sharon R., Candace S. Bos, and Jeanne Shay Schumm. 2010. Teaching Students Who Are
Exceptional, Diverse, and at Risk in the General Education Classroom. 5th ed. Boston: Pearson.
Ventura County Office of Education and the California Department of Education. 2011. Response to
Instruction and Intervention RtI2: An Implementation and Technical Assistance Guide for Districts and
Schools. (accessed March 20, 2014).
Vygotsky, Lev Semyonovich. 1978. Mind in Society: The Development of Higher Psychological Processes.
Cambridge, MA: Harvard University Press.
Walden University. 2010. Educators, Technology and 21st Century Skills: Dispelling Five Myths. Minneapolis,
MN: Walden University, Richard W. Riley College of Education. />(accessed March 20, 2014).
Walston, Jill, and Jill Carlivati McCarroll. 2010. Eighth-Grade Algebra: Findings from the Eighth-Grade Round
of the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K). NCES Publication

huffingtonpost.com/hunghsi-wu/math-education_b_1901299.html (accessed March 20, 2014).
Xin, Yan Ping, and Asha K. Jitendra. 1999. “The Effects of Instruction in Solving Mathematical Word
Problems for Students with Learning Problems: A Meta-Analysis.” Journal of Special Education
32:207–25.

California Mathematics Framework

References

883