Revitalizing Algebra: Unstructuring Tasks
Immediate results were mixed, though the teachers have continued to change over time. Through interviews with teachers, through reading their writing and listening to their planning for future work with their home departments, we observed an increased appreciation of the amount of structure in a mathematical task as a choice which can have important consequences (1) - (9). Their discussions indicate that they realized that there were careful choices and teaching moves required when leading low-structure activities, though they were not always sure what they were. Deconstructing the roles of students and teachers in low structure classrooms to understand how their roles differ from a traditional classroom was not something most participants did on their own. Participants began to focus on questioning as a key to facilitating low-structure tasks. It takes thoughtful reflection to become a good questioner who can create the "zone of proximal learning," and it seems that this is a fairly advanced developmental stage of teaching. One high school, which had already embraced many of the principles advocated by REAL, is just now focusing on the importance of the types of questions teachers ask in facilitating groups. Many of the teachers seemed to believe that using low-structure activities was an ideal to aspire to, and they realized that they must teach their students how to work together, take risks, make mistakes, look for multiple strategies, and explain their thinking.
We asked teachers to respond to questionnaires before and after the program began. Unfortunately, before it began we did not realize how crucial unstructuring would be in improving teacher practice. So, we did not ask whether they considered that a factor when planning lessons. However, in the post questionnaire, we asked to what extent "Unstructuring lessons so students can use their own strategies for solving problems" was a key consideration in their planning math lessons. Twenty-three percent of the teachers in participating schools ranked that aspect as one of their top three considerations. Sixty-five percent of the teachers ranked it with a 4 or a 5 on a 5 point scale as being a key consideration.
The REAL Project has collected data on academic achievement by algebra students in the partnership schools. Our originally planned direct work has been over for one year or more at the sites, but we have been able to continue work at several sites either directly, or indirectly by funding REAL-inspired projects. Roughly speaking, we have seen excellent recent results in the school involved in Ongoing Direct support, continuing improvement in the four schools receiving Ongoing Indirect support, and very poor results in the three schools where there is No Continuing support. On the one hand, it is satisfying to feel that our work can lead to improved results in schools. On the other hand, one of our hopes was to create lasting change in the culture of each math department.
The data from a school where we are funding ongoing direct work shows a truly impressive drop in algebra failure rates both collectively (down from 35% at project start to 25% last year), and disaggregated by ethnicity. Especially notable was the failure rate of African-Americans (down to 22.3% from 40% at project start), who are the second largest ethnic subgroup, and about a quarter of the student body.
At one school receiving indirect support we met our targets for reducing absenteeism in every ethnic group, and we met our passing rate targets for every ethnic group (except Asians). The absentee rates are down remarkably from the project start (down to 4.0 yearly absences/student from 12.3). Most encouragingly, the failure rate of African-American students has shown a big drop from 64% to 49% since the start of the program. This rate is still unacceptably high, but we are encouraged that significant change has occurred in the right direction. We are also pleased to report the overall failure rate dropped from 56.5% to 45.0%.
At a second school, receiving indirect support, the African-American failure rate has gone from 62.2% in the normal first year math course to 48.5%, which is very good progress. On the other hand, the failure rate for Latino students has increased from 30.6% to 45.6%. This presents a very mixed picture that we cannot explain but that could be related to changes in the Latino student population.
Two middle schools are receiving indirect support. The challenge in middle school is to give more students a chance to take algebra, while maintaining healthy passing rates. For this reason, our main benchmark for our two middle schools is the number of students passing algebra as a percentage of the total student population (not just a percentage of the number of students taking algebra). At one school the passing rate of students in their algebra classes has met our target and improved to 26.5% of all eighth grade students taking and passing algebra from an initial rate of 20.2%. of all eighth graders. At the second school the rate went from 11.2% to 27.2%.
