To Design for the Average is to Design for Nobody

I’ve been thinking a lot about the phrase “differentiated instruction” because it’s always felt redundant to me.  How is “differentiated instruction” different from “effective instruction”?  Are there ever really times when we want instruction to be “undifferentiated”?  What are the implications for lesson design?

I bring this point up because, in my humble opinion, thinking about differentiated instruction as something separate from “normal” instruction hinders our thinking about effective lesson plan design and prevents us from challenging some of our core assumptions about our teaching.  I’d like to speak a moment about some of these assumptions.

Assumption #1:  The Myth of the Average Student

I was blown away by this 99% Invisible podcast about the mathematical history of the average (arithmetic mean).  It’s very much worth the 30 minutes.  Give it a go on your next commute.

(H/t to Andrew Stadel for turning me on to this amazing podcast!)

Super quick recap:  No one ever really used averages except astronomers.  They used averages because their measurements were often crudely captured and the averages allowed them to adjust for errors and find better approximations for stuff like orbits and planet sizes.  It wasn’t until around the 1850s when the Scottish military started collecting data on the chest size of 5000 soldiers that someone (a Belgian dude named Adolphe Quetelet) decided to find the average chest size of a soldier.

Here’s a huge point to know:  The average chest size of the soldier became the IDEAL size for the average soldier.  This is a huge shift.  The average began to represent the ideal.  In other words, we assumed that the average sized person was the ideally sized person.

Fast forward a little bit.  In WWII, the US Air Force was losing pilots and airplanes at an alarming rate due to fatal crashes.  They finally figured out that maybe it was the cockpit design.  Up to that point, cockpits were standardized based on the averages of body measurements of (male) soldiers in the military.  The problem was the data they were using was several decades old and that many Americans were taller and larger than they were in the 1920s.  So the USAF decided to start measuring thousands of their current airmen on 10 metrics and that task fell to a Harvard dude named Gilbert Daniels.

You could argue that Gilbert Daniels helped us win the WWII because he asked a very important question.  After collecting the data and finding the average of these 10 metrics he wondered:  How many pilots measured average on all 10 metrics?

And his conclusion revolutionized how we thought about design.  He found out that not only was there no single average pilot on all 10 metrics, there wasn’t a pilot who was average on 4 metrics!  In fact, just 5% of the pilots were average on 3 metrics.

Gilbert’s analysis forced the USAF to realize that cockpits needed to be adjustable because there was no such thing as an average pilot.  This design thinking carries through to this day from cars (seatbelts, seats, steering wheels, etc) to the Bluetooth earbuds I just bought that came with different adapters to ensure a snug fit in everyone’s ear.  (It turns out that for a tall dude, I have very small ears.)

So, I’m wondering:  In what ways are we designing lessons for the average math student?  And how is that assumption detrimental to student learning?

There is no such thing as an average math student.  It’s a myth.  And believing in that myth is creating crushingly boring and ineffective lesson designs.

Assumption #2:  A 5th Grade Teacher Teaches 5th Grade Math Students

(I just picked 5th grade, but my point is true for teachers at all grade levels.)

A 5th grade math teacher teaches 3rd, 4th, 5th, and 6th grade math students.  If you look at their NWEA, SBAC, or any other test data, it will tell almost every teacher that his/her students are all over the place in terms of their abilities.

This reality is why teachers must know content below and beyond their grade level.  We need to be fluent in our understanding of the progressions and continually using resources like the progression documents from the University of Arizona and Graham Fletcher’s amazing progression videos in professional development workshops for teachers and principals.  (What other good resources are out there?  Please comment below and let’s add them here.)

The problem is made worse by the state adoption process that restricts the choices of curriculum writers to create lessons that are designed to meet the needs of students at different levels.  (Full disclosure:  I’m a published author of adopted math curriculum.)  To be adopted, the curriculum must be at grade level.  This reality forces writers to teach to the average student…the average student that doesn’t exist.

So teachers need to be aware of the inherent limitations of their curriculum.  It is written for a student that doesn’t exist.  Teachers must start adding in elements of universal design to make sure that their lessons are accessible to all learners.  All curriculum-based lessons must be modified or they will fail to lead to meaningful growth for students.

Embedding Differentiated Instruction into Standardized Lessons

So what are teachers to do about this?  The #MTBoS community in the Twitter world has been contributing solutions to this struggle for years.  Here are a few strategies that you can use as a teacher to rethink your pre-packaged curriculum lessons.

  1. Open up the problems for more student choice and voice. Numberless Word Problems, Open Middle, and 3-Act Math lessons are great examples where students have more authentic voice in creating their own understanding of the problem and gives them choices as they try to find a solution pathway.
  2. Think about ways to lower the floor of the lesson.  Ask:  What is the conceptual understanding that this lesson is trying to create?  How can I lower the floor as much as possible so all students can access what we’re talking about?  Creating a visual hook is always a good strategy.  Having manipulatives ready for students who need them is also a practice that should be routine. Dan Meyer’s headache/aspirin metaphor is another strategy to consider.
  3. Think about ways to raise the ceiling of the lesson.  Creating extension questions for stronger students is something to always consider for students who have met the lesson objective quickly.  Good questions can be:  Can you show me a different way?  Do you think this is the only solution?  You can also think of a more challenging extensions of the problem itself.  For example, if you’re finding out how many small bottles of ketchup are in the big bottle of ketchup, you can find an even larger bottle of ketchup for students to work with.

What are some other strategies that you would recommend to other teachers?

Conclusion

There is no average student.  The average classroom is differentiated.  I’m encouraging us to rethink “differentiated instruction” as being the default mindset as we design any learning experience for our students.  All instruction should be differentiated instruction.

As always, feedback and discussion is welcome.  What did I miss?  What did I get wrong?  Help me make this better in the comments section.

 

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