Why Use Non-Routine Problems?

-Do problems (1-10)

-Do problems (1-19) odds only

-Practice flashcards

-Do IXL problems for ____ standard

-Watch me do this example, now you do an example, now do your homework

If your assignments in math are similar to the list above, it may be time to introduce non-routine problems to your students! 

Why non-routine problems? 

Application

They help students make sense of how to apply mathematics, not simply follow a bunch of prescribed steps. You might have had the experience where you have students working on a new concept, and they seem to get it (yay!) but then you give them a problem where they have to apply the concept and they don't know where to begin! We need to give kids a chance to see that math is used to solve problems and those problems don't always look the same.

Enjoyment

Doing 100 of the same type of problem over and over is pretty boring! Math can be exciting and fun, but we have to show that to students. It's not exciting and fun if you only know how to do one type of problem and it is set up for you in one certain way. If you want your students to find enjoyment in mathematics, you need to show them that most problems or puzzles to solve can't be solved by filling in bubbles on an answer sheet.

Performance Based Tasks

I would argue that the two reasons above are all you need! But, just in case you need a little help convincing a "pace guide" driven administrator that you want to take a day away from the skill and drill and add a little non-routine spice to your lessons... here are the magic words: Performance Based Assessments. Yep, those common core tests (like PARCC, Smarter Balance, etc) use performance based assessments and many of them are, *gasp*, non-routine problems! So you can call it "test prep" if that makes someone happy. Just don't call it that to yourself or the kids!

Where can I get these magical tasks??

So, maybe you are sold on the idea of using non-routine problems with your class. Do you have to develop these yourself?! Nope! There are a lot out there ready to use. Here are my favorites:

MARS tasks (use for individuals, groups, or class discussions)

Formative Assessment Lessons (FAL) (mostly partners or groups)

Problems of the Month (individuals, groups)

Get it Together Activities (groups)

Other ideas for a few minutes left of class (no time for a full lesson, try some of these)


How often do I do these?

I would argue as often as possible! I aim to do a problem of the month, a Get it Together Activity, a FAL, and a MARS task each once a unit. If I can't get to one of them, I don't sweat it, but I do make an effort to make most of the work in my class around interesting problems. I know kids "need practice" with some procedures, but I also never really assign work like the list at the top of this post. We might practice in class on dry erase boards or in partners, then move towards application.

While I still have students that struggle, I can say that I notice my students much more willing to take on a challenging, non-routine problem now than at the beginning of the year. When I first start these with a new group of students, I hear a lot of "What?! How am I supposed to do this?!" Now I hear a lot of "I don't know how to do this, I know because I tried this and this and this." Still work to be done to get my students proficient at the math, but their improvement in perseverance is amazing!