1 / 34

Confirming the Overlapping Waves theory in children learning single-digit multiplication

Confirming the Overlapping Waves theory in children learning single-digit multiplication. Sanne van der Ven University of Amsterdam. Thanks to : Dr. Jan Boom Dr. Evelyn Kroesbergen Prof. dr. Paul Leseman. How to measure how children learn mathematics ?. Developing math knowledge.

azana
Download Presentation

Confirming the Overlapping Waves theory in children learning single-digit multiplication

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Confirming the Overlapping Waves theory in children learning single-digit multiplication Sanne van der Ven University of Amsterdam Thanksto: Dr. Jan Boom Dr. Evelyn Kroesbergen Prof. dr. Paul Leseman

  2. How tomeasurehowchildrenlearnmathematics?

  3. Developingmathknowledge Mathematics is more thanaccuracy on a test • Childrendevelop: how do theylearn? • Performance is more thanaccuracy:howdid a childreach the answer? • Why are somechildrenfasterlearnersthanothers?

  4. Strategies

  5. An example: strategies in addition ‘What is 4 + 5?’ • No understanding/guessing • Countingall • Counting on • Counting on fromlarger (min procedure) • Decomposition • Retrieval

  6. Strategies - Beware!

  7. Development: Overlapping Waves Siegler (1996)

  8. Aims of the study Aim 1 • Test overlapping waves model statistically Four steps: • Choosemathability • Measurethisabilitylongitudinally • Identifyandcategorizestrategies • Buildand test statistical model Aim 2 • Explainindividualdifferences in development

  9. Mathematics in the Netherlands • Social constructivism: ‘realistischrekenen’ (realistic mathematics) • Children construct theirownknowledge • Focused on understanding: math talk based on real world examples rather than drill and practice • Not evidence-based: Heavily debated!

  10. Example page workbook (grade 2)

  11. My study

  12. Assignment: identifystrategies In groups of 3, devise a meaningful way tocategorizechildren’sstrategiesfor single digit multiplication. Make sureyou span the entirelearningperiodfrombeginningto end, but alsotryto limit the number of categories!

  13. Apply your categorization – does it work? • Categorize the verbalandvisualexamples • Adaptyourcategoriesifnecessary. • You have a small selection: in totaltherewere 98 children * 8 weeks * 15 problems = 11,760 responses

  14. My own solution • Start broad, thennarrow down

  15. Initialcodingscheme:single strategies • Don’tknow • Guessing • Addition (8 x 6 = 14) • Repetition (7 x 4 = 7) • Other wrong strategies • Strategyunknown • Drawingandcounting • Fingercounting • Counting out loud (or silently) • Drawing a number line • Repeatedaddition • Repeatedaddition in smaller steps • Repeatedaddition in larger steps • Doubling • Using neighbours: 9x = 10x – x • Using neighbours: 6x = 5x + x • Using neighboursotherwise • Retrieval

  16. Initialcodingscheme:hybridstrategies • First repeatedaddition, continue on fingers • First repeatedaddition, thendoubling • First repeatedaddition, thencounting out loud • Reverse andrepeatedaddition • Reverse and double • Reverse and retrieval • Double, thenrepeatedaddition • Using a neighbour, thencounting

  17. Thenreduce the number of categories • Don’tknow • Guessing • Addition (8 x 6 = 14) • Repetition (7 x 4 = 7) • Other wrong strategies • Strategyunknown • Drawingandcounting • Fingercounting • Counting out loud (or silently) • Drawing a number line • Repeatedaddition • Repeatedaddition in smaller steps • Repeatedaddition in larger steps • Doubling • Using neighbours: 9x = 10x – x • Using neighbours: 6x = 5x + x • Using neighboursotherwise • Retrieval RepeatedAddition Wrong DerivedFacts Counting Retrieval

  18. Results - Descriptives Retrieval Derived Facts Repeated Addition Counting Wrong

  19. Results - Descriptives

  20. Retrieval Derived Facts Repeated Addition Counting Wrong

  21. So, howto model? • Combination of twotechniques in one model: • IRT (graded response model)  createscontinuousvariable (latent trait) • Latent growth curve modeling growth of this latent trait

  22. Graded response model: assumptions • Onestrategyused at a time • Strategies are ordered • Underlyingdimension (“mathematicalmaturity”) • Non-linearlyrelatedtostrategyuse

  23. Categorical Growth Intercept: - M = 0 - sd = 1.02 Slope: - M = 0.97 - sd = 0.90 Retrieval Derived Facts Repeated Addition Counting Wrong χ2(2151) = 2937.42, p < .001, NC = 1.37, CFI = .90, RMSEA = .06

  24. Contextualandplainproblems Retrieval Derived Facts Repeated Addition Counting Wrong

  25. Easy anddifficultproblems Retrieval Derived Facts Repeated Addition Counting Wrong

  26. Accuracy Intercept: - M = 0 - sd = 0.44 Slope: - M = 0.28 - sd = 0.45 χ2(1998) = 2071.75, p = .12, NC = 1.04, CFI = .96, RMSEA = .02

  27. Interrelations

  28. Differences in development • Working memory – relation has been shown in many studies • Anyideaswhy?

  29. Connectionisttheory

  30. strategy choice working memory accuracy Hypotheses

  31. Working memory tasks • Digit Span Backwards • Odd One Out • Keep Track 3 1 6 5  5 6 1 3 ?

  32. Questionsforfuture research • How general is the model? • Different mathabilities • Different ages • Different countries • Are therechildrenthatdeviatefrom the model, andwhy? • Why was there no relationshipbetweenworking memory and the twoslopes (development)? • Measureearlierduringdevelopment? • Should we promotesmarterstrategies, betterexecution, both, neither? • Perhapstailortoworking memory profiles?

  33. Questions? Retrieval Derived Facts Repeated Addition Counting Wrong

More Related