I hate word problem

Tagged Confusing, elementary school, math class, Muslims, news typos, Salt Lake Tribune, typos, word choice, word problems, writing

Today, I quizzed my Advanced Algebra 2 students and part of the quiz included Linear Programming problems. They did poorly. Part of it may be that we did it before Thanksgiving, and part of it may be they just don’t care about word problems. As they came into class today, several of them commented something along the lines of «I hate word problems. Why do we have to do word problems?» My answer was that word problems are the application of the mathematics, and it shows you where in the «real-world» that the mathematics is used. They weren’t thrilled.

Over the last few years, I have taught word problems less and less. Mainly, this has been because we have so much material to cover in Algebra 2 and I have to make sure they are prepared for state tests as well. But I also realize I am doing them a disservice. Word problems are the application. How are they going to be able to apply the mathematics?

So how do you get students to not hate word problems? I know part of the answer is along the lines of what Dan Meyer is doing, but, let’s face it, it’s kind of hard to do that with Algebra 2 topics. So, what’s the answer? How do you get students (particularly ones who have not done much with word problems for many reasons), to not hate word problems?

18 Comments

1. 

   Hi Dan.
   I haven’t watched the video, but this is an opportunity for me to put forward some radical ideas, so here goes:

   We teach the math, then we wrap it up in more, or less sometimes, artificial scenarios called word problems. The students know that this is a disguise for some sums, and will do anything to dig out the numbers, guess a procedure and get “the answer”.

   This is a cart before the horse situation. The sensible way would be first of all to look at situations familiar to the students, pose interesting, realistic problems, numerical or otherwise, and see what happens. Common sense will mostly get one to the end, and if not then a bit of “guidance”. Then an approach to the problems which looks for similarities, irrelevant details, and some prior knowledge will lead to a natural development of “theory”. This can be done at almost any level, from K to Bachelor degree, and is how a meaningful treatment of for example, abstract algebra, or vectors, or fractions can be created.
   I do like the three act approach, but it would be good to do this from the start. Then there would not be any “word problems”, only problems.
2. 

   I did watch the video, which reminded me that learning persistence can be a significant benefit of applied, 3-act problems. They do take longer than standard word problems, but students need to understand that many real problems do indeed require extended period of effort. Fortunately, good applied tasks (with an immediate and clear goal, student engagement in assembling information and tools, a satisfying and authentic conclusion and a challenging sequel) CAN keep students engaged long enough to reflect and learn.
   As a physics teacher (a discipline that relies on word problems even more heavily than mathematics), it is clear to me that including just a few well-developed authentic tasks during the year can build credibility about the value of both math and science–and it can change the way students approach the “routine” classroom work. A common mistake physics teachers make (especially now that “engineering design” has been added as a new responsibility) is to save their big authentic tasks (toothpick bridges, egg drop, etc.) until the end as capstone projects. That is too late to reap the full benefits.

3. 

   Hi, while watching this video a question is coming to me over and over: should we show these videos to our students BEFORE teaching them the necessary skills for solve them, like howardat58 says?
   Last year I showed some three act videos to my students and they felt so bad not knowing even how to pose a question or an objective to solve related to them…..and when we finally got to pose some questions to solve they felt pretty bad not knowing even which information they had to know or not having enough math skills to solve them….Maybe did I show the videos too early? Or is this a “normal” reaction when we challenge students with “real” math?

   For example, in the video of the basket ball throwing, how can they solve it if they have never heard about parabolic movement? if they don’t know anything about parabolas? When and how should we introduce these concepts to students, “before” or “after”? Thanks!!

4. 

   To Maria Guerrero
   But they do know about parabolas, they don’t necessarily know that the name is “parabola”. They have all thrown balls, or rocks(!). They can be prodded into seeing that since the path is a curve it is not going to have a y=mx+c equation. So what could it have? This is a chance to consider symmetry, and thus good reasons for placing any vertical axis through the apex, and there are other good reasons for placing the horizontal axis touching the apex. I’m sure that good reasons can be found for flipping the curve around the x axis, and we have a nice looking curve which gets bigger quicker than the x value, at least after a while. the question then is
   If it isn’t y=mx, what could it be? What could we have which is a bit more complex than x itself? OK, at this point, when silence has lasted for a minute or two some suggestions are in order. “How about y=x^2 or y=x^3 or y=x^99. Go on, plot them.”.

