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Thunder Math

Developed by Pashur Au Yeung

Built on math-education research

All eight of Thunder Math's modes follow established fluency standards and peer-reviewed studies, taught in a concrete → representational → abstract progression.

Add & Subtract

The strategy ladder — count on → make ten → bridging through ten → doubles → think-addition — follows established fluency standards and peer-reviewed studies:

  • National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common Core State Standards for Mathematics, 1.OA.C.6 & 2.OA.B.2. Washington, DC — add & subtract within 20 via counting on, making ten, decomposing to a ten, the addition–subtraction relationship, and known/equivalent sums.
  • Paliwal, V., & Baroody, A. J. (2020). Fostering the learning of subtraction concepts and the subtraction-as-addition reasoning strategy. Early Childhood Research Quarterly, 51, 403–415. doi:10.1016/j.ecresq.2019.05.008
  • Kullberg, A., Björklund, C., Runesson Kempe, U., Brkovic, I., Nord, M., & Maunula, T. (2024). Improvements in learning addition and subtraction when using a structural approach in first grade. Educational Studies in Mathematics, 117. doi:10.1007/s10649-024-10339-z

Times Tables

The array (groups) model and the structure-first ordering of the tables — anchor facts 2, 5, 10 → the 0× and 1× rules → 3, 4 → the hard cluster 6–9 — follow established standards and peer-reviewed studies:

  • Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children’s understanding and reasoning in multiplication. Educational Studies in Mathematics, 70(3), 217–241. doi:10.1007/s10649-008-9145-1
  • Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49. doi:10.1007/BF03217544
  • NRICH (Pennant, with Way & Askew), University of Cambridge, and NCETM — Arrays, Multiplication and Division / Arrays and Area Models (practitioner guidance).

Tens & Ones (Place Value)

Two-digit place value is built with base-ten blocks and the part-whole (number-bond) idea, following the concrete → pictorial → abstract progression:

  • Bruner, J. S. (1966). Toward a Theory of Instruction. Cambridge, MA: Belknap Press of Harvard University Press — the enactive–iconic–symbolic (concrete–pictorial–abstract) sequence.
  • Dienes, Z. P. (1960). Building Up Mathematics. London: Hutchinson Educational — base-ten / multi-base blocks that make “a ten is ten ones” visible.

Number Patterns

Skip-counting and number sequences build the awareness of pattern and structure that underpins multiplication and early algebra:

  • Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49. doi:10.1007/BF03217544
  • Clements, D. H., & Sarama, J. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach (1st ed.). New York: Routledge — counting and patterning learning trajectories.

How Many? (Subitizing)

Instantly recognising small quantities — on dice patterns and ten-frames — builds the number sense that underpins counting and arithmetic:

  • Clements, D. H. (1999). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5(7), 400–405.
  • Clements, D. H., & Sarama, J. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge — perceptual and conceptual subitizing in the early-number learning trajectory.

Number Bonds

Part-whole “number bonds” to 10 and 20 — the make-ten and missing-addend ideas, shown on a ten-frame — are the engine of fluent mental arithmetic (Common Core 1.OA.C.6):

  • Baroody, A. J. (2006). Why children have difficulties mastering the basic number combinations and how to help them. Teaching Children Mathematics, 13(1), 22–31.
  • Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45(3), 850–867. doi:10.1037/a0014939

Money (HK$)

Recognising coins and totalling them applies counting and addition in a concrete, real-world context, following the concrete → abstract progression:

  • Department for Education (2013). National Curriculum in England: Mathematics Programmes of Study, Year 1 (Measurement) — recognise and know the value of different denominations of coins and notes.
  • National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common Core State Standards for Mathematics, 2.MD.C.8. Washington, DC — solve word problems involving coins using the $ and ¢ symbols.

Number Line

Reading a number’s position on a 0–100 line builds the numerical-magnitude understanding that is a strong predictor of later mathematics achievement:

  • Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428–444. doi:10.1111/j.1467-8624.2004.00684.x
  • Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games—but not circular ones—improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101(3), 545–560. doi:10.1037/a0014239

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