We are using Math Exemplars and we love it. Our students love it as much as our teachers.
I use the Jigsaw Rubric in my Math Class for problem solving and love it! Makes students more accountable for their learning and affords them to see where and what they need to improve on.
I am determined to improve in math. The years I used Exemplars with fidelity my scores jumped tremendously; teachers actually assessed and enjoyed the art of teaching and students were always self assessing.
Dr. Jacqueline Peek-Davis School
I love the challenging problems that keep my students engaged in learning.
I have used Exemplars for the past 15 years, and I have yet to find any other resource that compares to it.
I teach both pre-service and regular teachers. These Exemplars are used to show students what constitutes good problem solving and assessment. I love them.
Thank you for a fabulous 2 days of training! We enjoyed everything we learned and are so excited to take our new knowledge back to our classrooms at JHE! You are truly an inspiration!
M. Kelley & A. Tidmore
From Park City
I have used Exemplars before in my classroom and my students love the tasks!
I have used Exemplars in my classroom for years as a regular classroom teacher. Your rubrics and tasks are well designed and fit the needs of my students.
Gifted Resource Teacher
My teachers and I enjoy using Exemplars ... We have found the math resource to be a great addition to our current curriculum.
Exemplars ... has solved the puzzle of how to find tasks that align to the standards. This resource is easy to navigate and enables me to differentiate instruction at the touch of a button ... The Preliminary Planning Sheets support me with teaching the standards of problem solving while choosing an Exemplar that is "just the right fit" academically for my students.
From New York City
Our school subscribes to the Exemplars Library. I find the formative tasks aligned to the Common Core are strong and can be easily embedded in any curriculum. Having a more accessible and more challenging version of each task provides teachers' support as they have the resources to problem solve across different levels of understanding in their classrooms. Both the teachers and administrators appreciate the Preliminary Planning Sheet and use this work to inform their instruction and support classroom observations. The summative tasks with detailed rationales make it possible for teachers to become confident in applying the criteria of the rubric and assessing student work accurately. Students are enjoying the tasks and are demonstrating a deeper understanding of the underlying concepts of the standards as they apply formal math language, accurate representations and connections. We are feeling positive that by embedding the Exemplars problem-solving tasks in our instruction and assessment we will see improved results in our state testing.
From New York City
Teachers are thrilled to have so many real-world tasks at their finger tips that are grouped by specific Common Core Standards. It is apparent that Exemplars gave a great deal of thought and consideration when designing this resource - it is intuitive and incredibly well organized. And most importantly, Problem Solving for the Common Core provides the rich learning opportunities for students that we were looking for.
New York City
From New York On New York City
The new Exemplars Problem Solving for Common Core is a welcome addition to the Exemplars' offerings. School districts currently searching for reliable problems to enact the spirit and content of Common Core at each grade will be delighted with this resource ... This can help teachers not only better understand the math of context -- rich problems -- but also help them anticipate varied student outcomes for evaluation.
Dr. Hal Melnick
Teacher & Leader Educator
Bank Street College of Education
New York City
From Cheetowaga, NY
I used your stuff in the 90's and loved it ... you were so Common Core before the Core.
From West Genesee
... Exemplars has problems which allow for the constructivist approach demanded by the Common Core.
Your work is fantastic! We are looking for a way to monitor the growth of a student as a scientist from grade to grade. Your rubrics will help us to begin this important work.
Elementary Science Curriculum Specialist
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 carries over to other mathematics tasks.
Deidre Greer, PhD.
Asst. Professor & Program Coordinator
Early Childhood Education
I was amazed to see the differentiation and the student examples. So many times we see the problems, but not actual student work. Thank you so much for allowing me to see student work and the DIFFERENT ideas so that it's not me creating "mini mes" but showing students how to arrive at the answer in many different ways!
This has been a great resource with the introduction of Common Core Math and ELA.
From New Jersey
I've used Exemplars in the past and find they are very useful for developing problem-solving strategies and mathematical communication.
With the increasing rigorous demand of high-stakes testing, Exemplars is a "must have" component to any mathematics program. I have been in education for over 18 years and have seen programs come and go. Exemplars is one of the few initiatives that has proved effective time and time again!
The content on these CD-ROMS can be easily integrated with some of the most popular science teaching kits ... This program will provide an invaluable service to schools ..."
NSTA Review Panel Member
From New York City
After being given a brief overview of Exemplars, I felt it was something that would be extremely helpful to teachers trying to implement the Core Standards into their teaching...
I am an elementary math coach whose job is to help teachers transition to the Core Curriculum. As we look at the Core and learn more, we see that students will need to write more and explain their thinking. Exemplars will help our students to begin writing more.
From New York City
Embedding Common Core aligned Exemplars tasks into our units of study has strengthened teachers understanding of the Common Core Learning Standards while improving student performance. Significant growth in student achievement has taken place across the grades in the Mathematical Practices ... even our youngest students do the work of real mathematicians to represent and solve authentic real-world problems.
T. Appel Peterson
From South Carolina
I was trained in Virginia Beach City Public Schools and used Math and Science activities with whole group instruction. After Virginia Beach, I moved to Yokota Air Force Base in Japan and taught at Yokota West Elementary School. Our school principal purchased Math and Science Exemplars and I used them with kindergarten - 4th grades. I am now in Laurel Bay and would like to use Math and Science Exemplars again. I am hooked and cannot imagine teaching without my Exemplars! Thanks so much!
From New Hampshire
With Exemplars we were preparing students to improve their problem-solving skills and writing skills. In addition, with the introduction of Exemplars rubrics, teachers were better informed of additional ways to assess student learning and were able to convey those expectations to students ...
Interdisciplinary Curr. Specialist K-12
I am a special education teacher and I have been using the math Exemplars with my students. They enjoy doing them and have actually asked to do them. I have noticed that with each problem we solve more and more students are trying to stretch their thinking so they can become 'Experts.'
