By now, I'm sure many of you have seen this picture floating around the world of social media...

with this caption...

"The dumbing down of elementary school children has reached epidemic proportions. They can no longer make any informed decisions due to the quantity of misinformation, falsities and deliberate use of distraction, all while imposing academic standards not even fit for a primate."

Many people immediately thought, WHAT? What are these teachers teaching our children? No wonder why our children are so "stupid".

Well... I have to tell you I had a similar reaction, but mine was more like, "Wow, that is BRILLIANT- way to go teach!"

Now, I am in no way here writing this post to say I am a for or against common core and that is not my purpose here today. However, I am becoming increasingly frustrated with the misconceptions and misunderstanding of what these standards are teaching our children. Let me start my explaining the "new way" in the above problem.

The work shown in that equation is nothing different than the way our brains work and process numbers. The reason it seems confusing is because we don't normally write it out on paper- our brain does all the work for us. In this problem, instead of subtracting, the student is doing reverse addition. Here's a visual...

So really, this type of thinking is not only not dumb, but also quite an advanced way of thinking. You see, for many of us growing up we just learned the algorithm. We were taught "the rules" and we followed them. We rarely veered off that path- and we thought we knew what we were doing, but in reality we were just following the steps our teacher taught us. Now in the 21st century, teachers are preparing students for careers that don't even exist yet and teaching them this type of critical, deep understanding of math concepts is essential for their futures and is not even close to making our students "stupid". In fact it is making them quite smart, much smarter than we were- like it or not, and capable of solving problems in many different ways.

As a teacher, it is my job to make sure my students are prepared for the world ahead of them. I can't sit here and say that teaching students this type of thinking is all cake and jellybeans.. No- It's frustrating, it's tiring, and sometimes makes me want to pull my hair out. Some nights I'm up until midnight trying to figure out a lesson that will best help my students understand WHY ... because critical, deep understanding is more important now than ever. Some nights I wonder if they'll ever get that concept I've been teaching them for 4 weeks. Some nights I wonder why in the world I chose this profession. But then, there's that day when a student explains their thinking like in the problem above, you see that light bulb, and you know that these new standards, the sleepless nights, the ridiculous acts you did to engage your students, the weeks you spent so patiently waiting for them to "get it"..is all worth it and that our children, our future, are ready for the lives that are ahead of them.

Great post! I love what the common core has done for the way students are expected to explain their thinking. It's really difficult for students to express their understanding of the problem if their brains work differently. I personally (if seeing the problem visually) would solve it the first way. If given it orally, would solve it the second way. In fact, I would have done 30 - 10 = 20 and totally disregarded the ones since they equal 0.

ReplyDeleteWhat I Have Learned

Thanks, I agree! I think one of the great things about it is that we provide so many methods for kids to solve problems so they can find what works best for them. Personally I would do the same thing with disregarding the ones since they are the same, but if it was a more difficult problem, I would totally add from smallest up to highest. I do it all the time, especially when dealing with money. :)

DeleteHello everyone. As a teaher with a17old experience so far I am convinced that all of the teachers should provide multiple ways of learning because of our pupils' multiple intelligences. There is no wrong or right way in Maths is the result is right. That's the magic of Maths. Although I find interesting your way, I propose an easier one 32-12= ? 32-2= 30 30-10=20 So 32-12=20 I am waiting your comments

DeleteWhat a wonderful post!!!!!! GREAT job, Ashley!!!!

ReplyDeleteSmiles - Lisa

Growing Firsties

Thanks!! :)

DeleteCould not have said it better. Well done! :) Jen

ReplyDeleteThanks, Jen! I appreciate it!

DeleteWhat's great is when the students share their strategies and another one says, "Well, you need two 10s to get to 32 so the difference is 20."

ReplyDeleteIsn't that the best?? :)

DeleteOr.... you could do math the correct, faster, more efficient way...

ReplyDeleteso you can apply the same principles to multiplication and it's far more useful:

Delete24 x 19

24 x 20 = 480

480 - 24 = 456

I find understanding algebraic relationships like that very useful, but what do I know Im just a computer scientist.

I'm not sure why you think this is incorrect. And it only seems longer because we are writing it out. Our brains work much faster. But you are certainly entitled to your opinion and me to mine.

DeleteAnother nice little articulation of approaching problems is a myth surrounding Decartes. His teacher asked him to do the sums from 1 to 100. He noticed that he could compute the result by computing 101+101 50 times. He apparently arrived at this by saying 1 and 100 = 101, 2 and 99 = 101 and so on.

