Guest blogger Katharine Beals, PhD is the author of “Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School.” She teaches at the University of Pennsylvania Graduate School of Education and at the Drexel University School of Education, specializing in the education of children on the autistic spectrum. She blogs about education at Kitchen Table Math and on her own blog, Out in Left Field.
By Katharine Beals
Why underestimate what children understand?
Recent anecdotes from parents and recommendations from educators suggest that the underestimation of American children is alive and well in the world of K-12 education. In particular, more and more teachers and education experts seem convinced that kids don’t really understand the words they read or the numbers they manipulate nearly as well as their parents claim they do. Thus, one mother learns from her daughter’s 2nd grade teacher that her child doesn’t understand the chapter books she’s been reading for pleasure since kindergarten. She should be reading picture books instead. Another mother learns that the multi-digit arithmetic that her 3rd grade son has been doing since preschool is mere calculation, devoid of conceptual understanding. He should be doing simpler calculations using manipulatives and repeated addition.
How, and why, have so many educators become so skeptical about children’s understanding?
How to become skeptical is child’s play. Simply ask the child a question that ostensibly probes comprehension, but is either vague enough, open-ended enough, or verbally challenging enough that the child is unlikely to give the “correct” answer: What is that? What is it about? Why did you do that? If further probing seems necessary, ask equally difficult follow-up questions.
Ground-breaking math education theorist Constance Kamii has shown how this works with place value in particular:
1. Show the child a number like this: 27
2. Place your finger on the left-most digit and ask the child what number it is.
3. When the child answers “two” rather than “twenty,” immediately conclude that he or she doesn’t understand place value.
4. Banish from your mind any suspicion that a child who can read “27″as “twenty seven” might simultaneously (a) know that the “2″ in “27″ is what contributes to twenty seven the value of twenty and (b) be assuming that you were asking about “2″ as a number rather than about “2″ as a digit.
How might you convince yourself that a 3rd grader doesn’t understand multi-digit arithmetic? Why not tap into her immature verbal skills? Ask her to elaborate how she subtracted 562 from 831. When she stumbles, ignore any suspicion that articulating why one borrowed from the 8 in the hundreds place and reduced the 8 to a 7 is beyond the verbal skills of your typical 8 or 9-year-old.
How might you convince yourself that a 2nd grader doesn’t understand his above-grade level chapter book? Here, a sufficiently open-ended question may do the trick. Ask him what the book is about, or what will happen next, or how the text relates to himself. Then interpret any hesitation, stumbling, vagueness, or reluctance to respond as an unequivocal sign of deficient comprehension. Dismiss any suspicion that this line of reasoning implies that a teenager who answers “What did you do today?” with “I don’t know” doesn’t comprehend his day.
Perhaps less obvious is why some educators seem determined to underestimate understanding. Here are a couple of possibilities. First, doing so may level the range of apparent abilities in a class of twenty-something children. Parents might think their children are ahead academically, but if they don’t really understand what they are doing, there’s less pressure to provide them with an accelerated curriculum. There’s also less of an apparent achievement gap to be troubled by.
Underestimating comprehension may also serve to avoid or postpone teaching harder material that, frankly, can be a pain in the neck to teach. Believing that children don’t understand place value, for example, gives you an excuse not to teach those pesky standard algorithms of arithmetic. Why? Because if children don’t understand place value, then they can’t understand borrowing and carrying (regrouping), let alone column multiplication and long division. And unless they understand how these procedures work from the get-go, educators claim (though mathematicians disagree), using them will permanently harm their mathematical development.
What’s particularly striking about this underestimation is how much it seems to have permeated the establishment’s take even on those children it itself identifies as “gifted.” For example, at the recent New England Conference on the Gifted and Talented, most of the math talks either expressed concerns about children’s comprehension of place value, and/or advocated the use of manipulatives in place of abstract math. The mathematically gifted kids I know, however, grasp place value and other aspects of arithmetic with only minimal exposure to manipulatives, and quickly advance to higher levels of abstraction by the time they hit first or second grade.
To stop holding our students back relative to their international peers, we need to stop asking them the wrong questions. Sometimes, indeed, no questions are necessary. If a child enjoys reading a particular book, then even if she fails to tell you what it’s about, she probably has a reasonable understanding of its content. If his multi-digit calculations are error-free, then even if he can’t clearly explain his steps in words, he probably has a reasonable understanding of his calculations. Comprehension may not be perfect—when is it ever so? — but the fact that it may need refinement is reason to encourage a child forward, not to stand in his or her way.