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SpringMath Theory of Change

Dr. Amanda VanDerHeyden developed the SpringMath Theory of Change to show how SpringMath facilitates math achievement — and ultimately math mastery.

SpringMath is web-based guidance to assess skills, deliver intervention, monitor progress, and adjust intervention weekly.1

Active ingredients

Increased alignment of intervention content with student need2

Increased alignment of intervention tactic with student need3

Increased correct intervention use4

Immediate effects

Child experiences higher quality instruction5

More efficient use of resources6

Decision accuracy improved7

Year-end effects

Mathematics achievement improved8

View the evidence behind the SpringMath Theory of Change by clicking on the respective number below.

    1. SpringMath is web-based guidance to assess skills, deliver intervention, monitor progress, and adjust intervention weekly.

    • VanDerHeyden, A. M., Codding, R. S., Martin, R., Desai, S., Maki, E., & McKevett, N. (in submission). Use of a web-based
      mathematics intervention tool to promote implementation and student learning. Manuscript submitted for publication.

    • VanDerHeyden, A. M. & Witt, J. C. (2005). Quantifying the context of assessment: Capturing the effect of base rates on teacher referral and a problem-solving model of identification. School Psychology Review, 34, 161-183.
      https://doi.org/10.1080/02796015.2005.12086281

    • VanDerHeyden, A. M., Witt, J. C., & Gilbertson, D. A (2007). Multi-Year Evaluation of the Effects of a Response to Intervention (RTI) Model on Identification of Children for Special Education. Journal of School Psychology, 45, 225-256.
      https://doi.org/10.1016/j.jsp.2006.11.004

    • VanDerHeyden, A. M., Witt, J. C., & Naquin, G. (2003). Development and validation of a process for screening referrals to
      special education. School Psychology Review, 32, 204-227. https://doi.org/10.1080/02796015.2003.12086194

    2. Increased alignment of intervention content with student need

    • Solomon, B., G., VanDerHeyden, A. M., Solomon, E. C., Korzeniewski, E. R., Payne, L. L., Campaña, K. V., & Dillon, C. R. (in submission). Mastery Measurement in Mathematics and the Goldilocks Effect. Manuscript submitted for publication.

    • VanDerHeyden, A. M., & Broussard, C. (2019). Construction and Examination of Math Subskill Mastery Measures. Advance Online Publication. Assessment for Effective Intervention. https://doi.org/10.1177/1534508419883947

    • VanDerHeyden, A. M., Broussard, C., & Burns, M. K. (2019). Classification agreement for gated screening in mathematics: Subskill mastery measurement and classwide intervention. Assessment for Effective Intervention. Advance Online Publication. https://doi.org/10.1177/1534508419882484

    • VanDerHeyden, A. M., Codding, R., Martin, R. (2017). Relative value of common screening measures in mathematics. School Psychology Review, 46, 65-87. https://doi.org/10.17105/SPR46-1.65-87

    • VanDerHeyden, A. M. & Witt, J. C. (2005). Quantifying the context of assessment: Capturing the effect of base rates on teacher referral and a problem-solving model of identification. School Psychology Review, 34, 161-183. https://doi.org/10.1080/02796015.2005.12086281

    • VanDerHeyden, A. M., Witt, J. C., Naquin, G., Noell, G. (2001). The reliability and validity of curriculum-based measurement readiness probes for kindergarten students. School Psychology Review, 30, 363-382. . https://doi.org/10.1080/02796015.2001.12086121

    3. Increased alignment of intervention tactic with student need

    • Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.), The fourth R: Research in the classroom (pp. 23–40). Columbus, OH: Merrill.

    • Burns, M. K., Codding, R. S., Boice, C. H., & Lukito, G. (2010). Meta-analysis of acquisition and fluency math interventions with instructional and frustration level skills: Evidence for a skill-by-treatment interaction. School Psychology Review, 39, 69-83. This meta-analysis demonstrated that when instructional tactics were aligned with student proficiency, learning improved and when instructional tactics were mis-aligned with student proficiency, learning declined. Burns and colleagues called this the “skill-by-treatment” interaction which is, in effect, an empirical demonstration of the Instructional Hierarchy.

    • Burns, M. K., VanDerHeyden, A. M., & Jiban, C. (2006). Assessing the instructional level for mathematics: A comparison of methods. School Psychology Review, 35, 401-418. In this study, Burns and colleagues demonstrated that attaining mastery level performance was associated with skill retention over time, generalization, and faster learning of more complex, related skills.

    4. Increased correct intervention use

    • 4Detrich, R., Keyworth, R., & States, J. (2008). Advances in evidence-based education: A roadmap to evidence-based education. Oakland, CA: The Wing Institute.

