Education: EDUC115N How to Learn Math
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Research Summary
Session 1 References
Community College Performance
The Carnegie Foundation for the Advancement of Teaching. “Strengthening Pre-collegiate Education in
Community Colleges: Project Summary and Recommendations.” A Report from Strengthening Precollegiate Education in Community Colleges (SPECC). Stanford, Calif.: The Carnegie Foundation for the
Advancement of Teaching, 2008.
Stereotype Threat
Steele, Claude M. (2011). Whistling Vivaldi: How stereotypes affect us and what we can do (issues of our
time). New York, NY: W. W. Norton and Company.
Steele, C. M. (1997). A threat in the air. How stereotypes shape intellectual identity and performance. The
American psychologist, 52(6), 613–629.
Spencer, S. J., Steele, C. M., & Quinn, D. M. (1999). Stereotype Threat and Women's Math Performance.
Journal of Experimental Social Psychology, 35(1), 4–28. doi:10.1006/jesp.1998.1373
Shih, M., Pittinsky, T. L., & Ambady, N. (1999). Stereotype susceptibility: Identity salience and shifts in
quantitative performance. Psychological Science, 10(1), 80–83. doi:10.1111/1467-9280.00111
Ambady, N., Shih, M., Kim, A., & Pittinsky, T. L. (2001). Stereotype susceptibility in children: Effects of
identity activation on quantitative performance. Psychological Science, 12(5), 385–390. doi:10.1111/14679280.00371
Perry, T., Steele, C., & Hilliard, A. (2003). Young, gifted, and black: Promoting high achievement among
african-americans. Boston, MA: Beacon Press.
Messages
Yeager, D. S., Purdie-Vaughns, V., Garcia, J., Apfel, N., Brzustoski, P., Master, A., et al. (2013). Breaking
the Cycle of Mistrust: Wise Interventions to Provide Critical Feedback Across the Racial Divide. Journal of
Experimental Psychology: General.
Cohen, G. L., Garcia, J., Apfel, N., & Master, A. (2006). Reducing the Racial Achievement Gap: A SocialPsychological Intervention. Science, New Series, 313(5791), 1307–1310.
Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting Interest and Performance in High School
Science Classes. Science, 326(5958), 1410–1412. doi:10.1126/science.1177067
Geoffrey L. Cohen, Julio Garcia, Nancy Apfel, and Allison Master. Reducing the Racial Achievement Gap:
A Social-Psychological Intervention. Science 1 September 2006: 313 (5791), 1307-1310.
[DOI:10.1126/science.1128317]
Walton, G. M., & Cohen, G. L. (2007). A question of belonging: Race, social fit, and achievement. Journal
of Personality and Social Psychology, 92(1), 82. doi:10.1037/0022-3514.92.1.82
A Mathematician’s Lament.
Lockhart, P. (2009). A mathematician's lament. New York, NY : Bellevue Literary Press.
Session 2 References
Brain Plasticity
Abiola, O. O., & Dhindsa, H. S. (2011). Improving classroom practices using our knowledge of how the
brain works. International Journal of Environmental & Science Education, 7(1), 71–81.
Woollett, K., & Maguire, E. A. (2011). Acquiring “the Knowledge” of London's Layout Drives Structural
Brain Changes. Current Biology, 21(24), 2109–2114. doi:10.1016/j.cub.2011.11.018
Maguire EA, Woollett K, Spiers HJ. (2006) London taxi drivers and bus drivers: a structural MRI and
neuropsychological analysis. Hippocampus. 16(12):1091-101.
http://www.today.com/id/36032653/ns/today-today_health/t/meet-girl-half-brain/#.UeGbixbfvCE
Karni, A., Meyer, G., Rey-Hipolito, P., Adams, M., Turner, R., Ungerleider, L. (1998). The acquisition of
skilled motor performance: Fast and slow experience-driven changes in primary motor cortex. Proc. Natl.
Acad. Sci. USA Vol. 95, pp. 861–868, February 1998. Colloquium Paper
Mindset
Dweck, Carol S. (2007). Mindset: The new psychology of success. New York, NY: Random House.
Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S., (2007). Implicit theories of intelligence predict
achievement across an adolescent transition: A longitudinal study and an intervention. Child Development,
78 (1). 246-263.
Dweck, C. (2009). Mindsets and equitable education. Educational Leadership.
Other Dweck references are available for download here:
http://www.stanford.edu/dept/psychology/cgi-bin/drupalm/cdweck
Session 3 References
Mistakes
Tugend, A. (2011). Better By Mistake. The Unexpected Benefits of Being Wrong. Riverhead Books: New
York.
