**Additional Key Research that Affected the Development of Perceptions Math's Curriculum & Manipulatives**

Research^{1} has shown that understanding fractions and whole-number division are early predictors of a student’s mathematical achievement in high school. The research further supports that mastery of fractions and division is important to develop an understanding of algebra and other high school mathematics. Watch a video of Dr. Seigler discussing the study and the implications. Research^{2} has also shown that an intervention should include explicit instruction that is systematic, cumulative, and multi-sensory. Additionally, interventionists should be proficient in the use of visual representations of mathematical ideas. The *Preceptions* Program uses *MasterPieces *and *MasterFractions* to support the instruction of place value, addition, subtraction, regrouping, multiplication, division, and fractions, and much more consistent with these research findings.

Butler, F. M., Miller, S. P., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. *Learning Disabilities Research & Practice*, *18*(2), 99-111.

Jayanthi, M., Gersten, R., & Baker, S. (2008). Mathematics instruction for students with learning disabilities or difficulty learning mathematics: A guide for teachers. *Center on Instruction*.

Maccini, P., & Hughes, C. A. (2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. *Learning Disabilities Research & Practice*, *15*(1), 10-21.

Maccini, P., & Ruhl, K. L. (2000). Effects of a graduated instructional sequence on the algebraic subtraction of integers by secondary students with learning disabilities. *Education and Treatment of Children*, 465-489.

Witzel, B. S. (2005). Using CRA to teach algebra to students with math difficulties in inclusive settings.*Learning Disabilities—A Contemporary Journal*, *3*(2), 49-60.

^{1}A 20 year longitudinal study on Early Predictors of High School Mathematics Achievement by Robert S. Seigler et al.^{2}Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools by Russell Gersten et al.