5. 

   @Maria, if a students wants to know whether the ball goes in, and has an intuition about its path, we’re in great shape. They want instruction. I try to use these tasks to motivate the need for explanation.

   For that particular lesson, students need a tool like Geogebra for modeling the parabola over the basketballs. Without that tool, the lesson would be quite frustrating, I’m sure.

6. 

   couldn’t disagree more.
   text books serve a purpose. particularly that of honing one’s practice with a view to competency that serves larger questions of interest to the learner.
   they ARE NOT meant to hook a student’s interest – that is incumbent upon the teacher and in fact upon the student’s own input.

   my very brightest and most curious students thrive most most vividly when they have text questions with which to hone their understanding. in fact they beg me to give them more to practice – and with good reason. Those very staid questions serve an entirely different purpose – to support their practical and natural inclinations of curiosity with rigour and raw skill acquisition.

   every resource has its place, and the professional teacher makes the most of every resource they have.

7. 

   mike:

   [textbooks] ARE NOT meant to hook a student’s interest

   Says who?

8. 

   Says me.

   Textbooks should supplement learning, not function as the primary catalyst to spark inquiry and I have to say I feel sorry for the students whose teacher relies on the text to function as such.

   Again, every resource has its place.

9. 

   @Dan and howardat58:

   Thanks for your answers! I do use Geogebra when I work with parabolic throwing (I don’t use Dan’s video, but I film my students using catapults they’ve built themselves), but I do all this work AFTER explaining how parabolic movement works, and how to draw a parabola in Geogebra. Should I be more daring and let them discover the concept by themselves? Do you achieve that? maybe your students are older than mines…. (15)

   If you get to do that I’ll try, for sure!

10. 

    Another terrific talk. Yes word problems are artificial and contain many assumptions. Your method of eliciting everything – question, information req’d and technique req’d sets up a student to independently become maths problem solvers to any problem, not just school/exam based. It’s very empowering. School at the moment does the opposite and kids believe it’s about passing an exam. I had a new student yesterday who told me that she ‘didn’t want to learn anything new’. A sad indictment of current methods at school. Love your passion Dan.

11. 

    Mr Meyer:

    I am NOT a math-teacher at any level, so I do not regularly follow your blog (though I am most keenly interested in enhancing the ‘effectiveness of math ‘learning+teaching’). I have developed a powerful ‘systems aid’ to problem solving and decision making, which I am promoting. This tool is called the ‘One Page Management System’ (OPMS). More information about the OPMS is available at the attachments to my post heading the thread “Democracy: how to achieve it?” – see http://mathforum.org/kb/thread.jspa?threadID=2419536.

    I have seen a fair number of your blog-posts, kindly brought to attention to participants at the forum ‘math-teach @ drexel’ by Richard Strausz (who IS a math teacher and who is also a regular follower [and admirer] of your blog).

    My comments on your blog: I think it is useful indeed – though it probably could be enhanced/improved quite significantly in many ways. This is based on my own judgement , as well as on the opinions of several of your followers, whose remarks and comments I have seen at your blog.

    I do believe you might like to take note of and respond to the serial and continuing put-downs by one Robert Hansen at the above-noted Math Forum of what I believe you are trying to accomplish vis-a-vis the ‘learning and teaching of math’. Robert Hansen’s latest quite vicious remarks appear at a thread he has titled “Dy/Scam’s Latest” (dt. Oct 21, 2014 6:01 AM, http://mathforum.org/kb/message.jspa?messageID=9625018).

    I do believe you should take note of his attacks on you and your blog. (If you’re willing to do a [tiny] bit of learning, alongside a fair bit of ‘unlearning’, the OPMS process would help you develop the most effective possible response to Robert Hansen’s rather vicious and damaging lies).

    Best wishes
    GS Chandy

12. 

