Helping Students with ADHD Solve Math Problems
David Johns, University of Delaware

"I did every problem in the book, and I didn't recognize one problem on the test." Students referred to my office because of difficulties with math and math-related courses tell a very similar story. "None of the problems looked like the ones we did in class or on the homework. The professors are out to trick students."

"Trick" is not a bad choice of words. According to University of Delaware math professor, Georgia Pyrros (1998), the critical skill in solving many problems is identifying the trick or key to the problem. This insight is what allows the problem solver to unravel the problem. Professor Pyrros also notes that many of the problems introduced in class have been around for hundreds of years. If a student wanted, he/she could find the same problem in Latin or Greek. As a result, she explains to students in her course on problem solving, professors have to play with the words and numbers so that the problems do not look alike.

Professors do not want students memorizing procedures, so they reconfigure the problems to alter how the problems look. If a student has stored away information with visual cues, a reconfigured problem won't fire off those connections, and the result is, "I don't recognize any of these problems!"

Mathematically gifted students proved to be better at solving verbal-spatial problems compared to artistically gifted students or a control group matched for IQ (Hermelin & O'Connor, 1986). One conclusion that can be drawn from this study is that mathematics ability includes more than spatial ability or general academic ability. Verbal ability apparently plays an important role in the process, and students gifted in mathematics appear to be capable of moving from verbal representations of a problem to spatial representations of a problem. The importance of these representations is illustrated by the diff iculty experienced by students when the two are combined to create word problems; the nemesis of all students who dread math.

Students with ADHD often encounter difficulties in math courses. They report making frequent "stupid mistakes." In college, they rarely receive the partial credit that improved their grades in high school math courses. Math is difficult because you have to hang on to meaningless information until it hooks up with meaning. For a student with ADHD, keeping meaningless information in his/her working memory long enough to apply it can be very difficult. Distractions and frustrations contribute to deficits in these students' short-term memories. Students with ADHD who are successful at math often have had a coach who made them stick to it and repeat it several times so that the connections were made. Thus, the common comment of a student with ADHD, "It takes me a lot longer to get stuff in, but once it is there it stays," is logical.

Math may also be difficult for students with ADHD because they are less likely to identify the trick to a problem. Difficulty with details lends itself to taking a big picture approach, and the trick can be a detail that only makes a cameo appearance.

So what does one do to help students with ADHD (or any students) who are having problems with math? First, check their background. Do they have the prerequisite skills needed for the kind of math they are attempting? When students with ADHD undergo psychoeducational assessment, their achievement test scores typically are consistent with their aptitude test scores. They have learned the material - maybe not in a fashion or rate to earn a good grade, but they have learned it. Given sufficient background, what follows is a systematic method to prepare for a problem-solving test. This approach emphasizes the use of multiple representations of problems as well as practice with key problems. The following chart depicts a format that can be useful to students during and after class, in order to practice and internalize math problems more effectively and efficiently.

Format For Organizing and Combining Math Lecture Notes And Homework Problems
(4) Homework Problems 1. 2. 3. 4. 5.	2) Steps in your own words: 1 . 2. 3. 4.	(1) Class: Nice Example 1 . 2. 3. 4.
(One extra step compared to this class example may be the trick to the problem.) (3) Rule or principle:   (5) Pick key problems and rework them to develop a feel for the problem:

The above diagram is an adaptation of the Cornell Notetaking System (Pauk, 1977).

(Note: example steps in numerical parentheses below correspond to steps in the diagram on the previous page.)

Step (1): Example: In general, a professor presents a clear, straight-forward example of a problem that works out nicely. Students report they never see one like it again. These notes are taken in class as presented.

Step (2): Steps-in-own-words: After class, a student goes back to the example and writes out the steps in his/her own words so that he/she can now follow a set of self-instructions.

Step (3): Rule or principle illustrated: Professors carefully select their examples to be clear examples of a particular rule or principle they wish to illustrate. Identifying and articulating the rule or principle helps to categorize the problem.

Step (4): Analogous homework problems: Students report that they use examples from class or in the book to solve homework problems. These problems are similar to the class and book examples, except that there is usually one step that is different. The rule or principle may be applied to another kind of function (e.g., natural log vs. log base 10), as this step is the trick to the problem, In some cases the problem may be an exception or variation to the rule or principle.

Step (5): Select key problems and rework them: Rather than solving every problem available, Professor Pyrros (1998) recommends picking key problems and reworking them to get a feel for them. She tells her calculus class to do these problems 22 times. When they recover, she emphasizes that, by redoing problems, you develop a feel for them. It is like a puzzle; you take it apart and put it together . . . until you can do it automatically.

 

Key Problems How do you know if it is a key problem? If the professor says so. If the professor gives repeated examples. If the problems are assigned or appear in a problem set.

 

Looking for Families or Categories of Problems To prepare for a test:  Pick key problems--discuss with others in class. Redo key problems and develop a feel for them.

By engaging in this structured practice strategy, students develop multiple representations of the problem: visual, verbal, categorical and/or logical, analogs and tactile. Repeated practice can help students develop internalized self-talk to guide the

 

General Problem-Solving Technique (Heuristic Device) What do they want to know? What do they give me? What does it look like? (draw a picture, diagram, graph, table, etc.) What do I know? (brainstorm) a.  Setup problem b.  Solve equation c.  Check answer to see if reasonable

Burrier, H. (1988). How to study math. Englewoood Cliff, NJ: Prentice Hall, Inc.

Hermelin, B. & O'Connor, N. (1986). Spatial representations in mathematically and artistically gifted children. British Journal of Educational Psychology, 56, pp. 150-157.

Pauk, W. (1997). How to study in college (6th Ed.). Boston: Houghton Mifflin Co.

Pyrros, Georgia (1998). Personal communication.