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Standards-based assessment and Instruction


Archive for the ‘Education’ Category

Where to Begin? Getting Started With Exemplars Science

Wednesday, September 27th, 2017

By Tracy Lavallee, 4th Grade Teacher and Exemplars Science Consultant

Exemplars Science is not a stand-alone program.

Rather it is a supplemental program to help schools and districts bring standards-aligned, inquiry and performance-based instruction and assessment into their classrooms. The tasks can be used in a multitude of ways, for both instructional and assessment purposes.


Tips for Getting Started With Exemplars Science

  • Begin by looking at your curriculum. What units of study are you currently teaching? What concepts and skills are you assessing? When do you assess your students’ understanding? Where might you add formative assessment? Where could you add more inquiry-rich tasks? Do you currently use a rubric for assessment?
  • Start small. Pick one task to add to your existing unit, for instruction or assessment. Try it out.
  • Work with colleagues. It is very helpful to meet with colleagues and discuss possible tasks to use for assessment. This will add consistency at grade levels and can provide opportunities for teachers to share and analyze student work together. These rich conversations can help facilitate more effective instruction and differentiation, and deepen students’ understanding of sometimes complex concepts. It is also an opportunity to help each other be the best teachers we can be for our students.

Ways to Use Exemplars Science

  • Pre-Assessment Task: Often we forget the importance of pre-assessing students to see what they already know about a particular concept. A pre-assessment is a powerful tool for teaching. It gives us a starting place. It helps us to identify any misconceptions students may have so that we can design our instruction to address those.
  • Anchor Task: An anchor task is used at the beginning of a unit to engage students with the content and the materials. It can also be used to pre-assess students’ prior knowledge and a way to elicit misconceptions students may have. But its main purpose is engagement with the phenomenon. For a unit on electrical circuits, “Can You Light the Bulb?” (a 3-5 Exemplars investigation) is a great anchor task to try. During this investigation, students use materials to explore how to light a bulb, engage with the big ideas of the unit, grapple with a problem, collaborate with others, and communicate their thinking and learning.
  • Inquiry/Content Task: Many of the Exemplars tasks may be used to enrich units of study by adding more inquiry-based learning. They are also designed to help students deepen their conceptual understanding. For example, the 3-5 investigation, “Learning About Electricity, Part 2: How Many Electrical Circuits Can You Make?” engages students with concepts of parallel and series circuits and helps them to understand and demonstrate the difference. It also provides an opportunity for students to practice inquiry skills such as observation, designing and testing ideas, gathering data and communicating explanations and solutions. Many Exemplars science tasks are effective for teaching and practicing the skills of science and engineering.
  • Formative Assessment: Formative assessments happen throughout a unit. They can be very intentional as a means to gather information about what your students know and are able to do at different points. They can also be very informal check-ins to see what instructional modifications or changes need to be made to help students with certain concepts and skills. An example of a formative assessment in a unit on electricity might include the task, “Can You Get Two Light Bulbs to Light?” In this setting, this 3-5 task may be used to check on students’ understanding of circuits and how they work. Most Exemplars tasks can be used for formative assessment purposes.
  • Cumulative Assessment: Cumulative assessments are an important part of classroom assessment. They not only ask students to demonstrate conceptual understanding but serve as real-world opportunity for them to apply that understanding. Exemplars performance tasks are designed to be real-world applications of knowledge and skills. The 3-5 investigation “Can You Wire a House?” may be used at the end of the unit to assess students’ understanding of the concepts and their ability to communicate their understanding. It also asks students to apply their understanding to solve a problem and design a possible solution.

These are just a few suggestions for getting started with Exemplars Science. There is no right or wrong way to begin. The important thing is to begin. Have fun with it! Our tasks are teacher- and student-tested and approved. We are also here to help you and your school as you implement Exemplars into your teaching and to support you as you go.

Why Science Standards?

Wednesday, September 27th, 2017

By Tracy Lavallee, 4th Grade Teacher and Exemplars Science Consultant

In 1985, the American Association for the Advancement of Science brought a group of scientists and educators together and created AAAS-Project 2061, which asserted what basic understandings were needed to ensure a scientifically literate citizenry.

From these understandings, the NRC (National Research Council) Science Standards were born. The NGSS (Next Generation Science Standards) then took these standards to the next level and included a more integrated, 3-dimensional approach, as well as one that focuses strongly on inquiry, mathematics, and engineering as part of that scientific literacy.

