Using Technology to Master Math Basics
By: Jack Fretwell
In math, learning the basic tables is often the first real challenge a student encounters. It follows, then, that the student who succeeds at basic computation is likely to go on to be reasonably successful at math. Unfortunately, the history of student success at these skills is not good. Traditional methods involving flashcards, timed drills, and rote memorization have tended to turn students off, and relatively few students recall being strikingly successful. To the contrary, the term "drill and kill" comes to many people's minds when the subject of basic computation arises.
In fact, the desire to escape from the drudgery of basic math led to its significant reduction in many classrooms as soon as calculators became widely available. However, teachers soon discovered (and the National Math Panel recently confirmed) that students lacking strong mental computation skills are disadvantaged when it comes to mastering more advanced math topics.
These findings would seem to put us back to square one. Luckily, that's not the case, for the same technology that produced the calculator, a device that enables some students to get by without strong mental skills, also produced the personal computer, a tool we can use to help students develop strong skills in a way that reverses "drill and kill."
In fact, we can give nearly all students a taste of feeling pretty good at math. Here's how. First, we define for students what it means to be pretty good. Then, we give them a small sample to show that they can do it. Next, we break the learning task into small, "bite-sized" chunks similar to the sample and let the student practice with them one by one until they've been mastered.
We develop a way for the student to track his or her progress, keeping score along the way and visually seeing the gains he or she is making. To keep it fun and free of pressure, we make it possible for the student to engage in all this while working independently at his or her own pace. Most importantly, we provide lots of positive reinforcement and feedback, especially at the "chunk" level.
Even a private tutor working one-on-one with a student would have a hard time fulfilling all these tasks, but a personal computer with the proper software handles them easily. To take just one example, look at defining the skill. Typically, we'd say being good at basic addition means being automatic and accurate—say, being able to solve 60 out of 60 basic problems in three minutes. Some teachers give drills like this all the time.
But, a beginner has no reason to believe that he or she can succeed at this task (and some never do). So, instead, we'll set the goal at being able to solve just one problem in three seconds and tackle those 60 problems one by one.
Without technology, we couldn't use this standard because it's practically impossible for a teacher to focus on problems one by one for each and every student, but a computer can do it easily. By timing each problem separately, the computer can show the student how close he or she is getting, until, sooner or later, the three-second mark is reached. It doesn't take long for these successes to add up, and soon the student comes to expect them.
The right software provides a number of additional functions that would ordinarily mean a great deal of extra work for teachers. Positive feedback, results tracking, practice assignments, and session scheduling can all be done by the computer in ways that combine to make the process not only rewarding to the student but much more efficient than traditional methodologies.
When comparing programs, look for the following capabilities:
* Does the program address the full range of computation from addition to division?
* Does the program address computation with negative as well as positive values?
* Will my students clearly understand the objectives of the program?
* Does the program set up and manage student sessions appropriately?
* Is there sufficient positive feedback for my students to enjoy working with the program? Is feedback immediate?
* Does the program allow me to monitor students' performance over time?
* Will the program work at an individual student's best pace for learning?
* Will students succeed at a rate that is challenging, but not frustrating?
* Does the program allow time for students to reflect on their work?
* Does the program use timing in a way that minimizes pressure?
* Does the program provide printed reports of student success?
* Does the program provide graphical reports of success and progress?
Using computers to strengthen mental computation offers excellent benefits to students, affecting not only their skills but also their overall attitude toward math. And, it relieves teachers of a burdensome and often unpleasant teaching task. However, any effective learning process takes time. Time during the school day is limited and so is access to computers.
Adding to the time factor are considerations involving the educational advantage of spacing many short sessions over time vs. having fewer longer sessions and the variations of learning pace among a class of students. The good news is that the speed with which learners develop math skills appears to be irrelevant. In fact, students taking more time sometimes show better retention.
A recommended approach, therefore, is to have all students engage your program and work through it from start to finish at their own pace. Your task should be to merely monitor progress to show your interest and offer encouragement. Minimize that some students complete the process ahead of others. Don't worry; even slower students who stay with the process will gain mastery at a much faster rate than with traditional methods.
Your reward? Be prepared for most students' computation skills to be anywhere from one-half to a full year ahead of traditional expectations. What effect will that have on their other math work?
Jack Fretwell is the founder and owner of Starboard Training Systems, www.capjax.com.
