How Good is this Cookie? Briefly discuss with your neighbor.
http://www.teachervision.fen.com/teac hing-methods-and-
management/rubrics/4522.html
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3210 TextureChewy Chewy in middle, crisp on edges Texture
either crispy/crunchy or 50% uncooked Texture resembles a dog
biscuit ColorGolden brown Either light from overcooking or light
from being 25% raw Either dark brown from overcooking or light from
undercooking Burned TasteHome-baked taste Quality store- bought
taste Tasteless Store-bought flavor, preservative aftertaste stale,
hard, chalky Richness Rich, creamy, high- fat flavor Medium fat
contents Low-fat contentsNonfat contents
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What affects a score?
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Rubrics
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What is a Rubric? A rubric is a scoring guide. Tool that
distinguishes teaching and learning by clearly stating criteria and
describing levels of quality. A rubric is an authentic assessment
tool used to measure students' work. A rubric is a working guide
for students and teachers, usually handed out before the assignment
begins in order to get students to think about the criteria on
which their work will be judged. Stein, M, D. Kinder, J. Slibert,
& D.W. Carnine, 2006, Designing Assessment for Mathematics, pg.
1 8
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Goal of a Rubric The purpose of the rubric is not only to
evaluate but also to help students increase their level of
performance by outlining a vision of success. (M. Stein, etc.,
2006, Designing Assessment for Mathematics) 9
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The rubric is the tool that binds assessment and student
achievement by making students and parents aware of expectation
from the onset. When this occurs, achievement at high level of
performance is a natural outcome. There are no surprises for
students during the evaluation process with the rubric. Rubrics
also make grading easier and less messy for teachers. (M. Stein,
etc., 2006, Designing Assessment for Mathematics) 10
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Types of Rubrics (4) General Rubrics Specific Rubrics Basic.
Give general view. A teacher might use a general rubric to review a
sample of papers for a task (Mathematics Assessment, 2005, pg. 120)
Specific to the task. Can make assigning scores easier, faster, and
more consistent. 11
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Types of Rubrics Cont. Analytic Rubrics Holistic Rubrics
Teacher scores separate, individual parts of the product or
performance first, then sums the individual scores to obtain a
total score (Moskal, 2000; Nitko, 2001). Uses multiple descriptors
for each criterion evaluated. Student has multiple opportunities to
be evaluated within same rubric. A performance is assessed several
times, using the lens of a separate criterion each time. (McTighe
& Wiggins, 1999, p. 273) A holistic rubric requires the teacher
to score the overall process or product as a whole, without judging
the component parts separately (Nitko, 2001) Has one performance
expectation description at each numerical level. The performance is
evaluated as a whole and often given as a single score. A rubric
used to obtain the overall impression of the quality of a
performance or product. (McTighe & Wiggins, 1999, p. 277)
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Remember: Rubrics Can Be A Complete Chart Description of Math
Involved List of Possible Techniques Involved Scale Other:
______________ THERE ARE MANY FORMATS FOR A RUBRIC! 13
Holistic Rubric Holistic ScaleHolistic Scale pg.2, 4, 6, 8, 21
DOROTHY IS RUNNING FOR PRESIDENT DOROTHY IS RUNNING FOR PRESIDENT
pg 11-13
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List
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Kid Friendly Analytic Rubric From Constructive Assessment in
Mathematics: How to Get It Going in Your District (Anderson
n.d.
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Other Kid Friendly Rubrics
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Self-Assessment Rubric
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Scale 5 children went home in cars, 2 children rode home on
bikes, 2 children walked. How many wheels took the children home?
Draw or write to explain your answers.
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Annotated Holistic Rubric This is a holistic rubric, but
includes performance indicators for the task. This helps teachers
justify why a certain score was given. Reys, Lindquist, Lambdin,
& Smith, 2006 Helping Children Learn Mathematics, pg. 77
(Base-ten block task on decimals.)
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Rubrics Can Be Used for Anything:
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Advantages to Using a Rubric [Rubrics] can assess thinking
skills, student understanding, and students ability to apply their
knowledge to mathematical tasks. (Designing Assessment for
Mathematics, pg. 1) Teachers can increase the quality of their
direct in instruction by providing focus, emphasis, and attention
to particular details as a model for students. Students, parents,
and teachers know expectations. This includes how much effort and
quality is expected. http://www.teachervision.fen.com/teachi
ng-methods-and- management/rubrics/4522.html 27
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Advantages to Using a Rubric Cont. Students can use rubrics as
a tool to develop their abilities (self assessment & active
involvement!). Rubrics can clarify for the students exactly what
their strengths and weaknesses are and enable their
self-assessment. (Charlesworth, 2005, Experiences in Math, pg. 46)
Teachers can reuse rubrics for various activities (some). Easy to
adapt to different levels of learners. 28
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What to Include in a Rubric (3) 1. Rubrics should be based
developed based on what you are looking for in your class.
