**Resources**

Some introductory videos about differentiated instruction:

**From Carol Tomlinson**

- A short video with suggestions of how to get started with DI: (4:56)
- Why differentiate? (3:02)
- DI as proactive instruction: (3:47)
- Two Misconceptions about DI: (3:31)
- Formative Assessment in a DI classroom: (1:07)

**What does differentiation in middle school math classrooms look like? Two examples:**

- Brent Loken (7:44) (a glimpse into one classroom, with no editorial comment)
- Marcel LeBlanc, Anglophone East Middle School (a narrated example of how one teacher differentiates for his students)

In the second unit of Phase III, we used a Races app designed by Janet Bowers to support students' ratio reasoning and found it to be very powerful.

Our design to use the Races app was based on lessons developed by Joanne Lobato and colleagues in their Math Talk project, funded by the National Science Foundation Award DRL-1416789.

**Our Presentations page** offers links to our power point presentations with basic information about differentiated instruction as well as samples of student work from the project.

**Additional References about Differentiation:**

Heacox, D. (2002). *Differentiating instruction in the regular classroom: How to reach and*

*teach all learners, grades 3-12.* Minneapolis, MN: Free Spirit Publishing.

Humphreys, C., & Parker, R. (2015). *Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10*. Stenhouse Publishers.

Laud, L. (2011). *Using formative assessment to differentiate mathematics instruction, *

*grades 4-10: Seven practices to maximize learning.* Thousand Oaks, CA, and Reston, VA:

Corwin and NCTM.

Parrish, S (2010). *Number talks: Helping children build mental math and computation strategies, grades K-5*. Math Solutions, 2010.

Small, M., & Lin, A. (2010). *More good questions: Great ways to differentiate secondary *

*mathematics instruction.* New York and Reston, VA: Teachers College Press and the

National Council of Teachers of Mathematics.

Tomlinson, C. A. (2005). *How to differentiate instruction in mixed-ability classrooms *

*(2nd ed.).* Upper Saddle River, NJ: Pearson.

Carol Tomlinson's website: http://www.caroltomlinson.com/

**Other References Cited: **

ACT (2010). A first look at the common core and college and career readiness. Retrieved July 9, 2012 from http://www.act.org/research/policymakers/pdf/FirstLook.pdf

Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. *Journal of the Learning Sciences, 2*(2), 141-178.

Chazan, D. & Yerushalmy, M. (2003). On appreciating the cognitive complexity of school algebra: Research on algebra learning and directions of curricular change. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), *A research companion to Principles and Standards for School Mathematics* (pp 123-135), Reston, VA: National Council of Teachers of Mathematics.

Gamoran, A., & Weinstein, M. (1998). Differentiation and opportunity in restructured schools. *American Journal of Education, 106*(3), 385-415.

Hackenberg, A. J. (2007). Units coordination and the construction of improper fractions: A revision of the splitting hypothesis. *Journal of Mathematical Behavior, 26*, 27-47.

Hackenberg, A. J. (2010). Students' reasoning with reversible multiplicative relationships. *Cognition and Instruction, 28*(4), 1-50.

Hackenberg, A. J. (2013). The fractional knowledge and algebraic reasoning of students with the first multiplicative concept. *Journal of Mathematical Behavior, 32*(3), 538-563.

Hackenberg, A. J., & Lee, M. Y. (2015). Relationships between students' fractional knowledge and equation writing. *Journal for Research in Mathematics Education, 46*(2), 196-243.

Hackenberg, A. J., & Tillema, E. S. (2009). Students' whole number multiplicative concepts: A critical constructive resource for fraction composition schemes. *Journal of Mathematical Behavior, 28*, 1-18.

National Mathematics Advisory Panel (NMAP). (2008). *Foundations for success: The final report of the national mathematics advisory panel*. Washington, DC: U.S. Department of Education.

Olive, J., & Caglayan, G. (2008). Learners' difficulties with quantitative units in algebraic word problems and the teachers's interpretation of those difficulties. *International Journal of Science and Mathematics Education, 6*, 269-292.

Steffe, L. P., & Olive, J. (2010). *Children's fractional knowledge*. New York: Springer.

Tomlinson, C. A., Brighton, C., Hertberg, H., Callahan, C. M., Moon, T. R., Brimijoin, K., Conover, L. A., & Reynolds, T. (2003). Differentiating instruction in response to student readiness, interest, and learning profile in academically diverse classrooms: A review of literature. *Journal for the Education of the Gifted, 27*(2/3), 119-145.

U.S. Department of Education, National Center for Education Statistics (2012). *Digest of Education Statistics, 2011* (NCES 2012-001), Chapter 2. Retrieved June 29, 2012 from http://nces.ed.gov/programs/digest/d11/ch_2.asp.