Tuesday, July 17, 2012

Common Core State Standards for Mathematics: Introduction & Performance-Based Assessments (PBAs)

Last week, I attended training on Common Core State Standard for Mathematics (CCSSM). As I stated in my preview post last week (see here), a large group of 3rd-8th grade teachers gathered to be trained on how to implement these new standards. We were split up by grade levels the majority of the time so we could focus in-depth on our specific focus standards. Since I teach 6th grade, I am going to be posting what I learned during my training with my fellow 6th grade teachers.

But before I get into all that, I wanted to share a quote that one of the head trainers shared that really stuck with me because it is so utterly true…

“You see what you look for…”

This applies to all aspects of life… When you are car shopping, you see the exact car you are looking for everywhere; pregnant women can easily spot other pregnant women, etc. This quote is especially true when it comes to teaching. If you look for the negative in your students that is all you will see. But, if you look for the positive in your students that is what you will see. The same goes for these new Common Core State Standards…if you look for the negative…that is all you will see. Teaching these new standards will be so much easier if everyone looks for the positive and sees the potential impact it can have on our students. With that said…Let’s get started!


As I stated last week, we all received a LOVELY book filled with lots of good information for our training. From this book, it is clear that the entire training was focused on a specific goal: Supporting RIGOROUS Mathematics Teaching and Learning. In order to reach this goal, there were 5 topics to cover:
  1. Performance-Based Assessment (PBA)
  2. Engaging In and Analyzing Teaching and Learning
  3. Enacting Instructional Tasks: Maintaining the Demands of the Tasks
  4. Analyzing the Demand of Instructional Tasks
  5. Illuminating Student Thinking: Assessing & Advancing Questions
Now, I don’t want to bore y’all to death by posting about all of these in one day…So, I am going to be writing about one or two of these topics over the next few days.


Introducing the CCSSM: Instead of throwing us into the entire ocean of CCSSM and seeing if we float or drown…the state has chosen specific standards out of the bunch for us to focus this year. Here are the TWO focus standards for 6th grade this year:
  1. Understand ratio concepts & use ratio reasoning to solve problems.
  2. Apply & extend previous understandings of arithmetic to algebraic expressions.
Starting this year, students will be expected to complete a Constructed Response Assessment (CRA) for Mathematics. The CRA will be given three times throughout the year (Oct., Feb., & May) and will focus only on the two focus standards. One of the good things about the CRA is that these test have no bearing on teacher evaluation yet…(Phew!) They are giving us 2 years to prepare and practice for the Partnership for Assessment of Readiness for College and Careers (PARCC) test that will be administered during the 2014 – 2015 school year. I personally think that two years is a good amount of time for us to get in the rhythm of teaching these new standards and to feel better prepared for when the PARCC is administered. I’m ready to Rock & Roll!! :)


Performance-Based Assessments (PBAs): During this first session, we were given problems to solve throughout the entire afternoon. Each problem they gave to us followed a certain framework that we will utilize when engaging our students in mathematical tasks. (I will divulge all the specifics on this framework tomorrow when I cover Engaging In and Analyzing Teaching and Learning) When given a problem, we first took time individually to solve the problems. Then we shared our answers/methods at our table and chose one of our methods to write on a large sheet of paper to share with the entire class. The entire class then discussed each method shared to decide if the person solving the problem clearly understood the concept at hand. It was seriously AMAZING to see how many different methods were used to solve one simple problem. I mean…seriously! One person drew an x & y axis chart, another created a table, others created an equations that were different from each other, but still reached the same conclusion. How COOL is that?! From this, it was immediately apparent to me how beneficial this structure would be to students.

One of the goals of this session was to deepen our understanding of the CCSS for mathematical practices and content. So, after we solved each problem, we would have to identify which of our focus standards and sub-standards were covered in the problem. We also had to identify which mathematical practices were covered as well. Through this process, we were able to understand how PBAs assess the CCSS for both content and practices.

The thing that I learned the most from this session was that it is clear that the PBAs will assess student conceptual understanding. With PBAs, students will no longer be given simple, low level problems that can be solved using calculators (punching numbers into a calculator does not show conceptual understanding). They will no longer be answering in multiple choice formatting. Students NEED to understand the overall concept of a problem and be able to explain/show how they arrived to their solution. For example, a word problem may be given with an answer that the student needs to agree or disagree with and explain/show why they agree or disagree. In this case, a calculator does nothing to help show the students overall conceptual understanding. There is no equation for them to punch in a calculator to generate an answer. They have to create their own method of solving the problem, whether it is creating an equation, table, tape diagram, double number line, etc., to show their conceptual understanding. HIGHER level of RIGOR!! I feel that this is so important for our students…and after the first day of training…I was pumped about the CCSSM (and still am)! :)


Well…that concludes my thoughts for the day. Hope I didn’t ramble on too much and that you can kind of get an idea of what the training was all about and where it is headed.

An interesting fact about the CCSSM in Tennessee is that the ENTIRE state is implementing the same focus standards in their grade levels this year. I know that in some other states, it is varies by districts. I’m curious at what y’all have been doing in other states to prepare for the CCSS. Have you had to attend training as well? What was it like for you?

Since I started with a quote, I'll end with a quote...

"Do not worry about your problems with mathematics, I assure you mine are far greater."  Albert Einstein

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