    Mr. Meyer,
    I must say that you have inspired many math teachers and I am one of them. I love the concept of 3-act math and only wish we had some more examples of you putting it to use in your classroom. I’ve tried it rather unsuccessfully in the past and am a bit stymied about why it hasn’t worked like I thought it would.
    I would like to comment on the criticisms I read here and elsewhere about your approach. I think it is obvious that teaching is an art form where the medium (students) is inconsistently delivered to the artist (teacher). It makes no sense whatsoever to me why someone who teaches one type of student at one level would criticize the techniques used by another teacher who teaches a different type of student at another level. For example, in reaction to this blog post “mike” comments that his best and brightest students beg him for more practice. Perhaps that has more to do with the way he practices his art, but I suspect it has just as much to do with the medium he is dealing with.
    As a teacher, I have never in my years of teaching, met a student who begged me for more word problems. If I had that problem, I certainly would fail to understand what you are getting at here. Since I don’t, I relate to you entirely.
    Thanks for your contributions to the improvement of math education.

13. 

    Movie’s stalling out on me… but I was just noticing earlier today that one of the strengths of our completely re-worked “Math Literacy” course is that we do, now, start with a “word problem” and then generate the math from the real situation, instead of teaching a math procedure and then artificially twisting some “real” situations. It works a lot better…

14. 

    (and meant to say that I got the video going in the meantime — we don’t exactly manage “three acts” but do achieve many of the same ends. And one of the guys in the first pilot section of it did, honestly, really want more word problems. )

15. 

    @Dan Thomander

    To be fair, not all my students beg for text book questions, but those seeking refinement certainly do. I spend weeks at a time not touching a text book in all my classes, including those who would shy at begging for more practice questions.

    The more my lessons are not my lessons at all, but rather my students’ lessons, the better they are. I try to get out of the way of their learning as much as possible. They’re not the medium, they’re the artists, to paraphrase your analogy.

    But speaking to my criticism of the other Dan’s commentary, early in the video he goes out of his way to say that he’s not picking and choosing text questions as Straw Man exemplars of poor practice and yet proceeds to do exactly that.
    Has *any* teacher ever thought that blindly pulling out a random question from a text as a lesson plan was likely to result in a quality lesson? I think not. But they serve a definite purpose for skill refinement and the text questions Dan selects as particularly poor actually serve that purpose as well as any.

    The 3-act lesson is a nice way of thinking about lessons, but not really new. What makes it effective is the passion, energy, and approach to the structure itself.

16. 

    We have been trying to incorporate more of the 3 act problems with our students. What is nice is the incorporation of multimedia for students to see how math correlates to life. But the biggest struggle that we are still having with our students when they start to work out the problem is the UNDERSTANDING. We have students that struggle too often with reading and then have issues trying to decide what they are truly suppose to be answering. To help them out I go through how to dissect a word problem with them first, you can see my poster at http://www.teacherspayteachers.com/Product/How-to-dissect-a-math-word-problem-1565684.
    What I really feel is the underlying issue for math word problems is one the application which the 3 act questions help solve but two do the students know what they are reading in order to solve.

17. 

    Yesterday at a conference in Australia a speaker commented on learning being visual – this is a big part of why what you share works.
    I explain making meaning as follows: you need both sides of the brain to make meaning.

    Left side of the brain Right side of brain
    If I say.. you see a picture of:
    black cat a black cat
    pink hippopotamus a pink hippopotamus (as
    ridiculous as it seems!)
    love ? (see how difficult this is as it
    has many meanings to each
    person let alone trying to get
    two people to have the same
    meaning!
    I say the word splunge which I know would have multiple spellings but what sort of picture do you have? A person doing the splits with a lunge, a long piece of sponge…

    I think this is a big part of why the visuals work so well – it allows us to create a shared meaning and then learn mathematics.

If you surveyed your classroom, how many students would say they like word problems?

20%? 10%? 5%? 

