My teaching buddy, Sonya New, and I are writing this post together! We have learned this week that we are FORMULA BABIES!! We ran across some problems where students need to write equations given 2 points and thought the students would just HAVE to have slope and point-slope formulas because that is how we learned to do it ourselves. BAHAHAHAHAHAHA!!
What an education we have received! I was so concerned about how they would find the "starting point" or y-intercept without formulas! Earlier this week Sonya's honors algebra realized that once they found the rate of change (slope) they could multiply the x coordinate by the slope and find the b (or starting point) by figuring out what to add or subtract to get y. I know that makes no sense when you read it! However, it took me and Sonya 2 WHOLE DAYS to realize that what they are doing is using the slope-intercept formula to solve for b. We felt STUPID!
ALSO, I had students to use tables to find rate of change and then extend the table "back" to zero to find the starting point or y-intercept. I had one student who hated the formulas yet got EVERY SINGLE PROBLEM correct using tables. Even problems with fractional slopes!! IT WAS AMAZING AND EYE-OPENING!!
Then we laughed about the fact that we are "formula babies" and have come to the conclusion that we need to understand that the logical (or NATURAL instead of FORMULA) way to write equations makes more sense to our students.
P.S. - Sonya is a new mother and I have had 3 breast-fed babies myself...so we couldn't resist the analogy.