Backed by Research

Proven by Practice
An old concept, made easy to implement
Daily math practice is not a new concept. It has been part of classrooms for decades, and has proven effective over time. While Formative Loop takes a unique digital approach to make running a daily individualized program easy, we built upon that existing methodology in designing much of our program. Digital programs are excellent additions to the classroom, but we believe strongly in the benefits of pencil-paper practice (read our blog post). Our program uses technology where it fits best in managing the program while providing students the mechanical practice of number formation and showing their work on paper.
White Paper - Efficacy of Formative Loop Numeracy
This case study provides a detailed analysis of implementing Formative Loop and the resulting impact on students.
When building Formative Loop, there were several papers from which we drew insights. They support the individualized learning design of Formative Loop, the sequence of our problems, and the content of our exercises. They also show the ways learning is enhanced when using pencil-paper vs. digital systems. Below is a list of papers we drew heavily from.

Baroody, A.J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise studies (pp. 1-34), Mahwah, NJ: Erlbaum.

Ferrari, M., Sternberg, R. J. (1998). The development of mental abilities and styles. In W. Damon (Ed.), Handbook of child psychology: Child psychology and practice (5th ed., Vol 2, pp. 899-946), New York: Wiley.

Hiebert, J., & Wearne, D (1996). Instruction, understanding, and skill in multidigit addition and subtraction. Cognitive and Instruction, 14, 251-283.

Isaacs, A., & Carroll, W. (1999). Strategies for basic fact instruction. Teaching Children Mathematics, 5(9), 508–515.

Steel, S. & Funnell, E. (2001). Learning multiplication facts: A study of children taught by discovery methods in England. Journal of Experimental Child Psychology, 79(1), 37–55.

Wong, M., & Evans, D. (2007). Improving basic multiplication fact recall for primary school students. Mathematics Education Research Journal, 19(1), 89–106.

Mueller, P., & Oppenheimer, D. (2014). The Pen Is Mightier Than the Keyboard. DOI:

Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy instruction with timed practice drills. Learning Disability Quarterly, 29, 269–289.