Does math HAVE a history?) Find out ways to learn what you never learned in school.
by Julie Brennan
I recommend the Mathematicians Are People, Too series so highly is because it started me earnestly looking at studying math through history, rather than treating the history as a supplemental interest addressed in high school, if at all. But some people have picked it up and asked, where's the math in it?
For my family, learning that these were real people overcoming real struggles, getting glimpses in their lives, learning how often luck and circumstances played a role in what they accomplished has been fascinating. It pulled me in to trying to understand *some* of their mathematics. I will never understand most of the math out there. But it is interesting to me to know what it can do. It opens up a whole world. I'll never be a mathematician myself, but I gain more insight into how math is woven into the fabric of our lives in many more ways than we realize.
I got another book yesterday that stated something in words I couldn't express well enough myself, *why* math history can help us understand and learn math. From "Learn From the Masters":
" . . . a deepening of mathematical knowledge [ can be ] intimidating, especially for a student who has lacked obvious structure in his or her mathematical learning. . . the history of mathematics can supply a structure of understanding relating reasons with results. History can provide a logic between the definition of a mathematical concept and its application."
"Mathematics as taught is perceived by most students as a subject devoid of history. The teacher [or curriculum] becomes the source of all that has to be leaned . . . the understanding of the process of mathematical creation and of the age-old grappling with mathematical problems are completely lost. . . "
"In the history of mathematics, we encounter many developments that were slow in coming to be accepted. Quite often, we find that mathematicians made important developmental advances which were disregarded later . . students face learning difficulties in areas similar to those we encounter in historical development."
In other words, for me, my children's cruising along and suddenly hitting a bump in understanding a type of symbolic notation such as fractions is NORMAL and EXPECTED. Some of the best minds in mathematical history had trouble grasping these concepts. For example, place value, the role of zero, negative numbers, symbols - these have taken many hundreds of years to develop. We ask children to learn and master these in a few short years in our traditional method of education, and they often have a sense they are slow if they don't grasp concepts in the order and timeframe presented.
I don't know about you, but if I am confronted with a puzzle, and I am completely stumped, seeing *how* someone worked through a similar puzzle, following their thought process in developing their solution, is far more helpful for me than being given a solution or procedure for solving it. One of my favorite proverbs which can be found in different forms in many cultures is: “Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand." For me, walking in their shoes involves me. For one thing, I SEE them struggle. Knowing someone more experienced than me struggles builds confidence for me. Math has always made me feel stupid, and I know I'm not alone! So knowing really smart people struggle with it is so encouraging to me. Attitude is more an indicator of success than aptitude, we all know this.
I'm not suggesting you run out and get Learn the Masters, it's just helping me write my courses, it addresses high school level only. But I feel that there is no reason why these ideas cannot be brought down to even kindergarten level. After all, kindergartners are learning about zero and place value, and these problems stumped and consumed the field of mathematics literally for centuries! The abstract notation can come later of course, but conceptually, these ideas can be brought out in their historical framework.
I love it when I run across things that explain instincts I've had but couldn't explain.
June 24, 2004