Skip to main content

Bite your tongue

Amanda has been doing the Art of Problem Solving Pre-Algebra course. It's about the opposite of, "do 100 problems almost the same using this technique.  Now do 100 more problems on the next technique."  They stress problem solving, applying techniques in creative ways, and learning through struggling with the topic.  To begin each chapter they give 5-6 problems that illustrate the topics in the chapter.  First the student struggles with the problems and maybe (or maybe not) discovers the methods used in the chapter to solve the problems and why they work.  Then the student reads the chapter to connect what she's learned through struggling with the mathematical theorems.

Some of the problems are really hard.  Sometimes Amanda sits staring at a problem not doing anything.  I've encouraged her to write something and she seems to be picking that up.  But it's not always obvious what to do so sometimes I help her to start.

The problem is that sometimes she's just on the cusp of solving a problem and my help actually detracts from her own solution, confusing the situation.  Sometimes my method isn't her method and gets in the way.  Sometimes she's just not ready.  So I need to do something different.

What I've worked out is that I can literally bite my tongue as she does the problem.  I can nod and say, "mmm-hmmm" when she's right, or signal that she's made a mistake.  But I don't give her any directions.  And she (often) solves the problem.

It's hard for her and hard for me.  Someone once said that the butterfly needs to struggle while getting out of the cocoon: if you help it, its wings don't fill and it will die.  But (in the case of children) struggle sometimes seems like a bad thing.  I have to remember that the struggle is part of the process, just as much as the answer. Maybe even my struggle to remain silent is part of the process.

Comments

Popular posts from this blog

Why you should study the history of math

  Why you should study the history of math In the mid 1300s a fad made its way around Italy. Mathematicians would challenge each other to “mathematical duels”. They would post problems for their opponents to solve, sometimes along with their solutions in coded poetry. The winners would get support and funding from rich patrons, the losers would descend into obscurity. One such contest, between Fiore and Tartaglia, involved a new method for solving the cubic. In order to win, Tartaglia worked day and night to find Fiore’s method---unfortunately, Fiore did not do the same and only knew his own method and no others. (*Recall that the formula for solutions to quadratic equations of the form use the quadratic formula, Giorlamo Cardano---physician, philosopher, astrologer and mathematician---convinced Tartaglia to share his method and promised never to reveal it. Then Cardano figured out a more general method, and wanted to share it, but was blocked by his promises. Fortunately (for Cardan

Southern butter mints---vegan edition

After the last post, we started to be able to see what the fuss was about.  The ones made with twice the butter were the best candy I have ever tasted.  Ever.  So then we started experimenting.  How long do you pull it?  Longer than you think.  And then pull a minute or two after that.  Suddenly every single batch was creaming, pretty much right after we would cut them. I tried adding less than double butter and I think they taste much better (more delicate, according to one taste tester). The latest experiment we did involved using Earth Balance instead of butter.  It cooked pretty much the same as usual, although I was distracted right at the moment I had to pull it off the stove so it cooked maybe a bit longer than usual.  Amanda and I each pulled a quarter, while Luke pulled the bigger half.  Luke's really wasn't turning very fast---perhaps because it was too hot when he took it off the marble.  Mine was turning faster than Amanda's so we traded for a while.  Aman

Southern Butter Mints part 1

Some friends of ours have a granddaughter getting married (and she's a friend of ours as well) and so I agreed to help out with the shower.  Apparently this is to be a "southern" shower, full of tradition and elegance, but not too far over the top. Among things that are needed for a shower are punch with great grandma's punch bowl, sandwiches with cream cheese and green pepper jelly, and southern pulled butter mints.  "Ah, nobody can make those anymore.  We used to know someone, but the tradition needs to be passed down."  Like a fool, I said that I'd be happy to give it a try.  I suffer greatly from "I got a PhD in math, how hard could X be?" where X is something like gardening, or quilting, or cleaning, etc.  It's always harder than I think it will be. "We'll call Mrs. X who makes these, maybe she'll pass down the method.  I hope you don't hate me!"  I was actually planning on doing research online, watching a fe