What is the best way to teach math word problems? I had developed different methods and implemented them in my class and they work very well, but still have students who have difficulties interpreting words into symbols.
I never had any issues with word problems, and I am not afraid of them. My lack of fear is probably my most important skill, I first learned to take word phrases and turn them into expressions and then connect the expressions into equations. There is a Spark outline on word problems that shows this method. I am not sure if this is the way word problems are taught in grade school, but it still serves me well. Now I understand these are simple word problems, but the ease with which they can be learned probably gave me confidence in doing more difficult ones. The sparks outline also give several methods to use in solving more difficult word problems. While not all problems can be solved using these methods, it does build confidence. In more difficult word problems that occur, for example, in Physics, if I do not understand the problem, I first make a drawing, and start writing out any equations that come from the diagram. Tables are also sometimes useful in solving some problems. I also need to write out what I am supposed to find, which is generally the last sentence of the problem. After this, I start looking for ways to find the answer. One thing that always gives me confidence is that the word problems in math or physics books have answers, something that is not always true in real life. A wise man said, if it wasn't for word problems, math would have no real use at all.
I agree with several of the previous posts. Vocabulary is vital, pictures are useful, and modeling and practice are a necessity. The last few years I have been using the "TIPS" strategy with my students, and have found it to be quite helpful as well.
If you are unfamiliar with "TIPS", is is a constructed response strategy that analyzes word problems to identify Thought (which operation is called for), Information (numbers to be used), Plan (the combination of the first two pieces to form an equation), and Solution (in sentence form).
This strategy involves quite a bit of teacher modeling and whole group practice initially, but after a few months the students generally have it down pretty well. What really sold me is the fact that I have seen a definite improvement on the problem solving portion of standardized tests since I have started using "TIPS" in my classroom.
I think the majority of us can sympathise with #10 and the dying a horrible math death! I agree with a number of editors who stress the need to use practical real life examples in math problems and questions. I also agree that creating flashcards or a crib sheet of how mathematical signs and symbols are translated can be really useful. Clearly though what is needed is lots of practice of questions that are carefully modelled by the teacher first and then given over for the students to complete which are carefully reviewed.
Something I left out of my earlier post on this topic--draw pictures! If they are buying 3 shirts at $20 a piece, and 2 jackets at $50 each, have them make symbols with each. If they are trying to "buy" carpet for an irregularly shaped area, draw it! I never would have made it through Physics without drawing pictures of what the problems were about....silly cannons.
I respond as someone who does not teach math and who is dyslexic. Numbers do not appear in my head the same way they are displayed on a page. I transpose them (3 and 5, 6 and 8, etc.), do weird things when I try to calculate them, etc. It's a visual problem; I do not view them in my head the same way they are viewed on the page and I then sometimes do weird things with them when trying to do calculations. When I am very tired, I also have trouble with words - the word is in my head but I cannot get it to come out of my mouth because I cannot visualize it; I cannot see the word in my brain. And I constantly reverse numbers (& words), so that I have to write some things down and or will them backwards every time. Funny thing is, if I've written it down, I often don't have to look at it later.
I think this is part of why word-based math problems have always been so difficult for me and why my math scores on standardized tests were always so low. Then one day I discovered a DOS-based computer game called Sherlock. It was the same word-based math problem you see in magazines all the time. A couple hosts a party for 5 other couples who all arrive in different color cars, bring a different food item, etc. You have to solve the problem of which couples are a couple, drove in what car, etc. Only in Sherlock, it's houses, people, road signs, foods, letters, etc. Oh, and most importantly, there are 6,999 iterations of this game. The clues are tiles which, when together, mean two items must be side-by-side, or a triple tile that means one item must be between two other items (or cannot be between them if it's got the circle around it), and so on. By process of elimination, you can solve the puzzle.
By the time I took my GRE (Graduate Record Exam), I had played over 4,000 iterations. When the dreaded math questions came, I quickly realized that some of them were Sherlock in a new skin. I grabbed some scrap paper and start drawing tiles. A number of the questions were about tree nursery plantings. The pine trees couldn't be planted next to that type of tree, etc. I got through these questions fairly quickly and continued converting these word-based math questions into visual tiles throughout the exam. I ended up with the highest math scores I've ever received in my life.