Special Education Teacher
From El Paso
Exemplars are open-ended word problems with hands-on activities that expose students to critical thinking! Great for whole groups or centers.
The presenter was extremely knowledgeable and has traveled all over the world for the purpose of finding strategies to help students understand numbers!
Lead Math Teacher
From West Virginia
Thank you for the great hands-on ideas!
1st Grade Teacher
Thank you – to coin a phrase – This old dog learned some new 'tricks!'
Middle School Teacher
Deb [the presenter] was so interesting, inspiring and encouraging – helped me feel as though I could truly do this in my classroom. My students will really benefit from this approach to learning.
I was extremely pleased with the workshop content and the delivery method used.
I enjoyed the workshop and facilitator. This [workshop] has given me a boost of energy to begin the new school year. I can't wait to start. Thank you so much!
4th Grade Teacher
From New York On Numbers and Operations
Hands down the most informative, practical and simply fun professional development session I have attended these past five years!
The tasks and rubrics that Exemplars has produced over the years are excellent resources for all three levels of the International Baccalaureate Organization (IBO) programs. The tasks exemplify the principals of the type and quality of the teaching and learning that the IBO requires: significant, relevant, and engaging work for students!
In my work with schools over the past 15 years I consistently use Exemplars as the model for high quality pre-assessment, formative assessment, and summative assessment tasks. The goals and standards for the tasks can always be aligned with central ideas, subject content, and the areas of interaction. The tasks are transdisciplinary and require that the students use what they have achieved in a new situation. That is the ultimate indication that the young people have learned something that the school has deemed worth knowing!
I am particularly charmed by the anchor papers. They provide an excellent indicator of what good work looks like so the teachers can immediately identify the levels of work that can be expected. In addition, the commentary on the anchor papers guide the teachers in using the rubrics so they may develop thoughtful and significant comments for the very important feedback they must give to their students.
I am certain that Exemplars has significantly improved the type and quality of assessments that are used in excellent schools! It has been my great pleasure to recommend Exemplars to every IBO school I work with. They in turn have greatly appreciated this very excellent resource and their students are certainly privileged to have had the opportunity show what they know, can do and understand in such a meaningful and relevant manner.
Because of Exemplars, I learned to think like a mathematician and if you do, you understand the problem a lot better. When I think like a mathematician, I explain the problem, look for patterns and get a strategy.
I love Exemplars... They changed my life because it made me smarter at math and made me love it.
I really loved Exemplars. They really challenge my mind. Exemplars really helped me in math... At the beginning of Exemplars I was never good, because I was an Apprentice, now I'm really good...I learned from Exemplars that there are so many different kinds of math, for example, adding, multiplication, division and subtraction.
'We need to start,' said my students last week. They told me to hurry up, read the problem and pass out the paper. This is a noticeable change in student attitudes toward problem solving. They are no longer meek, frightened, inhibited problem solvers.
Karen McKee's first grade classroom Easthampton, NY
I think all schools should have this kind of test.
A 4th grader upon completing an Exemplars problem
In this day and age of No Child Left Behind, assessment practices themselves are under assessment. Heidi Hayes Jacobs, president of Curriculum Designers, Inc. and educational consultant to thousands of schools nationally and internationally, advocates for the need to redefine assessment more comprehensively. Richard J. Stiggins works with teachers and learning communities and has found that assessment cannot function solely as an accountability measure through standardized test results and that teachers need to 'understand that assessment can work in positive ways to benefit learning, the time is right to add to our definition of good teaching the skillful use of assessment - doing it right and using it well.' (Classroom Assessment for Student Learning - 2004). Assessment is the third part of our curriculum office's triangle for improved student learning which intertwines curriculum, instruction and assessment (the Nashua Curriculum Instruction and Assessment 'CIA' model). By introducing Exemplars we have come to realize that we were providing the foundation for our teachers to begin moving toward formative assessment practices.
In 1995 the Nashua School District embarked on a full scale alignment of its Mathematics Curriculum K-12 with New Hampshire's Mathematics State Frameworks and the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics (1989). The state of New Hampshire began its state testing under the New Hampshire Educational Improvement and Assessment Program (NHEIAP) for students in grades three, six and 10. The goal of NHEIAP was to provide data to districts as they reviewed how well their programs of instruction were working to improve student learning.
Our district's Curriculum Area Research and Development (CARD) team for mathematics recognized that the teachers in grades three, six and 10 could not shoulder the responsibility for students' achievement. As a district, the CARD team identified student proficiency outcomes (spo's) for each grade level. It was during the 1995-1996 school year that the district set its sights on identifying materials that would aid teachers in improving how students solved problems, communicated that information, and how they demonstrated the connections within mathematics and the real world. Simultaneously, summer institutes were provided for elementary teachers where they explored how to introduce meaningful context through problems that could be interpreted mathematically, that used multiple strategies and helped to build understanding. They were expanding their tool box of teaching strategies in mathematics through problem solving. We came upon Exemplars materials with its prepared problem-solving tasks, and rubrics, which are designed to help teachers identify proficiency levels along with sample examples of students work. In January 1996, Ross Brewer, of Exemplars, provided professional development for our K-6 Mathematics Facilitators who learned how important it is to know why students are being assessed and what students need to know to be better at problem solving. Teachers learned that students should know the standard by which their work is measured. We were on our way to looking at a better way to assess students' learning and how to have students begin to take responsibility for their learning by enabling them to self-assess. From there we incorporated annual professional development for all teachers to become knowledgeable with this resource.
In addition to the Exemplars material, we were researching materials for our elementary mathematics program. When Everyday Mathematics (EM) was identified and implemented in 2001 - we continued to use Exemplars in conjunction with the newly adopted materials. During the summer, teacher leaders identified Exemplars problems that aligned with our EM expectations. We were delighted to see EM and Exemplars come together to complement each other and help us meet our program goals.
