Differentiation in The Math Room

In the classroom all of our students are unique and it is the teacher's obligation to treat and teach them as such. One of the more difficult aspects of teaching is making sure that your lessons are accessible to all students. The last thing you want to do is create barriers between your students and understanding.  It is easy to think of equal opportunity, accessible lessons and barrier free classes as taking the time to work with students who are achieving at a lower than average standard. This is can be problematic as you are no longer giving the attention to students who are gifted that they deserve. Take the following picture posted by @barrierfreemb on twitter as an example:

Equality vs. equity vs. the removal of systemic barriers #accessibility #DisabilityMatters pic.twitter.com/NBU3HwYfMU

— Barrier-Free MB (@barrierfreemb) May 12, 2016

The problem in this illustration is that the illustrated characters can't all see the ball game. In the first segment you see the characters each have an equally sized box; representing equality for all. Next we see that the boxes have been modified and individualized for each of the characters allowing them to all see; representing equity. In the final segment you see that the barrier that was put there in the first place being modified to allow all characters to see clearly without the need for boxes; representing the removal of systemic barriers.

When I look at this illustration I can so clearly see the connection to a key concept we've been recently introduced to that aims at creating an accessible lesson. The concept is to have your lessons built with a low floor and a high ceiling. This means that students who are achieving at a lower standard can access the same work that students who are achieving at a higher standard can.

One of the means of creating a low floor/high ceiling lesson is using techniques such as open ended questions as well as parallel tasks. Both of these aim to have students able to work on the same curricular expectations with the same task goals but at their own individual level. It is important to note this doesn't only benefit students at low and high standard achievement levels but also all the students in-between.

If you're new to creating open questions (like I am) it can be quite difficult to develop them yourselves. The important parts of open questions are that any student can access them.  An example could be asking students:

"How many apples are too many for a family"

instead of:

 "You are part of a family of 7. You each eat one apple per day 5 days a week. Apples last for one week before they go bad. How many apples should you buy for your family?"

Having this open ended question allows students to make it personal as well as control the complexity of it. One student may think of their family and easily say 20 apples are too many for my family. Another student may look at it more in depth by deciding how many people are in the family, how many apples they eat a day, if everyone eats an apple, etc. 

Marian Small, is very experienced at developing these type of questions. It is defiantly worth following her on twitter and her "good question of the week."

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Feel free to comment if you are currently working to use open questions in your classrooms.
Do you use them in math or other subjects?
What do you do to break down systemic barriers in your classroom to ensure you lessons are accessible to all?
What are you thoughts on equality vs equity?