forget the answer…
“As someone who has tried to explain to my struggling child that ‘the answer’ is not as important as how they arrived there, listen up. She doesn’t believe you.”
This was the opening line of a parent’s rant last week after her daughter broke into tears during the first 10 minutes of our session, then asked to go home. Her daughter, who I will refer to as “Kelly”, has just began the 6th grade, and excels in every subject, with the exception of math. In fact, adding to 10 is beyond her most days. She has tried flashcards, a slide rule, and her mom even even picked up an Abacus at a local garage sale hoping, to no avail, to provide some assistance. My friend Kelly cannot add or subtract.
I was lucky enough to hear Dr. Harry Wachs lecture about 8 years ago on his understanding of 1 to 1 correspondence, and how children need to “own” the idea that one thing is worth one thing. Although this concept might sound simple, and somewhat rudimentary, Dr. Wachs proclaimed that this basic concept was the foundation for all things mathematical. An idea I have tested in my own way several times, and every time Dr. Wachs is not only proven correct, but flawlessly accurate; as if you need any help from me to know how amazing he is. I don’t remember the reasoning, but I know Dr. Wachs explained that 1:1 correspondence should be taught with five objects or less. Perhaps because we have five fingers on one hand, perhaps because five is a small enough number to eliminate confusion, or perhaps that was just Dr. Wachs’ comfort level. Whatever his reason, I am not about to second guess it.
Kelly and I counted out five inch cubes and went through the initial steps of 1:1 correspondence. She counted them, I counted them, we stacked them different ways, spread them on the table, covered them with paper and she confirmed that no matter how they are positioned in space, there are always five blocks. We moved into simple addition and subtraction with her counting out the answer every time. “If you have 3 blocks, and I give you my 2 blocks, how many will you have? Please count them”. We worked this over and over again, slowly building our way up to 10 blocks. “If you have 10 blocks, and take away 3 blocks, how many are left? Please count them.” The process has taken a few weeks, and has been agonizing for both of us. Kelly’s mom has been watching every session, amazed that her 6th grade daughter is having such trouble with the simplest of problems. At one point mom opined “how can she be expected to multiply, divide, or even do fractions in 6th grade if she cannot even understand this?”. Touchè.
Last week both mom and Kelly had a meltdown during our session, and although it made for a tense few moments, it was a needed breakthrough. Kelly was able to admit to herself that her multiple compensations (and she has several) for finding the answer are no longer the best way, and in doing so, got out of her own way allowing for the beginning of a more solid understanding of math facts. Mom also came to an understanding albeit much more profound.
Right now, the answer is the least of our worries.