If you were asked to examine your practice, what would you keep, what would you toss, and what would you invent or re-imagine? In so many words our math department has been asked to do just that.

Adaptive challenges are difficult because their solutions require people to change their ways. Unlike known or routine problem solving for which past ways of thinking, relating, and operating are sufficient for achieving good outcomes, adaptive work demands three very tough human tasks: figuring out what to conserve from past practices, figuring out what to discard from past practices, and inventing new ways that build from the best of the past.–Adaptive Leadership

We’re deep in the muck trying to figure out how to raise student achievement and move students forward. We’re an upper middle class suburban district and our kids should be doing better. MAP is our yardstick. Like it or not that is the tool we use to measure growth.

Regardless of the yardstick, how do we move students forward? How committed are we to ensuring that student learning is maximized? We’re not super heroes, but what does it take (without killing the love of learning via excessive testing) to make sure students learn?

I’d like to limit the conversation to instructional decisions that are within our control. Besides a viable curriculum and the art of reteaching and reassessing, what else do you do? How do you differentiate for the capable student, but who is not ready to be placed in a higher track? Do you enrich or accelerate, and how?

I wrestle with these ideas as well as how to incorporate spaced vs. massed practice so the concept has a better chance of getting into long term memory.

What are the high leverage moves you’d recommend? I’m all ears.

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One of the most positive take-aways I have from your post is that your PLC acknowledges that there are things that you have been doing well. I am all for improving our practice. In fact, I think it is at the heart of what we do. But having been in the classroom for 27 years I have seen many “Greatest New Things” go by the wayside. Through the years some things have stuck around and gotten better and better. For me a good example of this is how the NCTM process standards were fleshed out and defined and how the Math Practices of the Common Core are in part based on those process standards.

I guess the “high leverage move” that has made the most difference for me has been to teach students how to be advocates for their own education. I think as a sixth grade math teacher it is a perfect time to explicitly teach students to recognize when they don’t understand something and to SPEAK up about it. The more students are given the opportunity to analyze their own work and figure out what they don’t know the better they become at learning.

A few years ago I attended a workshop by Carl Anderson the writing guru. He said something that has really stuck with me. Is your goal to make better writing or better writers. He said that if you were trying to make better writers you should do writing conferences with your students. He said that the hours and hours that teachers spend “correcting” papers does not help the students become better writers. I think there is a direct transfer to math. I have found that it is very powerful to sit with a student and assess their work. When I co-grade an assignment with a students, I don’t have to wonder what they were thinking. They are right there and sometimes they can tell me what they were thinking. Frankly, sometimes they don’t even know 🙂

The next step is to show the student an exemplar of a proficient paper and help them edit their own paper to a proficient level. We know that learning math is hard work, but we have to SHOW students what “hard work” looks like. I’m looking forward to reading what others are sharing – great discussion starter!

Diana, you offer some excellent suggestions. I am particularly interested in your idea of a math workshop. You didn’t exactly state it per se but but your description of conferencing with students reminds me of that and it is very timely. I had been talking with our reading specialist and she suggested I start a book study. I ended up purchasing Minds on Mathematics.

I routinely co-grade as a class, but the individual conferencing piece is limited to, “What kinds of problems do you need to work on?”

Thanks for being so thoughtful with your response. You’ve given me a lot to think about.

Mary, I always learn so much for a book study with my colleagues. My favorite books in the last few years were:

1) Judy Willis’s Learning to Love Math

2) Allen Mendler’s Motivating Students Who Don’t Care

3) Robert DuFour’s Leaders of Learning

4) Robyn Jackson’s Never Work Harder than Your Students.

Currently we are reading the new Common Core Mathematics in a PLC at Work by Diane Briars and TIm Kanold.

I have heard it called Math Workshop before, great descriptive phrase. I will look in to Minds on Mathematics. I look forward to hearing what you think.

Thanks so much for the list of books. I’m an avid reader and I’m going to suggest our math department that we consider a book study. Even if they don’t I’ll likely read them for my own PD. Thanks again!

For years I have made students grade their own work with me watching over them. It always amazes me the difference in the level of learning when I do that. The students who have small gaps in their knowledge tend to fix those. The students who are truly lost tend to ask me to help them more readily. This year, I stopped giving partial credit on exams and no more curves. A problem is right or it is wrong. If the students want to earn their points back, they have to write down the problem, work it out, and tell me where they missed the problem. That creates double grading duty on tests, but it is well worth the time. I have lost count this year on the number of students who have thanked me for doing this. Time and again they tell me how now they understand what they didn’t before. I never called it “co-grading” but that is a great term for it.

I wish I had the time for students to co-grade more of the students work. But I insist on it for unit tests and investigation check-ups. I still give partial credit because some of my struggling students will attempt a problem when they only know how to get started and not really how to do all the parts. Also our state test gives students partial credit on the open response questions and I really want to students to understand how important it is to try every part of the problems and show their work. I think this will remain important as we transition to the Performance-Based portion of the PARCC test.

Hi Alisa! As I write this I see an evolving definition of co-grading. I love the idea of having students actually assessing their work. Do you make copies of the key for each student and they go through and analyze each problem while you facilitate? They wouldn’t earn points back because I do a form a standards based grading, but certainly the process will help them when it comes time to reassess.

Thanks you so much for sharing!

I always go back to two areas of our work – (1) The questions we ask when we are discussing/lecturing/conversing with the students and (2) The questions we ask on assessments. I’ll comment on (2) first – I believe that we can spend all the time and energy we want telling students what we value about learning, but at the end of the day they take their cues from what we grade. If we place a point value on it, then the students know we mean it. I’m not saying that this is best, I am just saying that this is my interpretation of the reality of life. I try to spend my time and energy every day on (1). I think that modeling smart questioning and modeling curiosity and enquiry are the most powerful skills my students can walk away with. I always remember a conversation with a student before her AP Calc test. She told me she wasn’t nervous because “If I get stuck on a problem, I’ll just remember the questions you ask us to help get me through” I think that this is one of the best compliments I ever received as a teacher. By helping students to figure out a strategy to extricate themselves when they are confused – to ask themselves meaningful, leading questions – I think that they can grow tremendously as learners.

“Modeling smart questioning and modeling curiosity and enquiry are the most powerful skills my students can walk away with.”I’m at a loss for words because you so eloquently describe the core of teaching and learning. What you describe MUST be the foundation.Thanks for the kind words and the insightful editing. I would have seemed a bit smarter and more focused if I had restricted myself to the pull out quote above!

I wouldn’t say that. My favorite word you used was “extricated”!!

I do see the definition of co-grading evolving and deepening as we help students become responsible for their understanding. I also really liked mrdardy’s comments and I so agree that smart questioning and modeling curiosity are key.