(Charlesworth, 2005, Experiences in Math, pg. 46) 2. Take
categories from key steps, items that should always be in a
problem/graph, neatness, or CORE standards. 3. Levels of quality
that are expected. Students should be able to use the rubric to
self assess their assignment prior to turning it in and get that
score (or very close) when graded. 29
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Levels of Success Level 4Above expectations, outstanding. Level
3Meets expectations, acceptable. Level 2Needs revision or more
work. Level 1Shows need for reteaching. 31
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Keys to Using Rubrics Determine what your goal is. Only have
categories for things you want to see. Determine whether the rubric
is formative or summative by how you use the data. (Will you reuse
or is it specific to this time?) Determine the number of points on
your rubric. Some say that it is important to have an even number
of points possible, usually 4 or 6 because scorers are less
discriminating with an even point system. (Stenmark, 1991;
Danielson 1997) Anchor Papers. Have a good set of examples for each
rubric level. Share these examples with students! If these are not
shared, the rubric loses its effectiveness. 32
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Anchor Papers It is crucial to show students examples of each
rubric level. Many performance-based activities will come with a
rubric. Begin with that and adapt as needed. Many also come with
different examples of each quality level to help the teacher know
how to properly score. Share these with students. Work with other
grade level teachers to share samples. Let students practice
scoring samples. (Peer & Self.) You may need to get permission
from students and parents to use their paper as a sample. You may
want to remove the name. 33 Dorothy Anchor Papers Dorothy Anchor
Papers pg. 14-26
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Lets take a look at this problem. (We will be scoring student
samples.) Molly needs some green paper for her art project. She can
get 2 sheets for 4 cents or 4 sheets for 6 cents at another store.
Which is a better price? Explain your thinking at each step. 4
Sheets for 6 cents is a better deal. 35 (Mathematics Assessment,
2005, pg.126-128)
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Before Beginning to Score a Rubric Indentify: 36 the essential
mathematics the possible correct answers the practice implications
of the problem (for example, in this problem the number of pieces
of paper needed is knownstudents may or may not take this into
account) What specifics, if any, you would add to the
rubric(s).
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Idea for Scoring 37
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Lets Practice Scoring a Holistic Rubric 4 Fully accomplishes
the purpose of the task. Shows a good understanding and use of the
main ideas of the problem. Communicates thinking clearly, using
writing, calculations, diagrams and charts, or other
representations. 3 Substantially accomplishes the purposes of the
task. Shows a reasonable understanding and use of the main ideas of
the problems. Communicates thinking fairly well, but may use only
one representation. 2 Partially accomplishes the purpose of the
task. Shows partial but limited grasp of the main mathematical
ideas. Recorded work may be incomplete, misdirected, or not clearly
represented. 1 Shows little or no progress in accomplishing the
purpose of the task. Shows little understanding of the main
mathematical tasks. Work is almost or completely impossible to
decipher. (Mathematics Assessment, 2005, pg.120)
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Lets Practice Scoring an Analytic Rubric Understanding the
Problem 0 Complete misunderstanding of the problem. 3 Part of the
problem misunderstood or misinterpreted. 6 Complete understanding
of the problem. Planning a Solution 0 No attempt or totally
inappropriate plan. 3 Partially correct plan based on part of the
problem being interpreted correctly. 6 Plan could have led (or did
lead) to a correct solution if implemented properly. Getting an
Answer 0 No answer or wrong answer based on inappropriate plan. 1
Copying error; computational error; partial answer for a problem
with multiple answers. 3 Correct answer and correct label for the
answer. (Mathematics Assessment, 2005, pg.121, adapted)
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StudentHolistic Scores & CommentsAnalytic Score &
Comments Jeanette2Substantially accomplishes the task, recognizes
getting more for amount of money, communication missing.
Understanding 3 (no price comparing Planning0 (reasoning missing)
Answer3 Martha4Fully accomplishes the task; shows a grasp of the
concept, communication clear. Understanding6 Planning6 Correct
Answer3 Michael 3Partial understanding of purpose of task,
understood central idea. (Michael includes extra info that 4 is
more than 2, does not explain.) Understanding3 Planning3 Answer3
Mashonna1Shows little or no progress, doesnt seem to be getting it.
Needs reteaching. Understanding0 Planning0 Answer3 (No reasoning
given) (Mathematics Assessment, 2005, pg.129, adapted)
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Use a variety of expectations already in place to create a
rubric. Rubric Levels of Success CriteriaChecklistObjectives
Designing a Rubric 41
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Criteria vs. Rubrics CriteriaRubric Describes intent of
standard. Similar to learning objective. More detailed. Tells
levels of success. (MAIN DIFFERENCE!) Easy to turn criteria into a
rubric 42
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43
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Turning a Checklist into a Rubric If you have a checklist, you
can easily make it into a rubric. For example, a graph should
always have 1. A title. 2. Labels on both axis. 3. Be accurate. 4.
Be neat and readable. 5. Other ____________ 46
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47 TITLELABELSACCURACYNEATNESS 3 The graph contains a title
that clearly tells what the data shows. All parts of the graph
(units of measurement, rows, etc.) are correctly labeled. All data
is accurately represented on the graph. The graph is very neat and
easy to read. 2 The graph contains a title that suggests what the
data shows. Most parts of the graph are correctly labeled. Data
representation contains minor errors. The graph is generally neat
and readable. 1 The title does not reflect what the data shows. The
graph is incorrectly labeled. The data is inaccurately represented
and contains errors. The graph is sloppy and difficult to read. 0
The graph does not have a title The graph is not labeled. The data
is missing. The graph cannot be read.
