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May 2008Welcome to Exemplary Initiatives online!Exemplars is a community of users dedicated to helping schools become successful in standards-based performance assessment and instruction. Our monthly newsletter features short pieces from Exemplars users, as well as brief reflections on current education issues and trends that impact standards, assessment and instruction. If you would like to contribute, or have comments you would like to share, please get in touch with us at info@exemplars.com. We look forward to hearing from you. In This Issue:
What's New?: The Exemplars Assessment Suite1. The Planning Guide is designed to help plan an assessment. It is a digital version of the guide that we use in Exemplars workshops. It asks the critical questions: If I am going to use this particular task as an assessment piece, what do my students need to know and be able to do to meet the standard on this task, and what do I need to do to get them to that point? It really is a "backward planning" or Understanding by Design guide. It leads the assessor (user) through a series of questions, beginning with, What standards or Grade Level Expectations does this task address? It asks, What types of strategies might my students use to solve it? What representations might they use? To what mathematical language does this task lend itself? What connections can my students' make using this task? It encourages the assessor to explore alternative solutions, anticipating what students might do. Related tasks that can be used for instruction and exploration can also be recorded. The Planning Tool can be saved for future reference and editing as well as printed. To further assist teachers within the Planning Tool, there is a link to one that has already been filled out. 2. The Assessment Reporting and Analysis Tool helps teachers track their students' progress over time and make sense of their students' performance, individually or for an entire class. This tool generates progress reports on individual students as well as classes based on overall performance and the analytic criteria for each rubric. The assessment data can be exported to Excel or most student information systems, thus eliminating the need for double-entry. Graphs of individual students or the entire class may also be printed. 3. The Task Reflection Diary allows teachers to reflect on how things went. It helps them to look back and ask what went well and what they might do differently, either with the next assessment task or this same task next year. The diary asks not only how students performed but also how they reacted to the problem. It queries, What didn't my students know that they need to know to be successful on this problem? As they approach the same task next year they will be prepared. It concludes by asking, Where do I go from here? Once again, the diary can be saved as well as printed. Please give it a try and tell your colleagues about it. Go to www.assessment.exemplars.com to register or log in. From the Field: "Moving Math Instruction One Task at a Time"For the past seven years, the Institute for Student Achievement (ISA), an intermediary reform organization with either large high schools transitioning to small learning communities or with new small high schools, has been working with its partner to prepare low-income and minority students for success in college and beyond. Currently, there are 57 of these programs serving roughly 15,000 students in New York, New Jersey, Georgia and Louisiana. ISA also works with the National Center for Restructuring Education, Schools and Teaching (NCREST) at Teachers College, which serves as the organization's research partner in supporting schools. In addition to the professional development support ISA provides through coaching, workshops and institutes, ISA offers schools formative data in math and writing. The data from these assessments are intended to help schools develop their instructional capacity to support inquiry-based learning and literacy and numeracy across the curriculum. A need arose to provide useful formative data on students' ability to handle inquiry-based math tasks. After conducting a national search for companies that created math performance tasks, we identified Exemplars as the best fit given the quality of existing materials, the collection of student work samples, and the opportunity for professional development. Our idea was to create a team to share the work: the three ISA math coaches, two staff members from NCREST, and five New York City math teachers who regularly practiced inquiry in their classrooms. In a "train-the-trainers" model of professional development, our team worked with Aldo Bianchi from Exemplars in July to identify which performance task to administer to students first ("Tina's Quilt Squares") and how to introduce it to teachers. During one session in late August and another in mid-September, the team introduced Exemplars to the 46 New York City math teachers. The responses were overwhelmingly positive; teachers liked "Tina's Quilt Squares," the resource CD, and the focus on problem solving. Teachers enjoyed looking at students' problem-solving skills and discussing the sample papers with one another. It was a good start, but we are still pursuing a deeper goal - to support teachers' practice of inquiry-based instruction. This means, in part, working with teachers to learn about what makes a good performance task, how to revise performance tasks and how to create their own. To plan for this work, we brought Aldo to New York City again in late October to work with our team and with three teachers. These three teachers were our "focus group" as we experimented with different approaches to support creating tasks. After an intensive four-hour session, the two 9th-grade teachers collaborated to draft a task dealing with inequalities. The 10th-grade teacher, after taking time to identify what is most important for students to learn about triangles, drafted a task that asked to students to design various roofs for doghouses, and in doing so, generalize rules about the relationship between sides and angles. By the end, our 10th-grade teacher remarked, "This is good. Why haven't I been doing this all along?" A fuller discussion of the ISA project and Exemplars' role can be found here. From the Research Desk: "Mathematical Problem Solving: Its Effect on Achievement and Attitudes of Elementary School