Why is this important? Why do our students need to be scientifically literate citizens? The answer is obvious. If our children understand the why and the how of science, technology, and engineering, they are better able to make informed decisions as part of a democratic society. In order for students to do this, they must regularly engage with, investigate, and explain scientific phenomena.

Science education has long taken a back seat in schools across the country. The focus on math and literacy has forced many elementary schools and teachers to consider science education as optional, and only if there was time. It is very often a hit-or-miss opportunity for our students. It hasn’t been a priority in our schools for a long time. First AAAS and NRC, and now NGSS, are trying to change that.

The standards are not a curriculum. They are a scope and sequence of what our students should know and be able to do. They include not only the what, but the how. They also integrate reading, writing, and math and so much more. They connect concepts and allow students to explore these connections more deeply. They can become the heart and soul of what and how we teach.

Schools and teachers have the ability to bring this into their classrooms and to their students. It isn’t an add-on, but rather a way to enhance and enrich your students’ learning in new and significant ways. Science is all around us. It is a part of our everyday lives. Students are naturally curious and want to understand how the world works.

More than 20 years ago, Exemplars, a well-known name in math performance tasks, believed that science should be brought off the back burner. It started Exemplars Science, which was aligned to the NRC. Exemplars developed performance tasks to help teachers implement and assess these science standards. Over the years, the number of tasks has grown to include all strands of science as well as engineering. Like Exemplars Math, these tasks are teacher-developed and student-tested.

Exemplars recently edited and aligned its performance tasks with the NGSS as a way to help teachers navigate these new and perhaps unfamiliar standards. The posts in this blog series will be a way for us to help you navigate and implement the standards and Exemplars Science in your classroom.

Why science standards? Because, now more than ever, we need scientifically literate students. And because now you have Exemplars Science to help you bring these standards to life in your classroom and to inspire our future generation of citizens.

Time for Science

Wednesday, September 27th, 2017

By Tracy Lavallee, 4th Grade Teacher and Exemplars Science Consultant

Time. It seems we never have enough time. Not enough time to teach everything we need to teach. And science is usually the subject most affected by this lack of time.

It is easy to put it off and focus on other important things like math and literacy. But in doing so, we are doing a great disservice to our students.

Science education offers a multitude of opportunities for rich, engaging, and interdisciplinary learning. Science is the way of understanding the world in which our students live and scientific literacy is more important now than ever. Science opens up new ways of exploring, investigating, thinking, and explaining. It is hands-on and minds-on. The benefits of science are many: engagement, wonder, curiosity, enthusiasm, excitement, asking questions, solving problems, teamwork, and a desire to learn more. But, how do we find the time for this?

It involves getting creative with time and making the time for science. It involves a shift in our perception from seeing science as an extra, an add-on, to recognizing it is an important and integral part of our instructional program.

How Do We Find the Time?

Simple. We make the time. We think about the big picture of learning. We think about big concepts, big skills, and big ideas. Where does science fit in? Everywhere!

Are you teaching claims and evidence? Making models? Collecting and interpreting data? Doing a reading unit on weather or other non-fiction topics? Practicing writing procedures, opinions or non-fiction? Studying the history of inventions, the gold rush, or current events? The possibilities are endless for ways to integrate science into what we currently are teaching.

If we think about the habits of mind in science – perseverance, communication, questioning, curiosity, openness to new ideas, creativity, reasoning, logic, collaboration, and innovation to name a few – these are truly habits of mind we want our students to develop in all subjects and in life. Science fosters these naturally in our students and enables them to bring these habits of mind into all they do learn and experience.

NGSS can help us find the time. Each performance expectation has key integration components with the Common Core ELA and Math standards.

Exemplars Science can help too. Each science task has interdisciplinary links to social studies, language arts, mathematics, technology, outdoor learning and even music and movement!

Once you find the time, try taking it one step further. Try having science as your main theme, and integrate the rest of your instructional program into that theme. Not only does this help with time, but it allows students to see the inherent connections between all subjects and all things. Exemplars can help you do that as well.

Science doesn’t have to be a separate subject to be fit in when there are a few spare minutes. It can be the heart and soul of our instructional program. As teachers, it is within our power to engage students with all the wonders and phenomena of our natural world. We just have to make the time.

How Can Exemplars Support Best Practices in Science?

Wednesday, September 27th, 2017

By Tracy Lavallee, 4th Grade Teacher and Exemplars Science Consultant

Long gone are the days of the stand and deliver as an effective way to teach. Science instruction is now more about sense-making than memorization.

