Looking at patterns only helps to organize and sort the data. The patterns that emerge through data analysis serve as the basis for formulating hypotheses that lead to an improvement plan. Developing hypotheses is the process of formulating questions that explain the data. This questioning process helps to search and find meaning in the data.
All hypotheses should be expressed at this point. Hypotheses then can be disputed if evidence can be shown that disproves an explanation. Many hypotheses usually are offered, but eventually the list is reduced into just a few of the most valid theories.
| Problem: Achievement levels in math drop grade by grade until they are at very low levels in grades 6, 7, and 8. They pick up only slightly from grades 9 to 12. |
| Sample Hypotheses | Evidence to the Contrary? |
| Is it because there are more special education students in regular classes and it pulls our scores down? | REJECT. We checked special ed enrollments. They do increase from grades K-3 but then stabilize until grade 6, and then decline to grade 12. |
| Our standards are just too high. The tests are too difficult, year by year. | REJECT. We looked at test results nationally and in neighboring districts. Although mathematics performance is low nationally and statewide, our performance is particularly low compared to our neighbors and to the national sample. We have also studied the items and concur that the items are fair for the grade levels assessed. |
| Our math teachers in the intermediate and middle levels have not had the proper training to teach the current math standards. | ACCEPT AS A POSSIBILITY. We looked at the licenses, and the teachers do have appropriate credentials. However, we looked at the sequence and record of professional development activities, and no math professional development has been provided by our district in 10 years. |
| Our textbooks are not only out-of-date, but were not adopted in a logical grade-by-grade sequence. | ACCEPT AS A POSSIBILITY. We charted our math textbook adoptions. They range from 1981 to 1986 from five different publishers. We are long overdue for new materials adoption. |
| Our students are apathetic. They are turned off and just don't care enough to do their homework. | REJECT. We checked attendance rates and behavior problems, and see no real pattern there with math performance. Many of these same students perform well in other subjects. |
