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April 2005Welcome 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:
Integrating Exemplars With Your CurriculumExemplars focus is on real problem solving and assessment. It was not designed to be a curriculum, but rather a supplement to a curriculum. Schools and districts throughout the country have used it to enhance a variety of programs. By encouraging students to communicate their reasoning, Exemplars makes an ideal complement to a number of approaches to learning math. While Exemplars material can be used as an assessment tool or for the purpose of enhancing instruction, it can also stand by itself. Teachers will often use a task outside of the curriculum, to introduce their students to real-world problem solving. This approach enables students to learn critical problem-solving skills for the future. While this strategy is effective, we are finding more and more teachers want to specifically integrate Exemplars with the particular content they are studying. One reinforces the other instructionally and Exemplars problems provide a good indicator as to how well students really understand the material. To assist teachers we have aligned Exemplars to Everyday Mathematics and are in the process of aligning our material to Investigations. Many schools and districts have also aligned their own programs and standards with Exemplars. This issue of Exemplary Initiatives features three districts that have aligned our material to three different math programs, Everyday Mathematics, Investigations and Saxon Math. In each case, professional development has played an essential role in helping teachers understand how the two programs can work together. If you have a similar story, please share it with us so that others may learn from your success.
Exemplars and Saxon Math: The Perfect FitThe Early YearsWorking in a large urban school district such as Fort Worth can be a challenge, but with the hardship comes rewards. About 10 years ago, I had been moved from a self-contained class to teach just math to all of our grade four students, due to my love and success in the area of mathematics. My students gained over 50 percentage points on our state test. Some said that I had a "gift", others would comment, "You must have loved math in school." Neither was true. I had found the secret, Saxon Math. Two years after teaching Saxon Math, another reward became apparent. Due to their higher level of mastery, I now needed to search for higher-level challenges on my students' assessments. Discovering ExemplarsMuch to my delight, my principal allowed me to attend an annual Texas math conference, where I stumbled upon the Exemplars booth. I found the student samples, using problem-solving strategies, open-ended assessments and scoring rubrics, that I was looking for. I could not wait to try the samples out with my students. I returned to school the following month ready to merge Saxon Math and Exemplars. I must say that the fit was perfect. My students caught on to the rubrics quickly and began to apply their mathematics to these challenging assessments. I saw students that were able to represent and articulate their thinking on complex problems that I would have never considered using with them before. Exemplars BeginsWhen I was promoted to a mathematics instructional specialist, I was responsible for professional development training and district documents for pre-K through grade two for the entire Fort Worth district. This would be the first year for primary math to attend our famous Summer Math Institute, and I decided to train teachers on Exemplars as well as other items. I pulled in a cadre of successful teachers and trained them on the Exemplars assessment. They were hooked. That summer we trained a group of about 300 teachers on Exemplars and felt that we had just touched the surface. Soon after, we decided to add Exemplars to our new curriculum in all K-2 classrooms across the district. We added a day of instruction every six weeks to their current Saxon program. Professional development was the key to success. Once teachers were given the license to step back and assist, with the assurance that they would teach all of the required skills and concepts, they were amazed with the results. The Exemplars program was a great tool for helping all teachers learn how to help students take what they had learned in Saxon Math and transfer that understanding and knowledge to a different type of open-ended assessment. It was powerful to watch students begin to represent (draw, illustrate and show) their thinking using the high-order skills they had learned, and to communicate their knowledge about math as well. Looking to the FutureI recently moved to another position and passed the torch to other math specialists that had worked closely with me in the district. I told these wonderful professionals that they are in the lead in primary math in the country. With a product such as Saxon Math that provides such a strong and comprehensive math knowledge base and Exemplars that allows students to express their understanding at the highest level through open-ended assessment - they have the perfect fit. When I asked last week how primary math was going Mildred Sims, Fort Worth's math director made this comment, "People can leave and a weak program will die, however when the program is this good, it can stand on its own and will continue without the person that first had the vision." That is exactly what has happened in Fort Worth Independent School District. Both Saxon Math and Exemplars are going strong and will continue, I hope for many years to come.