Moser, J.S., Schroder, H.S., Heeter, C., Moran, T.P., Lee, Y.-H., 2011. Mind your errors: evidence for a
neural mechanism linking growth mindset to adaptive post-error adjustments. Psychological Science 22,
1484 – 1489.
Boaler Study of English Schools and Follow Up Study of Adults
Boaler, J. (2002). Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and
Their Impact on Student Learning. (Revised and Expanded Edition ed.). Mahwah, NJ: Lawrence Erlbaum
Association.
Boaler, J. (1998). Open and Closed Mathematics: Student Experiences and Understandings. Journal for
Research in Mathematics Education, 29(1), 41-62.
Boaler, J. (2012, 8-15 July). From Psychological Imprisonment to Intellectual Freedom - The Different
Roles that School Mathematics Can Take in Students' Lives. Paper presented at the 12th International
Congress on Mathematical Education, Seoul, Korea.
Ray Peacock
In:
Boaler, J. (2009) What’s Math Got To Do With It?How Parents and Teachers Can Help Children Learn to
Love Their Least Favorite Subject. Penguin: New York.
&
Boaler, J. (2010). The Elephant in the Classroom. Helping Children Learn & Love Maths. Souvenir Press:
London.
&
Boaler, J. (2011). Elefanten i klassrummet: Att hjälpa elever till ett lustfyllt lärande i matematik [The
elephant in the classroom: Helping children to a joyful learning in mathematics] (E. Trägårdh, Trans).
Stockholm, Sweden: Liber.
Didactic Contract
Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R.
Sutherland, & V. Warfield, Eds.). Dordrecht, Netherlands: Kluwer Academic Publishers.
Timed Tests
Ashcraft, M. (2002). Math Anxiety: Personal, Educational and Cognitive Consequences. Current
Directions in Psychological Science. 11, 5, 181-185.
Beilock, S. (2011). Choke: What the Secrets of the Brain Reveal about Getting it Right When you have To.
Simon & Schuster, Free Press: New York.
Beilock, S., Gunderson E., Ramirez, G., & Levine, S. (2009). Female Teachers’ Math Anxiety Affects
Girls Math Achievement. Proceedings of the National Academy of Sciences February 2, 2010, Vol 107, 5,
1860-1863.19-23.
Boaler, J. (July 3, 2012). Timed tests and the development of math anxiety. Education Week.
Faust, M.W. (1992). Analysis of Physiological Reactivity in Mathematics Anxiety. Unpublished doctoral
dissertation. Bowling Green State University, Bowling Green, Ohio.
Hembree, R. (1990). The Nature, Effects, and Relief of Mathematics Anxiety. Journal for Research in
Mathematics Education, 21, 33-46.
Lyons, I. and Beilock, S. (2011) Mathematics anxiety: separating the math from the anxiety. Cereb Cortex
22: 2102 – 2110.
Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (in press). Math anxiety, working Memory
and Math Achievement in Early Elementary School. Journal of Cognition and Development.
Richardson, F. C, & Woolfolk, R.L. (1980). Mathematics Anxiety. In I.G. Sarason (Ed), Test anxiety:
Theory, research and application (pp271-288). Hillsdale NJ:Erlbaum.
Young, C.B., Wu, S.S. & Menon, V. (2012). The Neurodevelopmental Basis of Math Anxiety.
Psychological Science Online First. March 20, 2012. doi:10.1177/0956797611429134
Number Sense
Boaler, J. (2009) What’s Math Got To Do With It? How Parents and Teachers Can Help Children Learn to
Love Their Least Favorite Subject. Penguin: New York.
Gray, E. and D. Tall. (1994). Duality, Ambiguity, and Flexibility: A "Proceptual" View of Simple
Arithmetic. Journal for Research in Mathematics Education, 1994. 25 (2), 116-140.
Seeley, Cathy (2009). Faster isn't Smarter (2009). Sausalito, CA:Math Solutions Publications
Some Good wesbites and apps to help with number Sense (recommened by Dan Meyer):
Motion Math
Conceptua Math
Buzz Math
ST Math
Dragon Box
Refraction
Laurent Schwartz:
Un mathématicien aux prises avec le siècle. Paris 1997, Autobiography, English translation: A
mathematician grappling with his century. Birkhäuser, 2001
Session 4 References
Cathy Humphrey’s Teaching:
Boaler, J., & Humphreys, C. (2005). Connecting mathematical ideas: middle school video cases to support
teaching and learning. Portsmouth, NH: Heinemann.
