Tool with metacognitive parental scaffolding for personalized, early informal math learning.


A good "numbersense", which is an understanding of fundamental math concepts, provides the foundation for success in formal math education [1,2]. Fundamental math concepts that compose this numbersense include: cardinality, the ability to assign numerical values to sets, ordinality, the ability to measure and compare objects, subitivity, the ability to approximate values without counting, symbolic labeling of numerical values, counting number strings, identifying shapes, and recognizing basic patterns [3-6]. Children who enter kindergarten with a good mathematical foundation perform better than their counterparts with a lower comprehension of basic math concepts and that this level of performance is a good indicator of future success (or struggle) with math throughout a child's education [7].


Children in the United States, specifically those with a lower socio-economic status (SES), are not equipped with a strong grasp of math fundamentals before entering school resulting in poor performance on math assessments when compared to other countries and their higher SES peers [8,9]. Furthermore, many gender biases surround math and STEM topics that creates a divide in preparedness of children based on gender [10]. Ultimately these socio-econominc and socio-cultural factors lead to underpresentation of low SES groups and females in STEM jobs.

These children do not have enough focused attention on learning math or access to resources needed to establish a firm grasp of math fundamentals prior to entering school, resulting in an inexperience with math fundamentals, few strategies to learn math, and poor performance [11].

Early math learning begins in the home and a child's primary 'teacher' is their caregiver/parent. However, components in early math learning that are lacking for undepresented groups includes parents who lack a solid math foundation, parents who do not emphasize math as part of early learning, no equity of access to relatable learning materials, lack of metacognitive skills in both parents and their children [10-12].

How this helps

This tool aims to provide scaffolding for parents that guides them on their child's math journey while encouraging a growth mindset [13] and "math talk", as well as, recommending learning activities for each stage of math development for their child. It does this by representing early math fundamentals in a topological graph with weighted edges where edges are represented using the zone of proximal development [14] and nodes are colored by states of: [Not learned, Ready to learn with help, Learning, Learned, Needs Reinforcement]. Nodes are interactive, in that clicking on a node will allow a parent to set that node as a goal (in the future a shortest path based on the child's current progress will be mapped out). Furthermore, when clicking on nodes links to activities will be provided for simple and cheap/free ways to teach the subject through informal play.

In its current state, parents will have to mark when a task is completed and whether or not the child is able to complete a test on the subject without help to mark a node completed see Where to go from here to see how in future work this will be improved by integrating native digital games for each subject.

Where to go from here

  • Add digital games to teach each subject
  • Add virtual agent to assist parents and children while playing
  • Integrate API and MVC for parent, children, activities, progress, etc
  • Add edge weight prediction algorithm to make learning paths more adaptive and personalized
  • Add shortest path visualization for parents
  • Improve UX


Heroku Version of POC


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[2] Craig, Dorothy V (2000). Computers and Young Children Technology, Math, and the Early Learner: Models for Learning. Tech. rep. 3.

[3] Ramani, Geetha B and Siegler, Robert S (2014). “How Informal Learning Activities Can Promote Children’s Numerical Knowledge”. In: The oxford handbook of numerical cognition, pp. 1135–1154. doi: 10.1093/oxfordhb/ 9780199642342.013.012.

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[6] Siegler, Robert S and Robinson, Mitchell (1982). “The Development of Nu- merical Understandings”. In: Advances in child development and behavior 16, pp. 241–312.

[7] Schacter, John and Jo, Booil (2016). “Improving low-income preschool- ers mathematics achievement with Math Shelf, a preschool tablet com- puter curriculum”. In: Computers in Human Behavior 55, pp. 223–229. issn: 07475632. doi: 10.1016/j.chb.2015.09.013.

[8] Ramani, Geetha B and Siegler, Robert S (2008). “Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games”. In: Child Development 79.2, pp. 375– 394.

[9] Aronin, Sara and Floyd, Kim K (2013). “Using an iPad in Inclusive Preschool Classrooms to Introduce STEM Concepts STEM Education”. In: Teaching Exceptional Children 45.4, pp. 34–39.

[10] Wang, Ming Te and Degol, Jessica L. (2017). “Gender Gap in Science, Tech- nology, Engineering, and Mathematics (STEM): Current Knowledge, Impli- cations for Practice, Policy, and Future Directions”. In: Educational Psychol- ogy Review 29.1, pp. 119–140. issn: 1573336X. doi: 10.1007/s10648-015- 9355-x.

[11] Ginsburg, Herbert P., Lee, Joon Sun, and Boyd, Judi Stevenson (2008). “Mathematics Education for Young Children: What It is and How to Pro- mote It”. In: Social Policy Report 22.1, pp. 1–24. issn: 2379-3988. doi: 10.1002/j.2379-3988.2008.tb00054.x.

[12] Committee on Developments in the Science of Learning and Committee on Learning Research and Educational Practice (2000). “How children learn”. In: How People Learn : Brain, Mind, Experience, and School: Expanded Edition. 2nd ed. National Academy Press. Chap. 4, pp. 79–113. doi: 10.4324/ 9781351039789-1.

[13] Dweck, Carol S (2008). Mindset: The new psychology of success. Random House Digital, Inc.

[14] Kozulin, A, Gindis, B, Ageyev, V, and Miller, S (2003). “The zone of prox- imal development”. In: Vygotsky’s educational theory in cultural context 1.2, pp. 39–64.

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