Getting the Whole Picture: Partnering Exemplars With Everyday MathematicsIn 2001, our Office of Mathematics saw the need for comprehensive reform in its math program. Although our students were tested according to statewide standards, our curriculum did not address those standards, nor did the instruction look and sound as the state's standards described. Our teachers were teaching mathematics the same way that they were taught mathematics. Rather than introducing a meaningful context through problems that could be interpreted mathematically, employing multiple strategies, building understanding and encouraging problem solving, we saw memorization of isolated skills and processes. Rather than communicating mathematical ideas verbally and in written form, our students were asked to complete worksheets and workbook pages. Rather than making connections among math content areas, our students were asked to look at skills in isolation. Our students were encouraged to reason mathematically, and therefore, they were not building the idea that mathematics makes sense. We had state standards that addressed appropriate delivery of instruction, but there was clearly a mismatch between those standards, our math curriculum and the real world. Recognizing the gap between our standards and practice, our district's Office of Mathematics initiated an ambitious, comprehensive effort to reform mathematics education in our schools with the support of the National Science Foundation. As part of this effort, a new math curriculum, Everyday Mathematics was adopted for our kindergarten through fifth-grade classrooms. Everyday Mathematics addressed many of the discrepancies between our standards and our practice. Practice was linked to the real world, helping our students make those crucial connections, and a balance existed between direct instruction, paired and group work, projects, and individual and group explorations. Children were expected to verbalize and write about their mathematical thinking and gain insight from the thoughts and strategies of others. However, our students were and still are expected to solve open-ended, problem-solving tasks on the statewide tests in third and fourth grade and explain their problem-solving strategies. Everyday Mathematics does not thoroughly address performance-based assessment tasks, and therefore, would not adequately prepare our children for what they need to face each year on their standardized tests. How could we meet this need for our children? Enter Exemplars. Exemplars had been used throughout the district in isolated schools, and our Office of Mathematics saw how well the material would complement Everyday Mathematics. Exemplars would fill the need for performance-based, open-ended assessment tasks. Furthermore, the Best of Math Exemplars CDs offered the ability to search for specific skills, concepts and standards, so it could be easily integrated into the Everyday Mathematics curriculum. The Office of Mathematics worked in collaboration with our Department of Instructional Technology to make the Exemplars CDs available on every networked computer in our district and to train all teachers, technology coordinators and administrators in its use. It also recommended a schedule of instruction, where teachers spend four days each week teaching the Everyday Mathematics scope and sequence and one day each week using a correlated Exemplars problem. A chart correlating the Everyday Mathematics learning goals to Exemplars problems (specific for each grade level) was printed and distributed to teachers to support them in this effort. By using Exemplars in conjunction with Everyday Mathematics, our classroom instruction now aligns more thoroughly with our state standards, delivers instruction utilizing appropriate methods, and prepares our children for that inevitable statewide assessment. Together, they guide our children to communicate mathematically, make those all-important connections and build mathematical understandings... for this we are grateful. Note: To assist schools/districts with the integration of Exemplars into their Everyday Mathematics curriculum, we have aligned our tasks on the Best of Math Exemplars CD-ROMS to Everyday Mathematics units. To view these samples and alignments please click here.
Integrating Technology, Exemplars and InvestigationsThe North East Independent School District's (NEISD) mathematical philosophy changed long before the NCTM Standards arrived in 2000. NEISD's guiding principle states, "All students must become fluent and flexible in dealing with quantitative information." Furthermore, the superintendent believes and expects that, "Each NEISD teacher of mathematics will create a classroom environment in which students will make sense of mathematics and acquire confidence in using it." The initial choice, to meet these expectations was the Investigations in Number, Data, and Space program. After using this series and seeing fine results, word spread. The daily, open-ended, problem-solving activities, intrinsic to this series, became catalysts for teachers to explore better assessments tools. As teachers became comfortable and familiar with the Investigations curriculum, they spent time researching assessment instruments that would reflect student growth and success, as well as gaps in their learning. Although much of the Investigations assessments relied on observation and looking at student work, teachers felt a more objective means of assessing student work was needed. They soon discovered Exemplars, which was purchased to mesh with the Investigations curriculum. With Exemplars, teachers could look at student work, determine performance levels, and have appropriate feedback for themselves, their students and parents. This information helped teachers to gather important data about each student as a mathematical learner, and to decide how to direct their instruction. Exemplars provided a way of assessing students' problem-solving and application skills. It tied together assessment results, curriculum and instruction. After five schools purchased Exemplars to use in conjunction with Investigations, several other NEISD schools felt it would fill their needs as well. In 2004, Exemplars tasks in both mathematics and science were purchased for all 17 Title I schools in the district. While supporting teachers using Exemplars, the district math specialists discovered that additional support, in the way of technology, would enhance its use and allow the sharing of ideas. An Exemplars web page was developed and installed on the NEISD intranet home page. It was made available to all those schools participating in Exemplars and could be accessed from home for planning purposes. District math specialists created a matrix that correlated the District Scope and Sequence math strands with Exemplars tasks. This allowed teachers to choose tasks in a timely manner with their Investigations lessons. A hotlink to each task was established as well as a hotlink directly to the Exemplars CDs and subscriptions. It was also important to create a page that gave easy access to Exemplars resources, such as a variety of rubrics, hints from teachers, tips that help engage students, etc. The continued use and integration of Exemplars into the Investigations curriculum reveals how positive the NEISD teachers feel about assimilating the two into a powerful tool for ongoing assessments. Note: Exemplars is in the process of aligning its math material to Investigations in Number, Data, and Space (K-5). These correlations will be made available on our web site as a free download in the fall of 2005. Investigations in Number, Data, and Space (K-5), Scott Foresman (original) now Dale Seymour (c) TERC, 1998.
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