Science is no longer a fixed set of facts and information to be memorized, but rather a way to experience and understand how our world works through a more open-ended and student-centered approach. It is no longer lab experiments with one correct answer, but rather an inquiry-based approach to designing and conducting investigations to answer students’ own questions about science concepts.

Science today helps students build on prior experiences and guides them through experiential opportunities that allow them to construct a deeper understanding of science concepts and to authentically use the skills of science. Science pedagogy has changed in many meaningful and important ways. Best practices in science have been around now for a while. But what are those best practices and how can Exemplars support them in the classroom?

What are Best Practices in the Science Classroom?

Best practices in science can best be defined as students thinking, doing, talking and collaborating about science. The effective science classroom is learner-, knowledge-, assessment-, and community-centered.

  • It means taking students from where they are with their prior knowledge and developing and guiding them to a deeper conceptual understanding.
  • It means engaging students with real-world ideas and problems and allowing them to grapple with and construct genuine meaning.
  • It means opportunities for rich discourse with others and to be reflective about how their preconceptions and misconceptions have changed.
  •  It means seeing science as dynamic and interconnected.

According to NSTA’s, Designing Effective Science Instruction: What Works in Science Classrooms,  (Anne Tweed, 2009) best practices mean that teachers should:

  •  Assess for prior student understanding of the science concepts.
  • Actively involve students in the learning process.
  • Help students be more metacognitive so that they can acknowledge the science concepts they understand, the goals for their learning, and the criteria for determining achievement of the learning goals.
  • Ensure that learning is interactive and include effective classroom discussions.

The Changing Role of Assessment

One of the most important aspects of effective instruction is the changing role of assessment. Assessment should be ongoing and shared with students. It is both formative for instruction and cumulative to assess student learning.

Formative assessment provides a way for teachers to focus instruction on what and how students are learning. Incorporating formative assessments as part of instruction results in creating an environment focused on learning for all.

Formative assessment is a process, one in which information about student learning is gathered and then used to modify teaching and learning activities to best meet the needs and interests of students. It also means involving students in the assessment process and helping them to be more reflective and engaged in their own learning.

Exemplars Supports Best Practices

Exemplars Science is a standards-based assessment program. It is designed to help teachers use formative and cumulative assessments in their classrooms in a more focused and intentional way. It offers teachers opportunities to assess students’ learning throughout a unit of study and engages students in their learning and assessment with performance-based tasks and rubrics.

Exemplars tasks are created by teachers and utilize the 5E model (Engagement, Exploration, Explanation, Elaboration, and Evaluation) for instruction and assessment. The tasks are aligned with both NRC and NGSS standards. They are hands-on and open-ended allowing students to construct and explain their understanding of concepts while using the skills of scientists and engineers. Exemplars can help teachers design and facilitate effective science instruction and assessment. Using Exemplars Science in the classroom is best practice.

Exemplars in Action: Tokyo International School

Monday, May 22nd, 2017

According to one student at Tokyo International School (TIS), “Our teachers want us to really understand the mathematics we learn.” That’s why Exemplars plays a vital part of the school’s approach to teaching problem solving. Watch the video below to see Exemplars in action in TIS’s first-grade class — and then read on to learn how our materials enhance the school’s approach to assessment.

Written By: Josef Kaufhold, TIS primary school teacher

Tokyo International School is a pre-K through 8th-grade school located in central Tokyo, Japan. Our 350 students represent more than 40 nationalities, making TIS a truly international school. For TIS, the Exemplars Library represents a step forward in assessing mathematical thinking.

As an International Baccalaureate Primary Years Program school, we are committed to finding resources that support students’ development of knowledge, concepts, skills, and attitudes. Exemplars tasks pose students with authentic problems that require them to demonstrate their understanding, knowledge, and skills. Through iconic representations, students visualize their conceptual understandings as they develop solutions.

Because the expectation that they show their mathematical thinking yields such detailed responses, we can effectively assess student understanding and thoroughly report on Common Core outcomes to our students and their families. Using Exemplars, we are able to assess students’ growth when comparing rubric scores for pre- and post-assessments. Alongside the rubrics, the anchor papers provide specific qualitative indicators of student performance.

