Student Written Word Problems.

 

There are reasons to have students write word problems.  Many of the problems that are found on the internet or in textbooks are not easy for my students to relate to.  For instance, anything involving a car and traveling from Los Angles to Seattle make no sense to my students because there are only one or two in town and you can't drive very far with one.  I think you can go eight miles to the new school and that is it.  Problems of that sort need to be rewritten using snow machines or all terrain vehicles.  Even problems with school buses do not work well unless there is one in town.

One reason to have students write their own word problems is that it gives the teacher a way to see if they understand the concept. In addition, it gives students a chance to create a real world application of the mathematical concept.  For instance, if students are learning about unit prices, they could write problems about shopping in the store and comparing two items to determine which is the better purchase.  Furthermore, writing word problems requires students to develop higher level critical thinking skills.  

When students write word problems, they write them with an idea of how they would solve the problem and if there is more than one method involved, they will think about which method might be better.  Writing word problems help students connect the mathematical concept with their background knowledge and with their own life's experience. 

One piece of research showed that although there was no indication of growth of students ability to write better and better word problems, there was a recordable change of attitude towards word problems. Furthermore, students who could solve an equation in standard form had difficulty with the same information when it was in a word problem. Once students began writing their own word problems, they started seeing a better connection between the equations and word problems. In addition, it also helped decrease student anxiety towards completing word problems. 

For the actual process, it is best to give students the answer or a few numbers to use in their word problem.    The answer might include variables such as x^2 + 4x + 4 or it might be 28 or you might give them numbers such as 3, 5, X.  You might even go so far as to tell them you want them to write a problem that uses multiplication and has an answer of 36.  

The majority of word problems usually involve a certain number of people who are doing something.  With this in mind, students choose the characters and what they are doing.  Usually, the characters are doing something like traveling, sharing things, buying something, deciding what happens if they add a foot to one set of wall or subtract a foot from the other set. 

So for an example, I might give my middle school students 45, 3, each and uses division.  So I have the parameters of the problem.  Since there is a 3, I might decide to have 3 friends, Joe, Mabel, and Frank.  Since I have to use division, it usually means they are sharing something so maybe there is a pile of 45 pieces of candy.  I have to use the word each, so if they are dividing the candy, I'd want to know how many pieces each person got.  

The final problem might read. Three friends,  Joe, Mabel, and Frank ,have a pile of 45 pieces of candy.  They want to share it equally among them.  How many pieces will each person get?

This is not something students can do one time and be experts.  It is going to take time for them to learn to write their own problems and it is not an easy process.  You should acknowledge that it will take time to learn to do this and that it can be difficult but with practice, it becomes easier. In addition, it should be taught, retaught, and taught again but over the span of weeks so students have an opportunity to get the understanding of the structure of word problems.

This is a good way to help students become less fearful of word problems and connect the words with the equations.  Let me know what you think, I'd love to hear.  Have a great day.

Student Written Word Problems

As we know students often have difficulty solving word problems because problems can have irrelevant information, use mathematical terminology, have higher vocabulary, and the syntax can be complex.

When students write word problems, they are able to base it on their frame of reference and interests.  For students who live in the bush of Alaska, trying to answer train problems for two trains, one leaving from New York City and one from Charleston, South Carolina make absolutely no sense.  Partly because there is only one railroad line in the whole state of Alaska that runs between Anchorage and Fairbanks.  There is a train running from Anchorage to Fairbanks during the day that stops at Denali National Park, and it returns at night, making the same stop.  The other possibility is the coal train heading to Healy to supply the electric plant.

Up here, students will write their problems using snow machines, four wheelers (ATVs) or boats because that is what they are used to.l. They do not have high rises so they'll use things like the main store, the airport, or possibly a hotel if there is one in town. They can use the problems in the book as a guide but adjust it to their particular circumstance.

Another advantage to having students write their own word problems is they see a connection between their lives and the real world.  In addition, they have to use their mathematical vocabulary outside of standard equations, use their creativity to plan the problem and they have to know how to solve it so they can provide a solution.

Furthermore, they have to translate the mathematical equation into words rather than words into equations.  Most word problems in textbooks do not ask students to create a problem, they ask them to solve it so they learn to create equations without necessarily understanding the concept.  The other thing is that most of the steps they've learned to use for solving word problems do not help them when writing the problems so it gives them an opportunity to see how people who work applied math problems go through.

If you stop to think about it, most of the worlds math questions tend to be based on observations which are expressed in words before it can be turned into equations.  By having students writing their own word problems, they are learning to express certain situations in written language which is part of learning to communicate mathematical ideas.  In addition, it helps students gain an understanding of the key steps needed to solve word problems.

According to several studies I read, having students write their own word problems, helps increase student ability to answer word problems.  In addition, it is a good way to incorporate reading and writing into the math curriculum and it helps students improve their ability to communicate.  Let me know what you think, I'd love to hear.  Have a great day.