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I teach 2nd grade like @char54: , although I'm in the States. I agree with her 100%. I've had so many students become confident math thinkers by allowing them to share their own, natural way of solving a problem (we call them strategies). It builds confidence and language skills, as well. Then we move into finding the most efficient strategies and finally the "traditional" methods.
I think a lot of adults say they aren't "math" people because they didn't get the chance to really understand how numbers work. We were all rushed into rote memorization of "rules" that didn't make sense. My hope is that this new cohort of learners will be "math" people because they've gotten to opportunities to gain that number sense.
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@woodentulip: in your example 32-12, how does one even begin to break apart the numbers? 12+3...Where did that come from?
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@char54: your examples and explanations are helpful.
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@joyfulkiwi :
@Mrs. Lemon-Lime: so what they're doing in that problem are "jumps" to the next "nice number"...Nice numbers are generally 10, 20, 30, etc. Then you add up all the jumps.
Basically for 32-12 you are finding the distance between the two numbers.
It's best explained on an open number line, I've shown a picture below. The top number line is what OPs original example above shows for 32-12. The bottom number line is a more efficient way of jumping... Instead of jumping 3 to 15, then 5 to 20, why not do a bigger jump of 8 to 20? That's why we spend so much time on the "friends of ten", 2+8, 7+3 etc . Soon students are able to make bigger jumps which allows them to solve the problems quicker.
But like I said, for that problem (32-12) jumps are not the most efficient strategy. It's much quicker to go 30-10 or use another mental math strategy. But students need time to develop their own strategies and realize there are more efficient ways to solve problems. You can't really rush them through the steps.
Hope the pic helps!
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@char54: Yes! I vote guest blog post too!! I have see way too many FB friends getting upset about common core/new math and talking about how education is getting so bad- and I wish there were more resources for them to learn about how these new strategies may actually be helping children.
@JoyfulKiwi: That's a great point. I failed basically every math class, and never received the help I truly needed. I floundered. As an adult, I'm much more self-sufficient and when I was learning math for my nursing program, I was able to find new effective ways that I can learn - and realized math never should have been as hard as it was for me.
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@char54: I think I do math like that in my head anyway without being taught. Like when I'm faced with 60-12 I just instinctively do 60-10=50 and then 50-2=48. For some reason I didn't develop number sense until I was an adult and had already struggled through AP classes!
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@spaniellove: right! A lot of us do that instinctively now as adults, now that we understand the concepts behind it. So the goal is to arm kids with the strategies to do that from a young age, rather than just follow a rote set of rules so that they don't have to struggle through more advanced math classes like so many of us did.
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@Mrs. Lion: What you said about depth of understanding-> BINGO. We want kids to be able to understand the math that they're doing, yes? Well, this is a way to do it.
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@char54: great example! Let me know if you do a guest post!
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@woodentulip: I'm pretty conflicted too. When i read all the articles that came out regarding New Math i was pretty annoyed. While i agree that a deeper understanding of the concepts is important, some may not necessarily need it to be successful in math.
There was a lot of hoopla over new math because of our declining test scores. I don't think it's because our kids are getting dumber, but new/discovery math doesn't allow them to get the answers faster. You're competing with students in countries/areas that still use rote memorization and it'll be much more difficult to compete. DH and i plan to supplement her math education. I am not completely against new math but i think memorization and drills have a place in learning basic math.
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@char54: a ha! Now I see the jumps and nice numbers.
+1 on your guest blog.
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@char54: exactly what I was going to say! I teach grade 2/3 and this is exactly my theory.
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Anyone else confused as to why this stuff even needs the "new math" labeling? I know we're mostly talking about that one example (subtraction) but it doesn't seem THAT different from what we (I) did in elementary.
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The big difference is that we don't automatically teach the standard algorithm but focus on using multiple strategies and "playing with numbers" to make them easy and manageable in their head. It is actually really interesting to watch kids do it on their own and explain their thinking. Providing students with these "strategies" allows them to truly understand math and not just follow steps. Most kids eventually get to the point of doing it the standard way, but not until they truly understand what is going on. I teach 2/3 and I have kids still using manipulatives to solve simple addition and subtraction to students who can do 3 and 4 digit questions in their head because they can play with the numbers.
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I understand how the explanation looks crazy, but once you understand the concept you can do math soooo fast in your head if you break everything into tens. You already do this with clock time - you break everything into :60's.
By the way, my 6th grade math teacher showed us this "new math" (in 1993) and I understood it in about 10 minutes.
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Hmm... "new" math looks closer to how my 5th/6th grade math teacher taught us math concepts, and she was one of my most memorable teachers of my entire K-12 education. I must have mastered abstract mathematical thinking at some point early on b/c math remained one of my very best subjects, and I went on to get a Ph.D. in a quantitative field. So while I don't know much about "new math", per se, it looks pretty promising to me.
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I remember getting really frustrated in math class as a child because I would use a different strategy/method and get the right answer, but the teacher wanted me to "show my work" and prove that I got the answer the way they wanted me to. I am all for anything that allows children a better grasp of math and science, and it sounds like "new math" is all about engaging the student in the process, rather than just teaching a formula and drilling it into their heads.
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@char54: your explanation is so much better than anything I found in google!
This, not so much:
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@googly-eyes: Actually the example made it sound pretty intuitive. The reality in many schools (at least with the curriculum we used) was that what they do on most days barely resembles math. There's no textbook, only a workbook and some manipulatives, and no teacher training. It takes years to go from the inklings of a concept to "so this is how you subtract", and you only really touch on a topic for very brief periods of time every year. Hence, "new math".
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@MrsScottish: ah sounds good to me then.
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@spaniellove: thanks for the explanation! I'm definitely coming around to this!
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@mrbee: @char54: I would LOVE a guest blog post on the subject.
That image was exactly what you described--one I grabbed from Facebook from a frustrated parent...and my eyes go crossed every time I see it.
Anything that would help parents navigate through these murky waters would be so appreciated!
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@Mrs. Lemon-Lime: That's where I get confused too. The numbers seem to appear out of nowhere and I want to crumple up the paper and throw it away.
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