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Exemplars is a community of users dedicated to helping schools and districts 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.
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In This Issue:
- From the Publisher's Desk: An Overview
- Exemplars: An Approach to Title I Success
- A Formula for Title I Success: Exemplars and NCTM Process Standards
- Exemplars and Title I: A First-Hand Account
- From the Field: Our Exemplars Transformation
- Exemplars Recognizes: Diane Leddy, Karen Kurzman and Tracy Lavallee-Walker
As you may know, Exemplars is used in many ways - assessment, instruction and professional development. Exemplars is also used in many classroom settings, including traditional, Title I, and Gifted and Talented. The spring issue of Exemplary Initiatives combines these two themes.
To begin, Carol McNair and Deb Armitage, two long-time Exemplars contributors and consultants, describe the characteristics of Exemplars performance tasks that make them valuable for instruction and assessment with Title I students. Deirdre Greer, a professor at Columbus State University, has been working with teachers at Brewer Elementary in Columbus, Georgia. In her interview, she describes firsthand how Exemplars is being used in assessment, instruction and professional development to improve the performance of Title I students as well as that of other students. Once again, it is the characteristics of Exemplars tasks that engage students and inform teachers.
We are often asked how to implement Exemplars in schools. Our final article written by Suzanne Hood, the Instructional Math Coach at Harbins Elementary in Gwinnett County, Georgia, provides an excellent description of how Exemplars was implemented to improve assessment and instruction in her school. Suzanne used data to inform teachers about the problem and introduced the consistent use of rubrics to score student work. With the help of a vertical math team "passionate about mathematics," materials for classroom use were created and professional development was used to facilitate the teaching of "real" problem solving. This is a story of genuine accomplishment. Many of the ideas Suzanne used were learned at Exemplars Summer Institutes.
In closing, we honor Diane Leddy, Karen Kurzman and Tracy Lavallee-Walker for their significant accomplishments.
I hope you enjoy this issue of Exemplary Initiatives and find it to be a helpful tool in your use and implementation of Exemplars.
Exemplars: An Approach to Title I Success
Exemplars standards-based performance tasks provide teachers with not only summative data about their Title I students' progress but also formative information. As a result, teachers can see what their students know, what they don't know and -- most important -- where student misconceptions lie so that corrective lessons can be planned.
With traditional assessments, students may not be engaged. Therefore, it is often difficult to judge if student effort stands in the way of performance. Exemplars real-world, problem-solving tasks were designed to engage students. With material that is differentiated at three levels, problems are made accessible to all students in a way that traditional assessments are not. Thoughtful interdisciplinary links also make tasks easily adaptable to particular units you are studying, thereby helping those students who need to see connections across the curriculum.
Many students often do not know what "good" math looks like, especially those who struggle. Exemplars annotated anchor papers can be used as teaching tools for students who need models of what good mathematics looks like and what they can do to strive toward excellence.
The Exemplars rubric also gives students the language to communicate about their math work so they may practice successful self- and peer-assessment. Giving Title I students the gift of mathematical discourse about their own math work can empower them in ways no math program can.
A Formula for Title I Success: Exemplars and NCTM Process Standards
Title I teachers are often challenged with assessing students' mathematical understanding. Traditional worksheets, chapter/unit tests, and norm-referenced tests typically do not provide enough support in discovering what a student truly understands about mathematical concepts. Teachers have found much-needed support from the research of the National Council of Teachers of Mathematics (NCTM) and Exemplars.
Like the NCTM standards, Exemplars material places a greater emphasis on the "process standards." By focusing on mathematical problem solving and communication, Title I teachers are able to look more closely at what students' work shows about their mathematical understanding. A stronger emphasis on process encourages teachers to demonstrate and support students in learning a variety of strategies for solving a problem. Exemplars encourages students to show different methods for arriving at answers to problems, and this variety of approaches provides the opportunity for teachers and students to discuss the merits of each strategy. The individual student can then embrace an approach that s/he is comfortable using to determine a correct outcome. By encouraging communication in mathematics, Title I teachers are better able to pinpoint where the problems in students' thinking arise -- and can therefore offer meaningful feedback that encourages students to focus on areas that need improvement.
This process of problem solving and communication helps students gain confidence in their ability to solve problems. Shifting the major emphasis from finding the correct answer (only) and placing it instead on the process and communication of "thinking" improves the mathematical disposition of many students. As a result, students become more comfortable with mathematical problems when they have a "tool kit" of possible strategies to consider, an understanding of mathematical language, and a belief that their way of solving a problem is just as valid as a neighbor's strategy.
Exemplars and Title I: A First-Hand Account
What first attracted you to Exemplars for use with Title I students?
Using Exemplars makes it easier to incorporate the process standards into every lesson, which is how those standards are intended to be taught. The Exemplars material help make this fact explicit for the teachers (and for my preservice teachers). Because the Exemplars tasks are aligned with both the Georgia Performance Standards and Investigations, it is easy to select tasks that are appropriate with any unit of study.
