Disclaimer: I hate high-stakes testing. Hate it. This post is not about high-stakes testing; it is about content that happens to be used in high-stakes testing. Imagine I’m writing about Holden Caulfield, and try to banish all memories of Catcher in the Rye plot pop quizzes from your mind.
My cousin asked me about my thoughts on common core. Here’s an actual paragraph from the common core website:
These standards define what students should understand and be able to do in their study of mathematics. But asking a student to understand something also means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One way for teachers to do that is to ask the student to justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.
This sounds awesome! I often think I understand something well, and then try to write it down only to realize that there are more subtleties than I thought, or that I had a fundamental misunderstanding, and in general that I am wrong.
On March 16th of this year I thought I had an answer to something I’m working on. Aaaand… today is August 27th and I’m still working on it. But I didn’t realize my answer wasn’t complete until I started writing, and I wrote “, because” and had nothing to follow it. This is frustrating and ridiculous, and I don’t expect every kid in America to become a mathematician and work on a problem for six months. But I do believe that trying to do something, thinking you’re right, and then trying to explain it and realize you’re wrong after six minutes is a good experience and makes you a better critical thinker. Question your beliefs, analyze your reasoning, explain yourself- all good things.
The above is all theoretical (I was a math and philosophy major in undergrad). So I looked up some common core examples.
Try doing multiplication in long drawn out word form like this one: 3, 6, 9 what is the 12th number in this sequence? My son can’t just read that and think the 12th number automatically. He has to write them out. He also cries over this type of math.
The problem itself is great (I’m also not opposed to crying). Most parents can help their kids with 12 times 3 equals 36 “automatically,” but figuring out why 12 times 3 is 36 is hard. This question offers justification first, and encourages the student to explore and discover multiplication for himself. I was quite bad at my times tables as a kid (I still remember nonsense like “Six and eight went out on a date. When they came back, they were 48!”) because it didn’t make any sense. But writing out a sequence 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 is just like practicing spelling or lay-ups, and it makes sense.
I started finding more examples of common core type problems, but I think talking about one of my own past experiences is more helpful.
During my first semester of graduate school, I sat down to my first analysis exam. I’d never been a big analysis fan (though now that I’ve taken it umpteen times I actually enjoy it!), and I felt a bit shaky about the material before I walked in the room. The professor handed out the exams and said “you have one hour.” If this isn’t clear to you by now, I’m good at math. But as I leafed through the problems I started silently FREAKING OUT. I felt something like vertigo, and also felt very very cold as I thought about trying to finish this exam in the allotted time. My hands were shaking and I was a little sweaty. This was my first experience at math anxiety and it was TERRIFYING. My skin is prickling as I type this, remembering the experience five years later.
I can only imagine what it must be like to feel that with math for years in elementary-high school. Math anxiety is real, and unfortunately contagious. There’s been some amount of backlash to common core/shaking up math education, and I’m certain that some of it is rooted in past traumatic memories of math anxiety. All I can say is, I support students, I believe in them, and that “the most important thing is to stay calm.”
If you google “common core math” you’ll get lots and lots of mild vitriol, but you also get some good stuff. Here’s a side-by-side comparison of some math problems and explanations of why they switched. Here’s a cool explanation of the new subtraction.
Here’s an article called “The Ten Dumbest Common Core Problems” that I’ve run into a lot [I dislike it because it doesn’t give credit to where any of the pictures/examples came from], and my thoughts on 1-10. Again, not an elementary-high school educator, just a math person:
- 7 + 7 = 10 + 4 = 14. Maybe adding a word like “number bonds” is strange and new, but memorizing that 7+7 = 14 can be hard (I’m a terrible memorizer, but a good reasoner). Breaking 7 into 3 and 4, and then pairing up to get a 10? That’s how I add large numbers quickly, and I had to figure that out myself. Helping kids learn the trick is great.
- Awesome, visualizing subtraction. See above explanation on the new subtraction.
- This is a worksheet with a typo. So… unclear why it’s included. If it didn’t have typo, it’d be a good sheet.
- This worksheet’s picture doesn’t make sense. But the math does. (Figure out what’s unknown if you have parts of a whole)
- More visualization of addition and subtraction. I literally did this with 12 year olds when I was 15, using quarters on a table.
- I like this one too.
- I always hated “carrying the one” so I’m all for the new addition.
- I don’t understand this. This doesn’t mean I hate it, it means I want to know what it says.
- This isn’t new; I did this worksheet as a child.
- Another typo
Final anecdote in this jumble of a blog post: how I learned to divide fractions. They tell you to just multiply by the reciprocal. Like I said, I’m bad at memorization, so I’d often do random nonsense that seemed sensible (divide the tops, multiply the bottoms). No matter what I tried on my own, I felt like I just couldn’t get this dividing fractions thing. One day, my dad drove me to Baker’s Square to buy a pie. He asked how school was going and I told him that I would never get how to divide fractions and I’d always get it wrong and math is dumb and I was just a sad little 8 year old sitting in that passenger seat. He said, okay, well, if we split this pie among our family, how much pie does each of us get? And I said “one fifth.” What about if just you and I take the pie? “One half.” What if I give you the pie? “One.” What if half a person gets a pie, how much pie does one person get? “Tw-OHHHHHHHHHH.” Crystal clear, this concept that had been frustrating me for weeks. Why do we use the reciprocal? Because if half a person eats a pie, that whole person eats TWO PIES.
That’s my happy story of understanding the madness behind the method. I’ve seen dozens of students who know to multiply by the reciprocal, but who don’t understand why, which makes word problems quite difficult. Conclusion: so far, I’m all for common core math. The important thing is to stay calm. And ask questions. And maybe not help your kids with homework?
Oh one more thing: I’m interested in giving back to the community/doing some volunteer work and putting my skills to use. I told my advisor yesterday that I don’t have any skills, and he responded that I have math skills and I should go find something like the free clinic for math. Do you have any recommendations for me to help people with my math skills?