Tuesday, February 19, 2013

Concepts vs. Procedures - Go Common Core!

I live in South Carolina and we will begin teaching math with Common Core next year. I know some of you have already started, and for some of you it is further in the distance. I have started taking a much deeper look at Common Core math lately, in order to prepare more for next year. I feel like I have a lot more preparing to do, but I am really excited about it actually! During a meeting I went to recently we discussed a book, that some of you may be familiar with, titled Adding It Up: Helping Children Learn Mathematics. This book really put things into perspective for me. I teach math all day, every day, so ‘getting it right’ is really important to me! I am sure all of you, self-contained or departmentalized, feel the same way.

I was NOT asked to write a review for this book. I was shown a few copies of pages from this book at a meeting recently, as I mentioned above, and I fell in LOVE with its message and the way in which it was written.

The section I am focusing on today is Chapter 4 (page 137)

“Adding It Up” divides proficiency into different categories:
1. Conceptual understanding: understanding of math 
concepts, operations, and relations.
2. Procedural fluency: skill in carrying out procedures 
flexibly, accurately, efficiently, and appropriately.
3. Strategic competence: ability to formulate, represent, 
and solve math problems.
4. Adaptive reasoning: capacity for logical thought, 
reflection, and justification.
5.  Productive disposition: routine inclination to see math as 
sensible, useful, and worthwhile, AND the belief in 
your own thoroughness and effectiveness.

One major thing that I really love about this article is that it puts a lot of the difficult to understand ideas into very simple examples. Finally! This is what I have needed regarding Common Core all along! For some reason, Common Core Standards are written in such a difficult to understand way that I have trouble finding the content and meaning in between all of the “words”. This book does not focus on specific standards, but it really helped me to see HOW I should be teaching math, and on what skills I should be focusing on with my students.

One of my favorite examples it gives is in the early part of the article when it describes that all children begin understanding numbers from a much earlier age than we think they begin…for example, a child may see that her sister received more candles than she received. I just love this example because it is SO true! I never really thought about that being an early phase a number sense (maybe because I teach 10 and 11 year olds!) but it is a really cool way to look at math for a young child.

So, back to what I mentioned above about the 5 different strands of learning in math…I really want to focus mostly on conceptual understanding and procedural understanding. Conceptual understanding, as stated in Adding It Up, “refers to an integrated and functional grasp of mathematical ideas.” Students with conceptual understanding are those students who understand WHY they are doing what they are doing in math…not the students that just follow the steps they learned from their teacher. These “step following” students are those with the procedural understanding. Going “Common Core”, we all know that we want to start leaning more toward the conceptual side of the scale. What is so great about the conceptual side is that once the students understand WHY you do something a certain way in Math, the procedures will come almost naturally!

Conceptual understanding, as discussed in the book, supports:
-The ability to learn new ideas by connecting to prior knowledge
-A student’s self-assessment after a problem is complete (i.e. Does that answer look right?)
-The ability of a student to represent a mathematical situation in many different ways.
-Making connections
…and obviously so much more!

Of course, the procedural understanding is important. This is how we solve problems and find answers. However, it is really important that student understands WHY they are doing something…not just going through the steps to get an answer….

I mean…that is SO last year…

If you want to read this yourself, you can purchase the book online OR you can click the link below to download it for FREE!! Just look to the left of the screen once you open the page below. It will have a spot where you can click to view the PDF version – you will need to sign in, but it allows you to just sign in as a guest!

Click here to download a free PDF of “Adding It Up”:

Happy reading! I really hope you all get something out of this great book like I did! If you do happen to read any part of this book, or if you already have read some of it, please comment and let me know if there is a part you feel is important for all of us to see! I would love to know!

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