In Memoriam Peter Caws: long multiplication

I love math, and it’s brought me a lot of joy over the years. I vividly remember the mind-blowing moment in high school when the math teacher introduced the unit circle and Pythagorean identities. After we’d slogged through a semester of trig, geometry (my least favorite math discipline), suddenly connected back to algebra (my favorite)! And one of my most satisfying adult experiences was discovering that I enjoyed calculus despite failing it in college the first time around. It was very hard but I earned straight As in Calculus I, II, and III in my 50s (undergrad at UMass, part of a computer science 2nd bachelor’s program).

None of that could have happened without my dad’s intervention in 4th grade, when I just could not comprehend long multiplication. I was on the road to classic math phobia – shared by my mother and brother, so a real possibility. The times table had already thoroughly spooked me, and it didn’t help that I skipped third grade (to this day I say of any gap in my education that it must have been covered in that year and I missed it). I remember being shocked that earlier generations were required to learn up to 12×12, because a hundred combinations already seemed impossible. (I never memorized the 6-7-8 section – I had to argue to get partial credit on my first calculus midterm for having correctly worked a difficult problem until I wrote 7*9 = 64…)

So 9-year-old me is required to know all the integer combos, and now I also have to know when to carry, how to move across the decimal places, and then add it up at the end? I could not handle it. I felt like my brain wasn’t up to it, that it was too complicated to ever understand, and that the people who could do it must have some special ability that I lacked.

I don’t remember asking my father for help. From a very young age I believed, due to a combination of nature (independence, stubbornness) and nurture (sink-or-swim parenting, a semi-feral childhood), that I was supposed to solve my own problems, and if I couldn’t, that was my failure. The notion of being “just a small child” didn’t cross my mind. But either I did ask, or he saw that I was struggling.

Peter worked with me patiently and gently for hours, typically in the mornings before school. The specifics have faded, but I vividly remember his tidy handwriting as he demonstrated the techniques, and most of all his faith and confidence in my ability to master it. He conveyed over and over again that he knew it was hard for me, that finding it difficult to grasp wasn’t a flaw, but that if I gave him my attention and didn’t give up, I would understand it eventually. Many times I broke down in sobs, insisting that I just didn’t and couldn’t get it, but he never lost his cool or threw in the towel.

There’s no memory of when the light dawned, and maybe it was a gradual change, but it can’t have taken very long. From then on I actively enjoyed long multiplication. I was still prone to errors, but I knew and understood how to do it, and it was one of the first techniques I added to my ever growing jack-of-all-trades-master-of-none toolset. Relishing good-enough skills – the ability to do something with a modicum of success if not at a high level – I also learned from him (see the previous post!) I am eternally grateful.

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