I have been wanting to do this for some time now. I have three charts I'd like to share with you to get your feedback. I've sent these charts to myself (2 jpeg, 1 gif) and each is about 190 Kb. I tried reducing the scanning resolution but the image quality suffered. Am therefore sending the list 1 image with this message plus two separate posts each containing one image and text to reduce the download time.

Unfortunately, I was only able to reconstruct these charts at the end of this school year. I am uncomfortable with what I see because trends were clearly present that, had they been acted on in the context of daily charting, could have spared this child relatively high social behavior error rates.

The lower portion of this chart shows the number of social behavior corrects and errors per minute relative to a 420 minute school day floor. The triangles reflect physical holding in response physical aggression toward teachers. The upper panel shows data from Steven's special education direct instruction math class. I believe the teacher is using Connecting Math Concepts, but couldn't verify the curriculum before the teacher left on summer break. Data points show problems correct per 2-minute timings and errors per 2-minutes. This teacher set 15 corrects/2-minutes with zero errors as the criteria for advancing from one level to the next.

First the social behavior data. What I observe is corrects dividing at 1.05 per minute per week while errors multiply by 1.05. The error trend could have been specified within the first month and half of school and effective action taken. My assessment of the situation when I was called in early December was that 1) the paras were giving too many warnings before taking effective action to correct errors, and 2) staff members had allowed the ratio of positives to negatives drop below 4:1.

To see this chart full size (if your browser can stand it), click on the chart.

In math, Steven's learning showed jaws in Level A but growth was slow at x1.3. Level B was almost flat with respect to corrects, but errors were dividing by 1.3. Just a word about Steven. When he came to us last year, he was a violent child. He could not read and could barely count. He had been in a program with two full time adults whose task it was to physical restrain him or escort him to time out. By the end of last year, he was acquiring reading skills from Reading Mastery and had been reintegrated into the general education setting. During the summer break a great deal of our progress got lost and that is why physical restraint counts appear on the chart.

The second chart shows Steven's progress since the 1999 Christmas break in both social behavior and math.

Following the Christmas break, staff members tightened up their responses to both social behavior corrects and errors, and they succeeded in holding close to our 4:1 ratio of positives to negatives. You can see that social corrects leveled out around mid February. Errors per minute, on the other hand, divided by 1.15 and for the first time, we see increasing numbers of zero error days. In early March, Steven was chosen "Student of the Month" by his classmates!

To see this chart full size (if your browser can stand it), click on the chart.

Steven continued to make progress in Math, passing one level every four weeks. I don't know if this is on pace or too slow; it is what it is. Corrects tended to multiply by 1.2 to 1.5 with low or zero error rates. What I noticed that I'd like comment on is an effect in Level G. There you can see two segments of three consecutive days in each. This is a departure from the weekly or biweekly timings usually plotted. These two segments show corrects that multiply by 1.8 and 2.0, respectively. These celerations suggest to me the potential for more rapid growth and movement through the curriculum levels with the addition of daily timings and charting.
 

This last chart illustrates the relation between social behavior errors per minute and the positives to negatives ratio. Data are plotted on log-log coordinates and reveal an inverse relationship. The power function accounts for 76% percent of the variation in the relationship between error rates and the positive:negative ratio. What it shows is a dramatic effect on the lowering of social behavior error rates with each unit increase in the pos:neg ratio. I constructed a similar chart for corrects versus errors per minute and found a very poor linear association through the power function.

What this suggests to me is a strong confirmation of Og's statement (and others on this list have said it too) that errors are independent of corrects. Ultimately the production of social behavior corrects must come under the control of natural classroom contingencies which is what I think happened here with the stabilized rate of corrects. The continued production of social behavior errors, however, was sensitive to the specific contingencies arranged by through our program which, in part, had to ensure greater benefit to appropriate social behavior than to errors.

Stuart Harder

Comments on the List Server:

In reply to Richard, who asked if Steven would continue working on these targets during the summer, and raising his aims:

I don't know if Steven is in the Summer Session. He should be, especially after last year's disastrous experience. The lack of a summer long program of social and academics was costly to Steven's progress in the 1999-00
school year for the first three months at least.

I will talk with his DI teacher about raising the aims.

From Sue Casson:

Stuart, while you in in there, _please_ find out what his 0-9 think/ write tool is. And if it's below 130, have him work on it. And set his aims to correspond with his 0-9 tool skill. (About 80% of tool skill would be aim.)
Move aim up as tool skill improves.

Also find out just what she is counting. It looks like on the chart they are counting problems. What kind of problems? Is he writing the problem out, or just writing answers? I would count digits written, it's more discrete.

Also, there's only two dots a week. When I used to supervise charts, I wouldn't even talk to someone until they had at least 4, if not 5, dots a week on the daily chart. Two dots is not enough practice. Sometimes you have to help teachers reorganize their classroom in order to get consistent fluency work done.

Your charts just look beautiful. They are so clear!

And later, from Sue Casson:

Stuart, are you saying 12 per minute on the chart for think/write "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2..."? Do you mean 12 digits per minute? On a two minute floor, so 24 digits a per 2 minutes? (Stu replied: I reported exactly what his teacher wrote on his add/subtract chart. He did not specify the sequence. Here is a cut down version of his add-subtract chart.)

Two minutes is too long a floor. That's a number every 5 seconds! Try it and see. Remember this isn't a zen meditation exercise! I'm surprised he's not smashing windows. You can add abitrary positives all you want for his conduct, but shorten those floors! Then you might actually generate some natural positives. For think/write digits 0-9 he could be put on a 15 second floor until he reaches 120-130 on the chart. Then drop it to 30 seconds and go to 130 on the chart again, then 40 or 45, to 130 on the chart, then a minute etc.

I just looked at his chart again,and he's a third grader, about 9 years? He should be able to make it up to 100-130, barring any physical difficulties.

If those components aren't there, raising the aim on his math problems isn't going to do anything but add to his what looks like his terrific burden of frustration and dis/dys/fluency (sorry, Ogden, I forgot how to spell it again. But hello!) The aim on his math problems should be counted in digits and 80% of his think/write 0-9 current aim (but building to 130 or so.)