Effective Personal Strategies for CBA
The following comments provide a glimpse of strategies that have been found to be effective in using CBA. They are not intended to be one-size-fits-all recommendations. The strategies have been proven on the complete gamut of students from Math for Technology II (students who have convinced themselves and everybody else that they can't learn algebra) through honors students.
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CBA offers flexibility that is unheard of in the usual algebra class. It is no problem at all to have different students working on a wide range of programs all at the same time, each getting the tutorial oversight of the program, telling him when he is on the wrong track. The teacher may spend only a few minutes lecturing at the beginning of the period (an exercise which is frequently futile, anyway). The bulk of the time I spend asking, "Now, who needs help?"
I find it very productive to let students re-do programs to improve their grade. My goal is to motivate them to master every topic, not to determine who gets an A for getting there first. I have no problem in letting them re-do programs, right up to the end of a report period. Tests, on the other hand, can be redone only during the assigned test period.
A convenient recording technique is to record partial grades in pencil (these result from exits from a program prior to completion), and to use a distinctively colored ink for the grade achieved at completion. Rather than split hairs over the difference between a 93 and a 94, I award 5 points if the Performance Summary screen shows either 15 or 16 correct (out of 16), the equivalent of an A. As a special incentive, perfect scores result in a circled 5 and the best students will re-do an entire program just to get the circle around their 5. Four points are awarded for 14 correct answers, the equivalent of a B. Three points are awarded for 13 correct answers, the equivalent of a C. Two points are awarded for 12 correct answers, the equivalent of a D. Only in a very special situation would 1 point be awarded.
Since students are encouraged to (and are eager to) improve their score, I must frequently change a grade. To facilitate this, the scores are recorded in the form of a five-spoke wheel. A four looks essentially like the letter X. As the scores are improved, it is a simple matter to add the required spoke to the wheel. Recording the added spokes with a color of ink that is different from that of the original grade retains information about the profile of progress.
The scoring plan was devised because I got tired of students carefully calculating what they had to do to get the grade with which they would be satisfied and then coasting. The trade-off for the ability to improve any and all grades is that the program component of a given student's grade will be the lowest grade that he/she has on any program during the report period. This first comes as a rude shock, but all have come to peace with the trade-off because of the encouragement that they get to succeed.
Once the course gets into the more complex programs, I offer the opportunity to improve any grade by one point by repeating the last four problems without an error. This means that, once a student has a passing grade, he can improve, say a D to an A, by successfully repeating the last four problems of the program three times without error (once for each point or missing spoke of the wheel). The better students often ask if they can improve their 5 to a circled 5 in that way. The response is, "No, I'm sorry, but the circle indicates no mistakes. If you want a circled 5, you'll have to repeat the entire program from scratch." Believe it or not, many do exactly that.
Special grading considerations
Since I use CBA in both Math for Tech II and Honors Algebra I classes, it is obviously necessary to make some adjustments. I find that we can achieve much more in the weaker classes than was possible prior to using CBA, including solving systems of equations and equations containing radicals, and a meaningful exposure to the derivation of the quadratic formula. To introduce some of the more difficult topics to one of the slower classes, I sometimes offer to assist the class to work the first four problems. A student who wants help will state his problem while I act as scribe at the board. If no one has any ideas, I will ask questions to prompt progress. Since all of the students will have similar problems for the the first four in most programs, assistance given to one will show the way for all.
Still, the most difficult of the programs are reserved for the honors classes. Also, at grading time, I find it advisable to "forgive" one or two programs in the weaker classes. This is because the pace of new programs has been gauged to challenge even the better students in the class which means that the lower end of the class is inevitably struggling to keep up. The goal is to keep hope alive in all. Each teacher will have to find the best way for themselves. Personally, I don't let it be known how lenient I intend to be or not to be. When a student asks, "What do I have to do to make a __", I reply, "Don't waste time trying to calculate; Just keep on keeping on".
Tests are scored a little differently too. Since a test consists of four problems on each of the four selected programs, the maximum possible score is again 16 correct answers. Since the students have the opportunity to re-do any portion of the test, I raise the ante on the test for the honors classes. Sixteen correct answers are required for an A, 15 for a B, 14 for a C, 13 for a D. I find it convenient to use a different color to record tests, and to record the results of each of the four programs separately, using four four-spoked wheels. In this case, each spoke represents a correct answer