Kids And Math: Mental Number Line Impacts Memory For Numbers
    By News Staff | September 9th 2010 01:00 AM | 3 comments | Print | E-mail | Track Comments
    Remembering numbers is one of the most basic things we do from a young age - early on, a combination lock or a phone number and later any number of things such as ATM codes, social security numbers, and more.

    In Western cultures, children learn to place numbers on a mental number line - smaller numbers to the left and spaced further apart than the larger numbers on the right. Then the number line changes to become more linear, with small and large numbers the same distance apart. Children whose number line has made this change are better at remembering numbers, according to a new study published in Psychological Science.

    For the study, Clarissa A. Thompson of the University of Oklahoma and Robert S. Siegler of Carnegie Mellon University looked at how children's memory for numbers relates to the way they represent numbers in their heads.    

    In one experiment, each child was given a stack of blank number lines, with "0" written below the left end and "20" written below the right end. Then the child heard a series of numbers from 1 through 19 and had to mark on each number line where they thought that number belonged. Then the experimenter told a story that included a few numbers. The child was asked to name four cartoon characters, to throw off their memory a bit. (Thomas the Tank Engine and Dora the Explorer were favorites.) After that, the experimenter asked questions about the story, like "How many forks did Colleen wash?" Children with a more linear number line were better at remembering the numbers in the story.

    "Young children's knowledge sometimes seems impressive, because they can count, 'one two three four five six seven eight nine ten,' but often they just learn by rote. Their counting doesn't have much to do with their understanding of how big the numbers are," says Thompson. But eventually these words get associated with the size of the numbers. Children normally start out with a logarithmic number line, which has more space between smaller numbers and crunches the larger numbers together at the top. Eventually they progress to a linear number line.

    In three experiments, Thompson and Siegler found that the more linear a child's number line, the better the child was at remembering numbers. This was true for preschoolers for numbers from 1-20 and for elementary school children for numbers from 1-1000. "We really do live in a world of numbers," says Thompson. "Some we only need to approximate, and others we need to remember exactly. Ability to estimate the sizes of numbers influences the ability to remember the numbers exactly."

    Citation: Clarissa A. Thompson, Robert S. Siegler, 'Linear Numerical-Magnitude Representations Aid Children’s Memory for Numbers', Psychological SciencePublished online before print July 19, 2010, doi: 10.1177/0956797610378309


    But please don't get carried away with the number line.  Here's a snippet from the introduction to "Geometry in a Modern Setting" (1969) by Gustave Choquet. 

    As soon as possible, the child must think of the set R of numbers as a totally ordered, commutative field: he must realize that when he is carrying out calculations, he is only using a small number of the properties of addition and of multiplication, the ones which mathematicians call the axioms for totally ordered commutative fields.

    Robert H. Olley / Quondam Physics Department / University of Reading / England
    "In Western cultures, children learn to place numbers on a mental number line - smaller numbers to the left and spaced further apart than the larger numbers on the right."

    I was never taught a number line anything even remotely like that. The ones I learned (this would have been very early 70s) all had evenly-spaced numbers.

    What kind of jackaninny teacher would try to do a logarithmic number line, and how do we get these teachers fired? All that would accomplish is forcing the kids to learn it a second time. Undoing crappy education is ALWAYS harder than getting it right the first time around.

    Great to see a study on this. I've oft wondered about our differing internal representations of numbers and time, how they vary per individual and culture, how they demonstrate they age at which concepts were learned, and how they influence our ability to negotiate numerical and temporal calculations. I look forward to reading more.

    ((Perhaps my number line was influenced by my mathematician father teaching me at a young age? It is vertical rather than horizontal, exists in 3D so i can zoom up/down its length or in/out for close/wide views (e.g. to fractional values), passes through a transparent surface at zero with negative numbers fading below into the depths, and fades into the distant sky past 100 - beyond that my visualization is of written numbers. My calendar clearly betrays its early origins - it is a big wheel, as infinitely zoom-able as my number line, and logarithmic in scale, with Jan (at the bottom right) getting a 6 degree arc and December a full 30 degrees.))