Test your number sense
How do children learn math—and why do some children struggle with it? The answers are in Number Sense and Number Nonsense, a straightforward, reader-friendly book for education professionals and researchers. More than a first-ever research synthesis, this highly accessible book brings math difficulties into clear focus, helping educators and psychologists get inside students’ heads so they can devise the best way to help children learn.
Take our test to better understand “number sense” and how some children struggle with it.
Where would you place "one billion" on this number line?
One billion goes all the way over here!
It’s only 1/1000 of a trillion. Studies have shown that it takes until second grade for children to accurately locate numbers on a 0-100 number line and until sixth grade for them to do so in the 0-1000 range.1 Some children lack such number sense.
1 Siegler, R.S., & Booth, J.L. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444; Siegler, R.S., & Opfer, J.E. (2003). The development of numerical estimation: Evidence of rmultiple representations of numerical quantity. Psychological Science, 14, 237-243.
Quickly and without counting can you tell which cloud has more dots?
Count them – you’ll see the one on the right has more dots. Some recent studies suggest that a child’s math achievement can be predicted from his or her ability to make rapid and accurate numerosity comparisons such as this,2 another mark of number sense.
2 Libertus, M.E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14, 1292-1300; Mazzocco, M.M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PloSone, 6(9), e23749.doi:10.1371/journal.pone.0023749.
Quickly, find all the Rs in A, and now, quickly, find all the Rs in B
Which was easier? For most people, it’s easier to distinguish a letter from digits, suggesting that the brain processes letters and digits separately. Studies have shown that postal workers who read mixed letter-digit zip codes all day—and children who text 2 each other like this—do not show any difference on these tasks. The brain is highly trainable through adulthood.[i]
3 Jonies, J., & Gleitman, H. (1972). A conceptual category effect in visual search: O as letter or as digit. Perception & Psychophysics, 12, 457-460; Polk, T.A., & Farah, M.J. (1995). Late experience alters vision. Nature, 376, 648-649; Polk, T.A., Stallcup, M., et al. (2002). Neural specialization for letter recognition. Journal of Cognitive Neuroscience, 14, 145-159
Without using pencil and paper, estimate the sum 12/13 + 7/8.
In one large survey, only 24% of typical 13-year-olds and only 37% of 17-year-olds picked the correct answer of 2. Even though 12/13 and 7/8 each is a bit less than 1, more than half the students picked 19 or 21, the sums of the numerators and denominators, respectively. Studies have shown that tweens and young adolescents overgeneralize whole number understanding to fractions and most can’t explain why fractions have two numbers.[i]
[i] Carpenter, T.P., Corbitt, M.K., et al. (1981). Results from the second mathematics assessment of the National Assessment of Educational Progress. Washington, DC: National Council of Teachers of Mathematics; Mazzocco, M.M.M., & Devlin, K.T. (2008). Parts and ‘holes’: Gaps in rational number sense among children with and without mathematical learning disabilities. Developmental Science, 11, 681-691.
Which figures on the right are in the same configuration as the one on the left?
One study of children as they moved through school demonstrated that their block-building skills in preschool predicted their high school math course selection, math grades, and scores on standardized math exams! Other studies add evidence that visual-spatial skills are crucial for math success and that children with weak visual-spatial skills are at risk for math failure. [i]
The correct answers for this classic measure of visual-spatial abilities are (A) the first and fourth alternatives, and (B) the second and third alternatives.
[i] Tartre, L.A. (1990). Spatial skills, gender, and mathematics. In E. Fennema & G. Leder (Eds.), Mathematics and gender (pp. 27-59). New York: Teachers College Press; Verdine, B.N., Golinkoff, R.M., et al. (2014). Deconstructing building blocks: Preschoolers’ spatial assembly performance relates to early mathematical skills. Child Development, 85, 1062-1076; Wolfgang, C.H., Stannard, L.L., & Jones, I. (2001). Block performance among preschoolers as a predictor of later school achievement in mathematics. Journal of Research in Childhood Education, 15, 173-181.