With Exemplars we were preparing students to improve their problem-solving skills and writing skills. In addition, with the introduction of Exemplars rubrics, teachers were better informed of additional ways to assess student learning and were able to convey those expectations to students. Rubrics were reviewed with students and samples of what constitutes good work were available. Our end of year district assessment incorporates an open-ended question some are direct Exemplars questions and others have been tweaked to meet the identified learning goals. Grade level teachers are responsible for scoring results as a team, providing sample papers of students' work and recording the data to compare against district results. The review of these results becomes the basis for introducing the Exemplars work with new hires and as a refresher for veteran staff as we focus on curricular areas in need of improvement. District results have been tracked since 1998, and each year we have data to inform us about students' progress at each grade level. From the state NHEIAP results, use of Exemplars has paid off. Our students in grades three and six have consistently reported higher scores compared to the state results. This has held true from 1998 through 2003. In October 2005 the state embarks upon the Tri-state New England Compact Assessment Program (NECAP). We are confident that our students will continue to perform well from the experiences they have with Exemplars. Finally, Exemplars has provided a conduit, which directly impacts our efforts with the implementation of the Nashua 'CIA' model.
Cecile M. Carlton
Interdisciplinary Curriculum Specialist K-12
From Atlanta Public Schools
"I have to admit that this workshop was PHENOMENAL... I feel so fortunate to have had the opportunity to attend this workshop with my fellow Atlanta Public Schools colleagues. Not only was it insightful and informative, but the presentation of the material covered was creatively done. She [the instructor] allowed us to make many of the activities she discussed. It seems as if both facilitators believe in the educational proverb: 'Tell me and I forget, teach me and I remember, involve me and I understand.'"
Mathematics Instructional Coach
Atlanta Public Schools
I have really enjoyed using Exemplars. Teaching students how to become better problem solvers has been easier and the students have a more concrete format in which to follow. The rubric is very user friendly. It has really allowed my high-achievers to reach a new level. Problem solving is usually a weakness for them, because they only want to get the right answer... this has opened their eyes to a new way to express themselves mathematically.
I am a special education teacher and I have been using the math Exemplars with my students. They enjoy doing them and have actually asked to do them. I have noticed that with each problem we solve more and more students are trying to stretch their thinking so they can become 'Experts.'
Special Education Teacher
A Principal's Reflections
I recently had the opportunity to reflect on our students' growth since they have been using Exemplars. What pleases me is the degree to which I see them developing the ability to explain their solutions using reasoning and strong language. This can be as simple as a kindergartener describing his/her picture solution; to the teacher who in turn records the student's idea; to our students at grade four who often utilize a full page of charts and explanations to "defend" and clarify their solutions. After selected students present their work to the class, every student is given a chance to expand their original solution. We have them use colored pencils to improve their first solution. There has been growth in our students' ability to collaborate in order to expand their own skills. Additionally, the sharing component provides the opportunity to practice communication and presentation to peers, which is an enhancement to our work in English Language Arts.
The level and complexity of Exemplars has enabled our students to gain exposure to more complex problems than we had ever offered them before. At the youngest grade levels, students are solving multi-step problems, and at all grade levels the subjects and "real life" feel of the problems gives students a natural desire to persevere, since the situations presented seem plausible.
Another great aspect about Exemplars is the more accessible versions that we use successfully with many of our students who struggle. The students are able to be successful with similar problems to their peers as opposed to requiring a different problem entirely and potentially feeling left out. The more challenging versions are used for our more talented math students as well!
On a final note, I review one Exemplars problem per month for each student, and I think it is a credit to the program that I look forward to seeing them each and every time. The problems generate excellent work from our students.
The School District of Lancaster, PA is committed to do whatever it takes to raise student achievement in their district. In order to meet this goal the teachers of Lancaster have been working with the Education Trust Foundation to analyze the rigor of assignments and student work. They have been using the Standards in Practice (SIP) process developed by Ruth Mitchell, to guide their work. Each of Lancaster's 18 schools (K-12) has a SIP Committee that meets regularly, and the results of these meetings are utilized when planning instruction.
The SIP model involves the following steps:
Each member of the committee:
- Completes a specified assignment or task
- Analyzes the demands of the assignment or task
- Identifies the standards that apply to this assignment
- Generates a rough scoring guide from the standards and the assignment
- Scores the student work using this guide
- Asks the questions: Will this work meet the standards? If not, what are we going to do about it?
- Then uses these results to plan action at the classroom, school, district, state levels, to ensure that all students meet the standards
To aid in their success with setting the standard, the Lancaster district has applied Exemplars to their SIP process. Patricia Jones, an Instructional Facilitator at Lafayette Elementary, SDOL, states in regard to Exemplars, "The examples of student work that show generalizations have been invaluable to push our thinking!"
Math Exemplars are chosen to support conceptual understanding of skills introduced in Everyday Math lessons. Discussions center not only on student needs and achievement - What does this student work tell us about learning in this classroom? What do students know and what are they able to do? Was the assignment well designed? Was it rigorous enough to help students achieve standards? - but give teachers the opportunity to reflect on their own professional practice - How do student results reflect my instruction? Do I need to be more explicit in presenting concepts? What misconceptions are present? What are my next steps?
The district of Lancaster has been utilizing Exemplars for the past five years to provide them with resources in math and science problem solving, and Melanie O'Rourke, a primary level teacher at Lafayette Elementary, SDOL, states that, "these tasks have been instrumental in our SIP sessions." Ms. Jones states that in the classroom, "Exemplars have enabled teachers to give students opportunities to apply math concepts in problem-solving situations. They provide situations to encourage dialogue among students in the classroom." Therefore, Exemplars became a helpful and measurable tool to assist their district in meeting the standard.
