Spiral Review 5-1

Ethan's homework for this week (Tuesday-Thursday evenings: 3 workpages + 1 hour of reading for each night) includes the following math problems:


Joylin is subtracting 97-43. She adds 4+23 before subtracting. What will she need to do?

a. Subtract 4 from the difference

b. Add 4 to the difference

c. Just find the difference

d. Subtract 2 from the difference


Ok....

WHY would she add 4+23? How is the number 27 going to help with this problem? What am I missing? I had Ethan chose answer c.

By Googling the problem I found sample worksheets with this problem and the exact same answers, only it says "She adds 4+43 before subtracting". Ok, now THAT would make sense. Typos happen - I get it. But how are 8 and 9 year olds supposed to understand a problem like that? At this age they still think adults are basically infalible. The idea of a typo on homework quite litterally flabergasts them.


Next question on the page is:

"Which property of addition is shown here: 0+7=7"

Honest question: Does it make me an idiot that I had to Google this? Ethan had no idea, so obviously the "review" wasn't working for him anyway. Why are they learning math theory in the 3rd grade? Is it more important for life-time sucess in mathmatics and applied mathmatics for 3rd graders to learn the names of all the addition and subtraction theories, or to memorize their basic addition, subtraction, multiplication, and division facts?


Speaking of multiplication facts, Ethan was supposed to have learned the 1, 2, 5, and 10 multiplication tables in the 2nd grade. He didn't, so we are already playing catch-up. Despite not being featured on any of his homework for the school year, he is supposedly learning his 3x facts in class. So why did we have the following problem on the "review":


What is the missing number in the table below?

Coaches ________________ Players

5 _____________________ 40

7 _____________________ 56

9 _____________________

12 ____________________ 96


Now for those of us who have learned our 8x facts, the answer is easily determined to be 72. However, THESE FACTS HAVE NOT YET BEEN COVERED IN CLASS. This was a REVIEW sheet, not a "challenge question".


Ethan tried subtracting 40-5 and then seeing if that answer equaled 56-7. I thought that was a good try, but obviously subtraction wasn't going to help him find commonality between those sets of numbers. He didn't like my suggesting of subtracting 56-40 and seeing what he got because "That only works for that side, it doesn't work for the other side. How do they match up?" He knew, on some instinctual level, that there was a relationship between the columns of numbers, but he didn't have the basic arithmetic skills to find the answer.


You know what happened then? He got so frustrated about "not knowing this stuff because we never talk about it" that he had a melt-down and had to take a break from homework.


"Spiral reviews" are the handmaidens of the "spiral process" of mathmatics education. Simply put, rather than memorizing facts through constant repetition until a concept is mastered, and then progressing to the next concept, students climb a winding staircase from concept to concept. If the student doesn't master the lesson on the first try, it is ok, because the next "spiral" through the material will catch them - hopefully.


For example: instead of doing pages upon pages of subtraction problems until the numbers are drilled into their sub concious, the child learns basic subtraction, number placement, how to do subtraction with number placement and place holders, subtraction theory, word problem strategies, how to "flip" a subtraction problem into an addition problem, estimating answers, and greater than/less than ALL IN a one or two week course! Still cannot remember what 14-9 is? That's ok, we'll catch it when we spiral through addition, number placement, word problems, subtraction to find addition, estimation, geometry and statistics during our NEXT spiral. Maybe. If you're lucky.

I fear for the future of the republic with education strategies like this. More pressing: I fear for my sanity while I struggle to properly educate these boys.