Common Core Math now and University later

[Tammi K]

A recent conversation with someone about the implementation of Common Core had me commenting that I was glad I was home-schooling as I'm free of the need to confuse my mathematical son with convoluted gibberish instead of actual instruction in the simple algorithms of mathematics.  

 

But, then I got to thinking about the new vocabulary that accompanies the Common Core math: friendly numbers, number bonds, etc  and the reliance on pictorial representation to solve problems instead of employing standard algorithms  and I got to wondering what happens to children NOT taught this way when they reach collegiate level.

 

Of course, this isn't a problem now because there standards and methods of implementation are just starting to be implemented. But, what will happen to, for instance, a third grader who continues to be taught at home by an 'old school' parent when he reaches college age along with the students taught in the Common Core manner.  

 

Do those of you who teach at a university level think that it will impact the way higher level math is taught?  I like to think that higher math is immune from the effects of poor lower level methodology and that pure math will always be pure math. But, I wonder.  Any thoughts?

[regentrude]

I do not think it will have any bearing on the way higher math is taught.

The only thing that matters is whether a student understands the concepts - it does not matter how this is achieved or what terminology is used (it is easy to learn different words for things, since the underlying concepts do not change). For what it's worth, following any standard algorithm without understanding will be useless in higher math. If the pictorial representations and other tools help to develop conceptual understanding, they can be a good thing. It is all a matter of implementation. I have not seen anything that indicates Common Core aligned curricula would NOT teach standard algorithms as well (which your post seems to claim.)

 

One possible problem could be that math education gets even poorer (because teachers are not qualified) and thus college courses have to be dumbed down further because students are even less prepared. This remains to be seen.

[Word Nerd]

Why do you assume the standard algorithms won't also be taught?

[Tammi K]

I do not think it will have any bearing on the way higher math is taught.

The only thing that matters is whether a student understands the concepts - it does not matter how this is achieved or what terminology is used (it is easy to learn different words for things, since the underlying concepts do not change). For what it's worth, following any standard algorithm without understanding will be useless in higher math.

The only possible problem could be that math education gets even poorer and thus college courses have to be dumbed down further because students are even less prepared. This remains to be seen.

 

I was hoping you would reply!  Good point about standard algorithms needing to be understood. The most common complaint I hear about common core is the pictorial representation of every problem. Of course, that has a place in instruction, right after concrete manipulation of object to develop a concept. I truly don't know enough about common core to know if/when the transition to standard algorithms is taught.   I suppose I envision college professors trying to draw 3d representations of the area under a curve and needing four chalkboards to do it.

 

[NASDAQ]

By the time the current Common Core five-year-olds go to university, Common Core will be several fads past already.

[Lang Syne Boardie]

By the time the current Common Core five-year-olds go to university, Common Core will be several fads past already.

Agreed. We will be up to OBE version 12.0 by then.

[regentrude]

I was hoping you would reply!  Good point about standard algorithms needing to be understood. The most common complaint I hear about common core is the pictorial representation of every problem. Of course, that has a place in instruction, right after concrete manipulation of object to develop a concept. I truly don't know enough about common core to know if/when the transition to standard algorithms is taught.   I suppose I envision college professors trying to draw 3d representations of the area under a curve and needing four chalkboards to do it.

 

 

Actually, pictorial representations are extremely important and will be incorporated in college courses. I require that my physics students draw a complete diagram for every problem they are solving. Any physics researcher begins with a sketch when he starts thinking about a new problem. It is the most important tool for visualizing and understanding.

 

I would surely hope that any college math instructor models drawing a graph and sketch for every problem before solving, and would require this from the students. Most students will be able to manipulate their integrals for example through memorization of the algorithm for finding the antiderivatives, yet they will be unable to apply this to concrete problems because they do not understand what it means that they do. Having to sketch that area in a suitable manner would be something I would mandate.

 

ETA: The problem comes when the pictorial representation is required when it is no longer sensible and becomes busy work. Forcing a child to draw out every addition or multiplication problem once the concept has been internalized and understood is overkill. But as long as the student is still thinking about a problem, pictures are immensely valuable. As I said, it is in the implementation.  A good teacher will know exactly how long to require which kind of visualization.

[Tammi K]

  A good teacher will know exactly how long to require which kind of visualization.

 

Absolutely! And that is where my understanding of common core is lacking.

 

The majority of the negatives I hear are based on the extended use of pictorial rep. at the expense of standard algorithms.   I was wondering how the long term use of pictorial reps would impact the instruction of upper level math.

 

[Dana]

Absolutely! And that is where my understanding of common core is lacking.

 

The majority of the negatives I hear are based on the extended use of pictorial rep. at the expense of standard algorithms. I was wondering how the long term use of pictorial reps would impact the instruction of upper level math.

 

I'd expect we'd just have more grad students from other countries instead of from the US.

 

I see that as an issue with how poorly prepared many teachers are at the K12 level...especially in math. It's been that way for years, unfortunately. Common core isn't going to make a change in that.

[ChristyB in TN]

I just wonder what convoluted methods are being used. I keep hearing this, but except for a brief explanation on NPR the other morning (which didn't sound convoluted to me) I just don't know the details.

I heard the same story and thought the same thing. My parents are really upset about common core and are angry with me for not being upset. It sort of reminds me of the 'new math' in the 70's and I thnk I remember similar reactions. The math I've seen makes sense it's just presented differently. I think it isn't an issue for me because I'm not political at all and listen to npr instead of watching cable news. It really seems like folks are less likely to adjust if they don't like the current administration?

I can't believe I'm writing this. I accept all explosions coming my way.

[ChristyB in TN]

It reminds me of the Singapore/Saxon wars, too. :) super fun stuff!

[mom2scouts]

My neighbor is a University math professor and I can't even imagine him changing the way he teaches his college courses because of Common Core.  He expects his students to have a grasp of the concepts and be able to use traditional algorithms to solve problems.

 

I'm not a fan of CC and it's mainly because the *implementation* of it is truly horrible in some places. (There's lots of other political things about it that bother me too, but we can save that for another discussion.)  The things teachers have been telling me about how it's being implemented in their schools are ridiculous.  In our local schools, even the teachers and parents don't really understand the methods of teaching math and the children are so confused.  All of the methods aren't bad, but they never seem to get far enough to teach traditional algorithms.

[Crimson Wife]

I just wonder what convoluted methods are being used.  I keep hearing this, but except for a brief explanation on NPR the other morning (which didn't sound convoluted to me) I just don't know the details.

 

Think wannabe Singapore/MiF but twisted into an incomprehensible mess by some poor B.Ed. who doesn't understand the underlying concepts.