How does Brewer Elementary specifically use Exemplars material with Title I students?
I am working with the teachers at Brewer this year to incorporate more formative assessment in mathematics. Using Exemplars is one of the ways we are accomplishing this. We are also working on problem solving in general. By using the Exemplars tasks and the scoring rubric, teachers are learning to help students become better at problem solving, reasoning and proof, communication, connections, and representation and to carry over those processes into the Investigations sessions.
What benefits do you think there are to using Exemplars material with Title I students?
The Exemplars tasks have proven to be engaging for our Title I students. Use of the student-scoring rubric helps students understand exactly what is expected of them as they solve problems. This knowledge then carries over to other mathematics tasks.
Have you seen any improvements, and if so, what specifically?
I have definitely seen improvement in students' ability to communicate mathematically. They are able to explain their solutions to problems both orally and in writing. Consequently, their thinking about ways to solve problems has improved as well.
What do Title I students like about Exemplars tasks?
The students usually find the Exemplars tasks very engaging. Most of the students keep working to meet the expectations and some enjoy working toward attaining an "Expert" level of achievement. On one occasion when I was doing a model lesson, I was using an Exemplars task and one of the students asked me, "Why is it when you are here, we keep on trying until we get the answer...?" I attribute part of the students' perseverance to the level of engagement of the Exemplars tasks.
Our Exemplars Transformation
Historically, problem solving has been a valued part of mathematical instruction at Harbins Elementary School. It has maintained a place of instructional importance and was often assessed at the end of each unit. Teaching computation was believed to be necessary for students to succeed at problem solving. As dedicated professionals, our teachers maintained high standards of academic excellence and used instructional methods they philosophically believed in to improve instruction. In our school, students were exposed to multiple methods of mathematical instruction in different classrooms, including manipulatives, inquiry-based instruction, cooperative learning, computational lessons and whole-group instruction.
Harbins Elementary used Exemplars three times a year for assessment purposes and assessed student performance using a rubric. This evidence was often referenced during parent-teacher conferences to communicate each student's mathematical abilities. However, there were inconsistencies. While the school data showed our students were excelling in problem solving, the standardized testing results did not indicate the same level of student achievement in problem solving. Second, although the use of Exemplars was valued by some teachers, the evidence as measured by student achievement suggested the effectiveness of its implementation was minimal. It became apparent that our school needed to revise its implementation of Exemplars.
As the Instructional Math Coach, responsibility for professional learning of mathematics is central to my duties and responsibilities. In that role, I attended the Exemplars Summer Institute. One of the most important goals was to revitalize the mathematical community at Harbins by passing along the multitude of ideas that were learned at the Exemplars Summer Institute and to redefine the use of Exemplars to drive instruction in mathematical problem solving.
I began by showing the inconsistencies between test score data and Exemplars results at different grade levels. To gauge the effectiveness of Exemplars use, I discussed with teachers how it was being used in the classroom. The Math Learning Lab (Math Model Classrooms) was the place to start the change process.
Through monthly meetings, collaborative work was done with a small group of teachers using book study, Exemplars newsletters and various research articles about mathematics. These sessions resulted in a team that aligned philosophically about its mathematical instructional beliefs. This vertical math team, representing kindergarten through grade five, was comprised of teachers who were passionate about mathematics. After sharing material from the Exemplars Summer Institute (preliminary planning sheets, self-assessment rubrics, and how to use the Exemplars rubric to score analytically and consistently), the Math Learning Lab team was convinced.
To foster further collaboration, a mission and vision statement was written to support our Numeracy Framework (a one-page document that is constructed and validated by the teachers at Harbins). It contains belief statements on the essentials of mathematics instruction. After the Exemplars Summer Institute, it was revised to reflect the new learning.
I presented the Exemplars assessment process to the Math Learning Lab team. Using the analytic rubric, I assessed to an overall standard of performance, without averaging across the criteria to attain a mean score. After discussion, the team agreed this assessment process would lead to improved student performance and should be part of the Numeracy Framework. This discussion created a foundation for future conversations about creating concise and consistent school-wide expectations.
The transition to using the new assessment process began with weekly staff-development sessions where Exemplars materials were assessed in grade-level teams. The trends were consistent and showed our students were falling short on the communication criterion. As a result, math journals were initiated along with math word walls in every classroom.
Our students were also struggling with the Problem-Solving Strategies component. In response to this, posters were created for every classroom highlighting each strategy that aligned with Georgia state standards. Interactive problem-solving strips were also created for students to use as support with math vocabulary and graphic organizers.
Teachers now feel confident in their ability to teach students about Problem-Solving Strategies, Reasoning and Proof, and Communication. The staff continues to develop confidence on the elements of Connections and Representation.