Exemplars problems engage curiosity and require commitment to solve. Students learn to cooperate and communicate effectively when working on these problems, which helps to develop positive attitudes towards mathematics. Through practice, students develop a strong, transferable grasp of the problem-solving process. Our staff has welcomed Exemplars into our balanced repertoire of tools used for effectively teaching math.

When Teacher Candidates “Do the Math” With Exemplars

Wednesday, April 19th, 2017

This blog is a reflection written by Dr. Courtney Baker, Ph.D., an Assistant Professor in Math Education Leadership at George Mason University, on her use of Exemplars with her elementary teacher candidates. The findings outlined in this piece would be beneficial to other professional development courses in a school or district setting.

Exploring Exemplars

Promoting discourse from rich tasks that move mathematical thinking forward challenges elementary teacher candidates, as their past experiences in working with both mathematics and children is often limited.

In teaching practice, the ability to come up with alternative approaches that vary from the traditional algorithm is necessary in order to anticipate student responses and to plan appropriate instructional opportunities. For new teacher candidates, however, this can represent a significant hurdle. Last semester, I incorporated resources from Exemplars into my practice to support my students with developing the background knowledge required to successfully anticipate student responses.

Upon my initial exploration of the Exemplars Library I was intrigued. How could I use these resources to not only introduce how children might authentically approach a particular problem, but also to elicit discussions centered on mathematics content? To meet these objectives, I needed to find a rich task that promoted a deep understanding of the pedagogical and content knowledge required to teach elementary mathematics. After looking through the expansive Library, I realized that multiple tasks met my needs as an instructor. I decided on a fifth-grade task titled “Crab Walk Relay Race.”

Doing the Math

I handed the pre-service teachers in my class hard copies of the corresponding overhead and created small groups to “do the math” collaboratively. I asked them to think about possible approaches using multiple representations (concrete, pictorial, and abstract) as well as possible student misconceptions. I wanted the teacher candidates to anticipate how a student might approach the task. I also wanted them to think critically about the manipulatives that would prove beneficial. My hope was for the teacher candidates to apply the knowledge gained from both their readings and fieldwork as they explored the Exemplars task. What happened in class, exceeded my expectations.

What started out as a 25-30 minute activity became a 60+ minute experience. Grounded in authenticity, the task promoted conversations that connected the teacher candidates’ background experiences with problem solving. Specifically, many of my students shared connections to either coaching sports teams or creating similar environments with children.

My class explained their strategies to one another as they tested their hypotheses. While they searched for an efficient strategy, they constantly compared their thinking to ensure that they were creating the most equitable teams. This continual communication allowed teacher candidates to share their thinking while using mathematically rich vocabulary.

Connecting to the Curriculum

After each group anticipated how students might approach the task, I provided them with the corresponding Exemplars Preliminary Planning Sheet. This resource proved to be an amazing support in the exploration of the mathematics content. Due to their limited experience with the standards, these pre-service teachers previously struggled to find connections between rich tasks and state standards. However, with the support of this document, my students were able to clearly articulate which mathematics standards the task was aligned with.

Analyzing Anchor Papers as Student Work Samples

At the heart of my activity was the analysis of student work samples. I took the levels (Novice, Apprentice, Practitioner and Expert) off of each anchor paper, and provided all samples to each group for evaluation. Initially, I thought that without the labels the teacher candidates would easily be able to sort and classify the student work samples. While I knew the discussion would center on determining what exactly each student knew, what I did not expect was the rich discussion that followed.

Teacher candidates were amazed at the variety of ways a student could approach the problem (many of which they had not anticipated). While some papers were easy to score, others were more challenging. Additionally, the anchor papers provided guidance to the depth of knowledge required to be identified as a successful problem solver. Their discussions centered on questions such as:

  • How do we define the difference between a student who is an Apprentice and one who is a Practitioner?
  • What questions could we ask the student to help them explain their thinking to us?
  • To what extent must a student display their knowledge to be identified as an Expert problem solver?
  • Is it possible for a student to identify a correct solution, but not be an Expert problem solver?

These questions arose organically from the use of this Exemplars task, and pushed my students’ understanding of problem solving.

Supporting Teacher Development

Preparing individuals to effectively teach elementary mathematics is a challenge, as it is impossible to provide each teacher candidate with all the knowledge and resources required to effectively teach elementary mathematics. Looking at how students might authentically approach a problem is essential for teachers to further their practice. Incorporating the Exemplars task into my teaching allowed teacher candidates to critically reflect on their practice and predict how students might approach problems through the analysis of these materials.