Ms. O'Rourke states, "Although the (SIP) process is at times painful, it is also rewarding to see the growth that occurs for both students and teachers. Keeping an eye on this goal has allowed us to work through and view the process as a process, forming trust among colleagues and resulting in the confidence and strength it takes to look closely at ourselves."
From Norfolk Public Schools
Norfolk is an urban district that is experiencing success because we've been focused on not only improving student achievement, but doing it for the long-haul.
We see the benefits of writing in mathematics; of using performance assessments in mathematics rather than simply relying on a multiple-choice assessment. Since we stress having students illustrate their thinking in words, pictures and numbers, Exemplars is a wonderful tool. Because it's written for and by teachers, our teachers understand what they are looking for as a result of the assessments.
We started using Exemplars with a small group of teachers that we felt would "run" with them. These teachers became our ambassadors and have worked to infuse Exemplars within our program. We even identified specific Exemplars tasks for use in our curriculum.
We use Exemplars as a professional development tool to get our teachers to look critically at what students know and illustrate for us. Last year we even had an Exemplars Study Group that met quarterly. Teachers were grouped by grade levels and worked on a task (to discuss the mathematics, the curriculum objectives embedded within the lesson, and to consider the rubric that would be used). The task was then given to their students and the teachers returned the next time to discuss the results. Teachers shared samples of student work and talked about strategies for improving all of their students' performance.
We are also using Exemplars at the K-5 level specifically as an assessment tool. One of the things that our elementary schools are doing is to chart the percent of students scoring at the different levels periodically so that as a grade level you can determine/describe student success (overall).
Norfolk Public Schools
Teaching STEM proved to be very time consuming last year and I love the [Exemplars] sample on breathing because the student gets to investigate the real-life situation instead of just watching!!
From Ft. Wayne
I work as a math/science facilitator going into elementary classrooms across the district with the main emphasis being problem solving strategies and advanced thinking questions -- A colleague shared a few sample Exemplars -- they have been amazing to use with kids. Teachers want to know where the ideas are coming from so they can continue along this same line. Great product!
K-5 Math/Science Facilitator
We use Math Exemplars and our math scores are above 90% across the board! We believe that Math Exemplars have helped our students understand math problem solving and explain their work on the ISTEP.
According to Tim McNamara, an Exemplars workshop leader, Eldorado, IL is, "home to some of the kindest, friendliest people you'd ever want to meet." Eldorado's economy once relied on coal mining. The mine has since closed and the community has fallen on hard economic times. The opportunities for good jobs once available to graduates have been lost. Knowing that Eldorado graduates would be entering a much different job market, middle school principal Rick Cox developed a strategy for improving the quality of their math program.
Mr. Cox contacted Exemplars in the Fall of 2000. Tim began assisting the Eldorado Middle School with the implementation of Exemplars to improve their students' math performance levels. The strategy included instituting Exemplars for both assessment and instruction, and providing teachers with professional development. He used an Illinois State Grant to fund the program.
Mr. Cox believes the strategy was successful. "In 1999, only 28% of our 8th grade students met or exceeded state standards." After the introduction of Exemplars, "In 2001, 56% of our 8th grade students met or exceeded the standards. In other words, we doubled the number of students passing the state test in the two-year time period."
Over the course of one academic year, Tim led three workshops with Eldorado teachers. The first focused on assessment, the second on content, and the third on instructional scope and sequence.
Teachers analyzed state assessment questions, compared them to Exemplars problems, discussed multiple strategies for solutions, rubrics, and assessing student work.
Teachers designed end-of-the-year assessments for each grade level based on the state standards, including both skills-based and more comprehensive performance-based Exemplars questions.
Teachers focused on laying out the curriculum for the entire school year using the state standards and Exemplars as benchmarks, with the textbook in a supporting role. Teachers used different colored index cards (one to represent a standard, one for a good class activity or web site, one for a skill-based question, and one for a performance-based question) and inserted them throughout the textbook, indicating where to place emphasis in their upcoming instruction and where to focus on assessment.
This scaffolding allowed each workshop to build on previous knowledge and gave teachers continuity as they implemented these changes. Rick Cox felt that these ongoing workshops made a tremendous difference for Eldorado's students.
Mr. Cox wanted to thank Exemplars for providing his students with such outstanding constructed-response items and for presenting his teachers with such extraordinary professional development.
I think that these tasks provide higher-level thinking skills and require students to take a look at the reasoning behind their answers.
Elementary School Teacher
Looking for a different way to get information about school testing out to the public? Try putting it on a McDonald's™ tray liner!
The Southwest Vermont Supervisory Union (SVSU) in Bennington was trying to help its local community gain a better understanding of what students need to demonstrate in order to be successful on their math assessments. One of the most difficult sections of the exam is problem solving. Here, students are not only expected to determine the correct strategy, but also to explain their answers in writing, using math language and representation. For four years SVSU has used Exemplars as a curriculum tool in teaching its students how to solve these types of problems.
In an effort to share with its community examples of the types of problems students are expected to solve, SVSU contacted the McDonald's Corporation for assistance in distributing information. The result was Exemplars tasks went out to lunch! Typical sample problems were recreated on the McDonald's™ tray liners allowing the community to see the kinds of problem-solving tasks their students were doing. Both McDonald's™ and Exemplars were glad to be part of this of this community effort. Exemplars was pleased to give permission for its problems to be displayed and McDonald's™ funded the printing and production of the tray liners. Exemplars problems will be featured in the Bennington McDonald's™ over a three-month period of time on five different sets of tray liners.
The public's response was amazing, with both local and regional media picking up the story! Two television stations broadcast the news. The Bennington Banner ran an article and editorial that commended the district for, "developing a unique way to let the community know the nature of the important test their children are taking." The Vermont School Boards Association and other districts have contacted SVSU to learn how they too can help broaden the community understanding by using Bennington's success as a model.