Mason, J., Burton, L. & Stacey, K. (1982). Thinking mathematically. London: Addison-Wesley.
Assessment
Black, P., & Wiliam, D. (1998). Inside the Black Box: Raising Standards through Classroom Assessment.
Phi Delta Kappan, October, 139-148.
Butler, R. (1988). Enhancing and Undermining Intrinsic Motivation: The Effects of Task-Involving and
Ego-Involving Evaluation on Interest and Performance. British Journal of Educational Psychology, 58, 114.
White, B., & Frederiksen, J. (1998). Inquiry, modeling and metacognition: making science accessible to all
students. Cognition and Instruction, 16(1), 3-118.
Ability Grouping
Burris, C.C., J.P. Heubert and H.M. Levin (2006), "Accelerating Mathematics Achievement Using
Heterogeneous Grouping", American Educational Research Journal, Vol. 43, No. 1, pp. 105-136.
Boaler, J. (2009) What’s Math Got To Do With It?How Parents and Teachers Can Help Children Learn to
Love Their Least Favorite Subject. Penguin: New York.
Boaler, J. (2010). The Elephant in the Classroom. Helping Children Learn & Love Maths. Souvenir Press:
London
Boaler, J. (2012, 8-15 July). From Psychological Imprisonment to Intellectual Freedom - The Different
Roles that School Mathematics Can Take in Students' Lives. Paper presented at the 12th International
Congress on Mathematical Education, Seoul, Korea.
Nunes, T., Bryant, P., Sylva, K., & Barros, R. (2009). Development of maths capabilities and confidence
in primary school. London: Department for Children, Schools and Families.
NRC. (2004). Engaging Schools: Fostering High School Students' Motivation to Learn. Rosenthal, R.;
Jacobson, L. (1968). Pygmalion in the classroom. New York: Holt, Rinehart & Winston.
Dixon, A. (2002) Editorial, FORUM, 44(1), pp. 1.
Kutnick, P., Sebba, J., Blatchford, P., Galton, M. (2005) The Effects of Pupul Grouping. A Literature
Review. Department for Education and Skills: London. Research Report, number 688.
Maggie Lampert:
Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven: Yale University Press.
Michelle Obama:
https://www.youtube.com/watch?v=_ObgwPR2Nzs&t=153
Japanese Math Video referenced, from the TIMSS study:
http://timssvideo.com/67
Mindset Websites:
http://mindsetonline.com
http://www.mindsetworks.com
Task Makeovers from Dan Meyer:
http://blog.mrmeyer.com/?p=17162
Session 5 References
Gray, E. M., & Tall, D. D. (1994). Duality, ambiguity, and flexibility: A “proceptual” view of simple
arithmetic. Journal for Research in Mathematics Education, 25, 116–146.
Slavit, D. (1998). The role of operation sense in transitions from arithmetic to algebraic thought.
Educational Studies in Mathematics, 37, 251–274.
Thurston, W. (1990). Mathematical Education. Notices of the AMS 37, 844–850.
Kieran, C. (2013). The false dichotomy in mathematics education between
conceptual understanding and procedural skills: An example from algebra.
In K.R. Leatham (Ed.), Vital directions for mathematics education research
(pp. 153-171). New York: Springer.
Kiernan, C. (1992). ‘The learning and teaching of school algebra,’ in D. Grouws (ed.), The Handbook of
Research on Mathematics Teaching and Learning. Macmillan, New York, 390-419.
Sawyer, W. W. (1964). Mathematician's delight. New York: Penguin Book.
Number Talks:
Boaler, J. (2009). What's Math Got To Do With It?: How Parents and Teachers Can Help Children Learn
to Love their Least Favorite Subject. New York: Penguin.
Harris, P.W. (2001). Building (Powerful) Numeracy for Middle and High school students. Portsmouth NH:
Heinemann:
Parker, R. (1993). Mathematical Power: Lessons from a Classroom. Portsmouth NH: Heinemann:
Parrish, S. (2010). Number talks: Helping children build mental math and computation strategies, grades
K-5. Sausalito, CA: Math Solutions Publications.
Parker, R. (1993). Mathematical power: Lessons from a classroom. Portsmouth, NH: Heinemann.
Mentioned websites/apps
Wolfram Alpha.
http://www.wolframalpha.com
http://doodlecastpro.com
http://www.airsquirrels.com/reflector/
Session 6 References
Pólya, G. (1957). How to solve it: A new aspect of mathematical method (2d ed.). Garden City, N.Y.:
Doubleday.
