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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.

Supporting the TEKS Mathematical Processes with Exemplars Performance Tasks and Rubric at the First Grade Level

Thursday, April 7th, 2016

Written By Exemplars Math Consultants: Deborah Armitage, M.Ed. and Dinah Chancellor, M.Ed.

Blog Series Overview:

Exemplars performance-based material is a supplemental resource that provides teachers with an effective way to implement the Math TEKS through problem solving. This blog represents Part 2 of a six-part series that features a problem-solving task linked to a Unit of Study for the Math TEKS and a student’s solution in grades K–5. Evidence of all seven Mathematical Process Standards will be exhibited by the end of the series.

The Exemplars Standards-Based Math Rubric allows teachers to examine student work against a set of analytic criteria that consists of the following categories: Problem Solving, Reasoning and Proof, Communication, Connections and Representation. There are four performance/achievement levels: Novice, Apprentice, Practitioner (meets the standard) and Expert. The Novice and Apprentice levels support a student’s progress towards being able to apply the criteria of a Practitioner and Expert. It is at these higher levels of achievement where support for the Mathematical Processes is found.

Exemplars problem-solving tasks provide students with an opportunity to apply their conceptual understanding of standards, mathematical processes and skills. Observing student anchor papers with assessment rationales that demonstrate the alignment between the Exemplars assessment rubric and the Math TEKS can be insightful for educators. Anchor papers and assessment rationales provide examples of what to look for in your own students’ work. Examples of Exemplars rubric criteria and the Mathematical Processes are embedded in the assessment rationales at the bottom of the page. The full version of our rubric may be accessed here. It is often helpful to have this in-hand while reviewing a piece of student work.

Blog 2: Observations at the First Grade Level

The second anchor paper and set of assessment rationales we’ll review in this series is taken from a first grade student’s solution for the task “A Birdbath.” In this piece, you’ll notice that the teacher has “scribed” the student’s oral explanation. This practice was also used with the Kindergarten task that was published in the first blog. Scribing allows teachers to fully capture the mathematical reasoning of early writers.

“A Birdbath” is one of a number of tasks aligned to the Strategies for Addition and Subtraction Unit designed by Exemplars for the new Math TEKS. This task could be used toward the end of the learning time allocated to this Unit. “A Birdbath” provides first grade students with an opportunity to apply different strategies to find the sum of addends six and 14 by decomposing six into five and one and decomposing 14 into 10 and four, or by finding the sum of six and four and adding that sum to 10. The student can use counters, ten frames, a Rekenrek, number lines or a tally chart to support her/his numerical thinking.

First Grade Task: A Birdbath

Leah counts the birds that came to her birdbath. In the morning, Leah counts six birds that came to her birdbath. In the afternoon, Leah counts fourteen birds that came to her birdbath. Leah says nineteen birds came to her birdbath. Is Leah correct? Show all of your mathematical thinking.

Math TEKS Alignment:

Exemplars Strategies for Addition & Subtraction Unit

The Strategies for Addition and Subtraction Unit involves understanding the processes of addition and subtraction in order to solve problems and answer questions such as:

  • If we know all of the parts, how can we find the whole?
  • If we know the whole and one of the parts, how can we find the missing part?
  • Given an equation, can you create an addition or subtraction situation to match it? How can you prove it matches the equation?

The standards covered in this Unit include:

1.3 Number & Operations:

  • 1.3A use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99.
  • 1.3D apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10.
  • 1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences.
  • 1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20.

1.5 Algebraic Reasoning:

  • 1.5D represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences.
  • 1.5G apply properties of operations to add and subtract two or three numbers such as if 2 + 3 =5 is known, then 3 + 2 = 5.
Mathematical Process Standards:
  • 1.1A Apply mathematics to problems arising in everyday life, society, and the workplace;
  • 1.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
  • 1.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
  • 1.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
  • 1.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

 

Supporting the TEKS Mathematical Processes with Exemplars Performance Tasks and Rubric at the Kindergarten Level

Tuesday, February 9th, 2016

Written By Exemplars Math Consultants: Deborah Armitage, M.Ed. and Dinah Chancellor, M.Ed.

