What Works in Elementary Math?

Euclid, the ancient Greek mathematician, is considered the inventor of geometry. His king heard about it, and wanted to learn geometry, but being a king, he was kind of busy. He called in Euclid, and asked him if there was a faster way. “I’m sorry sire,” said Euclid, “but there is no royal road to geometry.”

Skipping forward a couple thousand years, Marta Pellegrini, of the University of Florence in Italy, spent nine months with our group at Johns Hopkins University and led a review of research on effective programs for elementary mathematics  (Pellegrini, Lake, Inns & Slavin, 2018), which was recently released on our Best Evidence Encyclopedia (BEE). What we found was not so different from Euclid’s conclusion, but broader: There’s no royal road to anything in mathematics. Improving mathematics achievement isn’t easy. But it is not impossible.

Our review focused on 78 very high-quality studies (65 used random assignment). 61 programs were divided into eight categories: tutoring, technology, professional development for math content and pedagogy, instructional process programs, whole-school reform, social-emotional approaches, textbooks, and benchmark assessments.

Tutoring had the largest and most reliably positive impacts on math learning. Tutoring included one-to-one and one-to-small group services, and some tutors were certified teachers and some were paraprofessionals (teacher assistants). The successful tutoring models were all well-structured, and tutors received high-quality materials and professional development. Across 13 studies involving face-to-face tutoring, average outcomes were very positive. Surprisingly, tutors who were certified teachers (ES=+0.34) and paraprofessionals (ES=+0.32) obtained very similar student outcomes. Even more surprising, one-to-small group tutoring (ES=+0.32) was as effective as one-to-one (ES=+0.26).

Beyond tutoring, the category with the largest average impacts was instructional programs, classroom organization and management approaches, such as cooperative learning and the Good Behavior Game. The mean effect size was +0.25.

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After these two categories, there were only isolated studies with positive outcomes. 14 studies of technology approaches had an average effect size of only +0.07. 12 studies of professional development to improve teachers’ knowledge of math content and pedagogy found an average of only +0.04. One study of a social-emotional program called Positive Action found positive effects but seven other SEL studies did not, and the mean for this category was +0.03. One study of a whole-school reform model called the Center for Data-Driven Reform in Education (CDDRE), which helps schools do needs assessments, and then find, select, and implement proven programs, showed positive outcomes (ES=+0.24), but three other whole-school models found no positive effects. Among 16 studies of math curricula and software, only two, Math in Focus (ES=+0.25) and Math Expressions (ES=+0.11), found significant positive outcomes. On average, benchmark assessment approaches made no difference (ES=0.00).

Taken together, the findings of the 78 studies support a surprising conclusion. Few of the successful approaches had much to do with improving math pedagogy. Most were one-to-one or one-to-small group tutoring approaches that closely resemble tutoring models long used with great success in reading. A classroom management approach, PAX Good Behavior Game, and a social-emotional model, Positive Action, had no particular focus on math, yet both had positive effects on math (and reading). A whole-school reform approach, the Center for Data-Driven Reform in Education (CDDRE), helped schools do needs assessments and select proven programs appropriate to their needs, but CDDRE focused equally on reading and math, and had significantly positive outcomes in both subjects. In contrast, math curricula and professional development specifically designed for mathematics had only two positive examples among 28 programs.

The substantial difference in outcomes of tutoring and outcomes of technology applications is also interesting. The well-established positive impacts of one-to-one and one-to-small group tutoring, in reading as well as math, are often ascribed to the tutor’s ability to personalize instruction for each student. Computer-assisted instruction is also personalized, and has been expected, largely on this basis, to improve student achievement, especially in math (see Cheung & Slavin, 2013). Yet in math, and also reading, one-to-one and one-to-small group tutoring, by certified teachers and paraprofessionals, is far more effective than the average for technology approaches. The comparison of outcomes of personalized CAI and (personalized) tutoring make it unlikely that personalization is a key explanation for the effectiveness of tutoring. Tutors must contribute something powerful beyond personalization.

I have argued previously that what tutors contribute, in addition to personalization, is a human connection, encouragement, and praise. A tutored child wants to please his or her tutor, not by completing a set of computerized exercises, but by seeing a tutor’s eyes light up and voice respond when the tutee makes progress.