I actually did this in my science classes the other day.  Out of eighty-nine students over three class periods, representing sophomores through seniors, I had six students who claimed to like word problems and another three who did the half arm extension of, they kind of like word problems.  Let us give those students the benefit of the doubt and go with all nine students who claim to like word problems. Nine out of eighty-nine is a whopping 10.1%.  This is just about right for classes in a typical high school, when it comes to their desire to do word problems.

Why is there such a disdain for word problems?  Why do many students even balk at attempting word problems?  Why do word problems provoke fear in the hearts of the adolescent scholar?

As a science teacher, it is an absolute necessity that students work through the process of solving word problems.  I do not have the luxury of simply giving worksheets of repetitious, rote equation based problems.
Whether it is stoichiometry and gas law problems in chemistry or projectile motion or density problems in physics, students must be able to read a word problem, extract the necessary values and determine a method for solving for the unknown?

Over the years I have discussed this dilemma of word problems with the students who have made their way through my classroom. After years of gathering this anecdotal evidence, I have come up with three basic reasons that students avoid, dislike, or fear word problems: The Battle of the Left and Right Brain, The Language Barrier and The Lack of a Plan.

• The Battle of the Left and Right Brain
• Most students are dominant on one side of the brain.  They are either linear, numeric and organized on the leftt side of the brain or they are, artistic, verbal and feeling on the right side of the brain.  Word problems demand that students use both sides of the brain. Heaven forbid, that students use the left side for numbers and the right side for words simultaneously. They might blow a fuse. 
• For a word problem determining how far a person traveling on a plane for a certian period of time would travel at a given rate, students dominant on the left want to know the numbers, the formula and how to find an answer.  Students dominant on the right side of the brain want to know where they are going, what are they wearing and what movie is on the plane.
• Students on the left side of the brain can draw out the numbers but may confuse their significanance because the wording does not make sense.  Students on the right side, can decipher the words but do not necessarily have a purpose for the numbers.  
• A bridge needs to be created to bring the two sides together.  Left sided individuals need to create charts to transfer the numeric values into an organized meaningful process.  Right sided individuals can use diagrams to transfer the words into a meaningful mathematical purpose
• The Language Barrier
• How many word problems have just too much information. Most students get overwhelmed by the sheer wordiness of the word problems.  If their is general discomfort with the math that is only increased by superfluous wording and unfamiliar vocabulary. 
• For example: Johnny walks his shih tzu around his neighborhood every afternoon.  The evening constitutional usually takes about forty five minutes for the two of them to cover the five block trek through the neighborhood.  If the walk consists of one and a half miles, what is the average speed that they walk?
• There are forty nine words in this word problem.  The majority of them are not necessary to solve the problem. Many students would have difficulty with several of the words, shih tzu, constitutional and trek. While it is important to increase vocabulary and integrate science and language, students who have difficulty with word problems will simply avoid this type of  word problem due the seemingly imposing amount of words. 
• Students  must be given the opportunity to develop a sense of success with solving word problems gradually.  With time and greater success, students learn to identify the necessary information and filter out the wording that is unecessary to their problem solving. 
•  The Lack of a Plan
• Students need a problem solving plan.  Not a recipe, but an actual problem solving plan that is generic to all types of problems. 

• I believe the best example of a plan for Problem Solving comes from Rafe Esquith in his book, Teach Like Your Hair is On Fire:

 I have always appreciated the simplicity of this approach, wheter it is for Esquith’s grammar school students or AP Calculus students the plan holds true.  I also love the «Put Down Your Pencil» reminder for the brainstorming portion.  Too many students never get started because they don’t know where they are going.  This plan forces students to truly develop a means for determining where to start, where to end and the path to choose.  

By providing the proper approach, diffusing their fear and providing a concise plan to solve word problems, most teachers can give students the opportunity to develop success in solving word problems.  They may not ever like them, but they most definitely won’t avoid them.

Summary: A Teacher stands in front of a group of school children, writing on a chalk board. There are 3 or 4 children seated in desks, but only two (TOMMY and SALLY) have speaking parts. The kids are played by “adults” – and as the scene starts, they are doing typical bratty kid behaviors – thumping    spit balls, sticking their tongues out, etc. to let the audience know they are children, not adults. The teacher reads from a test booklet.
Style:  Light-hearted.   Duration:  8min
Actors: 4-5M/F

Characters
Teacher, Tommy, Sally, 2-3 other non-speaking parts.

