Dear Matt,

My materials have many word problems that require the students to read carefully in order to work them out. I find that students are very resistant to doing problems that require them to re-read or think hard and they come to me saying they don’t understand what the problem is asking. Should I read the problems to them emphasizing the important words or sentences? Many of them just give up if they don’t understand the problem right away. What can I do to make them more independent in figuring things out for themselves?

Worried teacher

Response:

Dear Worried:

Your question raises several different issues: students’ willingness to think hard, their difficulties with reading comprehension, and the types of problems we ask them to solve. Let’s look at each of those separately.

The most important thing you can do to help your students learn to think hard, and thus to learn mathematics, is not to take on the problem solving yourself. Often when students come to you (or any teacher) saying they don’t understand, they are hoping that you will do the heavy lifting for them. We live in a culture where we expect faster and faster speeds in most tasks of life. We want our computers, internet connections, and phones to be ever faster, our food to be served quickly, lines to move rapidly. In teaching problem solving, we are attempting to value the opposite of fast: sticking to a task, often for a prolonged time. Matt once had a poster he loved on the door of his math classroom that said: Patience, Persistence, Success, with an appealing picture of a sailboat on it. In order to build these qualities in students we must help them experience success and build their confidence through scaffolding and providing timely supports.

Precise reading is one of the basic skills required in mathematics, and students need to learn to do the careful analysis required for understanding mathematical text, which is very different from reading fiction or other most other types of reading. Exercises like those used for reading comprehension can be used to help your students improve these skills. New English-Language Arts standards include technical reading in all disciplines, including mathematics. Successful teachers often use a sequence of activities such as this during a lesson: Read the problem silently; read it aloud; explain it to a partner in your own words; ask a question about anything you don’t understand; work on it independently for five minutes, and then join a group and begin to share what you know and what you don’t know. This group work can continue for 20-25 minutes. One frequently used strategy that is not associated with increased understanding is focusing on key words. As often as not, this can be misleading, and is not a useful approach. A strategy that is helpful is encouraging students to use visual representations for the problem, such as diagrams, arrows, graphs, or pictures. A strategy used in many successful mathematics programs is that of modeling word problems. For an excellent explanation of this, see the “Modeling Word Problems” part of the Minnesota Mathematics Framework developed by SciMathMN. The driving question for this part of the Best Practice section of the Framework is How can I help my students understand and use the important information in a word problem? It can be found at SciMathMn

Good problems are not the same as exercises, which provide practice, but not necessarily thinking. Often the “word problems” found in textbooks are actually exercises, a way to provide additional practice in a particular procedure. Though you may want your students to be able to solve these exercise-problems, it is probably not necessary to spend too much valuable time on them. A larger goal is to help them develop skill in solving non-routine problems, ones that are not easily solved by performing a procedure currently being studied. An important role for you as a teacher is to select good problems. Terry Wyberg, immediate Past-President of MCTM, says that a primary characteristic of a good mathematics teacher is that s/he is a “good picker” of rich and interesting problems. The context of the problem can be a way to provide both motivation and understanding, remembering that the goal is learning mathematics. Realistic problems, using students’ experiences, can also help- students make sense of the situation, so they are not trying to read about something that is unfamiliar to them, or about which they do not care.

It is not clear from your question what grade level students you teach, and your question applies to students at all grades. There are special issues regarding word problems for algebra, since typically much algebraic work involves translating word problems into equations in order to solve them. It may help students to remind them to use any variable or term that helps them make sense of the problem, such as b for Barbie’s candy and k for Ken’s. Many students mistakenly believe that they must use Xs and Ys, reinforcing the belief that algebra is the intensive study of the last three letters of the alphabet. Translating a situation into an equation can also be explored by working backwards – translate an equation back into a situation with words. Remind students that any method that helps them reach a solution is acceptable. Some students are more comfortable using more informal methods to solve, others will use formal and abstract strategies easily. Both will work, and much enriching mathematics can be studied by encouraging students to compare and contrast different solution methods.

So, to sum up:

• Don’t take the thinking away from your students; some struggle is necessary in order to learn
• Support persistence and build confidence
• Help them learn to read mathematics carefully
• Teach modeling techniques for approaching word problems
• Pick good problems
• Accept informal approaches

Matt

Matt Mentor, a wise and experienced teacher, offers advice about teaching mathematics topics to beginning teachers. Of course, experienced teachers can join in as well.

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