Blog Series Overview:

Exemplars performance-based material is a supplemental resource that provides teachers with an effective way to implement the Math TEKS through problem solving. This blog represents Part 1 of a six-part series that features a problem-solving task linked to a Unit of Study for the Math TEKS and a student’s solution in grades K–5. Evidence of all seven Mathematical Process Standards will be exhibited by the end of the series.

The Exemplars Standards-Based Math Rubric allows teachers to examine student work against a set of analytic criteria that consists of the following categories: Problem Solving, Reasoning and Proof, Communication, Connections and Representation. There are four performance/achievement levels: Novice, Apprentice, Practitioner (meets the standard) and Expert. The Novice and Apprentice levels support a student’s progress towards being able to apply the criteria of a Practitioner and Expert. It is at these higher levels of achievement where support for the Mathematical Processes is found.

Exemplars problem-solving tasks provide students with an opportunity to apply their conceptual understanding of standards, mathematical processes and skills. Observing student anchor papers with scoring rationales that demonstrate the alignment between the Exemplars assessment rubric and the Math TEKS can be insightful for educators. Anchor papers and scoring rationales provide examples of what to look for in your own students’ work. Examples of Exemplars rubric criteria and the Mathematical Processes are embedded in the scoring rationales at the bottom of the page. The full version of our rubric may be accessed here. It is often helpful to have this in hand while reviewing a piece of student work.

Blog 1: Observations at the Kindergarten Level

The first anchor paper and set of assessment rationales we’ll review in this series is taken from a Kindergarten student’s solution for the task “Boots.” You will notice that the teacher has “scribed” the student’s oral explanation. This method allows teachers to fully capture the mathematical reasoning of early writers.

“Boots” is one of a number of Exemplars tasks aligned to the Counting and Cardinality Unit designed by Exemplars for the new Math TEKS. This task could be used toward the end of the learning time allocated to this Unit. Prior to “Boots” being given, students have already completed a number of tasks with questions that state, “How many ears?”, “How many shoes?”, “How many balloons?”, etc. “Boots” gives students an opportunity to bring a stronger understanding of the concept how many to their solutions.

Kindergarten Task: Boots

Five students wear boots to go outside for recess. When the students come in from recess they must put all boots on a rubber mat to dry. The teacher counts seven boots on the mat. The teacher thinks some boots are missing. Is the teacher correct? Show and tell how you know.

Task Alignments

The Counting and Cardinality Unit involves understanding numbers and how they are used to name quantities and to answer questions, such as:

  • How many balls is the clown juggling?
  • Do you have enough cups for each member of your group to have one?

The TEKS standards covered in this Unit include K.2 Numbers and Operations:

  • K.2A count forward and backward to at least 20 with and without objects.
  • K.2B read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures.
  • K.2C count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order.
  • K.2D recognize instantly the quantity of a small group of objects in organized and random arrangements.

Mathematical Process Standards: K.1A, K.1B, K.1C, K.1D, K.1E and K.1G

Why A Focused Mathematics Curriculum Matters and How Exemplars Can Help Texas Educators

Monday, November 3rd, 2014

Written By: Dinah Chancellor, Exemplars Math Consultant

Prior to 2006, many states—including Texas—had a math curriculum that was perceived to be “an inch deep and a mile wide.” Teachers were required to teach a large number of math skills that spiraled from grade to grade and seemed both disconnected and fragmented. When Texas’ own Cathy Seeley became President of the National Council of Teachers of Mathematics (NCTM), she determined that a more focused mathematics curriculum that was built around fewer “big ideas” would give students and teachers the luxury of time—time to plumb the depths of major math concepts, and time to form a foundation of connected mathematical understandings.

Therefore, in 2006 NCTM published the Curriculum Focal Points—A Quest for Coherence. The Texas response to the Curriculum Focal Points was the new state assessment program—STAAR—the State of Texas Assessment of Academic Readiness taken by students in grades 3-8. STAAR focuses on fewer skills at each grade level and it is expected that these skills will be taught at greater depth. When the new math TEKS were written, released in April 2012 and implemented in the fall of 2014, the writing teams focused on fewer skills at each grade level. Teachers are expected to address these skills and understandings by teaching rich lessons in which students make critical connections between foundational big ideas in mathematics. Because of the need to teach a focused mathematics curriculum, it does not make sense to teach each of the new math TEKS in isolation.

