Sunday, October 23, 2016

Helping Students "Make Sense" of Problems

math practice standards
Teaching math is a complicated venture--to say the least.  Between figuring out how to meet the needs of all our students, balance a jam-packed curriculum, worry about interventions and enrichment--and then throw in fire drills, strep throat epidemics, students gone on vacations, meetings...it's a wonder we get anything done!

The one thing I always use to "center" myself is the Standards for Mathematical Practice--or "Math Behaviors", if you prefer.  These "ways of being" in math class are the glue that holds my  math class together...whether my students are above or below grade level--and no matter if we are doing addition or fractions or measurement.

One of these standards is often called the "perseverance" standard...and people do a GREAT job of teaching students that word and stressing that "I can" spirit in their classrooms.  That being said--"perseverance" is only a small part of that standard and we cannot forget the rest.  This standard talks about sticking with problems--but perhaps more importantly talks about MAKING SENSE of problems...using a thoughtful, logical, and organize process to dig in to the information presented and to tackle it.  It's hard to persevere on a problem until you have "decoded" it!
perseverance
This is one of the posters in my "kid friendly" math standards posters resources.
So the other day I decided to give my students one of my open ended challenges--with NO preliminary work.  I didn't read it to them.  I didn't give them any hints or talk them through it.  I told them--your goal today is to figure out WHAT this problem is asking, think about how to get started, and how you will organize your work.  I told them I would read them any word they struggled on (not reading class!) but it would be up to them to try to "decode" the problem.  I built up the energy...told them I KNEW they could do it and explained we would start tackling it alone but then would move into partnerships to compare notes and to get started.

So off they went!  I walked around and circulated...asked a few questions here and there--mostly things like, "What have you figured out so far?" and "Tell me what you notice." to try to get a sense for what they were gleaning from the problem.
math challenges
After five minutes or so, I then partnered students up to compare notes.  I started to see some great stuff...highlighters came out.  Students were pointing out information and underlining it.  I heard things like "OHHHH...now I get it!" and "I totally missed that part!".  After a while longer, we came back as a class and talked about our findings--and also talked about the power of partners!  It was pretty evident to students that two heads were definitely better than one in this case!
math workshop
At that point, I put a copy of the problem under the document camera and we shared out our findings.  I used highlighters and my pen to showcase what students told me they had found in the problem and what they were noticing about getting it started.  After a few more minutes of processing, I was pretty sure that partnerships were ready to go tackle it! They were chomping at the bit to get going, and I am pretty sure that taking the time to process on this problem was just as valuable as actually working the problem itself!  I quickly reminded them about working precisely and in an organized fashion (our recent goal) and sent them off on their way.
math practices
From beginning to end, my students worked for 45 minutes on this problem this day--and could have done another 15.  We finished up the next day and had a ton of fun sharing our different solutions.  I love hearing the students' logic about which solution made the most sense for them.  I think I have some entrepreneurs in training in my class!
math challenges

So today's food for thought?  Think about how much work YOU are doing for your students by helping them get started...and consider how many opportunities you are giving them to try to learn how to make sense of tricky problems on their own.  Want to try 
the Marco Problem with YOUR class?  It's one of the three challenges in Set 1 of my "Open Ended Challenges" resource..  Click the image below if you want to see more!

math word problems
 Also available in this bundled set of 9 challenges!
open ended problems

Thanks for stopping by!

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