Mathematical Practices and Mathematics Common Ground

Finding common ground when talking about the new Common Core standards for math has not been easy.  The ODE is still in the process of completing the Content Elaborations for the Ohio Math Standards. PARCC has released their own suggested framework. Teachers are trying to come to terms with a shift to teaching more about less, especially in the elementary grades.  Traditional math programs, existing integrated math programs and secondary course offerings don't neatly align to the new content. There are significant shifts in content from one grade level to another.  Textbook publishers are playing catch up to the new curriculum.

Eight.  No, it is not my lucky number or how many pieces of chocolate I ate as I sat down to plan for my upcoming math team meetings. (that was only 3)  Eight is the number of mathematical practices that serve as a single thread across all grade and ability levels.  Eight is the common ground.  The Mathematical Practices don't describe what math facts a student should know or the order that they should acquire knowledge of geometric concepts.  The 8 Mathematical Practices define how a student should be able to act and think as a mathematician, whether they are doing basic addition or Calculus BC.  These are not just good mathematical skills, in many cases they are good for science, social studies and language arts thinking as well.  As teachers sit down together to work on creating lessons that will begin to transition their math curriculum to the new Common Core model curriculum, they need to start on common ground, framing each lesson within the concepts of the 8 mathematical practices.

The 8 Mathematical Practices 

1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning

Learn more about the 8 Mathematical Practices
Resources

• Engage NY - Instructional Shifts for Common Core Math
• Carroll County Public Schools - Mathematical Practices Resources Mini posters - 8 mathematical Practices, template for evaluating lessons based on mathematical practices, lesson plan template.
• Inside Mathematics  Good explanations of mathematical practices with example lesson videos. (various grade levels spans elementary, middle and high school)
• Mathematics Assessment Project ( University of California Berkeley)  example lessons for each mathematical practice (MS and HS)  The  MAP also has formative assessment lessons for HS and MS math.  Also great are the performance tasks, aligned to the 8 mathematical practices, written for experts, novice and beginner level students that can be used for summative assessment http://map.mathshell.org/materials/tasks.php   Finally, professional development articles and activities http://map.mathshell.org/materials/pd.php including handouts, examples, videos and interactives.
• Teaching Number Sense - how number sense is similar to phonemic awareness. ( Reading Rockets.org)
• Thinkmath.org  K-5 version of the 8 Mathematical Practices
• Chittenden East Supervisory Union - good summaries and discussions of the 8 mathematical practices.
• Teaching Problem Solving Skills  (Waterloo University Centre for Teaching Excellence)
• Understanding the 8 Mathematical Practices   a K-4 Progression created by Mesa Public Schools