Woot Math’s design and development sought to leverage multiple principles from research from cognitive science with established evidence, and other practices that have extensively established evidence for the learning of mathematics. These have included sources such as the various Practice Guides from What Works Clearinghouse (IES, U.S. Dept. Education), and seminal works such as Adding it Up and How People Learn (from the National Research Council and National Academies, respectively).
Woot Math has been designed and developed to help teachers through its support of important strategies that are widely identified as best practices. For example, the WWC Practice Guide on Improving Mathematical Problem Solving in Grades 4-8 gives the following recommendations: prepare problems and use them in whole-class instruction; assist students in monitoring and reflecting on the problem-solving process; and expose students to multiple problem-solving strategies (Woodward et al., 2012).
Woot Math has also been designed and developed to leverage the best research from cognitive science about how people learn. In a recent review of laboratory and classroom studies, Booth and colleagues (2017) describe the evidence for eight cognitive science principles that are especially promising for improving mathematics instruction, namely: feedback, scaffolding, distributed practice, interleaved practice, worked examples, error reflection, linking between abstract and concrete representations, and comparing and contrasting multiple instances. Each of these principles was incorporated into the design of Woot Math. Here are some examples, with citations of research published by the Woot Math team: All tasks in Woot Math provide immediate feedback to students. Woot Math’s adaptive learning and practice capabilities adaptively schedule both distributed and interleaved practice based on Bayesian predictive models of student knowledge along with blocks of practice and other techniques to boost student confidence (Montero et al., 2018; Khajah, Mozer, Kelly, & Milne, 2018; Milne, Kelly, & Webb, 2014). Unlike other leading intelligent tutoring platforms that use a “hint system,” Woot Math provides worked examples both for scaffolding and for just-in-time (isomorphic-task) help. A recent year-long randomized study of fifth grade students found that worked examples significantly improved transfer of student outcomes to algebra (Hallinen & Booth, 2018). Woot Math’s connected-classroom and formative assessment capabilities place focus on worked examples, error reflection, and comparison and contrast across approaches (Bush & Milne, 2018a; Bush & Milne, 2018b; Bush, Marks, & Milne, 2017). Woot Math emphasizes high-quality virtual manipulatives and uses them to create linkages between concrete and abstract representations (Marks & Wyberg, 2016).
Having a valid basis in research is a necessary element of an effective product for education, but it is not enough. It is equally important for the product to be easily used by teachers and students and to naturally fit into the requirements of their classroom. Because of this fact, Woot Math has been carefully designed and developed for ease of use and to minimize the friction of adoption in real classrooms. This has been done through extensive work with teachers and students and iterative updates to the products through the process of co-design and design-based implementation research (Penuel et al., 2011).
Bellman, A., Foshay, W. R., & Gremillion, D. (2014). A Developmental Model for Adaptive and Differentiated Instruction Using Classroom Networking Technology. In The Mathematics Teacher in the Digital Era (pp. 91-110). Springer, Dordrecht.
Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: principles, policy & practice, 5(1), 7-74.
Booth, J. L., McGinn, K. M., Barbieri, C., Begolli, K. N., Chang, B., Miller-Cotto, D., Young, L. K. & Davenport, J. L. (2017). Evidence for cognitive science principles that impact learning in mathematics. In Acquisition of complex arithmetic skills and higher-order mathematics concepts (pp. 297-325). Academic Press.
Booth, J.L., Newton, K.J., Pendergast, L.H., & Barbieri, C. (2018). Opening the door to algebra: The role of fraction knowledge in algebra learning. Proceedings of International Conference of the Learning Sciences, ICLS, 3(2018-June), pp. 1581-1582.
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.
Bush J. (In Preparation). Evaluation of Software-Based Formative Assessment Intervention with Digital Manipulatives to Support Student Conceptual Understandings of Fractions. Approved for Doctoral Prospectus. University of Colorado, School of Education.
