I recently was invited to attend training for the new constructed response assessment for common core for 6th – 8th grade mathematics. My system has decided that the high school teachers will help the middle school teachers grade the assessments. We are doing this for two reasons. The first is to gain knowledge of what is to come in 2014 for us and the second is it takes a long time to grade them. I personally was anxious to see how my own child (a 6th grader) was going to be assessed.
I knew I would love the new common core, but I had no idea how much. As I sat and listened to a 6th grade math teacher speak about how the common core had changed her classroom, I had to hold myself back from shouting “amen” and “preach it, sister.” Each grade has two focus standards that all lessons revolve around. For sixth grade, one of them is “understand ratio concepts and use ratio reasoning to solve problems.” (How many time have you said: “If my kids could only understand fractions…”) This teacher stated that she no longer teaches her students ‘cross multiply and divide’. She said that is an algorithm or trick we teach them, but it does not lead to a deep understanding of ratios and proportional reasoning. (I was crying for joy inside!)
Common core has identified six key principles for mathematical practices. This is what the students are assessed on. The content is interwoven into the these six practices.
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
The teacher I observed had a poster on her wall for each practice. She said she constantly refers to them when working on problems with her students. As we began to grade the sample assessments, it was obvious that the eight mathematical practices were vital to earn a successful score on the assessment. I loved that the students did not have to work the problem using on method, however, they did have to show their work and reasoning. As a grader, you could not assume anything. If a student did not show how he or she arrived at an answer, they did not receive credit for several of the categories above. If it was necessary to perform a process more than once, like finding the slope of a line, the student would have to calculate the slope using the same method each time, while showing their work, to receive credit for the repeated reasoning practice.
Overall the grading of the assessments reminded me of the Advanced Placement Calculus training I went through and how that test is graded. Students have to justify arguments and show their work. Answers are no longer enough and your method for finding the answer must be mathematically sound. The sixth grade teacher told us that she spend a class period with her students looking over the sample tests and the scoring rubrics and discussing why some students didn’t receive full credit. One of the benefits for students was that they discovered they could work the same problem using different methods and still receive full credit as long as they showed and explained their work.
I would strongly encourage you to contact your state to gain access to any practice assessments and grading rubrics released. In TN, the items are password protected or I would share them. (I like my job and want to keep it 🙂 I plan on encouraging our Algebra 1 teachers to begin implementing the 8th grade assessments we have access to online. Overall, I learned a lot from the training and I have high hopes for the future math students. It will take a few years to see the results, but I believe mathematics education is finally moving in the right direction in the United States.