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>
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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.

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!

#teach180: This year’s first classroom

It’s been too long and I didn’t do much worthy of a #teach180 tweet today so I’m doing a #teach180 blog post instead. Going to try to blog at least once a week during this school year, we’ll see how it goes. Be forewarned that there are a lot of pictures in this post!

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I’m traveling between three classrooms and two offices this year. It’s a pain. Thankfully the classrooms, my students, and my co-teachers are generally awesome and so far it’s been worth it. The first classroom is really long! When you walk in, you’re in a small entryway. On one side of this entryway is a supply table which has calculators and anything students leave behind. Don’t freak out too much, the keys are mine.

 

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Right past the supply table is the weekly schedule board and the teacher space. I didn’t take a picture of the board, but it’s broken down by day and each day has two parts to it:

  • broad topic (this week’s is probability)
  • daily question we’re working toward being able to answer (“what happens when events depend on each other?”, “what happens when probability changes based on given information?”, “how many different outcomes are possible for this experiment?”, etc.)

 

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On the far left of the board I also have the weekly homework assignment posted. On the far right of the board I have my weekly paper holder. Our copiers are unreliable, so I try to only make copies once or twice a week for all of my classes. I also don’t take work home during the week and rarely on the weekends, so this helps me keep organized.

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Currently students are in sets of two or three facing the front of the room. The teacher I’m sharing the room with and I have developed four seating patterns that we think we’ll be using regularly throughout the year:

  • black, which is individual seats (for standard assessment days)
  • green, which is the sets of two or three that they’re currently in (for notes or partner work)
  • green, which is two teams facing each other with students in pairs (for debates and games)
  • red, which is groups of four to five (for small group work)

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In the front of the classroom there’s a cabinet in the corner, which is where we have supplies that students can always use. Right now it’s pretty empty and only contains scrap paper, scissors, pencils, colored pencils, and highlighters. There’s also my “student of the week” trophy and two dinosaurs that I occasionally give to students who need them.

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Immediately to the right of that cabinet is our school rules bulletin board, which currently has the schedules, tardy policy, and electronic device policy. My classroom-sharing teacher is planning on changing the tree scene with each season.

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On the far end of the classroom are two boards for student use. One has the 2016 Challenge thanks to Sarah Carter at mathequalslove, and the other has Sudoku thanks to Christie Bradshaw at Radical4Math. Students can use these during our study hall time or if they finish something early in class.

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Finally, in one set of cabinets in the corner my students have personal boxes. This is where students can keep personal supplies, papers they don’t want to lose, etc. from day to day and it’s also where I put work when students are absent and where I pass back 98% of papers to. All of the cabinets are built into the wall and a lot of my stuff is in electronic form so this was a good way for me to utilize that space!

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So that’s my current AFDA classroom. I’m in there for first block every day from now until the end of January, when my schedule changes and I’ll be moving again for the spring… sigh. Bonus pictures below of decorations on our math department office windows. A handful of quotes I’ve collected over the past few years that are school-appropriate and potentially teenage-worthy as well as a collection of photos from Sara Van Der Werf’s Math Wall of Shame.

 

Tracking Student Achievement #MTBoSBlaugust

I blogged previously about how next year our math department has decided to move toward a department-wide grade replacement policy (see #MTBoS30 Day 9: Grade Replacement vs. Standards Based Grading) and I’ve been working on figuring out how I can still include students in the process. I enjoyed using Dan Meyer’s concept checklist over the last two years. Sometimes it was a hassle, but for the students that actually kept track of theirs they enjoyed knowing what their strengths and weaknesses were (and getting those stickers!)

Last spring semester I taught a new class called Algebra, Functions, and Data Analysis – this is a class that is not tested by the state but still has standards. I mostly used stuff from the other teacher who was teaching AFDA at the same time as me and only glanced through the standards before teaching the course… good job, past me. But, we live and learn. There were some days that seemed too easy and repetitive and others that seemed totally over my students’ heads, and the same was true about the quizzes and projects they completed as assessment. I didn’t really enjoy that, but I felt a little overwhelmed without a planning period so I kept pushing through. Well I’ve finally sat down and looked at the standards and boy did we do some interesting things. We taught multiple things that definitely are not required! Some of which I’ll be keeping, and some of which will probably get tossed.

ANYWHO, I digress… After reviewing our curriculum map and the state standards, and a little inspiration from someone on Twitter (I forget who) I made up slightly new Achievement Trackers. My plan is to have students keep these at the front of their assessment section of their binders so they’re easy to find.

Things I Like:

  • students being cognizant of what grades they’re earning (and hopefully why!)
  • helps me better plan lessons and assessments
  • the students have less to keep track of compared to the old concept checklist

Things I’m Not Sure I Like:

  • some of the wording isn’t necessarily the most student friendly/some boxes have a lot of text
  • it will take up two pieces of paper front/back
  • the homework section at the beginning of each unit

Let me know what you think and if you have any suggestions!

Time to try this blogging thing out.

My profile says I’m “fresh out of college” but that’s technically not true. I’m currently in my second year of teaching after graduating from Robert Morris University in 2014. I “joined” the #mtbos on twitter in 2013 and frequent blogs such as Kate Nowak’s Function of Time and Sarah Hagan’s Math = Love. After one year in the classroom, I feel like I’m ready to give blogging a shot myself.

So now,  to introduce myself. My name is Rose Roberts, and I am a math teacher. I currently teach at Warhill High School (Go Lions!) in Williamsburg, VA. I grew up in Adrian, MI (Go Maples!) and went to college at RMU (Go Colonials!). Our school has a block schedule right now, meaning I teach 3 out of 4 blocks each day and the math classes are seen on both A and B days. Last year I taught two sections of year-long Algebra I with a collaborating teacher, and semester-long Geometry. I’m currently teaching the same things this year, but next semester I’ll be switching from semester-long Geometry to Algebra, Functions, and Data Analysis (AFDA, an optional precursor to Algebra II).

My biggest goals this year are:

  • have increased classroom management
  • involve students more in goal-setting and keeping track of their grades and achievement levels
  • expand concept-based grading from semester-long Geometry to AFDA (haven’t implemented it in year-long Algebra I yet, but that will be a goal next year if I am teaching it again)
  • have a higher Algebra I pass rate
  • blog once a week

As a end-note, we’re one month in to school and some of the new things I’m implementing are really trying my patience (and sometimes the patience of my students) but I have faith that by June it will all work out.