Ashli Black, over at Learning to Fold, recently posted this little bit of wit and whimsy.  The post essentially recounts her experience in algebra classes and compares it to the experience of contestants on an extremely confusing, quite vague, and thus hilarious math game show.  Ashli makes the point that, “As that kid without conceptual understanding in algebra, this skit is pretty much exactly what it was like in class for me. Confusing, almost no stated rules I understood, and at any moment the scene might change or I might be shoved in a box for not achieving Wangernumb.”  Ashli considers the difference between teaching for conceptual understanding and teaching for procedural understanding in her post, but it got me thinking about my own students.  I often think my students are holding their breath, waiting for me to tell them their answer was in fact “Numberwang.”

My goal as a special educator is to communicate the day’s lesson or task so the students will be able to access, understand, and apply the mathematical content.  This often leads to accommodation, modification, and differentiation of everything for everyone.  When one thinks of accommodations the first things that come to mind are standardized testing accommodations.  The general list usually looks something like this:

• Oral reading (either by an adult or a tape)
• Large print
• Magnification devices
• Sign language
• Braille and Nemeth Code (a specific type of Braille used for math and science notations)
• Tactile graphics (e.g.; 3-D topographical maps, 2-D raised line drawings)
• Manipulatives (e.g.; geometric solids, real coins & currency, abacus)
• Audio amplification devices (e.g., hearing aids)
• Screen reader  (Adapted from Special Connections, 2005b)

But in the world of special education the idea of accommodations and modifications take on a different meaning.  Every lesson should be modified and differentiated so each student has the greatest chance to access, understand, and utilize the mathematical goals of the class.  Rick Wormeli recounts this anecdote while describing differentiation:

If we know only one model of instruction or one way to teach something, we’re setting our students and ourselves up for failure. Professor, author, and literacy expert, Kylene Beers freely admits that for years she had only two ways to differentiate instruction for students who struggled: teach louder and slower.

In special education classes each student has their own needs to access and understand the content in a lesson.  For instance lets consider just giving instructions to launch a math task: a student with autism would need the instructions clearly laid out ahead of time; a student with auditory processing disorder would need to be able to read the instructions; a student with dyslexia would need to hear the instructions read aloud; a student with a developmental disability may need concrete visual cues attached to the instructions.

This is only for the introduction of the task and instructions.  All of these students then benefit from the use of hands-on manipulatives, direct modeling, graphic organizers, scaffolding of the task, breaking the task into manageable chunks, and various other methods of differentiation during a lesson, and I haven’t even mentioned the accommodations and modifications students with disabilities may require to participate successfully in a whole group reflection of the lesson or task.

And all of this takes place in the same room.  For instance, earlier in the year two of my students were working as partners on a task involving cuisenaire rods.  This is what it looked like:

This is an example of differentiated written communication.

After these students completed the task, the way they communicated their thinking was in different, modified ways.  One student recorded the group’s work by hand and the other used his Chromebook.

Then this week on twitter Carl Oliver asked a very good question…

Is there a twitter chat for people who try to teach with non-routine problems and lots of class discussion?

— Carl Oliver (@carloliwitter) February 9, 2015

There wasn’t one and so this idea has turned into #probchat, which Carl will be blogging about soon.  This is going to be a rich and interesting chat about teaching with rich and interesting problems.  If you’re new to problem-based learning then Geoff Krall has you covered, and there is a wide variety of resources for such problems; just a couple of examples include: The Math Forum, NRICH, Mathematics Assessment Project, Mathalicious, and Open Middle.  There were several ideas of what the focus of the chat would be, one of my favorites was proposed by Bridget Dunbar:

@carloliwitter @Veganmathbeagle @bkdidact @nrichmaths assign a problem to solve for the week–and then chat has to do with implementation??

— Bridget Dunbar (@BridgetDunbar) February 9, 2015

Assigning problems to teachers and then discussing how to implement for their students is such a great idea.  Teachers need to continue to think of how their students see, understand, and process the content of their lessons.

My major concern is making sure any chat about problem-based teaching (launching, working and communicating thinking) needs to include thoughts on how to modify and differentiate each piece of the process and accommodate diverse learners, special ed or not.  Every teacher has a student who feels like Ashli did in algebra class, and we as teachers need to make sure no student feels like they are trying to get numberwang!