Establishing a Multidimensional Classroom

NOTE: This is the third in a series of posts about Complex Instruction

In the last post, I wrote about how status affects all interactions between humans–none more so that those between teenagers.

If a teacher assigns a group of students a task of typical academic work, the student who is perceived as getting the best grades in that subject is likely to dominate the group, regardless of the merit of their ideas in the specific task.

Elizabeth Cohen, Designing Groupwork: Strategies for the Heterogeneous Classroom

Some teachers want that and intentionally pre-select groups so that each group has at least one “strong student” to lead the group. I made that mistake until Lani taught me a solution to that and much more when I went back to get my Masters in Teaching. In a later post, I hope to explain the specifics of why this is a bad idea–despite its good intentions. Ideally, though, we should want groups of students to make decisions based on the merit, logic, and reasoning of the ideas presented and not the status of the group members.

However, our students are slaves to status. They will make decisions based on status unless we do something to counteract it. The entire system of Complex Instruction is built on fighting status and creating equity in the classroom, but the first step towards a solution is establishing a multidimensional classroom (those thinking about spacetime and fifth dimensions should settle down). A multidimensional classroom is just one in which there are many ways to be smart. Despite this sounding very simple, many of the classrooms I’ve seen–especially math–are very one-dimensional.

In fact, when you ask most Americans what it means to be good at math, there are three common answers. Being good at math, the fallacy goes, means that a person…

  1. can do math quickly
  2. can do math in one’s head
  3. doesn’t make mistakes

All three of these, of course, are completely false.

The 2014 winner of the Fields Medal (“the Nobel Prize of Mathematics”), Maryam Mirzakhani, is a self-described “slow thinker“. Students that think too quickly often think quite shallowly and miss mathematical connections (as a former student who embarrassingly cared a lot about finishing first, I speak from experience). There are many opportunities for creativity in deliberate thinking. With regards to the fallacy of needing to do math in one’s head to be good at math, research on the neuroscience of math learning shows that thinking mathematically involves using distributed networks of the brain that involve visual processing regions. Someone that does math only in their head will show less neurological activity–less connections being made–than someone who uses visuals (paper, their hand, technology, whatever). The third fallacy, that good mathematicians don’t make mistakes, is like saying that good athletes don’t ever have a bad game and is so absurd that I don’t know whether to refute it with a link to an article or an entire book, Mathematical Mindsets, by Jo Boaler.

There are many ways to be good at math just like there are many ways to be good at cooking. Making a delicious dessert or a six-minute stir-fry or a health-conscious casserole all require vastly different skills but nonetheless display culinary acumen. Being good at math or dancing or writing or Australian Rules Football–or anything–is no different. It should be accepted that there are many ways to be successful at any discipline.

Every teacher should think deeply about what it means to be good in their discipline. The important step, however, is communicating these skills to our students. After all, if you think identifying connections between Shakespeare and Sorkin makes a student a strong writer but she thinks she sucks at writing because she can’t spell, then you’re fighting an uphill battle. I think every teacher, at the beginning of the year, should ask their students what it means to be good at their discipline. When they hear their students’ responses, I think they’ll understand why there are so many status issues in schools and why it’s so important to create a dialogue in the differences between what’s valued by teachers and what’s valued by their students.

One of the mistakes I’ve made in the past is not communicating these skills effectively enough to my students. So about seven years ago, I compiled/created a list that I call “An Expert Mathematician…” and I share it with students.  In it, students see 48 skills, like:

An Expert Mathematician…
… can restate a problem in their own words
… organizes a plan of attack
… spends more and more time stuck without giving up
… creates models/diagrams/pictures or uses manipulatives
… discovers new problems (i.e. extensions)
… asks creative, outside-the-box questions
… communicates clearly, concisely, and convincingly

In the second assignment of the year, students must identify one of the skills at which they are already good. Even though perhaps a majority of students enter my class claiming that they’re not good at math, a quick look at the list enables everyone to find at least one strength. Students then must artistically render their chosen skill on a piece of computer paper. If I’m good, I’ll have squared away an entire wall of my classroom to display these skills so that–throughout the school year–any time a student displays one of the skills, I can point it out to them and the class. But I’ll write more about that in the next installment about Assigning Competence.



One thought on “Establishing a Multidimensional Classroom

  1. This is fascinating and very helpful. I think I’m going to ask my students what it means to be “good” at math…I think this could be really eye-opening for them. I love the idea of slow thinking by the way. Oh and I see you made a reference to Habits of Mind…I strongly recommend “Intellectual Character” by Ron Ritchhart for further reading on this topic.


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