As is often the case with educational reforms, ASCS has been very proactive and supportive in the transition to the Common Core Standards. After reading their April 2013 Education Update article “Making Mathematicians,” I spent some time on their Common Core Website. I highly recommend this website if you are just beginning your journey of understanding the vision of the Common Core standards implementation. One of the sections I read was an example lesson on formative assessment of algebra content related to a standard on the structure of algebra.

After years of focus in the classroom on standardized multiple-choice tests, one of the greatest challenges for teachers, particularly those with no other experience, will be developing methods of formative assessment of how much their students “understand” the concepts of mathematics. This goal is very different than testing if students can “do” mathematics using multiple- choice questions. I have often discussed in my trainings how helpful Thinking Maps can be as tools for formative assessment. As I studied the example lesson on the website I was visualizing brace maps, tree maps, and bridge maps.

For example:

I also remembered an experience from a long-ago conference I attended. I cannot remember who the speaker was but I distinctly remember two very important points that I adopted in my classroom.  First, provide feedback on formative assessments, rather than grades. Provide some form of feedback (indications of problems containing mistakes, leading questions, reminders of applicable rules, etc.) in pencil on student work, then hand the work back to students for corrections. Certainly we want to hold students accountable for making progress, but that is not the same thing as assigning a “grade” to a summative assessment.

The second point which was an epiphany for me and many others, numbers can be flexible. Most of my career was in a district where grades were assigned as numbers, with 70 being a passing grade.  Often when I was giving my students a quick “check-up” on relatively new material, or very difficult material, I might only give 3 to 5 problems to solve. If there are only 3 problems, missing one would normally produce a failing grade! Was that really the point I wanted to make with my students? I can remember my own daughter’s Algebra I teacher who gave a 4 question quiz on solving systems of equations, counted them 25 points each and gave NO PARTIAL CREDIT for correctly applying the processes learned if there was one arithmetic error which resulted in an incorrect solution. It’s no wonder we have killed the joy in learning mathematics in many students through practices like these.

The point the speaker made was you can assign any value you want to the problems, even when grading on a 100 point scale! For example, I began giving 4 question quizzes where each question might count 15 points or I might give 5 problems and ask them to work any three. I can assure you my students were in a rigorous environment and as a group scored very well on state tests. I believe one of the reasons was my flexibility and my efforts to support their progress in learning rather than providing punitive assessments.

As we implement the Common Core Standards and mathematics practices and push students to display deep conceptual understandings, we will need to continue to explore ways to support their learning through meaningful formative assessments which move them forward with confidence.  What are some ideas you can share for using Thinking Maps for formative assessment?