Thinking Mathematically

Our Classroom Poster of the 8 Mathematical Practices!

Last spring I had the chance to gain a different perspective of our classroom, seeing it in action, not as the teacher who needs to make sure that engagement is high and problems are appropriately challenging, but as an outside observer. What I noticed amazed me and had me thinking and reflecting on what THINKING MATHEMATICALLY means in the new day and age of the CCSS.

As luck would have it, the ASCD Education Update for April arrived in my mailbox soon after and had me thinking even more about how our pedagogy has shifted thanks to the demands of the CCSS. The opening article was titled Making Mathematicians, about the types of shifts in thinking that are required to effectively implement the common core in math. As article author Laura Varlas stated, "The math standards represent a shift from the focus on skills and procedures of the past decade toward a conceptual understanding of mathematics, balancing practices with content and asking students to explain mathematical reasoning."

To get our students thinking about the importance of the mathematical practices, Celina infused theatre and movement to help our students connect and remember what each practice means. Our students now proudly throw their hands in the air and say, "Persevere", and work their way through Reason, What's the Evidence?, Connect and Reflect, What Resources?, Wipe it Out/No More/Back it Up, One Big Whole Break It Up! and Details. The ownership of creating a set of movements we could work with as well as the continued return to these Mathematical Practices for self-assessment and goal setting has truly transformed the way our students think about and DO math.

So what evidence did I observe? Students were persevering through a multi-step "Problem of the Week" about compounding deposits, discussing with partners and using rich math language with ease. These POW's challenged and incorporated many operations that could be considered beyond their grade level, yet they were actively engaged, using evidence and reasoning in their commentary with their math partners. Students sought out calculators when they needed them, and checked their work through a different strategy.

This only highlighted in my mind the ways in which the CCSS demand that math is approached differently. Students must build a strong conceptual understanding through building models, recognizing part-whole relationships, decomposing numbers, looking for patterns, estimating, strategizing, looking for examples and non-examples, solving problems and learning math vocabulary through rich contexts, as well as analyzing attributes and making connections.

Thanks to our work with the CCSS, problems have become puzzles to ponder and attack, rather than something that requires the use of one rote process. Our classroom norms have now enveloped the idea of students routinely explaining their thinking and processing as a fundamental part of what they do. As Steven Lienwand states in the foreword of Math Misconceptions (Bamberger, Oberdorf, Shultz-Ferrell 2010) "mistakes and confusion are powerful learning opportunities".  Each discussion highlights reasoning and application as opposed to discreet procedures or skills.

Many people might skip right past these practices but as stated in Putting the Practices Into Action (O'Connell, SanGiovanni 2013)they actually "highlight the level to which math content must be known, focusing on the application, reasoning, communication and representation of the content -- they are actually the heart and soul of the Common Core State Standards." (pg. xi)

Let the reflection continue! ~Ann