Differentiation

Last week, I attended a training for our district's new vendor assessments.  While I'm reserving my opinion about the vendor assessments and the data we will obtain from the testing, I found a comment by the trainer to be particularly troubling.  The assessment provides a report with a number assigned for the student's skill level with mathematics that the teacher can then use to find activities to help differentiate instruction in the classroom.  My concern with this process is that the majority of the materials provided were worksheets with little instruction involved.  Differentiation is NOT providing more work for students but rather helping to tailor instruction to the learning needs of the student.

In my math classroom, I prefer that all students are working on the same problem.  A rich mathematical task has multiple entry points so that most students are able to begin working on the problem.  An excellent example is NCTM's House Numbers problem:  http://illuminations.nctm.org/LessonDetail.aspx?id=L225

It takes a few minutes to introduce the problem and be sure students understand any associated vocabulary.  Once I have made sure all students understand the parameters of the problem - for example, that the sum of the digits is 4 and that all of the digits must be different - they are ready to begin!  Because there are many correct answers for this problem, students are successful if they find one correct answer or if they find many.  The challenge is to find as many house numbers as possible.  Questions such as, "How do you know you've found them all?" and "How did you decide what numbers would work?" help students to reason and justify their mathematical thinking.  Students are practicing adding in a much more engaging way rather than solving math facts on a worksheet.  You can further differentiation by giving students a calculator to check the sums, pairing them with a student working just above their level, or providing a framework to help them organize their thinking (such as an organized list).  The idea is to see what students need before providing too much support.

The best part of this type of differentiation is that when you discuss the problem, all of the students were involved in the problem and can participate and contribute to the discussion!