Information Technology Coordinator
From New York
I have been using the math Exemplars K-8 for the past 6 years. I am a former NYC Math Coach and I have seen Exemplars improve my students Mathematics skills and thinking
If you are a student at our school, you will have heard the term, Exemplars. Exemplars are extended tasks in which 6th graders work in cooperative groups to plan strategies and find solutions. Initially, students are presented with a particular mathematical situation and asked to brainstorm individual strategies for "attacking" such a problem.
Our students have been preparing early for the new 8th grade state assessments by working diligently on Exemplars tasks.
The 6th graders recently completed the Exemplars "Mary Quite Contrary: How Does Your Garden Grow?" Students were grouped in teams and given a large sheet of poster paper on which they planned a strategy. Students were directed to map out all ideas on this paper whether in picture or words...
From New York
I find your samples and your rubrics very useful in my consulting work with teaching teams that include students with disabilities and in my work with teachers on differentiating instruction.
From Columbia University
Going into September there were no illusions about how difficult it would be to introduce teachers to a new set of materials, familiarize them with the assessment tasks, learn how to use the Exemplars rubric, and, in the case of New York City teachers, begin to create additional performance tasks for their students to meet the DOE requirements. 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. In early October we brought Aldo back to run a scoring conference where the teachers closely examined the Exemplars rubric and then applied it to samples of student work from "Tina's Quilt Squares" in advance of scoring their own students' work.
The response from teachers was again very positive; 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?"
At the start of November, we brought together all the New York City 9th-grade teachers in preparation for their second assessment administration. Over the course of six hours, the teachers worked in small groups clustered around the same topics in algebra. Some identified problems from the Exemplars "Best of Secondary" resource CD and then revised the tasks to fit into their upcoming curriculum; others started from scratch and created tasks that employed the key concepts they want students to learn. Our ISA/NCREST team circulated to facilitate groups, make suggestions and ask questions to prompt further discussion.
It was a long day, one that we will repeat in late November with 10th-grade teachers, but it was well worth the effort. Teachers were discussing not only content and skills but algebraic concepts and problem-solving strategies that are key components of inquiry instruction in math. Our New York City teachers took another step along the path of preparing students for college, and now we're working to take that step with teachers in Atlanta, Baton Rouge, Buffalo and other school systems partnering with ISA.
Research Associate - NCREST
Teachers College, Columbia University
Exemplars is a wonderful tool for differentiating mathematics and reaching the needs of a variety of students Pre K-12. At Glacier Edge Elementary, we enjoy using the software to challenge students in grades K-5. One of the best features is that there are three levels of accessibility for each problem, so more children are able to solve just right math problems, extending a particular strand in mathematics. The PDF files are easy to print and show additional features that our staff appreciate: the amount of time and materials needed, scoring rubrics and solutions, specific concepts/skills per problem, standards met, and teaching tips for staff and/or parent volunteers.
The catchy titles are irresistible. "Domino Dilemma" is just one example that will really catch kids' attention! One of the best programs available to really stretch talented students, is Exemplars!
Learning Resource Coordinator
This is just one example of what we are doing with Exemplars in Southwest Iowa.
I work with up to 31 school districts. There is now a heavy emphasis on problem solving. The trend has changed from curriculums with a weight on computation to those of process, communication...all those NCTM process standards. Our agency, through grant money, purchased an Exemplars CD for every building participating in our Enhancing Education Through Technology project. Just yesterday I worked with a building (Pre-K-6) in Sidney, IA. Each grade level selected up to 18 Exemplars tasks that they will incorporate throughout the year. Each grade level recorded the titles of their chosen tasks so we could see if there were overlaps. Teachers will alter the tasks to better match the curriculum at their grade level - especially so one grade level is not engaging students in the same exact tasks as another grade level. We need to expect more as we climb the grade-level ladder. This district has developed a form in which the students use (primary grade teachers and students work together to complete it) that focuses the students (and teachers) on George Polya's Four-Step Problem Solving method. They have also developed and tested a rubric to score the student work. This took time and lots of research, but it was well worth it. The reflection sheets that were completed after yesterday's search for problem solving were out of this world! The teachers love this product! They cannot believe what they have at their fingertips!
Exemplars is a product that I would personally buy should I return to the classroom.
Inservice training for teachers can be a real challenge in a large school district. It's tempting to just "present" the information, mandate the implementation and hold teachers responsible for the quality of that implementation. Choosing this format creates a void between teaching the teachers and classroom follow-up. Just as Madeline Hunter and so many others have advocated the importance of modeling for students, it is likewise important to model for teachers. With the advent of "No Child Left Behind," it has become increasingly essential that we look at "No Teacher Left Behind."
One important step in the direction of making professional development more meaningful to teachers has been to model instruction in a variety of realistic settings. During the fall of 2003, Exemplars consultant Deb Armitage was in Calcasieu Parish Schools for seven days. She spent two of the days in several schools across Calcasieu Parish in southwest Louisiana. Schools were selected to reflect a wide range of socio-economic backgrounds and student achievement. Teachers were scheduled to observe a model lesson in grade two, three or four in their school or in one nearby, which meant minimal time out of their own classrooms. These observations were tied to a full day of inservice training either the day before or the day following the model lessons.
This teacher-friendly format of tying the model lessons to the day of professional development in problem solving, communication and assessment, has given teachers the opportunity to see the application of specific strategies in a realistic setting. It gave them a model to either practice as presented or to adapt to their own situations. It gave them a springboard for moving forward.
Implementing constructed-response problems has often proven difficult for teachers. Since it is an integral part of the Louisiana accountability system, it has become increasingly important that this part of mathematics not be skimmed past or even omitted from the elementary curriculum. Exemplars has been a leader in providing high-quality, real-life, open-ended problems for students for many years. While teachers had previously been exposed to the materials, even "inserviced" in their application, the actual classroom use of the Exemplars problems had been scattered prior to this year.