Sharing this Exemplars task with my students made for a great discussion that furthered their understanding of teaching elementary mathematics, and highlighted the complexities of problem solving. It also provided teacher candidates with a quality resource that they can potentially access as they enter into classrooms of their own.

Exemplars in the Classroom: “They Want to Become Experts.”

Sunday, November 27th, 2016

Written By: Danielle Descarfino, Fifth Grade Teacher at P.S. 94 in Brooklyn

Getting Started

From the beginning of the school year, I used Exemplars problem-solving tasks regularly to create routines that have helped my fifth grade students grow and succeed. Following the Problem-Solving Procedure is a central part of this.

Although each task is different, the procedure helps kids internalize a framework for approaching a problem. I provided each student with his or her own color copy (in a sheet protector for safe keeping.) Each time we begin an Exemplars task, the students take out their Problem-Solving Procedures and refer to it. I also have a poster-sized version prominently displayed in the classroom, which I hold up and point to while guiding and facilitating tasks.

Building Background Knowledge

My class is made up of English Language Learners and former English Language Learners, so I anticipate that reading and understanding the problem may be especially challenging for them. We read the problem together, I ask questions to activate their background knowledge, and I often provide pictures that help them visualize the problem.

For example, we recently completed “A New Aquarium,” a 5.MD.C.5a task involving volume. We had been working on this math concept for only a few days and this was our first volume Exemplars task. Before reading the problem, I displayed a photo of an aquarium on the Smart Board and discussed the following questions with the class:

  • What is an aquarium?
  • What type of solid is this aquarium?
  • How could you figure out how much space this aquarium takes up? What steps would you take?

Although many students initially were not familiar with the word “aquarium,” after this discussion, they understood that an aquarium is a fish tank and a rectangular prism, which meant that we would be calculating its volume to find out how much space it takes up. Using visual aids and background questions to ensure that students understand the situation in the problem has been very helpful when completing Exemplars with English Language Learners.


We always utilize the differentiated Exemplars tasks. Students are aware of which problem-solving group they are in and know where to sit when it is time for an Exemplars task. One group gets the More Accessible Version; they are guided through the problem as they work with the Special Education teacher at a kidney-shaped table. The other two groups receive the Grade Level and More Challenging versions and sit with their groups in desk clusters, like a team of problem solvers.

For the Grade Level and More Challenging groups, we discuss background information, read the problem out loud, annotate it, and write our “I have to find …” statements. Then the students go on to work with their groups to complete the task while the teacher takes on the role of a facilitator, conferring with groups. Students share ideas, address misconceptions, and explain their mathematical reasoning to one another as they solve.

Motivating Students

I love hanging Exemplars tasks on bulletin boards. I think it’s useful for students to look at the page and see all of the different ways their classmates organize and express their mathematical thinking through equations, representations, and writing.

From day one, I have made it clear that it is expected that their finished work clearly communicate their problem-solving steps to the reader. Not only should the students make an effort to write neatly, but they should also organize their problem-solving steps on the page in a way that makes sense. Sometimes if a student is not showing all of their steps or it is unclear, I’ll say, “I am confused. When I look at your paper, I don’t understand the steps you took to solve the problem.” When the students have the understanding that a goal is to communicate their math thinking to a reader, it helps them create a higher-quality finished product.

Another great way to motivate students is through mathematical connections. I have given a strong emphasis to connections, as I initially noticed that once students solve the problem, they feel like they are done! This is not the case, because noticing mathematical connections, patterns, and alternate strategies really helps students understand mathematics on a deeper level and practice critical thinking skills.

To help them stretch their thinking, I discourage students from writing “boring” connections, like “This number is greater than that number” or “John ate the least amount of pizza.” Instead, I encourage them to use mathematical language, create a second representation, show steps to solving with alternate strategies, convert fractions/decimals/percents, or extend the problem by adding to the story in the original problem. Once they get the hang of it, they start being more creative, going above and beyond to make more complex math connections. During the volume unit, I taught students how to use grid paper to make scaled models of rectangular prisms. When completing these tasks, many students decided to build models to represent the rectangular prisms in the task and attach them to make 3-D Exemplars. They looked great, and the students loved making them!

Peer Assessing

At the beginning of the year, I explained each portion of the Exemplars rubric to the students. The rubrics are very student-friendly and I find that they inspire students to want to become Experts.