Now, I still have one roadblock in Algebra 3; I get to one point and cannot visualize the problem well enough to grasp the concepts, so I never get beyond that point. But for most other match problems and issues, I have found that if I can find a way to visualize it, I can solve it.
The key is to help the student find a way to unlock what is blocking them. Do they need to see it graphically so they can then express it in words? Do they need to learn how to take simple math problems first and write them out in words? Will their success in that, and lots and lots of practice, help them move to doing them more complex problems?
I think continued variety will help you get more students able to succeed. Use every "trick" you can think of because that next one you try might just be the key to unlocking someone's barrier!
I agree with post #2. I always had trouble with word problems, though my reading scores were through the roof. It was a panic-stricken young me who attempted a reading problem test. It was very difficult to see the language in terms of the abstract math issue, and then to have to set up the equation? Impossible. Of course, as I have gotten older and more sure of myself, the difficulty has lessened, but as an adolescent, I felt that I would die a horrible math death.
I think the best way to teach word problems really depends on the learning style of the student. One student may learn word problems very easily when taught one way, while another may be totally confused. The key is really finding out how to make the word problem relevant to the individual student.
All of the above posters are correct. There is one more thing to try, which isn't a specific technique, but more of an incentive. I teach a high school math class for kids who have REALLY been struggling with math. I try to use word problems that they will actually use in their lives, and I tell them I do not want them cheated out of their money. If they don't know how to figure out how much of something they will need, and how to figure out how much they should be charged, they may very well be cheated.
Most of the students I have helped with Math have also been really low readers. I think that some of them are so intimidated by the fact that not only do they have to figure out how to do the math they also have to deal with reading and comprehending, which is something they cannot do very well to begin with.
I agree with the above post regarding Math as a language. Since the calculator revolution, I find students have a more difficult time visualizing and therefore using the language of mathematics. Story problems are an attempt to bridge that gap and force them to visualize the math they are working with, but 1) we don't really try to teach them how to reason through such problems, and 2) students are just looking for the right answer, not the correct route to get there.
I think we should require them to generate a graphic that illustrates the math from each problem. That is, in addition to just showing their work, they should be able to translate the problem into a visual aid that shows they know the language.
That is exactly what I proposed in my project. One of the reasons was languages issues, but not inly for special needs but also for non-english speakers. In this case awe could use help from the ESL teacher to incorporate math vocabulary in her class.
It is actually an action project but no results were actually obtained so I do not really know if these techniques would work or not.
Great question! Although I spent most of my years as an English teacher, I did spend two years as a 9th grade coach of math and English teachers, so I saw firsthand the issue you are describing.
I think it's a language issue, rather than a math issue. In other words, the student has difficulty seeing math as a language.
To help this type of student, I would check first to make sure there is no disability--if there is, it could be a processing issue that requires some intervention that a special education resource teacher might be able to help you devise.
If there is not a special education situation, I would still borrow a page from the special ed. teacher's handbook and provide this student with a "word bank" of sorts: a vocabulary list of the math words, with the definition being the symbol. For example, "greater than": >
I'd let the student use the word bank as much as s/he needs in order to build confidence. Flash cards are helpful also.
When the student has built a strong math vocabulary, word problems become less of a problem!
i am person who loves to solve tricky sums. i love word problems because words are used less than signs.
Interesting question. I am of opinion that the word problems can be given by using day to day materials that are known to them. Say for examble, There are sixty five coupons in a box. Out of it 34 coupons were issued. How many coupons will be available in the box. Instead of starting teaching with coupons, we go with known things such as balls, ice creams, etc. Since these things are known to children, we can easily go near to them. Above all, I feel it is very much needed as well as a must that every teacher should behave as children when they are with children. So that novel ideas will come from that children itself. we can make use of it.
I'm having trouble on these math word problems and I have to do like 8 more. Cn you help me on these 5?
20. The longest side of a triangle is twice as long as the shortest side and the remaining side is 25 cm. If the perimeter is 70 cm, find the length and the widt
i think this is the solution but do reply the correct one if i am wrong!
let the shortest side be x
the longest side will be 2x
adding all the sides of the triangle
so, the shortest side 15
the longet side 15*2=30