Our principal is an advocate of the mission of the National Staff Development Council: "Every teacher should have high-quality professional learning as part of their workday." Two times a year, each grade level collaborates in a half-day session with Math Learning Lab team members to discuss and plan for the utilization of best practices in mathematics. They also work as a team to assess their instructional needs. Grade levels meet bi-weekly to collaborate on strategies and to share instructional techniques used with Exemplars classroom instruction.
Student Exemplars were assessed for grade-level consistency and to find trends that needed instruction. Students were then taught how to self-assess their own Exemplars work. A book each month was also given to teachers based on a math-literature connection. The overarching goal is to create life-long mathematicians equipped with a toolbox of strategies and the confidence to use those strategies in varied mathematical problems.
The requirements for the Harbins Math Profile or portfolio were also changed in response to the Exemplars Summer Institute. In the past, three Exemplars tasks were used with the same content, but with different computational amounts and varied scenarios. There are now nine interim Exemplars assessments that are used. These assessments incorporate the Academic Knowledge and Skills curriculum (AKS) for Gwinnett County Public Schools that align with our state standards and grade-level instructional calendars.
Our district has also adopted a Math Continuum, which facilitates the school-wide transformation for using Exemplars. An entire section in this document is devoted to problem solving, where Exemplars evidence of student progress can be recorded. During parent-teacher conferences, portfolios of student Exemplars are reviewed. Student's problem-solving abilities (as noted on the Continuum) are discussed with parents. Exemplars are also modeled for parents at the annual Instructional Fair, an event in the school building where parents can see firsthand how Exemplars are taught in the classroom.
Today, teachers are encouraged to use Exemplars weekly. Grade levels that have taken the initiative and implemented the process are seeing strong results in their standardized testing data. In order for success to be attainable, research indicates that students should use a school-wide problem-solving plan and have a vertical alignment of problem-solving strategies. Each grade level in our school uses the same problem-solving strategy, and the strategies come from our state standards.
Support from the math team is a vital element in the success of our math program and the implementation of Exemplars. The team's efforts of organizing the math closet materials and creating math graphic organizers are necessary to maintaining consistency in grades K-5.
Even as our standardized testing results continue to improve, we also noticed an interesting trend in our Cognitive Abilities Test (CogAT) scores. Our students were showing gains in their CogAT scores after using Exemplars. CogAT scores can change over time as a result of the right kind of instruction. Our school believes that these increases are attributed to teaching that requires students to think at higher levels as required by the use of Exemplars. Students are being taught how to think critically with mathematics using Exemplars and are using that knowledge and applying it to a multitude of problem-solving situations.
In conclusion, Exemplars have been a fundamental element in transforming mathematical instruction at Harbins. Significant gains are observed in fifth grade after students have experienced Exemplars consistently during their elementary school experience. Instruction is differentiated using Exemplars and students are nurtured in a rich mathematical community. Critical thinking is a natural part of the mathematical day and Harbins's students are thriving on the rigor of these tasks. Deb Armitage, an Exemplars consultant, was an essential element in the success that many teachers have experienced as a result of Exemplars training. The Exemplars Summer Institute was a nurturing bed of ideas about Exemplars that ignited the fire of mathematical passion in this Instructional Math Coach.
Exemplars Recognizes: Diane Leddy, Karen Kurzman and Tracy Lavallee-Walker
Exemplars would like to congratulate Diane Leddy, a grade three, four and five teacher at The Newton School in South Strafford, VT. She was named by the State Board of Education as the 2009 Vermont Teacher of the Year.
Diane is the originator of the "Painted Essay" concept that forms a key element of our Developing Writers publication, edited by Karen Kurzman.
Karen Kurzman is also congratulated as a contributor to the recently published Writing for Understanding. This publication is a product of the Vermont Writing Collaborative and is published and available through Authentic Education, Hopewell, NJ.
Tracy Lavallee-Walker has contributed to Exemplars Science on many levels. She has written and edited tasks, aligned them to key textbooks and science kits, created curriculum extension links to literature and language arts, and offered Exemplars professional development around the country.
Exemplars is proud to acknowledge the fine work of Tracy Lavallee-Walker and her school, Underhill I.D., which was profiled in the Burlington Free Press this fall. Tracy is currently a fourth-grade teacher.
According to the article written by Molly Walsh of the Burlington Free Press, "In a state where only 48 percent of fourth-graders scored at or above proficiency on the state science test [NECAP], the small school in the shadow of Mount Mansfield posted a 100 percent proficiency rate."
Principal Cindy Makin told Walsh, "Underhill I.D.'s curriculum is carefully aligned to state standards ... drills aren't part of the program. Science instruction emphasizes field work and hands-on projects and labs."
This goal is exemplified by Tracy Lavallee-Walker who said, "... doing experiments and making direct connections to the real world keep students engaged." She continued, "We could just stand up here and talk about it, but the knowledge won't stay. To me, my goal is, more than anything, to get the kids excited about science."
Great work, Tracy!