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Keys to Design a Rubric 1. Decide the type of rubric. (chart,
scale, list, etc.) 2. Determine what you would like to see in the
task. These will be your categories. 3. Next you need to determine
the quality levels acceptable .. How many levels? 48
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Determining Levels of Success a) Identify the key mathematical
elements that determine whether a paper is acceptable (4) or
unacceptable (1). b) Identify specific differences between a paper
that is barely unacceptable (2) and one that is clearly
unacceptable (1). c) Give specific criteria for distinguishing
between a paper that is acceptable, but just so-so (3), and one
that clearly shows good understanding (4) in the task, correctly
applies appropriate mathematical tools to the task, and uses clear
mathematical reasoning to explain the solution process. (Huetink
& Munshin, 2000, Teaching Mathematics for the 21 st Century:
Methods and Activities for Grades 6-12) 49
Lets Practice Developing Our Own Rubrics . Take the remainder
of the time (__ minutes) to discover some of these sites.
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Step by Step Help in Designing a Rubric 52 A step-by-step
process for designing scoring rubrics for classroom use is
presented below. Information for these procedures was compiled from
various sources (Airasian, 2000 & 2001; Mertler, 2001;
Montgomery, 2001; Nitko, 2001; Tombari & Borich, 1999). The
steps will be summarized and discussed, followed by presentations
of two sample scoring rubrics. Step 1: Re-examine the learning
objectives to be addressed by the task. This allows you to match
your scoring guide with your objectives and actual instruction.
Step 2: Identify specific observable attributes that you want to
see (as well as those you dont want to see) your students
demonstrate in their product, process, or performance. Specify the
characteristics, skills, or behaviors that you will be looking for,
as well as common mistakes you do not want to see. Step 3:
Brainstorm characteristics that describe each attribute. Identify
ways to describe above average, average, and below average
performance for each observable attribute identified in Step 2.
Step 4a: For holistic rubrics, write thorough narrative
descriptions for excellent work and poor work incorporating each
attribute into the description. Describe the highest and lowest
levels of performance combining the descriptors for all attributes.
http://pareonline.net/getvn.asp?v=7&n=25
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Step by Step Help in Designing a Rubric Cont. 53 Step 4b: For
analytic rubrics, write thorough narrative descriptions for
excellent work and poor work for each individual attribute.
Describe the highest and lowest levels of performance using the
descriptors for each attribute separately. Step 5a: For holistic
rubrics, complete the rubric by describing other levels on the
continuum that ranges from excellent to poor work for the
collective attributes. Write descriptions for all intermediate
levels of performance. Step 5b: For analytic rubrics, complete the
rubric by describing other levels on the continuum that ranges from
excellent to poor work for each attribute. Write descriptions for
all intermediate levels of performance for each attribute
separately. Step 6: Collect samples of student work that exemplify
each level. These will help you score in the future by serving as
benchmarks. Step 7: Revise the rubric, as necessary. Be prepared to
reflect on the effectiveness of the rubric and revise it prior to
its next implementation.
http://pareonline.net/getvn.asp?v=7&n=25
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Summary of Steps 54
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Example Upper Elementary Math 55 Mr. Harris, a fourth-grade
teacher, is planning a unit on the topic of data analysis, focusing
primarily on the skills of estimation and interpretation of graphs.
Specifically, at the end of this unit, he wants to be able to
assess his students' mastery of the following instructional
objectives: 1. Students will properly interpret a bar graph. 2.
Students will accurately estimate values from within a bar graph.
(step 1) Since the purpose of his performance task is summative in
nature - the results will be incorporated into the students'
grades, he decides to develop a holistic rubric. He identifies the
following four attributes on which to focus his rubric: estimation,
mathematical computation, conclusions, and communication of
explanations (steps 2 & 3). Finally, he begins drafting
descriptions of the various levels of performance for the
observable attributes (steps 4 & 5). The final rubric for his
task appears in Table 4.
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Mr. Harriss Rubric 56 Table 4: Math Performance Task Scoring
Rubric Data Analysis Name _____________________________ Date
___________ Score Description 4 Makes accurate estimations. Uses
appropriate mathematical operations with no mistakes. Draws logical
conclusions supported by graph. Sound explanations of thinking. 3
Makes good estimations. Uses appropriate mathematical operations
with few mistakes. Draws logical conclusions supported by graph.
Good explanations of thinking. 2 Attempts estimations, although
many inaccurate. Uses inappropriate mathematical operations, but
with no mistakes. Draws conclusions not supported by graph. Offers
little explanation. 1 Makes inaccurate estimations. Uses
inappropriate mathematical operations. Draws no conclusions related
to graph. Offers no explanations of thinking. 0No response/task not
attempted. http://pareonline.net/getvn.asp?v=7&n=25