Each time I assess Exemplars, I use the rubric along with a sticky note full of feedback. The sticky note always contains one “Glow,” something the student did well, and one “Grow,” something the student could improve upon. At the beginning of the year, I let the students know that when they become more comfortable with Exemplars, they would learn how to peer assess. After a few months, I told the students that they were ready to peer assess one another’s work. They were so excited! This made them feel proud that they had reached a new level of expertise in problem solving and feel empowered that they were now trusted to assess a classmate’s work.

To peer assess, they do exactly as the teacher has done all year: complete the student rubric and use a sticky note to write “Glow and Grow” feedback. An example of this can be seen below. From the start, I was so impressed at how well the students were able to assess one another’s work with Exemplars. I found that regularly providing students with written feedback and referring to the rubric when expressing expectations is a great way to model peer-assessment. Furthermore, the experience of assessing Exemplars helps students get new ideas from their classmates and become more aware of how their own work will be graded.

Task: A New Aquarium

(More Accessible Version)

Joseph has a new rectangular aquarium. The aquarium has a length of four feet, a width of two feet, and a height of two feet. What is the volume of Joseph’s new aquarium? An aquarium holds one inch in length of fish for each twelve square inches of the area of the base of the aquarium. Joseph can buy fish in two different sizes—about three inches in length or about five inches in length. About how many three-inch fish can Joseph put in the new aquarium? About how many five-inch fish can Joseph put in the new aquarium? Show all your mathematical thinking. 

Danielle’s Biography

Danielle Descarfino is a fifth grade teacher at P.S. 94 in Sunset Park, Brooklyn. She graduated from Fordham University with a Masters of Science in Teaching English to Speakers of Other Languages. Danielle grew up in Tappan, New York, and currently lives in Brooklyn. She was inspired to become a teacher after spending time as a volunteer teaching English at an orphanage and community center in Salvador, Brazil.

A Problem-Solving Lab to Support the Math Practices

Monday, October 31st, 2016

Written By: Donna Krachenfels & Debra Sander, Teachers from PS 54

The school administrators at PS 54 had a vision to create a math laboratory based on the eight Standards of Mathematical Practice. The idea was to create a setting in which students could focus on multi-step problem solving.

The Exemplars program has given our students many opportunities to build and strengthen their problem-solving skills. Students were also able to strengthen their close reading skills as they reread problems multiple times to identify and think about the relevant information necessary to find a solution. Collaboration allowed students to become confident in their problem-solving skills and increased their abilities to construct viable arguments as they defended their solutions and critiqued the solutions of their classmates. Students were not afraid to take risks as they tried different representations and strategies to solve problems. As a result of the Exemplars math program, our students became more confident and more independent problem solvers.

The math laboratory is in its second year at PS 54. Last year, our data saw increased math scores for the classes that participated in the problem-solving lab. This year, the trend continued and all general education students passed the state math exam.

Special thanks goes to Exemplars professional development consultant Deb Armitage for all of her help and support. She is a true math educator!

Preparing for the New Math TEKS: Using Rubrics to Guide Teachers and Students

Thursday, October 6th, 2016

By: Ross Brewer, Ph.D., Exemplars President

As you begin preparing your staff to focus on the new math TEKS this year, rubrics should play a key role in terms of helping your teachers and students achieve success with the new standards.

 What are rubrics?

A rubric is a guide used for assessing student work. It consists of criteria that describe what is being assessed as well as different levels of performance.

Rubrics do three things:

  1. The criteria in a rubric tell us what is considered important enough to assess.
  2. The levels of performance in a rubric allow us to determine work that meets the standard and that which does not.
  3. The levels of performance in a rubric also allow us to distinguish between different levels of student achievement among the set criteria.

Why should teachers use them?

The assessment shifts in the new math TEKS pose challenges for many students. The use of rubrics allow teachers to more easily identify these areas and address them.

For Consistency. Rubrics help teachers consistently assess students from problem to problem and with other teachers through a common lens. As a result, both teachers and students have a much better sense of where students stand with regard to meeting the standards.

 To Guide Instruction. Because rubrics focus on different dimensions of performance, teachers gain important, more precise information about how they need to adjust their teaching and learning activities to close the gap between a student’s performance and meeting the standard.

To Guide Feedback. Similarly, the criteria of the rubric guides teachers in the kind of feedback they offer students in order to help them improve performance. Here are four guiding questions that teachers can use as part of this process:

  • What do we know the student knows?
  • What are they ready to learn?
  • What do they need to practice?
  • What do they need to be retaught?

How do students benefit?

