Wednesday, July 18, 2012

Common Core State Standards for Mathematics: Engaging In & Analyzing Teaching and Learning

Life is like riding a bike. It is impossible to maintain your balance while standing still.” Linda Brakeall

If you are just joining in today…you may want to stop by my previous posts to get up to speed! :) (see here and here)

As I shared yesterday, I left the first day of training excited about this entire process! So, I’m going to continue to share the next topic we covered in training.

Engaging In & Analyzing Teaching and Learning: This session was CRAZY! Once again, we were given a problem to solve. Only this time the problem was a little more complex. Now, it wasn’t complex in the fact that it was hard to solve…no…it was complex in the fact that it dealt with number of eggs in small, medium, and large cartons. (sounds simple when I say it like that, but trust me…it wasn’t!) You really had to focus on whether or not the problem was talking about # of eggs or # of cartons AND/OR how many eggs were in an x amount of cartons. You had to be sure that you labeled everything in your solution correctly to show that you fully understood the task at hand...Haha! Makes me want to pull my hair out thinking about it! But it was such a great exercise to show how frustrating math can be for our students...

Anyhow, it was in this session that we learned how we are to start incorporating mathematical tasks in our classroom. (Tasks is another name for problems.) These tasks are higher-level problems that can be worked over a longer period of time. I will probably set up one task a week that my students will work on solving. We were given a framework to guide us in how to present this to our students. (See pic)
Mathematical Tasks Framework:

  1. Set-Up of the Task
  • Teacher introduces task to students to engage learning

  1. Private Think Time (Generate Solutions)
  • Students take time to individually think about and solve the problem (5-10 min.)
  • Teacher monitors student work (walk around)

  1. Explore Time / Small-Group Problem Solving
  • Students get into small groups to share/compare solutions.
  • Teacher monitors student discussion --> assessing and advancing student learning by asking questions to facilitate learning

  1. Share, Discuss & Analyze (Whole Group)
  • Students share, compare, focus & discuss their solutions with the entire class.
  • During discussion, students are to put ideas into their own words, add onto ideas of others, make connections between solutions, and ask questions about ideas shared.
  • Teacher continues to assess and advance student learning by asking questions to facilitate discussions.

Now, this is NOT something that is done everyday in place of the lessons we ‘normally’ teach. This is just a framework for when we implement these mathematical tasks in the classroom. These task will help students better prepare for the CRA that they will be expected to take throughout this upcoming year.

The purpose of these tasks are determine whether there is a shared understanding of teaching and learning. Can student’s take the concept that has been taught to them and apply it to everyday life? Can they show/explain how they generate solutions to a task utilizing equations, tables, tape diagrams, double number lines, words, etc.? You may be saying tape diagram…double number line?? It was something that was new to us as well…so I thought I would share examples of what these are. They make sense and are great methods to show our students as other ways to solve problems! :) (Please excuse my messy handwriting…)

The one important thing that I got from this framework is that it is STUDENT DRIVEN and TEACHER FACILITATED. I know that sounds scary to some teachers out there…allowing students to take more control... but I think it is FANTASTIC! What better way to motivate students than to let them feel in control of their own learning… 

So that’s where I’m going to leave off for today…I was going to post about Maintaining the Demands of the Tasks, but my assistant just text me to let me know my room is all finished being deep cleaned (carpet shampooed, tiles waxed, etc.) So, with that being said, I am off to begin setting up my classroom! Yippee!! SUPER excited!! :)

Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.” Archimedes


  1. I like the double number line. Thanks for sharing!

    Teach on a Limb

  2. When I took my Methods Of Teaching Math class, it was based on teaching problem solving strategies along with math. The process was very similar to this! We were supposed to use it in ALL of our lessons, though!

  3. You have really good ideas! Thanks for sharing! I'm your newest follower!

    Teaching Special Kids