Preschool math lessons:

Do kids need to be in a classroom to learn?

© 2008 - 2013 Gwen Dewar, Ph.D., all rights reserved

Preschool math lessons might have long-term effects.

But do these lessons have to happen in an school setting? Popular media reports imply that they do. But I doubt it.

In 2008, the popular media were abuzz with a new study about children's math achievement published in the journal Science (Melhuish et al 2008a).

According to the headlines, the study’s main finding was that preschool attendance gives kids a boost in math skills that lasts until they are at least 10 years old. And to some writers, the political implications seemed clear: We should adopt a policy of universal preschool attendance.

But if you actually read the study, you get a different picture.

The study reports that the most important predictors of math achievement were maternal education and the quality of the preschoolers’ home learning environment.

Attendance of a preschool had a positive effect, too.

But the effect applied only to a select group of “highly effective” preschools -- schools that produced students who knew more about math upon graduation than would be expected on the basis of their prior attainments, home advantages, and so forth (Melhuish et al 2008b).

Those preschools rated as moderately effective were not associated with better math skills.

More details? Let’s look.

The early years: Preschool influences on mathematics achievement

University of London Professor Edward Melhuish and his colleagues (2008a; 2008b) were interested in the variables that influence long-term math achievement in kids. They tracked British children from age 3 until their 6th year in primary school (when they were about 10 years old).

The researchers looked at all sorts of things that might influence math achievement in primary school, including these social factors:

• Parent’s socioeconomic status

• Total family annual salary

• Ethnicity

• Mother’s level of education

• Father’s level of education

• Home learning environment

• Preschool effectiveness

• Primary school effectiveness

Which variables had the greatest impact?

In order of their importance, the variables linked with the greatest positive effects on math achievement were:

1. Mother with college degree or professional qualifications (0.50)

2. Highest-quality home learning environment (0.40)

3. Indian ethnicity (0.35)

4. Attending an highly effective primary school (.33)

5. Being in the highest income bracket (0.31)

6. Attending a highly effective preschool (0.26)

7. Father with college degree or professional qualifications (0.23)

8. Medium-quality home learning environment (.21)

The numbers in parentheses are a measure of each variable’s effect. As you can see, maternal education was far and away the largest effect. Next was the home learning environment.

These effects weren’t just sizeable. They were also highly statistically significant, meaning, in this case, that the chance of getting these results by accident were less than one-tenth of one percent.

Moreover, the positive effects of maternal education and home learning environment were just as big for low-income as they were for high-income kids.

And the effects were independent, meaning that high-quality home environments were linked with better outcomes even after controlling for high income, parents' education levels, and so forth.

What is the moral of this story? I suppose it depends on your interests. If you are a parent, the most important message may be that your home environment can have a big impact on your child's math achievement -- one that may outstrip sending your child to the most effective preschool.

Even variable #3--Indian ethnicity--may reflect the influence of parenting, if Indian parents, like other parents of Asian ethnicity, are more likely to adopt attitudes that promote math achievement (Sammons et al 2007; Stevenson and Lee 1990).

And yet the popular headlines proclaimed a different moral: “Preschool helps boost math skills.” Not exactly untrue. But it's rather misleading, given that only the subset of "highly effective" preschools were found to make a difference.

Why the spin? I think it’s pretty clear. Many of the popular articles I’ve seen link the study with the argument for universal preschool. People want to believe that preschool will set kids on a course for high mathematics achievement. And perhaps it will--if kids are lucky enough to attend “highly effective” preschools.

But--as noted below--this research doesn’t tell us why some preschools were “highly effective” and others were not. And, in any case, most parents have few choices when it comes to finding the right preschool.

By contrast, parents have a lot of personal control over their preschooler’s home learning environment.

So wouldn’t it be more helpful if these popular accounts covered that aspect of the story?

What is a “highly effective” home learning environment?

To answer this question, Melhuish and colleagues conducted a series of parent interviews and devised a checklist of activities that kids might do with their parents.

Then the researchers analyzed which of these activities predicted better math scores for 10 year olds. As it turns out, the social activities on their checklist had little to do with math achievement.