Fullilove, R. E., & Treisman, P. U. (1990). Mathematics achievement among African American
undergraduates at the University of California, Berkeley: An evaluation of the Mathematics Workshop
Program. Journal of Negro Education, 59 (30), 463-478.
Burton, L.: 1999, ‘The Practices of mathematicians: What do they tell us about coming to know
mathematics?’, Educational Studies in Mathematics 37, 121–143.
Hersh, R. (1999). What is Mathematics, Really? New York: Oxford University Press.
Wilder, R. (1984). ‘The Role of Intuition,’ in Campbell, D. & Higgins, John
(eds). Mathematics. People. Problems. Results: Volume
Wadsworth.
ii. Belmont, CA:
Davis, P., R. Hersh, L. Steen, & William C. Waterhouse. (1983) The Mathematical Experience and
Mathematics Tomorrow. Physics Today 36.11: 76.
Davis, P., R. Hersh, R. (1999). The Mathematical Experience. Mariner Books.
Session 7 References
Algebra:
Confrey, J. (1998, September). What do we know about K-14 students’ learning of algebra. In The nature
and role of Algebra in the K-14 curriculum: Proceedings of a national symposium (pp. 37-40). National
Academies Press.
Hacker, A. (2012). Is Algebra Necessary? New York Times.
Moses, R., & Cobb, C. E. (2002). Radical equations: Civil rights from Mississippi to the Algebra Project.
Beacon Press.
Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on
mathematics teaching and learning. New York, NY: Macmillan.
Kieran, C. (2013). The false dichotomy in mathematics education between conceptual understanding and
procedural skills: An example from algebra. In K.R. Leatham (Ed.), Vital directions for mathematics
education research (pp. 153-171). New York: Springer.
http://blogs.oregonstate.edu/smedcohort2010/files/2011/02/Smith-Hillen-Catania_2007.pdf
Smith, M. S., Hillen, A. F., & Catania, C. L. (2007). Using Pattern Tasks to Develop Mathematical
Understandings and Set Classroom Norms. Mathematics Teaching in the Middle School, 13(1), 38–44.
http://blogs.oregonstate.edu/smedcohort2010/files/2011/02/Smith-Hillen-Catania_2007.pdf
Küchemann, D. (1978). Children's Understanding of Numerical Variables. Mathematics in School, 7(4),
23–26.
Kuchemann, D.: 1981, ‘Algebra’, in K. Hart (ed.), Children’s Understanding of Mathematics: 11-16,
Murray, London, pp. 102–119.
Mason, J., Graham, A., & Johnston-Wilder, S. (2012). Developing Thinking in Algebra. Sage.
Confrey, J. (1998, September). What do we know about K-14 students’ learning of algebra. In The nature
and role of Algebra in the K-14 curriculum: Proceedings of a national symposium (pp. 37-40). National
Academies Press.
Moses, R., & Cobb, C. E. (2002). Radical equations: Civil rights from Mississippi to the Algebra Project.
Beacon Press.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational studies in mathematics,
12(3), 317-326.
Kozol, J. (2012). Savage inequalities: Children in America's schools. Random House Digital, Inc.
Harvard Calculus:
http://www.math.harvard.edu/~knill/pedagogy/harvardcalculus/
Bell, A. W., Malone, J. A., & Taylor, P. C. (1989). Algebra-an exploratory teaching
experiment. Shell Centre for Mathematical Education, University of Nottingham.
Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers, Grades 6-10. Heinemann, 361
Hanover Street, Portsmouth, NH 03801-3912.
RAND, M. S. P. (2002, October). Mathematical proficiency for all students: Toward a strategic research and
development program in mathematics education (DRU-2773-OERI). Arlington, VA: RAND Education & Science
and Technology Policy Institute.
Jo’s summer school teaching in:
Boaler, J. (2009). What's Math Got To Do With It?: How Parents and Teachers Can Help Children Learn
to Love their Least Favorite Subject. New York: Penguin.
Mathematics Assessment Resource Service
Sources for Algebra Tasks:
Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers, Grades 6-10. Heinemann, 361
Hanover Street, Portsmouth, NH 03801-3912.
The DVD and book, "Thinking mathematically: Integrating arithmetic and algebra in elementary school"
by T.P. Carpenter, M.L. Franke, and L. Levi (2003); Portsmouth, NH: Heinemann.
