*How do children develop an understanding of math concepts?*

Research suggests that the mind is hard‐wired to view the world numerically.[i] Children begin to understand and use numbers very early in life, and can distinguish between different quantities of objects as early as six months of age.[ii] As they grow, children learn to count, to understand numbers as symbols for representing quantities, to discriminate between different quantities, and to put things in numerical order.[iii] This *numerical competence* is the foundation for the development of more complex math skills.

Formal math activities like counting and using numbers rely in part on *number sense*, an innate human awareness of how numbers work. Number sense includes the intuitive ability to distinguish between quantities, understand how numbers are related to each other, and perceive what happens when quantities are combined or separated (i.e. addition and subtraction).[iv] Students typically enter school with a basic number sense that has been forming since infancy.

Research shows that children who struggle with math, such as those with the learning disability *dyscalculia*, often have impaired number sense.[v] Dyscalculia, which affects six percent of students, is characterized by problems with counting, calculating, measuring, estimating quantity, and doing calculations “in one’s head.”[vi] Research suggests that dyscalculia and other math learning challenges may be rooted in difficulties with *number sense*.[vii] On the other hand, a large body of research demonstrates that gender is *not* a factor in whether a child struggles to learn math. There are no innate differences between men and women in math and spatial reasoning abilities.[viii]

The section below highlights some key findings from the research on how children learn math.

Basic number skills — the understanding of numbers as symbols, the ability to count and put things in numerical order, and the ability to discriminate between different quantities — are the foundation for more advanced math achievement. Children who have strong numerical competence by kindergarten and first grade perform better on standardized math tests later in elementary school.[ix] Those who lack basic number skills can continue to fall behind their peers as they progress through elementary and secondary math classes.[x]

In the traditional approach to teaching mathematics, often an instructor poses a math problem, a student responds, and the instructor evaluates their solution.[xi] However, recent research supports a more interactive approach that asks students to explain their mathematical reasoning rather than simply provide an answer or show calculations.[xii] There are many ways a student can tackle the same problem, and even end up with the same solution,[xiii] so teasing apart the mathematical reasoning behind a solution can help instructors identify and address flaws in students’ mathematical thinking.[xiv]

*Spatial ability* is the capacity to visualize and mentally manipulate objects; for example, to imagine what an object would look like if it were rotated. Spatial ability plays an important role in math learning, and is a strong predictor of a student’s achievement in math, science, and engineering.[xv] While some people naturally develop strong spatial ability, a large body of research demonstrates that it can also be learned through activities ranging from video games, to blocks and puzzles, to instructor‐led spatial lessons.[xvi] Spatial training can even improve performance on tasks that are not explicitly spatial.[xvi] In one study, for instance, children who received training in the mental rotation of objects performed better on arithmetic exercises than those who did not receive the training.[xvii]

The Number Processing topic explores how the brain works to understand numbers, including the different ways children develop this skill.

The Numerical Understanding subtopic explores how children develop an understanding of numbers, and interventions that can support this learning.

The Neuroscience & Education subtopic explores how the field of neuroscience can inform practices in education, including curriculum and product design, and research in schools.

The Learning Counting subtopic explores how children develop counting skills and an understanding of what numbers represent.

The Learning Arithmetic subtopic explores the ways people develop and remember addition, subtraction, multiplication and division skills. It includes studies on methods of instruction, the brain processes that are used to learn arithmetic, and factors that lead to differences in how individuals learn arithmetic.

The Gender & Spatial Skills subtopic includes research on differences between male and female students’ spatial thinking skills, and how this affects their performance in math, science, and engineering.

The Spatial Memory subtopic explores how the brain stores information about locations, and helps people navigate and find locations.

The Math Interventions subtopic includes research and evaluations on various interventions to improve children’s math skills. There is a particular focus on students with learning disabilities, and who are struggling in math.

*Explore this topic in the Network View or Chord View of the Research Map.*

Citations

[i] The Neural Development of an Abstract Concept of Number [Article] Cantlon JF, Libertus ME, Pinel P, Dehaene S, Brannon EM, Pelphrey KA,*J COGNITIVE NEUROSCI* (2009),

[ii] John D.Bransford, Ann L.Brown, and Rodney R.Cocking, editors (2000) *How People Learn Brain, Mind, Experience, and School*. Chapter 4 — “How Children Learn”

[iii] Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In Kilpatrick, J., Martin, W. B., & Schifter, D. E. (Eds.), A research companion to principles and standards for school mathematics (pp. 219‐233). Reston, VA: National Council of Teachers of Mathematics.

[iv] Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. *School Psychology Review, 39(2)*, 181.

[v] Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia [Article] [15 different authors],*COGNITION* (2010).

[vi] Cortiella, C., & Horowitz, S. H. (2014). The state of learning disabilities: Facts, trends and emerging issues. *New York: National Center for Learning Disabilities*.

[vii] Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia [Article] [15 different authors],*COGNITION* (2010), Symbolic and nonsymbolic number comparison in children with and without dyscalculia [Article] Mussolin C, Mejias S, Noel MP,*COGNITION* (2010),

[viii] Sex differences in intrinsic aptitude for mathematics and science? A critical review [Review] Spelke ES,*AM PSYCHOL* (2005),

[ix] Validating a Number Sense Screening Tool for Use in Kindergarten and First Grade: Prediction of Mathematics Proficiency… [Article] Jordan NC, Glutting J, Ramineni C, Watkins MW,*SCHOOL PSYCHOL REV* *(2010)*, Cognitive Predictors of Achievement Growth in Mathematics: A 5‐Year Longitudinal Study [Article] Geary DC,*DEV PSYCHOL (2011)*,

[x] Validating a Number Sense Screening Tool for Use in Kindergarten and First Grade: Prediction of Mathematics Proficiency… [Article] Jordan NC, Glutting J, Ramineni C, Watkins MW,*SCHOOL PSYCHOL REV (2010)*,

[xi] Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. *Second handbook of research on mathematics teaching and learning, 1*, 225‐256.

[xii] Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. *Second handbook of research on mathematics teaching and learning, 1*, 225‐256. http://www.air.org/sites/default/files/downloads/report/An‐UpClose‐Look‐at‐Student‐Centered‐Math‐ Teaching.pdf

[xiii] Siegler, R. S. (2003). Implications of cognitive science research for mathematics education. In Kilpatrick, J., Martin, W. B., & Schifter, D. E. (Eds.), A research companion to principles and standards for school mathematics (pp. 219‐233). Reston, VA: National Council of Teachers of Mathematics.

[xiv] http://www.air.org/sites/default/files/downloads/report/An‐UpClose‐Look‐at‐Student‐Centered‐ Math‐Teaching.pdf

[xv] Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817–835. doi:10.1037/a0016127 Shea, D. L., Lubinski, D., & Benbow, C. P. (2001). Importance of assessing spatial ability in intellectually talented young adolescents: A 20‐year longitudinal study. Journal of Educational Psychology, 93(3), 604–614. doi:10.1037/0022‐0663.93.3.604

[xvi] Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: a meta‐analysis of training studies. *Psychological bulletin, 139(2)*, 352.

[xvii] Cheng, Y. L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. *Journal of Cognition and Development, 15(1)*, 2‐11.