If this is the secret of the effect of tutoring (beyond personalization), perhaps a similar explanation extends to other approaches that happen to improve mathematics performance without using especially innovative approaches to mathematics content or pedagogy. Approaches such as PAX Good Behavior Game and Positive Action, targeted on behavior and social-emotional skills, respectively, focus on children’s motivations, emotions, and behaviors. In the secondary grades, a program called Building Assets, Reducing Risk (BARR) (Corsello & Sharma, 2015) has an equal focus on social-emotional development, not math, but it also has significant positive effects on math (as well as reading). A study in Chile of a program called Conecta Ideas found substantial positive effects in fourth grade math by having students practice together in preparation for bimonthly math “tournaments” in competition with other schools. Both content and pedagogy were the same in experimental and control classes, but the excitement engendered by the tournaments led to substantial impacts (ES=+0.30 on national tests).

We need breakthroughs in mathematics teaching. Perhaps we have been looking in the wrong places, expecting that improved content and pedagogy will be the key to better learning. They will surely be involved, but perhaps it will turn out that math does not live only in students’ heads, but must also live in their hearts.

There may be no royal road to mathematics, but perhaps there is an emotional road. Wouldn’t it be astonishing if math, the most cerebral of subjects, turns out more than anything else to depend as much on heart as brain?

References

Cheung, A., & Slavin, R. E. (2013). The effectiveness of educational technology applications for enhancing mathematics achievement in K-12 classrooms: A meta-analysis. Educational Research Review, 9, 88-113.

Corsello, M., & Sharma, A. (2015). The Building Assets-Reducing Risks Program: Replication and expansion of an effective strategy to turn around low-achieving schools: i3 development grant final report. Biddeford, ME, Consello Consulting.

Inns, A., Lake, C., Pellegrini, M., & Slavin, R. (2018, March 3). Effective programs for struggling readers: A best-evidence synthesis. Paper presented at the annual meeting of the Society for Research on Educational Effectiveness, Washington, DC.

Pellegrini, M., Inns, A., & Slavin, R. (2018, March 3). Effective programs in elementary mathematics: A best-evidence synthesis. Paper presented at the annual meeting of the Society for Research on Educational Effectiveness, Washington, DC.

Photo credit: By Los Angeles Times Photographic Archive, no photographer stated. [CC BY 4.0  (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons

This blog was developed with support from the Laura and John Arnold Foundation. The views expressed here do not necessarily reflect those of the Foundation.

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5 thoughts on “What Works in Elementary Math?

  1. If Math concepts are not made accessible to students, they get tensed & confused. This in turn makes teachers also uncomfortable & upset. In many cases, teachers resort to negative comments or focus on students who seem to understand or ignore the weaker students. In general it vitiates the classroom environment. In this way inappropriate math pedagogy also leads to a negative learning environment. So it would not be correct to say that pedagogy does not have a significant effect. This aspect needs to be studied. (This is based on my experience in Indian classrooms)

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    1. Thanks for writing! I completely agree that pedagogy and content knowledge are essential. What our review discovered, however, is that math improvement approaches focused on giving teachers better understanding of math content and pedagogy did not make any difference in student learning. Perhaps teachers already know enough about content and pedagogy, so more professional development on those topics do not make much difference.

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      1. “Perhaps teachers already know enough about content and pedagogy, so more professional development on those topics do not make much difference” – This is definitely not the case in the Indian school system.

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  2. I am curious as to whether this,or any, study looked into the amount of preparation elementary teachers are given in mathematic (and science) pre-service as compared to literacy. I have noticed it is very lacking and disproportional.

    Also, in the blog, it is noted, “The successful tutoring models were all well-structured, and tutors received high-quality materials and professional development. ” but then later states that PD was not effective. I find this contradictory. PD is helpful for educators at any and all levels – as long as it is quality PD. If in their undergraduate studies, Mathematics were not addressed fully and their understanding is not strong, good PD can help fill that void.
    Thank you

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  3. Thanks for your comments. In my blog on our math review, I did not state that professional development (PD) was ineffective. Virtually all effective programs in mathematics require high-quality professional development. What matters, however, is what the professional development is intended to do. We found that professional development to teachers or paraprofessionals to deliver one-to-one or one-to-small group tutoring was extremely effective, as was professional development to implement innovations in classroom organization and management. What was not found to be effective in our review was professional development to improve teachers’ knowledge of mathematics content and pedagogy. It may be that teachers already have enough knowledge of mathematics content and pedagogy, so they do not benefit from more PD along those lines. Yet whatever the reason, we found 12 very high-quality studies of programs that provided extensive PD in math content and pedagogy to elementary teachers, and not one had a significant impact on student learning. The average effect was near zero. This is not what any of us expected, but it is what we found and reported.

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