Bush J, Milne B. (2018a) Making Mathematical Thinking Visible Through Technology. Proceedings of International Conference of the Learning Sciences, ICLS, 3(2018-June)
Bush J, Milne B. (2018b). Technology to Support Students’ Learning Mathematics from Other Students Work. Proceedings of International Conference of the Learning Sciences, ICLS, 3(2018-June)
Bush JB, Marks K, & Milne RB. (2017). Design Considerations for a Web-Based Formative Assessment tool to Support Collaborative Learning in Mathematics. Contributed paper to the International Society for Design and Development in Education (ISDDE) Annual Conference, Berkeley, California.
Hallinen, N.R. & Booth, J.L. (2018). Don’t just do it, explain it: A 5th grade worked examples curriculum supports transfer to algebra content. Proceedings of International Conference of the Learning Sciences, ICLS, 3(2018-June), pp. 1647-1648.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of educational research, 77(1), 81-112.
Khajah MM, Mozer MC, Kelly S, Milne B. (2018). Boosting Engagement with Educational Software Using Near Wins. In International Conference on Artificial Intelligence in Education. pp. 171-175. Springer.
Kobett, B. M., & Wray, J. A. (2016). The formative 5: Everyday assessment techniques for every math classroom. Corwin Press.
Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2003). Using a translation model for curriculum development and classroom instruction. In R. Lesh, & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Routledge.
Madda, MJ. (2016). Which Edtech Companies Are Producing the Best Research-Based Products? EdSurge. Nov 9 2016. Retrieved from https://www.edsurge.com/news/2016-11-09-which-edtech-companies-are-producing-the-best-research-based-products
Marks K & Wyberg T. (2016) Making Sense of Fractions: The Journey Is the Destination. NCTM 2016 Annual Conference, San Francisco, CA.
Milne B, Wyberg T. (2014). Effectiveness of Personalizing Instructive Software for Rational Numbers: A Randomized Controlled Trial. Fourth International Realistic Mathematics Education Conference.
Montero S, Arora A, Kelly S, Milne B, Mozer M. (2018). Does Deep Knowledge Tracing Model Interactions Among Skills?. In Proceedings of the Eleventh International Conference on Educational Data Mining. Educational Data Mining Society Press.
Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Virtual and Personal Learning Environments, 4(3), 35-50.
National Academies of Sciences, Engineering, and Medicine. (2000). How people learn. (Bransford et al). National academy press.
National Academies of Sciences, Engineering, and Medicine. (2018). How people learn II: Learners, contexts, and cultures. (Marrett et al). National Academies Press.
National Research Council. (2001) Adding it up: Helping children learn mathematics. National Academies Press.
NCTM. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA
Penuel, W. R., Fishman, B. J., Cheng, B., & Sabelli, N. (2011). Organizing research and development at the intersection of learning, implementation, and design. Educational Researcher, 40(7), 331-337.
Roschelle, J., Penuel, W. R., & Abrahamson, L. (2004). The networked classroom. Educational Leadership, 61(5), 50-54.
Sarama, J., & Clements, D. H. (2009). Concrete computer manipulatives in mathematics education. Child Development Perspectives. 3(3), 145–150. doi:10.1111/j.1750-8606.2009.00095.x
Shaffer, D. W., & Kaput, J. J. (1998). Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education. Educational Studies in Mathematics, 37(2), 97–119. doi:10.1023/A:1003590914788
Siegler, R., Carpenter, T., Fennell, F., et al. (2010). Developing Effective Fractions Instruction for Kindergarten through 8th Grade. IES Practice Guide. NCEE 2010-4039. What Works Clearinghouse.
Trigueros, M., Lozano, M. D., & Sandoval, I. (2014). Integrating technology in the primary school mathematics classroom: The role of the teacher. In The mathematics teacher in the digital era (pp. 111-138). Springer, Dordrecht.
Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., … & Ogbuehi, P. (2012). Improving Mathematical Problem Solving in Grades 4 through 8. IES Practice Guide. NCEE 2012-4055. What Works Clearinghouse.
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