Script

TEACHER: Okay, children, settle down, settle down. We have a lot of work to do. Your third grade standardized exams are coming up in a few weeks, and the Math section is very important. Today, we are going to be reviewing word problems.

TOMMY: Ugh! I hate word problems!

SALLY: Ms. Hudson, Tommy thumped a spitball at Sarah!

TEACHER: Sally, we’ve talked about being a tattle-tale. If Sarah has a problem with Tommy, she should speak up.

TOMMY:That’s a fib! It was Martin. I was minding my own business…

TEACHER: (sternly) Children, that’s enough. Time for word problems. Write this down carefully as I read it aloud…
(The children settle in and prepare to write.)

TEACHER:(continues) “Mr. Smith and Miss Thompson are getting married in June. Mr. Smith has a job working as an electrician, earning $51,000 dollars a year. Miss Thompson is a part-time secretary, earning $17,500 a year. Once married, they will combine their salaries. What will be their total household income?”

SALLY: (raises her hand quickly) Ms. Hudson!

TEACHER: Yes, Sally?

SALLY: Why does the woman have to be the secretary? I think she should be the electrician. I like electricity. I could be an electrician.

TEACHER: I’m sure you would make a fine electrician, Sally. But I didn’t write the problem. Please just calculate the sum of their two incomes and…

TOMMY:You have to be smart to be an electrician. Girls are too stupid.

TEACHER: Tommy, Tommy. That is not nice. We don’t call anyone stupid. Now, back to the math problem.

SALLY: Ms. Hudson?

TEACHER: (sighs, growing frustrated) Yes, Sally?

SALLY: Can Miss Thompson be an electrician and a mommy?

TEACHER: (abrupt) Okay, kids. The answer is 68,500 dollars. Write that down. Next problem. (takes a breath) “After their marriage, Mr. Smith and Miss Thompson will need a place to live. Mr. Smith has suggested they move into a one-bedroom apartment in the city with a monthly rent of $975 dollars. Miss Thompson prefers that they purchase a small two-bedroom cottage in the suburbs with a monthly mortgage payment of $1240 dollars. What is the difference between the two options?”

SALLY: Ms. Hudson, will the cottage have a picket fence? My mommy says every home needs to have a picket fence. And a breakfast nook. And a bay window. Will the cottage have those things?

TOMMY: I think the apartment sounds cool! I bet there’s a swimming pool on the roof, and a weight room, and … and… I bet it’s near the ballpark and the football stadium and the river and he can go fast in his speedboat on the weekend and … and…!

TEACHER: Tommy! Sally! Please quiet down. Your questions are completely irrelevant to the word problem.

TOMMY: Ms. Hudson, what does irrelevant mean?

SALLY: It means that boys are cavemen.

TEACHER: Sally!

SALLY: Well, whenever my dad talks about watching football games at the stadium with his buddies, my mommy calls him a cave man.

TOMMY: Well, my dad says my mom is an ice queen.    Ms. Hudson, what’s an ice queen?

TEACHER: Enough. Remember, word problems! So, what we want to do here is to subtract 975 from 1240 and the result is the difference.

SALLY: Ms. Hudson?

TEACHER: —The answer is 265. (exasperated, quickly) Question three. “Mr. Smith works 55 hours a week and Miss Thompson works 22 hours a week. Calculate the average of the two work weeks.”

SALLY: 55 hours sounds like a lot of work. My mommy says my daddy works too much.

TOMMY: My daddy says that my mommy shops too much.

SALLY: My mommy says that daddy should stay home from work so they can talk more. Daddy never talks to her—

TOMMY: My dad never talks to my mom either! Hey, we have a lot in common!

(They giggle and start to focus on each other lovingly.)

TOMMY: I like your pigtails.

SALLY: I like your freckles.

TEACHER: Ugh, I hate word problems.
…………………………………………………………………………

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