    • Fixsen, D. L., & Blasé, K. A. (1993). Creating new realities: Program development and dissemination. Journal of Applied Behavior Analysis, 26, 597-615. https://doi.org/10.1901/jaba.1993.26-597

    • Joyce, B. R., & Showers, B. (1981). Transfer of Training: The Contribution of "Coaching." Journal of Education, 163, 163-172. https://doi.org/10.1177/002205748116300208

    • National Implementation Research Network. https://nirn.fpg.unc.edu/national-implementation-research-network

    • VanDerHeyden, A. M., McLaughlin, T., Algina, J., & Snyder, P. (2012). Randomized evaluation of a supplemental grade-wide mathematics intervention. American Education Research Journal, 49, 1251-1284. https://doi.org/10.3102/0002831212462736

    • Witt, J. C., Noell, G. H., LaFleur, L. H., & Mortenson, B. P. (1997). Teacher use of interventions in general education settings: Measurement and analysis of the independent variable. Journal of Applied Behavior Analysis, 30, 693-696. https://doi.org/10.1901/jaba.1997.30-693

    5. Child experiences higher quality instruction

    • VanDerHeyden, A. M., & Burns, M. K. (2005). Using curriculum-based assessment and curriculum-based measurement to guide elementary mathematics instruction: Effect on individual and group accountability scores. Assessment for Effective Intervention, 30, 15-31. https://doi.org/10.1177/073724770503000302

    • VanDerHeyden, A. M. & Codding, R. (2015). Practical effects of classwide mathematics intervention. School Psychology Review, 44, 169-190. https://doi.org/10.17105/spr-13-0087.1

    • VanDerHeyden, A. M., McLaughlin, T., Algina, J., & Snyder, P. (2012). Randomized evaluation of a supplemental grade-wide mathematics intervention. American Education Research Journal, 49, 1251-1284. https://doi.org/10.3102/0002831212462736

    • VanDerHeyden, A. M., Witt, J. C., & Gilbertson, D. A (2007). Multi-Year Evaluation of the Effects of a Response to Intervention (RTI) Model on Identification of Children for Special Education. Journal of School Psychology, 45, 225-256. https://doi.org/10.1016/j.jsp.2006.11.004

    6. More efficient use of resources

    • Barrett, C. A., & VanDerHeyden, A. M. (2020). A cost-effectiveness analysis of classwide math intervention. Journal of School Psychology, 80, 54-65. https://doi.org/10.1016/j.jsp.2020.04.002

    • Codding, R., VanDerHeyden, Martin, R. J., & Perrault, L. (2016). Manipulating Treatment Dose: Evaluating the Frequency of a Small Group Intervention Targeting Whole Number Operations. Learning Disabilities Research & Practice, 31, 208-220. https://doi.org/10.1111/ldrp.121206

    7. Decision accuracy improved

    • VanDerHeyden, A. M. (2010). Determining early mathematical risk: Ideas for extending the research. School Psychology Review, 39, 196-202. https://doi.org/10.1080/02796015.2010.12087773

    • VanDerHeyden, A. M. (2013). Universal screening may not be for everyone: Using a threshold model as a smarter way to determine risk. School Psychology Review, 42, 402-414. https://doi.org/10.1080/02796015.2013.12087462

    • VanDerHeyden, A. M. & Witt, J. C. (2005). Quantifying the context of assessment: Capturing the effect of base rates on teacher referral and a problem-solving model of identification. School Psychology Review, 34, 161-183. https://doi.org/10.1080/02796015.2005.12086281

    • VanDerHeyden, A. M., Witt, J. C., & Gilbertson, D. A (2007). Multi-Year Evaluation of the Effects of a Response to Intervention (RTI) Model on Identification of Children for Special Education. Journal of School Psychology, 45, 225-256. https://doi.org/10.1016/j.jsp.2006.11.004

    • VanDerHeyden, A. M., Witt, J. C., & Naquin, G. (2003). Development and validation of a process for screening referrals to special education. School Psychology Review, 32, 204-227. https://doi.org/10.1080/02796015.2003.12086194

    8. Mathematics achievement improved

    • VanDerHeyden, A. M., & Burns, M. K. (2005). Using curriculum-based assessment and curriculum-based measurement to guide elementary mathematics instruction: Effect on individual and group accountability scores. Assessment for Effective Intervention, 30, 15-31. https://doi.org/10.1177/073724770503000302

    • VanDerHeyden, A. M. & Codding, R. (2015). Practical effects of classwide mathematics intervention. School Psychology Review, 44, 169-190. https://doi.org/10.17105/spr-13-0087.1

    • VanDerHeyden, A. M., McLaughlin, T., Algina, J., & Snyder, P. (2012). Randomized evaluation of a supplemental grade-wide mathematics intervention. American Education Research Journal, 49, 1251-1284. https://doi.org/10.3102/0002831212462736

    • VanDerHeyden, A. M., Witt, J. C., & Gilbertson, D. A (2007). Multi-Year Evaluation of the Effects of a Response to Intervention (RTI) Model on Identification of Children for Special Education. Journal of School Psychology, 45, 225-256. https://doi.org/10.1016/j.jsp.2006.11.004