Following the reformatted training, teachers have been more responsive in implementing strategies taught than they were when material was given but not modeled. The added dimension of actual classroom modeling has made teachers more comfortable with the process. Within the schools, teachers have been participating in learning communities supporting each other both within and across grade levels. It has promoted teacher/staff discourse and a sense of mathematical community. Exemplars consultant, Deb Armitage, will return toward the end of the academic year to give teachers the opportunity to solidify the learning process through feedback and follow-up training. One additional benefit of using the modeling format has been that teachers not only saw an Exemplars mathematics lesson modeled as intended, but they have also had the opportunity to see numerous quality strategies for communicating with students. They have seen students enticed to communicate their thoughts to peers as well as communicating their explanations on paper. Teachers have seen best practices for establishing a working community in the classroom.
When teachers use Exemplars they know who needs more modeling and which children are able to become more independent. It is always used as a process to move the children to the next level.
I feel that Exemplars has enabled our students to score well on our state and local mathematics assessments, not only in problem solving, but in all areas of mathematics. SCSD2's math scores are among the highest in the state, and I feel our K-5 mathematics curriculums (Everyday Mathematics and Exemplars) and the quality of our teachers' instruction are responsible for those scores.
I find that the kids really enjoy the use of Exemplars. It is a change of pace and the opportunity to think out of the box. Another great feature is the opportunity Exemplars offers for kids to learn from other kids!
From my own experience, I found that Exemplars has also had a positive impact on the Social Studies and Science curriculum.
K-5 Math Coordinator
From Clear Creek Independent School District
Many thanks for sending Dr. Jeri Thompson to our district for Exemplars science training. Jeri was excellent in her knowledge, skills, and expertise. We are completely satisfied with her remarkable work. We plan to have Dr. Thompson return for continued professional development in the future. Again, thank you for providing this exemplary service.
Elementary Science Coordinator
Clear Creek ISD
From Socorro Independent School District
We have used Exemplars in our school for the past year. We are a Pre-K-5 school with a population of about 1,350 students. I was introduced to Exemplars through the USI Collaborative for Excellence at the University of Texas at El Paso. I was a USI mentor until this past school year. We purchased the Best of Exemplars for our own school....
Using the Exemplars has added strength and depth to our mathematics program. Our primary math curriculum is Investigations in Number, Data, and Space a standards-based program. The two fit nicely together because both require students to explain their reasoning and show their work using numbers, pictures, and words...
Elementary School Teacher
Socorro Independent School District
The Exemplars program is designed to assess students' problem-solving and mathematical-communication skills. It also supports higher-level thinking and extension of mathematical reasoning.
From Los Alamos
Several years ago, Connie Witt tried to implement a standards-based curriculum and grading system into her school district, Los Alamos. At that time, she received little feedback or enthusiasm from her colleagues. Nevertheless, she pushed on. Determined to turn things around, Connie purchased Exemplars with her own money and began to apply basic standards-based skills. As Connie states, "I tried to introduce all of this when I first went back to the classroom a few years ago. No one understood what I was trying to do." After years of hard work, the Los Alamos school district has become extremely successful in using Exemplars and in, "Making a paradigm shift from focusing on instruction to focusing on student learning and using formative assessment to drive instruction." She began with the principals in her district, teaching them how to assess student work using rubrics. For many it was the first time they had ever looked at student work in this way. By collecting sample math tasks and rubrics from Exemplars web site, and student work from their own schools, Connie led them through the process of working in pairs and using rubrics to evaluate student work. She found this "mini training" highly effective and explained, "They were amazed at the power of the conversations they had around the student work."
She has since conducted similar training sessions with teachers, which has resulted in a whole new approach to staff development. Connie states, "We're moving away from district-wide, one size fits all trainings to peer coaching at sites." This has become a valuable tool to Los Alamos in teaching the use of rubrics and self-assessment.
The principals were thrilled Exemplars enabled them to provide their teachers and students with high quality rubrics and benchmark student work. The rubrics have also become a helpful tool for parents in understanding the standards-based (no letter grades) report cards.
Next on their agenda is to begin using Exemplars Reading, Writing and Research material to help develop their language arts assessment. Connie states, "We've started a 4-8 vertical alignment team for language arts and are trying to design a collection of developmentally appropriate sets of rubrics, 'style' sheets/guidelines, etc." They anticipate the same level of success they experienced with Exemplars math materials.
Exemplars math problems and rubrics have been available to Amphitheater teachers since 1998. The materials were distributed through our District Math Team. Each school received information and explanations from their site leader. Classes covering the use of problems and the rubrics were also included in the district professional development program. In addition, the District Math Specialist provided in-service to individual schools.
As a result, many teachers, as well as teams of teachers, adopted the Exemplars materials for use in their Career Ladder professional development plans.
Anecdotal evidence suggests that teachers in classrooms utilizing Exemplars materials on a regular basis saw in their students not only improved mathematical thinking on a day-to-day basis, but an increased ability to understand standardized testing materials as well.
Math Resource Teacher
From San Carlos
Learning With and From Each Other
Working Together to Implement Assessment
Exemplars Multiple Problems, Multiple Solutions
Betty Casey, is the principal of White Oaks School in San Carlos, California. Before taking that position, she was the curriculum facilitator in Burlingame, CA. Ms. Casey described the several ways she used Exemplars with her teachers in Burlingame. She explains how in Burlingame, Exemplars tasks are:
- Applied as a tool to teach assessment
- Used to "hammer out" the district's assessment plan
- Implemented as a vehicle to promote discussion on assessment and the implications it has on teaching
A Tool to Teach Assessment
After a few monthly meetings devoted to reading and discussion about assessment, Exemplars tasks were introduced. Teachers used the tasks in their classrooms. The following month they returned with the student work the tasks generated, assessed the work together and discussed what they learned. They also chose tasks for the next session.
