As we wrote in previous posts, fluency is important. Basic math facts do not go away but are used throughout the upper grades in more abstract and involved contexts. If the students’ minds are burdened with having to reestablish basic facts and concepts, they’ll be like music students not fluent with their basic scales, burdened and frustrated later when they come across those scales in a piece of music.

The progress chart, found in the middle of every partner page, builds on the good practice started with the graphic and partner pages. It uses those pages to keep practice grounded in experience, so there are no tricks or drills separated from a physical context that is understood. It takes what is good about timing exercises and leaves behind the problems. It both measures and improves performance. It develops further the understanding, speed, and accuracy needed for work in the upper grades.

The overall time and increments in the progress chart differ between lessons based on our experience in the classroom and tutoring. You may find it helpful to read the earlier posts in this series, A Model for Using Guided Discovery in a Math Lesson, if you haven’t already, as these steps are sequential.

Here’s a model for working with the progress chart.

1. After students are oriented and comfortable with a graphic and accompanying partner page, ask for a volunteer to do a timing experiment with you. While they say the answers on the partner page, time them to see how many seconds it takes them to get a perfect score (with the help of the graphic page if needed). You can say that it’s their first time doing this so it doesn’t matter if they’re fast or slow; this helps relieve a sense of anxiety. To avoid the tension sometimes associated with racing, do not begin timing with “ready, set, go!”; simply begin the timing when they say the first answer. Their partner should continue checking to make sure the answers are correct as explained in the post on the partner pages. When they finish, tell them their time and have them circle all the times on the progress chart that they beat.

There is no target time. However long it takes to get a perfect score is the objective at this point. Because of their previous work with the graphic and partner pages, many students will move comfortably into this timed approach. The problems are better understood and they’re becoming more familiar to them. To keep this from being a rote exercise, change the direction in which they solve the problems.

2. Now ask the class to look at their partners and decide who is partner A and who is partner B. When you say “begin,” all the A’s will say the answers and the B’s will check the answers and keep track of the time with you. When they’re done, they can look up and you’ll give them their time.

3. The times that are beat are circled and the partners switch roles.

4. The partners continue taking turns, comfortably and joyfully improving their times by increasing their familiarity with the material. After the initial work on the graphic page, reinforced and expanded on with the partner page, the progress chart creates even greater competence and confidence with the concepts, procedures, and facts.

This is very different from enforced time tests, where students do as many problems as they can in a predetermined time—which often means that they fail to answer some problems, and answer others incorrectly. Our emphasis is on correctness, thoroughness, and understanding every bit as much as time. The students correct themselves as they go; all of the problems are answered correctly. Therefore, no wrong answers are written and reinforced, and no answers need to be given to them. They don’t miss needed practice on certain problems because of not finishing the exercise in a predetermined time. The voluntary character of working with the progress chart creates a happy feeling. And our experience continues to be that students’ natural inclination is to keep going to improve their time, and in so doing, their understanding and fluency.