But the activities associated with literacy and numeracy had significant, positive effects on better-than-expected math achievement. These were:

  • being read to
  • going to the library
  • playing with numbers
  • painting and drawing
  • being taught letters
  • being taught numbers
  • being taught songs/poems/rhymes

Why were these activities effective? Melhuish and colleagues think they were valuable in several respects. Kids learned specific facts and skills. But they probably also benefited in other, more general ways, "learning how to learn" (Melhuish et al 2008b).

What is a “highly effective” preschool?

As noted above, the researchers defined a preschool as “effective” if its students performed better than could be expected based on the students’ personal characteristics (like prior educational attainment and family background).

But that doesn’t explain why some preschools were more effective than others. What did these schools do differently? The study doesn’t tell us that. And it’s not because the researchers didn’t try to figure it out.

The study that Melhuish and his colleagues have published in Science is part of a larger research program that has been going on for several years. If you check out their other reports, you’ll find that the researchers visited preschools to rate their quality (Sylva et al 2004; Samms et al 2007).

But it turns out that these preschool quality ratings didn’t predict long-term achievement in math.

As a result, researchers can’t say why some preschools were more effective than others. Not based on this study.

So what's the crucial factor?

Research at tracking specific math skills may help us figure it out.

Evidence is accumulating that one of the most important predictor of long-term mathematics achievement is a young child's understanding of the meaning of numbers -- understanding the quantity that a number represents and being able to compare that quantity with others.

For instance, studies suggest that kindergarteners and first graders who are good comparing numerical magnitudes go on to perform better on standardized math tests (De Smedt et al 2009; Mazzocco et al 2011; Sasanguie et al 2012; Sasanguie et al 2013).

Might Melhuish's "highly effective" preschools have done a better job of getting kids to think about quantity? It's plausible. 

For more information about specific activities that may boost number sense, see this evidence guide to preschool math lessons.

Copyright © 2006-2021 by Gwen Dewar, Ph.D.; all rights reserved.
For educational purposes only. If you suspect you have a medical problem, please see a physician.

References: Must preschool math lessons take place in a classroom?

De Smedt B, Verschaffel L, Ghesquière P. 2009. The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. J Exp Child Psychol. 103(4):469-79.

Mazzocco MM, Feigenson L, and Halberda J. 2011. Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS One. 6(9):e23749.

Melhuish EC, Sylva K, Sammons P, Siraj-Blatchford I, Taggart B, Phan MB, and Malin A. 2008a. The early years. Preschool influences on mathematics achievement. Science. 321(5893):1161-2

Melhuish EC, Sylva K, Sammons P, Siraj-Blatchford I, Taggart B, Phan MB, and Malin A. 2008b. Supporting online material for: Preschool influences on mathematics achievement. Science. 321(5893):1161-2. Accessed on August 29, 2008 at

Sammons P, Sylva K, Melhuish E, Siraj-Blatchford I, Taggart B, Grabbe Y and Barreau S. 2007. The Effective Pre-School and Primary Education 3-11 Project (EPPE 3-11): Influences on Children’s Attainment and Progress in Key Stage 2: Cognitive Outcomes in Year 5. London: DfES / Institute of Education, University of London.

Sasanguie D, Göbel SM, Moll K, Smets K, and Reynvoet B. 2013. Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement? J Exp Child Psychol. 114(3):418-31.

Sasanguie D, De Smedt B, Defever E, and Reynvoet B. 2012. Association between basic numerical abilities and mathematics achievement. Br J Dev Psychol. 30(Pt 2):344-57.

Stevenson HW and Lee SY. 1990. Contexts of achievement: a study of American, Chinese, and Japanese children. Monogr Soc Res Child Dev. 55(1-2):1-123.

Sylva K, Melhuish E, Sammons P, Siraj-Blatchford I, Taggart B and Elliot K. 2004. The effective provision of preschool education (EPPE) project: Technical paper 12. final report: Effective pre-school education. London: DfES / Institute of Education, University of London.

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