Why are word problems so hard?

Before going any further, I have no answer for the question posed in the post title. If you have good research on this subject please share.

 

My students really have gone above and beyond my expectations for our unit on systems of linear equations and inequalities, but there is still so much struggle happening, and not all of it is productive.

We worked on systems of inequalities and linear programming for about four days this past week and based on their quizzes the students procedurally understand how to solve these problems. But when I gave them their assessments on Friday there was some serious struggle.

The assessments were word problem heavy. I allowed students to do this open note so they could view the word problems we’d been working on all unit and hopefully use them as a guide. The majority of my students did not finish this assessment in the time allotted, and as they were turning them in I saw a lot of mistakes. I’m going to provide feedback on them and allow them to fix/finish on Monday before I grade them and hopefully that will help, but I’m still not pleased with it.

<blockquote class=”twitter-tweet” data-lang=”en”><p lang=”en” dir=”ltr”>So many tiny misconceptions about expressions and equations that I wasn't tuned into until now.</p>&mdash; Kent Haines (@KentHaines) <a href=”https://twitter.com/KentHaines/status/804415131006353408″>December 1, 2016</a></blockquote>
//platform.twitter.com/widgets.js

I’ve been following more and more elementary and middle school math people on Twitter trying to understand where these ideas and issues come from. Kent Haines, above, is seeing similar struggles with expressions in his middle school math classes that I am still seeing with juniors in my AFDA class. These teachers have helped give me ideas for supports and different types of lessons but I haven’t found answers. I teach a lot of students with special needs; more than a third of my AFDA class has some sort of educational plan in place. But even my non-diagnosed students struggle with word problems. Even my readers, the students who love and excel in English, struggle with word problems. WHAT GIVES?!?

This might be what finally kicks me into a master’s degree, or at least into reading more educational research. I need to understand. I don’t understand what it is about word problems that seems to cause everyone, even students with at- or above-grade-level reading levels, to suddenly lose math focus and ability and I want to.

P.S. I don’t really want to be a special educator (shout-out to them; good special educators are the hardest working and best teachers I know) but I honestly hope that I never stop teaching collaborative classes. These kids teach me more than they’ll ever know.

Advertisements

Systems of Equations: Take 2

We started systems of linear equations on Monday in AFDA and things could not be going better! Now don’t get me wrong, students are still struggling. But they are making sense of word problems, using different methods to solve problems, getting better at using technology, and learning how to ask for assistance. It’s great.

Monday was our first day but we didn’t actually do anything involving systems. We spent the beginning of class doing our warm-up and going over the quiz and midterm that had been taken last week. The rest of the block we worked on numberless word problems. I got this idea from Julia Finneyfrock and it was exactly what my group of students needed because they did exactly what was expected – when they didn’t think about the problem, they just added the numbers up! So we worked on reading comprehension, drew pictures, acted things out, made estimates, wrote different equations on the board… we thought. And they thought they were easy, but I know this time was well spent.

Tuesday the students started off with guess and check word problems. All I did was give each student a copy of these problems, read the problems aloud one at a time, and encouraged them while they worked. We talked strategy, used technology, students collaborated, and the pride they displayed when they finally worked out the answer was palpable.

We worked through examples using each method by writing and solving more systems using word problems on Tuesday and Wednesday as well. The class did the majority of these problems together and some students remembered some of these methods from Algebra 1 but most did (do) not. The students were then grouped into 2-4 each and each group was assigned 1-2 word problems from the matching portion of the packet linked. Each group had to identify their match, get it peer checked, and then show their work for solving and explain what the answers meant in the context of the problem.

Today, the students again worked in groups but today was more rote practice. Groups of 3 worked together to find the solution to different systems, with each member using a different method and making sure they all got the same (correct) answer. I found my worksheet on TeachersPayTeachers but you could really use any worksheet and just assign students different methods for each problem I suppose. I  don’t know whether or not the purpose of this got through to all of my students but I know it did for some; I worked through a substitution problem involving fractions with a girl and she said “All of that just for (7, 0)? Isn’t there an easier way?”

You might have noticed that missing within all of this are the different types of solutions to systems of equations. Not to worry! We’ll be addressing that on Monday with one of my favorite MAP activities: Classifying Solutions to Systems of Equations. The students will take their first quiz of the unit after that, so I guess that will be the real test. But the conversations that we and they have been having are giving me really good vibes about this unit!