Ms. Casey sees this process as non-threatening and invaluable to the teachers. It allows them to learn assessment through hands-on experience, while promoting discussions with their peers on the assessment practices of their school. Teachers are learning with and from one another.
Constructing the District's Assessment Plan
Ms. Casey assembled an assessment community built of teachers, principals, and parents. The main objective of this group was to construct the assessment plan for the district. They selected tasks for grades 3, 5, and 7, to be used as assessment tools within the curriculum for the upcoming year. This was important as assessment results would be reported. They found Exemplars tasks to be extremely helpful in this process.
A Vehicle to Promote Discussion on Assessment
"These were great sessions!", states Ms. Casey, in regard to their School Improvement Planning day. Teachers at each grade level received Exemplars tasks, and over the course of the next month the math mentor and Ms. Casey met with each teacher, assisting them in assessing their students' work. The real importance of this activity was in the discussion that it generated about the assessment criteria and the implications for teaching.
Ms. Casey also suggests making sure that every educator in the school has access to Exemplars, either via their computer network, or in the school's professional library. She has always made herself available to do any of the tasks with any class, and she states that, "So far, it's been great fun!"
From Kent School District
We have adopted the Exemplars program here in the Kent School District as a supplement to our Everyday Math program. We aligned our Everyday Math lessons with the Essential Learnings for each grade level and then aligned Exemplars to that. Each of our teachers has been given an implementation guide. This guide tells them which lessons in Everyday Math, Problem Solvers, Games and Exemplars to teach during any given month. They can easily cross reference their lessons with the EALRs as well as use it as a guide to their monthly planning.
In order to access specific Exemplars problems for various grade levels we have placed them on an Intranet system by grade and by month. Now all a teacher has to do is open up the Implementation Guide or their grade level, find the month and click on the exact Exemplars task they need to teach. They can print out one copy for themselves or multiple copies for their whole class! We have made using the Exemplars program easy and accessible for the teachers and in turn they are comfortable using it.
Kent School District
I did not grow up feeling mathematically empowered. I felt that math was a subject for "gifted" students and that average kids like myself would survive required math classes with minimal understanding. I learned quickly that memorization was the key to a passing grade. And after high school, who needed it!
Then I entered the world of classroom teaching and found myself on the opposite side of the teacher's desk. Looking out I saw a room full of smiling faces eager to embrace the subjects of math and science! There was no fear of failure in their eyes. There was no misconception about who can "do math" and who would be just another average Joe. Their [elementary] age did not hinder their enthusiasm to tackle the "hard stuff." They were ready. I wasn't! It was time for me to make some major changes in my whole philosophy about math, kids and learning. The first thing I did was take classes, workshops and training in math instruction. I reached out to colleagues I thought were strong teachers, and eventually learned that my own mathematical education was not a fault of mine, but the result of poor instruction. I had the misfortune of taking high school algebra and geometry [I didn't dare go beyond that!] with teachers who catered to the cream of the class, and failed to recognize I needed their support and attention, too. I was not about to become one of those teachers!
The Alaska Math Consortium offers classes for teachers just like me - math phobics! I signed up and spent three weeks of my summer realizing that I not only could "do math" but I loved it! I took the Advanced Institute the following summer and eventually became a facilitator myself. I searched for other classes, which addressed instruction in a more meaningful and hands-on approach. The more I learned, the more I longed to be stretched and challenged. To this day, I still have my eyes open for workshops or opportunities to further my knowledge in math, even with retirement just around the corner! I was drawn to classes, which broke math concepts down to a concrete level, using manipulatives to develop the visual thinker in me. [Oh, the delight I found when I learned about base ten blocks and algebra tiles!]
While my own mathematical needs were met through these classes, they also shaped my personal philosophy about math instruction. I have become more sensitive to the needs of all my students. The way I teach math is not unlike the way I look at reading instruction. New learning is based on prior knowledge. Students need to explore and manipulate objects in order to make sense of the mathematical world. As a teacher, it is my role to support their learning with as much scaffolding as they require in order to feel successful. As they become more confident learners, the support system is eventually removed - piece-by-piece. Students also learn best when they are guided to make discoveries on their own. "Drill and kill" techniques cannot lead to mastery as effectively as providing children with enough opportunities to practice through exploration and games. Playing "Go Fish For Ten" can help even the youngest students eventually realize that 14 + 6 = 20 "because 4 and 6 are 10 friends and 10 and that other 10 make 20!" I continue to use materials which allow my students "to see" their way through math concepts.
Over the years, I felt that my recipes for math were solid, with just the right ingredients to provide my students with a balanced program. Everyone was happy. Still, there was something missing. I knew that I needed something more - a dessert - involving math problem solving. I went in search of such a recipe on the Internet and came across the site for Exemplars. As I read it over, my mouth began to drool! This is exactly what I needed. So, when I came into some money [The Presidential Award for Excellence in Mathematical Teaching provided me with a check!] I signed up for the closest Exemplars workshop to Alaska, which happened to be in Texas!
The workshop's presenter was Deb Armitage, a former classroom teacher from Vermont. She literally kept me on the edge of my chair. I even held off "bathroom breaks" for fear I'd miss something she said. First she presented the overall idea behind Exemplars. Then she handed out problems, which had been tried and tested, just like a recipe in a test kitchen! We went over both the problems and the students' work, analyzing what children knew and could explain, and what was still missing. The rubric was invaluable for this! Finally, we got to roll up our sleeves, donned an apron and started cooking ourselves. Using the information Deb taught us and the rubric, we set about scoring problems. The more we did, the more we wanted to do! Who would have thought that sitting for two days in a windowless room could be so wonderful. The time flew!