To assist Texas educators in achieving this goal, Exemplars latest K–5 product, Problem Solving for the TEKS, groups the individual math TEKS student expectations into rich Units of Study. Four or more instructional tasks/formative assessments and one or more summative assessment is provided to address the big mathematical ideas within each Unit. Tasks are meant to supplement a school or district’s existing curriculum. Teachers may choose to use all or only a few of the instructional tasks/formative assessments in a Unit. The summative assessments include anchor papers that exemplify each of the performance levels in the Exemplars Rubric—Novice, Apprentice, Practitioner (meets the standard) and Expert.

A Look at a Sample Unit

The Place Value Unit represents one of eleven Units in the third grade. The math TEKS covered in this Unit include: 3.2A, 3.2B, 3.2C, 3.2D. These math TEKS were grouped together to provide a cohesive Unit that enables 3rd grade students to understand the Properties of Place Value and to apply this understanding to compare and order whole numbers. See the full list of Units of Study for K–5.

How Might a Teacher Use the Tasks in This Unit?

As the Place Value Unit progresses, a teacher may want to use one of the instructional tasks to teach students the expectations of the Exemplars Assessment Rubric. A lesson using the task “Tables for a Party” may include the following steps:

  •  Whole Group: Read the task together and ask students to underline the question, identify important information in the problem and summarize the task by restating what the question is asking them to do. Example: I need to find out how many tables need to be set up for 34 students with no more than 10 students sitting at each table. On the Exemplars Rubric, this step is scored in the category for Problem Solving—Does the student understand the problem?
  •  Small Group: Ask students to work together, think of a plan, and write it down. Example: I will draw a diagram of tables with students sitting at them. At this point, students will implement their plan to solve the problem.

Example:

(Refer to the task Planning Sheet for additional examples of solution strategies.)

 Students will check their plan to make sure it works and put a box around their answer.

Example:

On the Exemplars Rubric, this step is scored in the category for Problem Solving—Does the student have a plan? Does the student get the correct answer? It is also scored in the category for Reasoning and Proof—Does the student show a systematic implementation of the plan?

Small Group: Ask students to polish their papers—

  • Organize your solution.
  • Explain your plan and how it solved the problem.
  • Create a representation—such as a diagram with a key, use a model (such as manipulatives), use a table, use a number line.
  • Use mathematical vocabulary and/or symbolic representation.
  • Label your solution.
  • Show your answer. Put a box around it. Make sure it answers the question.

On the Exemplars Rubric this step is scored in the category for Communication—Does the student use at least two mathematical vocabulary words, at least two correct symbolic representations or one of each? It is also scored in the category for Representation—Is the representation correct and appropriate to the solution?

 Small Group: Finally, make a connection—

  • Make an observation.
  • Identify and describe a pattern.
  • Make a comparison between this task and other tasks. Explain how the math is similar.
  • Identify a rule.
  • Create a hypothesis or conjecture to test.
  • Solve the problem using a different strategy to prove the original solution is correct.
  • Recreate the problem and show a different solution.

On the Exemplars Rubric, this step is scored in category for Connections—Does the student include a mathematically relevant connection? Making connections requires students to look at their solutions and reflect.

Using Anchor Papers & Scoring Rationales

Anchor papers and assessment rationales are provided with every summative assessment task. These problem-solving tasks are given at the end of a Unit of Study to assess students’ understanding. A summative assessment must represent a student’s total independent solution. One Hundred Miles is the summative assessment for the grade 3 Place Value Unit.

Anchor papers and scoring rationales provide a great way to show both teachers (in professional development sessions) and students the expectations of the Exemplars Rubric; i.e. What a Practitioner (meets the standard) piece of student work looks like. Analyzing Exemplars anchor paper solutions and rationales at the Practitioner and Expert levels help students polish their own work and measure their own progress toward a specific goal. Analyzing the Novice and Apprentice samples can help identify for students where the work falls short of the goal and specifically how the papers could improve.

To view other sample tasks and anchor papers for grades K–5, you can sign up for a free 30-day Trial for Problem Solving for the TEKS.

 

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