The Order of Operations is wrong

This says it all.

Complex instruction and group-worthy tasks: my favorite math supply

If there is one thing I can’t live without it’s the knowledge gained from good professional development. I’ve sat through some awful PD, where the presenter’s material is as empty as a blank Word document—with the only visible sign of life is a flashing cursor. Not this year. I experienced something called Complex Instruction and I’ve been weaving it into my daily practice.

Complex Instruction is an alternative that addresses the limitations of ability grouping and tracking. It calls upon each student to contribute their own individual intellectual strengths to the group task.–Stanford University

I’ve previously written about some middle school math tasks we’ve created during our professional development this year (led by Evanston High School teacher Zach Herrmann), but here’s the big picture—at least my interpretation of why and how Zach implements Complex Instruction. Zach, if I get it wrong or if you want to clarify, please comment.

Why Complex Instruction—abbreviated

According to Stanford University Complex Instruction is about achieving equity in the classroom. The goal “is to provide academic access and success for all students in heterogeneous classrooms.” It is accomplished using a variation of cooperative learning where students of various abilities and backgrounds make meaningful contributions to the task. Simply put, students “don’t fail to participate because they are too shy or don’t want to participate. They don’t participate because other children in the group see them as having nothing to offer…In short, they have low academic status within the group.” (University of Vermont).

Complex tasks designed with multiple entry points lowers the barriers allowing all students an opportunity to learn. See Dan Meyer’s recent post on Equity, Race, and the Opportunity to Learn.

How it works—establishing norms and accountability

Students are empowered when the teacher creates an environment where the students are considered the authority, where most questions can be answered using the groups’ collective resources. As such each student is held accountable for the success of the group. It begins at the start of the year by setting norms, explicitly teaching, and reinforcing the expectations of what effective group work looks like and sounds like. How does the group demonstrate overall patience with others? How does an individual demonstrate patience while explaining the solution to others? How do you acknowledge and honor a valued contribution? How does the group encourage all members to participate equally? What does it mean to be a productive and responsible group?

These norms are then woven in with the eight mathematical practices. It is the responsibility of the group to make sure all members understand how one or more solutions to a task are found.

How it works—creating group-worthy tasks

Tasks are considered group-worthy if they are complex and have multiple entry points so that all learners can access the problem. The tasks are open ended, have multiple representations, and may have more than one solution.  (Boaler)

Additionally, clear criteria are provided for group and individual accountability. Several high school tasks created by the Complex Instruction Consortium can be found here.

I’m not aware of any middle school tasks aside from few our district has created so if you know of some please share.

How it works—facilitating the learning

Students recognize that they should utilize each other as the primary resource. At times a group huddle may be needed. If the teacher sees several groups asking the same question, a representative from each group is then called to a group huddle where the teacher provides some insight. Or resource cards with information are provided. The resource cards are designed to allow more entry paths towards solving the problem. The onus is on the students to make sure everyone in the group contributes and can explain how to complete the task.

There’s a whole lot more to complex instruction but this is the gist.

In the fall

Within the first two weeks of school next year I plan to explicitly teach the behaviors and expectations of positive group interactions. I think that part is very similar to Socratic Circles. If I have time, before the year is out, I may even record a group of students working on a task. A picture or video is worth a thousand words.

But it’s not just about the behavior. It’s about best practice. I have students with a WIDE range of abilities in the same classroom. Everyone deserves access.

My apologies if this reads more like Dan Meyer’s Math Recap. Nothing wrong with Math Recap, it’s just the format may not be what readers expect from a blog post on my favorite math supply. I hope it became clear as to why I termed this as is my favorite “supply”.

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The Differentiation Domino

Daniel Schnieder and I are on a similar journey. He recently wrote a thoughtful piece in which he discovered the domino effect while implementing Standards Based Grading. His post focused on three dominoes—standards, assessments, and grading—and how his move to SBG has resulted in a reevaluation of every aspect of teaching and learning. He concludes by suggesting there are at least 50 more dominoes in the chain.

I think one of those fifty dominoes combine differentiation with formative assessment.

I thought I knew differentiation—content, process, product, readiness, etc. But today I realized how much there is to learn. I watched portions of a Carol Ann Tomlinson webinar, Common Core State Standards: Where Does Differentiation Fit? and learned how the MARS project is transforming differentiation by using formative assessment to facilitate student thinking and problem solving.

In the past I used formative assessment to differentiate instruction by groupings or as a reactionary tool for when students didn’t get it. If you read the previous sentence closely, I’m differentiating before or after a lesson or task. What’s different is how Tomlinson suggests using differentiation and formative assessment during a mathematical task.

Here’s an example. In this MARS task students work independently for 15-20 minutes to solve and graph an inequalities problem. After the allotted time, the work is collected and analyzed based on the 8 Mathematical Practices (Not all practices may be present in the task).

Is the student having trouble getting started, or misinterpreting the problem (Make Sense of Problems)? Is there an organization of thought, or is work haphazard (Construct a Viable Argument/Attend to Precision)? Did the student present a variety of mathematical models (Reason Abstractly and Quantitatively/Model with Mathematics)?

The differentiated feedback is given to the student in the form of questions. Can you organize your numbers in a certain way? How would someone unfamiliar with your solution understand your work?

When the students resume the task the next class period they are given 10-15 minutes to review the feedback and answer questions. They are then paired or organized into triads to collaborate—combining ideas and creating a new and improved solution.

This particular task is designed for high school, but MARS has a variety of problem solving and concept development tasks for middle and high school. You can take your pick of Classroom Challenges.

What I’ve been doing

The mathematical tasks our math department created this year use questioning to differentiate and guide problem solving but not in the same manner. Those tasks are much more group worthy in nature and the questions are presented to the groups as resource cards to allow for multiple entry points.

They both serve a purpose but the MARS example allows for differentiation based on a formative assessment, not on anticipated misconceptions.

In the fall, I had planned on introducing the students to the mathematical practices and collaborative work through a series of short group worthy tasks. It will serve them better if I differentiate by using the approach suggested by Tomlinson and the MARS classroom challenges.