Kieran, C. (2013). The false dichotomy in mathematics education between conceptual understanding and
procedural skills: An example from algebra. In K.R. Leatham (Ed.), Vital directions for mathematics
education research (pp. 153-171). New York: Springer.
http://www.utdanacenter.org/k12mathbenchmarks/tasks/tasks.php
Session 8 References
Rose, Hilary (1998). Reflections on PUS, PUM and Weakening of Panglossian Cultural Tendencies. The
Production of a Public Understanding of Mathematics. Birmingham, England: University of Birmingham,
p4
Boaler, J. (1993). The role of contexts in the mathematics classroom: do they make mathematics more “real”? For
the Learning of Mathematics, 13(2), 12-17.
Boaler, J. (2009). What's Math Got To Do With It?: How Parents and Teachers Can Help Children Learn
to Love their Least Favorite Subject. New York: Penguin.
Dan Meyer on contexts:
(blog.mrmeyer.com/?p=8002), (http://blog.mrmeyer.com/?p=17162), (http://threeacts.mrmeyer.com/).
Grouws, D., Tarr, J., Chávez, O., Sears, R., Taylan, D., & Soria, V. (2013). Curriculum and
Implementation Effects on High-School Students’ Mathematics Learning from Curricula Representing
Subject-Specific and Integrated Content Organizations. Journal for Research in Mathematics Education,
44(2), 416-463.
Tarr, J. E., Grouws, D. A., Chávez, Ó., & Soria, V. M. (2013). The Effects of Content Organization and
Curriculum Implementation on Students' Mathematics Learning in Second-Year High School Courses.
Journal for Research in Mathematics Education, 44(4), 683-729.
Jo’s research:
Boaler, J. (2009). What's Math Got To Do With It?: How Parents and Teachers Can Help Children Learn
to Love their Least Favorite Subject. New York: Penguin.
Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for
research in mathematics education, 41-62.
Boaler, J. (2002). Experiencing School Mathematics: Traditional and Reform Approaches To Teaching and
Their Impact on Student Learning, Revised and (Hardback)(Series: Studies in Mathematical Thinking and
Learning Series).
Boaler, J. (2005, September). The 'Psychological Prisons' from which they never escaped: The role of
ability grouping in reproducing social class inequalities. In Forum (Vol. 47, No. 2, pp. 135-144).
Symposium Journals.
Papers available for download from:
www.joboaler.com
Flannery, S. (2000). In code: A mathematical journey. Algonquin Books.
Advice for parents:
http://yano.co.uk/2012/05/dont-let-maths-muddle-you-2/
http://www.racetonowhere.com
A selection of Keith Devlin’s books:
Devlin, K. J. (2000). The math gene: How mathematical thinking evolved and why numbers are like gossip.
New York: Basic Books.
Devlin, K. (1996). Mathematics: the science of patterns: the search for order in life, mind and the universe.
Macmillan.
Devlin, K. (2000). The language of mathematics: making the invisible visible. Macmillan.
Jo’s response to the attacks on her work:
http://stanford.edu/~joboaler/
Resources for mathematics puzzles.
Flannery, S. (2002), In Code: A Mathematical Journey. Algonquin Books.
Boaler, J. (2009) What’s Math Got to Do With It? Penguin: New York. Appendix A
Puzzle books, in order of difficulty.
Bolt, B. (1984) The Amazing Mathematical Amusement Arcade. Cambridge, England: Cambridge
University Press.
Bolt, B. (1992) Mathematical Cavalcade. Cambridge, England: Cambridge University Press.
Bolt, B. (1993) A Pandora’s Mathematical Box. Cambridge, England: Cambridge University Press.
Bolt, B. (1995) A Mathematical Jamboree. Cambridge, England: Cambridge University Press.
Tanton, J. (2001). Solve This: Math Activities for Students and Clubs. Washington DC: Mathematical
Association of America.
Cornelius M., & Parr A. (1991). What’s Your Game? Cambridge, England: Cambridge University Press.
Berlekamp, E. & Rodgers, T. (1999) The Mathematician and Pied Puzzler: A collection in tribute to Martin
Gardner. Natick, Mass: A K Peters.
Gardner, M (1987). Riddles of the Sphinx: And other mathematical puzzle tales. Washington DC:
Mathematical Association of America
Gardner, M (2000). Mathematical puzzle tales. Washington DC: Mathematical Association of America
Gardner, M (2001). The Colossal Book of Mathematics. New York: W.W Norton
Moscovich, I. (2005) Knotty Number Problems & Other Puzzles. New York:Sterling
Bergekamp, E. R., Conway, J.H & Guy, R.K. (2001). Winning Ways for your Mathematical Plays. 2nd ed.
Wellesley, Mass: AK Peters
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