What a math classroom should look like, sound like, and feel like

During my first class of the semester last Thursday, I asked students in my Advanced Pedagogical Content Knowledge for Intermediate Mathematics course to describe their experiences as a student of mathematics.  Here are some of their comments:

I find it frustrating that these students - who are young enough to have been in my own 4th grade class - had these types of experiences in math class.  Students thought that perhaps their memories were stronger for high school math classes rather than elementary school classes.  Are these experiences listed above what we want for our high school students?

It was refreshing to hear what my students thought a math classroom should look like, sound like, and feel like.  Here are some of their thoughts:

I am looking forward to expanding on these ideas with my class this semester!

Principles to Action: Using ideas for professional development

I have been reading NCTM's Principles to Actions: Ensuring Mathematical Success for All.

 This book is a wonderful resource for educators wanting to learn more about mathematics education based on current educational research.  One of the areas emphasized is "Facilitate Meaningful Mathematical Discourse".  While the focus is on students, I have also used this idea to facilitate meaningful conversation among colleagues about our mathematics instruction.  We had 20 classroom teachers attend an early morning "Math Summit" at our building in November.  Out of the conversation, we identified retention of basic facts as a common source of frustration and a topic we wanted to explore further.

In December, we met again and sorted the standards for grades K-5 related to number sense, computation, and fluency. After discussion around the progression of learning across grade levels and observing that students should know from memory the basic facts for addition, subtraction, multiplication, and division by the end of grade 3, we read Gabriel T. Matney's article "Early Mathematics Fluency with CCSS-M".  Currently, we are discussing in an on-line forum how we might define fluency and how we use number of the day, number talks, and problem solving to build fluency.  Teachers are expanding their definition for fluency far beyond speed with recall of basic facts.  We've had great discussions!

In Principles to Actions, there is a chart that describes the actions students are taking when participating in meaningful mathematical discourse.  These include:

• Presenting and explaining ideas, reasoning, and representations to one another in pair, small-group, and whole-class discourse.
• Listening carefully to and critiquing the reasoning of peers, using examples to support or counterexamples to refute arguments.
• Seeking to understand the approaches used by peers by asking clarifying questions, trying out others' strategies, and describing the approaches used by others.
• Identifying how different approaches to solving a task are the same and how they are different.

I am excited by the energy and enthusiasm teachers bring to our conversation about fluency.  They are engaging in all of the behaviors of meaningful mathematical discourse!  Our next question for discussion is to describe an application of a number of the day, number talk, and/or problem solving that is used to connect to fluency.  I'm looking forward to the sharing of ideas!