Giving Students Extra Information

{NOTE: This post will appear in the Winter 2018 edition of Wahpe Woyaka, SDCTM's quarterly newsletter.}

In Dan Meyer’s 2010 Ted Talk “Math Class Needs a Makeover”, Dan suggests that the types of problems typically found in textbooks don’t require students to think critically due to the amount of information given to students in the context of the problem.  Far too often students are given exactly the information needed to solve a problem.  Consequently, students come to believe that all pieces of given information must be used as part of the solution-finding process.

The following example was part of a set of practice problems for a lesson on isosceles triangles found in a certain textbook. 

Students were asked to “find the value of x”.

For those of you who remember the converse of the base angles theorem for isosceles triangles, you can see the problem gives students exactly enough information to solve.  {Set the two expressions equal to one another and solve the resulting two step linear equation.}  One might claim that a student could correctly solve this problem by simply guessing the two expressions are equal to each other without actually understanding the theorem.

I’m not here to say that we should overload students with oodles of useless information in a given problem.  However, by adding one or two additional pieces of information to this same problem, we can deepen the level of thought that needs to be applied by students to solve the problem.

Here is the same problem as above, only I added one piece of given information. 

I invite you to think about the different misconceptions that this new problem could identify versus the previous problem.  {To be clear, the problem is still solved by setting 3x + 13 = 5x +2.}  Two mistakes that my students made because of the change:

·       Set the wrong two expressions equal to each other.  {Ex: 3x + 13 = 2x + 35}

·       Set the sum of the three expressions equal to 180. 

{3x + 13 + 5x + 2 + 4x + 16 = 180}

          Additionally, I had a number of students solve the problem correctly but ask “what are we supposed to do with the 4x + 16”.

          By giving students information that is irrelevant to the problem, we can raise the level of thinking done by students. 

          [Side note: Dan offers a strategy to help students become better at deciding what information is and is not important for a given problem.  I invite you to dig into his 3-ACT tasks for more information.  Here and here as well.]

         


UPDATE: In my original post, it was brought to my attention that my triangle was not accurate.  I have attempted to fix the error and appreciate the feedback.  Thanks @Teachmathtorr for helping me be a better teacher!