I dreaded the thought of leaving Texas without the support of another colleague in my own district. I was the only Alaskan among so many Texans! But, I didn't really have to worry. Deb became my email support person. The more we emailed, the more confidence I gained. And so, now I really feel I have the perfect math program, complete with dessert! I felt so excited about my ability to teach students how to solve problems that I initiated a Math Club for third-fifth graders. [I teach a K-1 Multiage program.] We meet once a week after school just to solve math problems. They love it and so do their parents!
I'll be retiring at the end of this school year. While I have lots of plans for my retirement, one is to continue to keep cooking up great math recipes for kids. As a volunteer, I will be excited to work with students in the area of math. When I think about packing up my classroom for the last time, many things will be tossed or given to other teachers. But I will never give up my Exemplars Math binder! That's my recipe book! And whenever anyone asks about math, I hop up on my soapbox and shout the praises of EXEMPLARS!
"In a career of more than 20 years in education and going to professional development meetings, there have only been one or two experiences that have changed the way I approach teaching. The Exemplars workshop has been one of them."
From Claremont Graduate University
In a number of recent studies comparing approaches to teaching mathematics in countries around the world, a list of 'best practices principles' have been identified. The Exemplars math program reflects the most important of these 'best practices principles,' and offers teachers a curriculum for teaching mathematics and assessing mathematical expertise from a contextual, problem focused point of view. The program is terrific.
Ph.D. Professor of Psychology
Claremont Graduate University
From Jefferson County Public Schools
My favorite experience with Math Exemplars occurred when I was completing my administrative internship as an assistant principal at a middle school. One of my primary responsibilities was to discipline students. If a student was suspended, it was required that a parent come to the school and take the student home.
On one occasion, a mother was unable to pick up her student right away, so he needed to stay in my office until she arrived. I gave him a Math Exemplars problem to work on to keep him busy. He loved it! He was engaged in the problem and truly enjoyed solving it. When his mother arrived, he was excited to show her what he had accomplished. The mother told me that this was one of her son's most positive experiences.
Jefferson County Public Schools
From Round Rock
Questions that puzzled many of our school board members, campus principals, community members, administration staff, teachers and students were:
- How do we know what students really know?
- Do students and parents understand what we expect students to be able to do well?
- Is what I consider acceptable, considered acceptable by others?
- Are students really making the connections in their learning?
- Will students recognize the connections in future or unique situations?
Searching for answers to questions such as these was the catalyst for developing district academic standards. In conjunction with this development was the development of assessments that would provide evidence of meeting the standard. We wanted assessments that would tell us more than what most multiple-choice assessments were able to provide. At this point, Exemplars moved to center front stage for mathematics. Several campuses in our district had been engaged in 'The New Standards' language arts or mathematics project and were familiar with the idea of performance tasks. Scoring with a rubric and establishing benchmark papers challenged most math teachers. With Exemplars, that was no longer a monumental problem, since annotated benchmark papers are provided with each task.
We are now in our fourth year of using Exemplars. We have a district license and every campus and every math teacher regularly uses an Exemplars problem either for assessment or instruction. These campuses really see the benefits and enjoy watching their students grow mathematically. They have provided the opportunity for students to bring forth their knowledge, apply that knowledge in solving fun, challenging problems and communicate their thinking.
Mary Alice Hatchett
Director of Mathematics (retired)
Round Rock ISD
From Santa Rosa
Exemplars helps bridge the gap between standards on a page and students and teachers in the classroom.
If I think about all the strategies teachers have used to try to improve student achievement in math, the Exemplars program was the most powerful.
This is an excellent resource! Thanks for making it available. Exemplars are a wonderful tool for our highly capable math students. They encourage them to show their work, explain their thinking and label their answers.
I think the Exemplars are great. My students have really done well with word problems since I have started using some of the Exemplars.
"I love Exemplars. In fact, it is all I want to do with the kids. I am amazed at the thought processes it evokes from the children. Exemplars gives a perfect view into the child's thinking and their minds. Exemplars tasks also give the child who has difficulty grasping math concepts the opportunity to explore, and apply techniques and thoughts to the mathematical process."
From Alaska On Exemplars Summer Institutes
Using the information Deb [the presenter] taught us and the rubric, we set about scoring problems. The more we did, the more we wanted to do! Who would have thought that sitting for two days in a windowless room could be so wonderful. The time flew!
From Tacoma School District
If you walk into a Tacoma classroom during math instruction, you will see kids huddled around an Exemplars task, cooperatively selecting their problem-solving strategy. Rich conversations will follow, in which students will not only defend their solutions, but also get a chance to study alternative strategies unveiled by other groups assigned to solve that very same problem.
In the fall of 1997, Tacoma schools implemented a promotion policy where students in grade 5 are required to demonstrate their proficiency in literacy and mathematical problem solving as a condition for being promoted to the sixth grade. The policy's mathematics component requires students to communicate their thinking as well as work towards an accurate solution to an extended problem. With the increased demand on student performance, it became clear to our personnel that instruction needed to change in order to prepare students for this more rigorous assessment. Yet many staff members lacked training in how to weave problem solving throughout their daily math instruction.
After searching through the myriad of problem-solving materials offered, Exemplars was chosen by Tacoma as one vehicle for helping staff and students move in this new direction.
Knowing the importance of staff development, we offered multiple workshops designed to acquaint the staff with Exemplars and how to teach towards the Exemplars rubric. Sample problems were sent regularly to schools and the Best of Math Exemplars CD-ROM was provided for each of our 46 buildings. We needed to educate the parents as well so we offered workshops around the district to acquaint them with several problem-solving strategies. Ross Brewer flew to Tacoma on two occasions to work with groups of teachers and students as we all struggled to give up some of our tried and true math practices in order to free up time to delve into problem-solving on a more regular basis.
Tacoma School District