Just for kicks, I threw up a volume of revolution problem on the whiteboard in the lunch room when I came in Friday morning. As the girls from Fundamentals of Research filtered in I was pleased to see them drawn to the puzzle. I watched in amusement as they made the problem so much more complex than it really was. It wasn’t the Calculus that stumped them but the failure to recognize simple things: the radius was equal to y which was proportionate to x. They solved it before going to class so I gave them another: could they apply the method of slicing to derive the equation for the volume of a pyramid?
After returning from their visit to the Neuroscience Lab they enthusiastically attempted to tackle this problem, filling the white board with symbols, equations, formulae and sketches. Finally at around 3:30 they found their solution – “He figured it out” they reported, pointing to Lance, the lone boy in the group. “At least it wasn’t one of those kid geniuses in the String Theory class – we would have really felt stupid then,” commented Amanda. Almost on cue, 11 year old Dylan pops his head into the room to report “I got the cross section part. I just forgot one part of the calculus.” My response – “That’s great Dylan, but aren’t you supposed to be in class.” As he returns to class, I close the door, face Lance and the girls: “You didn’t hear that.”
This first week of camp has been such a joy. We have the nicest kids and I’m having a blast tucking in little bonus math tutoring here and there to a very receptive group. It brings back so many memories of people I’ve tutored over the years.
The first person I tutored was my mother. I was in 4th grade when she decided to try to earn her GED. The report showing that she passed the math but failed the English would remain tucked in the top left corner of her dresser mirror for three decades until she finally earned her GED at age 65. My determination to help my mother fulfill a dream destroyed by the Allies Napalm campaign in Japan yielded an ability to teach myself math. I clearly remember the moment of clarity when lying on my bedroom floor with her GED study guide in front of me, I realized I could do anything I wanted to these equations as long as I did the same things to both sides – it was a missing piece to the puzzle I’d pondered for days.
Since that time, I have tutored hundreds of other math students, including several who remain indelibly etched in my memory.
There was the retired school superintendent, now an Alzheimer’s patient determined not to lose her memory without a fight. I slowly watched her deteriorate from not remembering what we did last week to not remembering what we did 5 minutes ago. I admired her courage and determination and felt honored that her loyal husband trusted me to lift her spirit during hours of self-designed experimental treatment.
There was a young boy, a Fetal Alcohol Syndrome victim, who I hoped to at least teach to count money and tell time before the social workers finally removed him from his mother’s house.
There was the middle school girl, who first came to me failing math who I once tutored by camp lantern after driving to her house after a hurricane. Although by that meeting, she had a solid A for the marking period and knew the material well, she needed me to validate her belief that she could Ace the next day’s test and see her first ever A in math on her report card.
As I coach new tutors working for HEROES Academy, I talk to them as much about relationship building and psychology as I do about math. The most important principal I teach them is to help build the student’s confidence. I don’t believe that distributing false praise, watered-down curriculum or inflated grades builds confidence. Children interpret such tactics as evidence that I don’t really believe in their ability. I believe that confidence is developed with the knowledge that they have a solid foundation and experience with successfully solving problems that challenge them.
For a struggling student, this often means working on material that was covered two or three years ago which often makes both parents and students nervous. They come hoping for a magic potion that will insure a passing grade on the next weeks’ exam. What they need is not a quick fix but a long term plan to build a solid foundation.
With gifted kids, I face other challenges. These children often like to fly through material, ready to devour the next concept as soon as they swallow the current one. I’ve met young children with impressive comprehension of regression, integration or linear algebra but have huge gaps in their math education. These children often are not happy when I suggest that we do a chapter by chapter assessment beginning in Algebra I to identify and fill in those holes.
I encountered that just last week after my theoretical physics instructor, Dr. Michael Park, talked to me about the math background of the students in his class. I asked each of the boys to take an algebra test. I received strong resistance, each boy claiming that it was beneath him.
Yesterday, I was working with one of these boys. After graphing a few parabolas, he recalled that he had done this before and was impatient to move on to something new. His complaint was that he needed to get through algebra so he could start calculus.
It’s because I know he can master calculus and beyond that won’t rush him. I pulled out the multiplication tower of math to explain this to him. “If I want to build a short tower, I can build it fast because I don’t have to worry about the strength of the foundation.” I explain to him as I start to haphazardly throw these Jenga-like blocks on top of each other. “But if the foundation isn’t strong, the tower will collapse.” I continue as they all fall down.
“If you want to build a tall tower; if you want to get to higher level math; then you have to take your time and make sure each level is solid before you move on.” I conclude as I carefully build my tower, aligning each level before stacking on new blocks.
If I believe a child can reach for the stars, I am careful to make sure that their foundation is strong before I encourage them to proceed to the next rung on the ladder. Allowing children to progress to new material before they fully understand the required prerequisites, is telling that child that I don’t really believe he or she is really able to understand math. We need to believe that our children CAN really understand math. We need to act on that belief by holding them to a standard that will prepare them to successfully travel along the path to higher learning. They will build confidence as we demonstrate our faith in them. This confidence plus a solid foundation will equal unlimited ability.