Students"The treatment group was comprised of 164 students in seven classrooms in one school in grades 2, 3 and 4. Teachers in these classrooms agreed to supplement the regular district mathematics curriculum with 10 non-routine mathematics problems. The non-routine problems were Exemplars problems. Students in the treatment group completed a survey and solved one Exemplars problem independently as a first step in the study. At the end of the study, they solved another Exemplars problem independently and filled out a second survey. Teachers in the comparison group also filled out a survey and were interviewed by Devens-Seligman. Teachers were trained how to present problems and to debrief solutions after the problems had been completed. A comparison group in the same school (TS) as the treatment group was comprised of 164 students in five classrooms in grades 2, 3 and 5. Classes in this comparison group followed the regular district mathematics curriculum without the supplemental Exemplars problems. Students in the comparison group solved an Exemplars problem at the end of the study and completed a survey. A second comparison group (M), in a different school, was comprised of 164 students in seven classrooms in grades 2, 3 and 4. Classes in this comparison group followed the regular district mathematics curriculum without the supplemental Exemplars problems. Students in this comparison group also solved an Exemplars problem at the end of the study and completed a survey. Students in the three groups were similar. Most of the student participants qualified as economically disadvantaged: 88% at one school and 87% at the other. Additionally, 43% of the students at the treatment school and 51% of the students at the neighboring school are classified as Second Language Learners with Spanish as their first language. The teachers shared similar backgrounds as well. Research Questions Guiding the Research
Students in all three groups took the California State Test (CST) and the district mathematics assessment before the study in 2005 and after the study in 2006. Scores on the CST increased for all students between 2005 and 2006. Students in the treatment group, who had been using Exemplars problems on a regular basis, had the greatest increase in scores. This was also the only group whose increase in scores was statistically significant. Students were also tested using a District Summative Assessment (DSA), which is designed to measure student mastery of California Standards. The test does not evaluate students' ability to solve non-routine problems. Scores were compared for all three groups for 2005 and 2006. Scores for the treatment group increased slightly between 2005 and 2006 indicating that they had gained a full year in mathematics achievement as reflected on the DSA. Scores for the two comparison groups declined, slightly for one group and significantly for the other. The increase in scores for the treatment group was not statistically significant. Devens-Seligman concludes: "The instructional time designated for problem solving in place of traditional textbook lessons did not result in lower scores on the CST or DSA. Instead, the inclusion of problem solving as part of the mathematics curriculum appears to have enhanced the mathematical achievement of students who participated in this study." (Devens-Seligman 2007, 93)
Students in the treatment group scored significantly higher on the post non-routine problem than students in the two comparison groups. However, the growth in problem-solving ability was not significantly greater between the pre- and post-non-routine problems for the treatment group.
Students in all three groups were asked to compare solving non-routine problems with "regular textbook practice problems." At most, 20% of students preferred the regular textbook problems in all three groups. A plurality of students in the treatment group and one comparison group preferred non-routine problems. In the other comparison group, a slight plurality felt the same about textbook and non-routine problems, but nearly as many in that group preferred non-routine problems. Students were also asked if problem solving helped them understand mathematics better. Students in all three groups responded similarly. Among all students, 54% reported that problem solving helped them understand mathematics "a lot better" and 33% responded "a little better." Devens-Seligman concludes: "In summary, the results of this study favor the rejection of the Null Hypothesis. Attitudes about mathematics remained positive when non-routine problem were included as part of mathematics instructions. For the students in this study, both their attitudes and understanding of mathematics improved as a result of solving non-routine problems. " (Devens-Seligman 2007,113)
Most teachers reported that it was important to assign more non-routine problems to help their students become strong problem solvers. When asked how solving non-routine problems impacted on students' understanding of basic facts and procedures and math concepts, five of the seven teachers reported an improvement in basic facts and procedures and two said that there had been no change. With regard to math concepts, all seven teachers reported an improvement in their students' understanding of math concepts. Teachers in the treatment group reported that their students' persistence in problem solving increased over the course of the year as their students engaged in more problem solving. This view was supported by the students themselves when comparing the amount of time they reported spending on solving difficult problems in October and June. The treatment group also reported spending significantly more time solving problems than either of the comparison groups. Devens-Seligman, Judy. 2007. Mathematical Problem Solving: Its Effect on Achievement and Attitudes of Elementary School Students. PhD diss. Claremont: Claremont Graduate University. NSTA Recommends Approves Exemplars Science CDsExemplars Best of Science K-5 and 6-8 CD-ROMs were recently reviewed by the National Science Teachers Association (NSTA). Both products are included in the digital and print publication NSTA Recommends, which determines the best available supplements for science teaching. Materials are reviewed by "top-flight" teachers and other science educators. To read a review of each product, please click on the links below: |
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