DeleteThe point is that he intrinsically understood something about the nature of this function. To wit, he basically came up with:

n(n+1)/2

I sincerely believe in helping students explore the multiple ways you can arrive at a result. It will help students understand the nature of numeric algebra better.

This kind of idea sounds quite similar to the Numeracy Project that we have here in NZ. Sometimes it's frustrating and teachers get so annoyed planning it and teaching it but the kids need to be able to understand what they are doing and why. I combine both styles as I teach the higher level kids. Thanks :)

ReplyDeleteIt can absolutely be frustrating but I think it is all worth it. It's so important that they understand the WHY so they can apply their learning to other areas and problems as well. Thanks for your feedback!

DeleteThere are always more than one perspective. It is important for students to know how and to know why, but not all students will develop the most efficient strategies on their own. Direct instruction is still important to ensure students develop computational speed and accuracy. Sure addition is easier, but subtraction as the inverse operation to addition is still a more valid and important concept for students to learn.

ReplyDeleteI agree and this is why we teach students multiple ways to solve a problem. Students can find the way that works best for them. Thanks for your feedback! :)

DeleteI do agree that students need to think critically but this method seems like the "long way" and not the most efficient way to solve the problem. They should learn how to break apart 32 and 12 and understand the place value of each part of the number. Isn't there a better way for us to challenge our students to think critically? The Common Core is simply the work of Bill and Melinda Gates who seem to think they have the magic solution to what's wrong with education. I would have more respect for CC if it was developed by educators.

ReplyDeleteI think that this way is simply showing students how their brains work. This will help internalize it and they will be able to do the math in there head. Of course, if this method does not work with a student then we try other ways. That's why we teach so many different ways, so that students can find the best method that works for them. The most important thing is that they understand the WHY. Thanks for your feedback!

DeleteThis makes so much sense. I've had difficulty with tradtional subtraction for years until I learned that adding to subtract works best for me. 2nd grade would've been a cake walk and maybe algebra wouldn't have been so hard later.

ReplyDeleteLoved your post. The more choices, strategies, examples, ideas, etc. that kiddos can have at their disposal the better. I did well in math, but many times didn't know the "why". I am so happy that kiddos must really understand the why and have many ways to show it.

ReplyDeleteYes, and IF your brain can wrap itself around this easily (or better than the "traditional" way) then it is a good strategy. BUT...if not, then it is nothing but confusing. I look at these types of strategies as just that...strategies. Another way to look at numbers. In my 5th grade class I take the time to teach several strategies, including these "new" ways to think of numbers, then I tell the kids, choose a strategy that works best for you. Choose one that "your brain likes". The "new" ccss are not THE answer, they are simply "another way" of doing things. I don't think it's right, fair or even reasonable to expect EVERY student to "get it" this way. Some brains do just fine understanding things other ways. For some, this will be helpful. One more trick to pull out of our hats to help students "get it".

ReplyDeleteI agree with Holly. Yes, our brains work faster than we can work out the problem, BUT honestly, the way you solved it is slower than simply subtracting the one (tens place) from 3 (thirties place) and adding a 0! I homeschooled our children (one's a business owner, another a Christian school principal and youngest, recently out of the Marines, is working on Homeland Security degree while working part time doing security at a big company in town) successfully in math and they didn't even like math. Our one child uses business math all the time. If it's not broken, don't fix it! And now I work with after school children in a local public school after school program in which I help with their homework. So I'm seeing some of the ridiculously long math problems. Of course, Common Core is more than math teaching propaganda to our impressionable children. One example is having fourth graders pick 2 of the Bill of Rights they would like to get rid of and write their own amendment to replace it. If one is listening to our liberal congressmen and senators, they are wanting to replace the "outdated" constitution. Another example is children reading about adult situations such as pregnancies. Don't remember the details now, but this CC is the worst thing to dome down the pike for education. It's to undermine our nation's sovereignty and have our kids be exposed to adult themes that are totally inappropriate! As if we don't have enough sex crimes committed by teens as well as teen pregnancy! (There's a very sexually, perverted, explicit novel the 10 graders are to read in the curriculum.)

ReplyDeleteWhoever wrote this is clearly trying to advertise the stupidity of cc as something great while it surely is not. Whoever agrees with this is buying into this without thinking. This is indoctrination. This is dumbing down at its best. All systems work and evolve best with efficiency and simplicity. Einstein said, stupidity is infinite!

ReplyDeleteI clearly stated that this post was not for or against common core. I was only explaining the problem above and the misunderstandings that have come along with it. It is NOT common core- it's basic understanding of math. You seem to have written your comment without thinking.

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