I know, I know. This Slice of Life Challenge is all about writing. We’re supposed to be writing stories and poems about things that we have seen or experienced in recent days. Well, the experience that I am about to write about did happen this past week and has me extremely excited. Also, the math nerd had to come out of me at some point.
So, are the Common Core Math Standards really that terrible?
No, no they are not. In fact, they are actually pretty great.
Many parents, teachers, administrators, and school districts have been all up in arms about these new standards, but I really don’t understand why. Maybe they don’t really understand what they are all about. When they first came out, the writers claimed that they were clearer – more easily understood so that anyone who plays any part in education would know exactly what the students should be learning.
I have to be honest and say that they really are not clearer. I think that a bunch of brilliant mathematicians got together and wrote these things, not understanding that everyone has not seen or understood math the way they have. It even took a lot of decoding on the part of me and my two math coach colleagues to fully understand what they were asking of us – and we are “math people.”
But once you understand what they are asking and you get down to the nitty gritty of teaching and using some of the “new” strategies, I promise you are going to see some amazing things from your students.
I’m going to talk a little bit about fractions – a skill that most teachers dread teaching.
Why do they dread it?
They dread it because students usually don’t understand them and hate learning about them.
Why don’t students understand them?
They don’t understand because in the past they were only taught the process of adding, subtracting, multiplying and dividing them. They were shown the algorithms and expected to just remember how to do them, without attaching any sort of meaning to it.
Take, for example, multiplying two fractions together.
3/4 x 6/10 = 18/40 = 9/20
Many of us were taught to just multiply the numerators together, multiply the denominators together, get an answer, and simplify if needed.
Simple enough, right? Most students can do this if shown the steps. But do they really know what happened here?
I think back to when I used teach fractions in this manner. Students would come up with the correct solutions but a few things happened:
- They could do the problem when we were working on the unit and taking the test, but if given the problem later, they couldn’t. They would forget the steps to multiplying because they didn’t really understand what was happening when they multiplied two fractions together.
- They didn’t know that 9/20 was smaller than 6/10. They saw two bigger numerals and just assumed that they ended up with a larger number.
- They thought they ended up with a larger number because they were taught from 3rd grade and up that multiplying numbers led to larger numbers.
- They didn’t realize that when they multiplied the two fractions, they were actually taking part of a part, which in turn would leave them with less than what they began with.
A big part of the CCSS for math relies on the use of concrete materials or models to help students see what is happening. They must also have a strong math vocabulary to go along with these models. Having this as a base will allow them to think more abstractly about the numbers – or understand them when only seeing numbers.
Let’s go back to the problem above. 3/4 x 6/10
If the students understand that the symbol “x” means “of” in this problem, they will know that they are finding part of 6/10, specifically 3/4 of it.
Having them create a model will give them a visual to go along with this.
This model shows us 6/10. We can clearly see that we don’t have a whole object, but just some of the object.
Now, if I want to take 3/4 of it, I would have to cut the model into fourths and shade only three of those fourths. But, I only shade three of the six – or the part – that I originally had.
This leaves the students understanding where they got the 18/40, understanding that they took a part of part, and SEEING why they end up with less than what they began with. If they also have an understanding of simplifying fractions, they will know that 9/20 is equivalent to, or the same amount as, 18/40.
An additional part of the standards rely on the students using their prior knowledge to see some sort of pattern and solve problems on their own – without the teacher just telling or showing them what to do.
I’m currently working with a 5th grade class that already has an understanding of what the “x” symbol means when it comes to fractions, what regular and improper fractions are, how to draw models for a fraction times a fraction, and how to use the algorithm of just multiplying across.
The other day, the classroom teacher and I posed a problem to them that builds on their schema of fractions.
We first asked them if they could draw 6/5. We did not show them, we had them explore and try on their own. With their understanding that an improper fraction is at least one whole and possibly some left over pieces, they ALL were able to do so without our help.
Next we asked them to show us 3/4 of it. Again, they were able to break it up to find the part they were looking for.
As you can see, the only issue that most of the students had was coming up with the correct denominator. Most of them thought it was 40 because the two whole objects were broken up into 40 pieces total, which is really not an unreasonable mistake. (Although I must include here, that since they do know the standard algorithm for multiplying fractions, some of them did think there was something “not right” about their answer being 18/40 – something they would have just passed right over in the past.) This showed us as teachers that although the students had a ton of fraction knowledge, their understanding of what a denominator actually is was a bit off. We were able to tailor our conversation according to that. Once we discussed the true definition of the denominator being the total number of pieces it takes to make one whole and not just the total number of pieces there are, they understood their mistake.
The point I am trying to make is that although the Common Core Standards may seem to be a bit wordy and hard to understand at times, they are actually helping our students to understand the math more. These kids are not just memorizing the process of how to do something and then forgetting that process later. They are actually seeing what is happening, knowing where the process comes from, and using that knowledge to solve problems (on their own) that build off of it – not just waiting for us to give them the solutions.
Now I think that is pretty darn awesome!
My thoughts about PARCC on the other hand…well, that’s another long story for a different slice. 😉