Helping Students Talk about Strategies

Students sometimes have difficulty sharing their thinking about strategies.  Others struggle to see similarities and differences in computation methods.  The discussions that we have with students in our classrooms are important in helping them build further understanding.  To help students see the ways in which different methods of multiplication are similar and different, I made posters for each method and posted them around the classroom.  Students were then asked to stand by the method they would use to solve the problem.  The group standing by their strategy had the task of explaining how it worked to the rest of the class.  I then asked the class to stand by a different poster - but one that they felt was most similar to the way they chose to solve the problem the first time.  Students had to explain their choice and how the two methods were similar.

Another idea for this instructional strategy would be to have students stand by a method they do not understand.  Other students in the class could act ask experts to help explain the method.  Recording student ideas on a chart would be beneficial so that students could later refer to their ideas.  The ideas that students share during the class discussion also provides the teacher with important feedback about student understanding and potential misconceptions.

The posters we used are shown below with the partial products method for multiplication, the traditional method, and methods students had invented during class.  There was also a poster for students who might have used a strategy that was not posted.  Similar posters could be made for addition strategies, subtraction strategies, division strategies, and many other mathematical concepts!

How would you use this idea?

Navigating away from "mile wide and inch deep"

The analogy of math curricula as a river has been used frequently, with  the familiar "mile wide and inch deep" used often.  It is a compact way to describe a set of standards that tried to "cover" many different topics and left many students struggling to master math concepts.

With the Common Core, what is the alternative analogy?  Someone recently asked, "Is the curricula now an inch wide and a mile deep?"  That does not seem like an appropriate way to describe the Common Core.  I'm sure that many analogies will emerge as people become more familiar with the Common Core.

The big idea of the Common Core is to help students develop those important mathematical practices.  Children are naturally curious and wonder about many things.  We want to nurture this curiosity but all too often in mathematics students are taught a "rule" without understanding why it works.  The Common Core is going to push ALL of us to further consider the WHY things work.

For example, my son is in second grade.  Recently he came home from school and was proud that he could identify any number as either even or odd.  After giving him a couple of numbers to identify, I asked him whether he knew why 43, for example, was odd.  He recited the rule about the ones place having a 3 so it was odd.  We then had a discussion about why the ones place was important.  Any number that is a multiple of 10, 100 and so on will always be even because it can be grouped in pairs.  So if you think of 43 as 40 + 3 then you know there will be 20 pairs in the 40 and that there can only be one pair made from the 3 with one remaining.  We looked at several other numbers to test this theory and my son talked about what he noticed in the relationships of the numbers.

THIS is what we can do as educators to help implement the Common Core.  Think about WHY the rules in mathematics work.  If you aren't sure yourself, don't be afraid to ask your students.  They are curious by nature and will enjoy working alongside you to notice patterns and relationships in mathematics.

Standards for Mathematical Practices

When the National Council of Teachers of Mathematics (NCTM) developed the Principles and Standards for School Mathematics in 2000, it was with an intention that mathematics instruction would emphasize both content and process.  Within the document, NCTM describes five content standards (number and operations, algebra, geometry, measurement, and data analysis/probability) and five process standards (problem solving, reasoning/proof, communication, connections, and representation).  Many times the process standards were overlooked.

In the development of the Common Core State Standards, there has been a more intentional focus on the Standards for Mathematical Practices.  While content standards provide a "what" we teach in mathematics, the mathematical practices provide the "how" we do it.

I attended several wonderful sessions at the recent annual conference held by the Ohio Council of Teachers of Mathematics in Columbus.  I am attaching one of the many useful ideas I found - ideas for what those mathematical practices look like in the classroom.  A word of caution - this is not an all-inclusive list!  I do not see this as a checklist of "must-dos" but rather a tool to help you reflect on your own teaching.  Do these phrases describe your classroom?  If so, where are they strongest?  Where might you place a different emphasis?  How can these practices help you differentiate instruction?  It might be useful in planning lessons to be sure that you are addressing a variety of the practices.

Happy teaching!  :-)

Standards for Mathematical Practices

Welcome to Implementing CCSS-M in Central Ohio!

I dropped the "Planning" part of the title since many of us are moving into full implementation of the Common Core.  Please use this area to share questions, ideas, and resources!