Monday, July 30, 2012

Mathematical Mindset: Embedding the Standards for Mathematical Practice into the Elementary School Classroom

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I'm intrigued by the Standards for Mathematical Practice outlined in the Common Core State Standards Initiative because I believe the standards prepare students for facile, deep and meaningful thinking related to mathematics and information in general.  I've been waiting all summer long for my colleague's interpretation of the 8 standards noted above.  I could wait no longer, and as I prepare my classroom design and content outline for the year ahead, I knew I had to plan for these optimal thinking/working strategies.

Below I've created an initial draft as to how I will teach and embed the Standards for Mathematical Practice into my year's initial work with students and throughout the year.  I welcome your ideas and feedback as I'm at the starting point with regard to this endeavor and I have plenty of time to revise and enrich this initial plan. Thanks in advance for your consult.

1. Make sense of problems and persevere in solving them.
We'll begin the year by talking about problems, and that the first step to solving any problem is understanding what the problem is.  We'll define "problem," identify problems (in math and other areas), and then discuss the hard work and stick-to-it-ness it takes to be a successful problem solver.  Then throughout the year we'll solve math problems starting with identifying what the problem is, creating a process for solution, estimating the time it will take to solve the problem and persevering to solve the problems mainly in a collaborative effort.

2. Reason abstractly and quantitatively.
Whenever possible we'll use charts, diagrams and tables to turn our problems into equations with numbers and variables.  We'll look carefully at the relationships and patterns inherent in our problem, and chart those using mathematical expressions and numbers.  

3. Construct viable arguments and critique the reasoning of others.
Now this is a challenging standard since it requires careful listening and apt communication in our hurried, busy 21st century learning environment.  Hence we'll start the year with a meaningful, complex problem that's near and dear to all: classroom rules and logical consequences for off-task behavior.  We'll work together to understand the problem.  Students will create viable arguments and critique the reasoning of others as we come up with optimal protocols for logical consequences for off-task behavior and classroom rules. We'll use this as a stepping stone and practice for the methods for sharing our mathematical thinking and problem solving throughout the year.

4. Model with Mathematics
We'll talk about models in general.  What is a model?  When do you use one?  Where do you see models?  What are the advantages of using models?  How and why does a mathematician use a  model. Then as we begin our "Fact Smart" unit we'll make mathematical models for numbers using Google docs and other venues to show the many arrays possible for a variety of numbers.  Similarly throughout the year we'll use a lot of technology and other venues to make models of all the mathematical principles we are learning about and exploring.

5. Use Appropriate Tools Strategically.
I am glad that I am reading this before I set up my classroom. I had already planned a learning tool-kit center, but now I'll create that center with more gusto.  I want to put the tools (mathematical and others) in good storage units labeled with the specific, correct titles.  I also want our virtual and expression/symbol tools and key vocabulary (math word wall) to be noted correctly on the bulletin board above the learning tool kit center.  I will make special effort to introduce this area of the room to students in a thoughtful way at the start of the year.  Then when we're solving problems, I'll make sure to ask up front, 'What tools should we use to solve this problem?"

6. Attend to Precision
I always like to tell students aout the library design project when an architect forgot to account for the weight of the books--an error of precision.  We'll talk about when precision is very important, and when it's not so important.  We'll build in some real-world, meaningful math problems at the start of the year to focus on how we check for precision.  We'll create a list of possible precision check-in activities to help one make sure that their answer and/or process is accurate.  I'll also mention more stories about precision during the year including medical, construction and cooking stories where lack of precision made a significant difference.

7. Make Use of Structure
As mathematicians and learners in general, we'll become astute observers of the world around us and the mathematical problems before us.  We'll notice size, shape, order, patterns, repetition, commonalities and differences.  Our observations will help us to make accurate predictions and choose optimal processes.  We'll slow down enough and take the time to notice, discuss, chart and make predictions related to structure.

8. Look for and Express Regularity in Repeated Reasoning
We will discuss the way we solve equations, and we will look for more varied and efficient ways to express and solve number sentences and problems.  We'll chart, write about and share our discoveries with classmates near and far, online and off. 

Sample Fourth Grade Problems