Rubrics provide students with important information about what is expected and what kind of work meets the standard. Rubrics allow students to self-assess as they work on and complete problems. Meeting the standard becomes a process in which students can understand where they have been, where they are now and where they need to go. A rubric is a guide for this journey rather than a blind walk through an assessment maze.

Important research shows that teaching students to be strong self-assessors and peer-assessors are among the most effective educational interventions that teachers can take. If students know what is expected and how to assess their effort as they complete their work, they will perform at much higher levels than students who do not have this knowledge. Similarly, if students assess one another’s work they learn from each other as they describe and discuss their solutions. Research indicates that lower performing students benefit the most from these strategies.

Rubrics to Support the New Math TEKS.

Exemplars assessment rubric criteria reflect the TEKS Mathematical Process Standards and parallel the NCTM Process Standards. Exemplars rubric consists of four performance levels (Novice, Apprentice, Practitioner (meets standard) and Expert) and five assessment categories (Problem Solving, Reasoning and Proof, Communication, Connections and Representation).

Our rubrics are a free resource. To help teachers see the connection between our assessment rubric and the TEKS Mathematical Process Standards, we have developed the following document: Math Exemplars: A Perfect Complement for the TEKS Mathematical Process Standards aligns each of the Process Standards to the corresponding sections of the Exemplars assessment rubric.

It’s never too young to start.

Students can begin to self-assess in Kindergarten. At Exemplars, we encourage younger students to start by using a simple thumbs up, thumbs sideways, thumbs down assessment as seen in the video at the bottom of the page.

Our most popular student rubric is the Exemplars Jigsaw Rubric. This rubric has visual and  verbal descriptions of each criterion in the Exemplars Standard Rubric along with the four levels of performance. Using this rubric, students are able to:

  • Self-monitor.
  • Self-correct.
  • Use feedback to guide their learning process.

How to introduce rubrics into the classroom.

In order for students to fully understand the rubric that is being used to assess their performance, they need to be introduced to the general concept first. Teachers often begin this process by developing rubrics with students that do not address a specific content area. Instead, they create rubrics around classroom management, playground behavior, homework, lunchroom behavior, following criteria with a substitute teacher, etc. For specific tips and examples, click here.

After building a number of rubrics with students, a teacher can introduce the Exemplars assessment rubric. To do this effectively, we suggest that teachers discuss the various criteria and levels of performance with their class. Once this has been done,  a piece of student work can be put on an overhead. Then, using our assessment rubric, ask students to assess it. Let them discuss any difference in opinion so they may better understand each criterion and the four performance levels. Going through this process helps students develop a solid understanding of what an assessment guide is and allows them to focus on the set criteria and performance levels.

Deidre Greer, professor at Columbus State University, works with students at a Title I elementary school in Georgia. Greer states that in her experience,

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.

At Exemplars, we believe that rubrics are an effective tool for teachers and students alike. In order to be successful with the learning expectations set forth by the new math TEKS, it is important for students to understand what is required of them and for teachers to be on the same “assessment” page. Rubrics can help.

To learn more about Exemplars rubrics and to view additional samples, click here.

7 Things I’ve Learned on My Journey to Implementing Problem Solving in the Classroom

Monday, October 3rd, 2016

Written By: Suzanne Hood, Instructional Coach, Georgia

I’ve always believed in the power of students to use their own childlike curiosity to problem solve. These problem-solving experiences happen for our students naturally, through the math they use in cooking, playing games and playing with toys, among other things. Problem solving is a life-long skill all mathematicians use. The true power of a mathematician is the ability to see math in all situations and solve problems using a toolbox of proven strategies.

While I believe that students are innate problem solvers, I also believe that learned algorithmic thinking corrupts a child’s natural ability to problem solve and discourages perseverance. Although I have met many teachers who share my belief that problem solving should be the focus of the math, many struggle to create this culture in their classroom.

This is becoming more apparent—and the stakes of ignoring problem solving much higher—as we approach testing season. The classrooms that will likely fall behind in this new era are those who insist on teaching math through algorithmic thinking. Conversely, I am convinced that teachers who use problem solving to teach math, supported by materials like Exemplars, will have students who score proficiently on the state assessment and are more prepared for success beyond the classroom.

