Would the real “real world” please stand up.

I really appreciate Dan Meyer’s post on real world vs fake world and getting the MTBOS to help define what makes a problem “real world.”  He put a call out to Mathalicious (specifically), which is a team of highly-skilled designers of “real world” math problems.  Mathalicious states in a  post concerning the purpose of two types of tasks problem solving tasks and application tasks:

While the purpose of problem solving tasks is to help students develop a deeper understanding of math, the purpose of application tasks is to use math to develop a deeper understanding of how the world works. It’s pretty Radiolab like that. [Link to Radiolab added.]

 

As math teachers, we need to be able to integrate both types of tasks into our courses.  I am making an effort to use both by using Dan’s 3-Act tasks (which have a more problem-solving flavor) and Mathalicious.com (which have the ever-expanding real-world tasks). My battle is with how much time I devote to these types of tasks, which, as you can imagine, take a lot of class time.  Mathalicious rightly states this toward the end of the post:

Instead of discussing which type of activity – procedural, conceptual, or applied – we should use, a more constructive conversation would be about how often and when. For instance, is it more effective to start a unit on linear functions with an open-ended problem (e.g. Dan’s Groceries), an application activity (e.g. our Domino Effect), or a procedural task (e.g. Khan Academy’s activity on  slope-intercept form)? Also, within the unit, how much time should we allocate to each type of activity, i.e. how much time should we spend in each world?

I highly encourage everyone to read Dan’s original post (including the comments!) and Mathalicious’s reply.

 

 

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Desmos–Function Carnival and Des-man

The team at Desmos has two really good activities:

1.  Function Carnival–Students graph the motion on three rides.  They can do this in class on computers or iPads. The teacher dashboard rocks too.  I made a quick handout here.

FunctionCarnivalImage

2.  Des-man–students make faces using functions.  This will also help reinforce domain and range.  I have made a quick handout for that one too.

des-man

Updated 3/20:  Here is a quick video of the teacher dashboard for both the Function carnival (0:00-2:10) and Des-Man (2:10-End) that we did in our workshop with about 20 participants on using tablets in the classroom.  There is a little down time that I failed to edit out. I also want to give a big shout-out to Desmos for responding rapidly to a small issue we were having.