So how can teachers help their classrooms make this critical transition to problem solving? My personal story of transformation, which began after participating in one of Exemplars’ Summer Institutes, offers a path forward. This was when I realized two important things: first, I needed to work on my own personal proficiency in teaching problem solving. And second, I wasn’t alone; veteran teachers confessed their frustration in teaching problem solving, and many admitted their backgrounds did not include support in how to instruct students through the problem-solving process. Here are seven things I’ve learned on my journey to becoming an educator fully committed to teaching mathematics through a problem-solving approach.

1. Nurture a community of trust.

Based on my experience as a Mathematical Instructional Coach in Georgia, I believe it is essential to nurture relationships and establish a community of trust between teachers, so that discussions are authentic and all voices are included. Trust is a prerequisite for being able to assess the strengths, weaknesses and gaps of teacher readiness in the classroom. Only when teachers feel they are in an environment where they can share their knowledge, their doubts and their pedagogical weaknesses, will they be able to feel comfortable.

2. Establish a baseline of teacher readiness.

Evaluating teacher readiness and needs and getting them on the same page is an important first step. How can you get teacher teams to have collegial conversations when everyone has a totally different math background? Do all teachers even want a problem-solving classroom? Do they know what that means? Asking these questions can be illuminating, albeit tough. As such, using universally agreed-upon protocols such as those from the National School Reform Facility can establish a baseline to work from, encourage collaboration, and support an atmosphere of trust.

3. Assess student work so you can see where the gaps are.

One way to assess teacher acuity and readiness in teaching problem solving is by assessing student work using an Exemplars task. Here’s how it worked for me: At the first Professional Learning session, I asked teachers to bring classroom samples from their most recent classroom Exemplars task. As a community, we agreed to facilitate the discussion with the protocol Atlas – Learning From Student Work. As I observed teachers at the meeting, I noticed that while some teachers were proud to display their samples, others pretended to forget their samples or chose to stick their student work in their tote bag. As we used the Exemplars standards-based rubric to score our samples, it became clear that our understanding of the skills needed to meet the standards did not align. The journey began; teachers began to talk about problem solving.

4. As a team, align your mathematical beliefs towards problem solving.

When we began, we knew we shared some foundational mathematical beliefs. We also knew that we needed to solidify a shared understanding of how a mathematics culture transfers knowledge from the teacher to the student. We used the Math Framework (a document listing all the mathematical beliefs of the faculty) as a tool to target instructional strengths and weaknesses. As a team, we revised the document to build cohesion and a shared understanding of our beliefs. Next, I had the team read a book rooted in Vygotsky’s constructivist theory to increase our group’s understanding of the problem-solving trajectory. Because we had been working hard to build an atmosphere of trust, teachers felt safe sharing their struggles and personal hardships with teaching problem solving. We discovered that we shared similar experiences, and that we all believed our students would be successful at any problem if we just taught them the necessary skill set. The student samples, however, told a different story.

5. Create simple tools to help teachers and students internalize the standards and assess their progress.

At our next meeting, we reviewed Exemplars student work samples and discovered a misconception: we thought we knew how to teach problem solving, but we were actually teaching skills in isolation. Why? Quite simply, it turns out that many teachers lacked background knowledge about the Standards of Problem Solving. To facilitate the understanding of the standards, I created posters with clear icons for each standard. These anchor charts would support teachers and students. It worked. Now, teachers could explain each standard. Each classroom in our building displayed the posters. It was a great reference for both students and teachers. We made a replica of the posters into a small book that students put in folders for their own reference. Students used the folders as portfolios to track their problem-solving progress, and created data notebooks to reflect on their growth and set goals for their next Exemplars task. Using data notebooks empowered kids to self-reflect on their own progress.

6. Hold individual meetings with students to track progress and set goals.

Currently, I am encouraging teachers to hold one-on-one Exemplars conferences with their students. Individual conferences support differentiated instruction, meet students where they are, and set goals for the next problem-solving task. Although this approach makes some teachers uneasy at first, they become more confident over time. Allowing other teachers or coaches to observe and co-teach the process can lead to greater transparency and effect change in teacher practice.

7. You may not get the teacher of the year award, but you’ll still be changing students’ lives.

At the beginning of my career, I thought Oprah would call me to announce my Disney Teacher of the Year Award. While this hasn’t happened yet, I do have countless memories of the sparkle in a child’s eye when he or she announces, “I get it!” I believe I have the responsibility to show up every day prepared to change the lives of children and equip them with the skills to be life-long mathematicians. Exemplars provides the problem-solving tools necessary to guide teaching and build capacity for each child’s mathematical journey.

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