1. Briefly discuss with your neighbor.
How Good is this Cookie?
Briefly discuss with your neighbor.
Need: Cookies! We are going to ‘score’ these cookies three different ways. (1) Discuss

2. Did you both have
the same opinion?
Why or why not?

3. Judge the cookie again. Rate from 0-12.
Now, we’ll score from looking for specific things that make a good cookie.
(2) Rate just by 1-12.

4. 3 2 1 Texture Chewy Chewy in middle, crisp on edges
Texture
Chewy
Chewy in middle, crisp on edges
Texture either crispy/crunchy or 50% uncooked
Texture resembles a dog biscuit
Color
Golden brown
Either light from overcooking or light from being 25% raw
Either dark brown from overcooking or light from undercooking
Burned
Taste
Home-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 contents
Nonfat contents
(3) Justify your score/rating

5. Did you both have the same opinion this time?
Why or why not? Was it closer?
Which way was easier to judge?
Which way is better?

6. What affects a score?
Was your score/rating of the cookie the same all three times? Why or why not?
Who is checking
When they are checking
How they feel when they are checking
(Sometimes) Behavior of student
For assessment results to be valid, we need a valid tool for scoring. RUBRICS!
Without rubrics, teachers would have a hard time scoring performance-based tasks, journals, and other key assessment tools.
We don’t want a score to be an opinion. We want the student to receive the same score no matter who is correcting the assessment.

7. Rubrics
Alternative names for rubrics: Scales, Grading Scale, etc. Sometimes “Rubrics” is hard & intimidating for students. But then, I’ve found they love to know the teacher jargon. Decide what the needs are of your class.

8. 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.
I also like this: Why use rubrics? According to Heidi Goodrich Andrade:
Rubrics help students and teachers define "quality."
When students use rubrics regularly to judge their own work, they begin to accept more responsibility for the end product. It cuts down on the "am I done yet?" questions.
Rubrics reduce the time teachers spend grading student work and makes it easier for teachers to explain to students why they got the grade they did and what they can do to improve.
Parents usually like the rubrics concept once they understand it, and they find rubrics useful when helping with homework. As one teacher says: "They know exactly what their child needs to do to be successful."
Stein, M, D. Kinder, J. Slibert, & D.W. Carnine, 2006, “Designing Assessment for Mathematics, pg. 1”

9. 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)
We want the task to seem achievable! This is what rubrics do!

10. (M. Stein, etc., 2006, Designing Assessment for Mathematics)
“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)
Rubrics meet all of the goals for assessment. One student actually didn’t like rubrics for this very reason: “If you get something wrong,” she said, “your teacher can prove you knew what you were supposed to do!” (Marcus 1995).

11. Types of Rubrics (4) Basic. Give ‘general’ view.
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.
Rubrics are less often categorized general and specific. General rubrics are more often thought of, not necessarily written. (Like “sifting through.” Teachers often have a rubric as they go through data. They will separate the work into three piles. 1 does not understand. 2 Developing understanding. 3 Understands the idea and can apply and communicate it.

12. Let’s look at some samples:
Types of Rubrics Cont.
Analytic Rubrics
Holistic Rubrics
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)
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)
An analytic and holistic rubric can be general or specific. We use these two categories more. Analytical rubrics are usually part of formative assessment; holistic rubrics are usually part of a summative assessment.
Let’s look at some samples:

13. 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!
We generally think of a graph/table format. There are many other types though! Another type that fits within any category is KID FRIENDLY! Make sure that you use language and formats that students can understand!

14. Analytic Rubric Ontario's Standards Pg. 16-17
This rubric is analytic. It can be reused for additional problems like this. It helps guide students to reflect on what they know and what they still need additional practice with. This is usually a formative assessment. Teachers can pull students with lower scores for additional practice.
the advantage to the use of analytic rubrics is quite substantial. The degree of feedback offered to students-and to teachers-is significant. Students receive specific feedback on their performance with respect to each of the individual scoring criteria-something that does not happen when using holistic rubrics (Nitko, 2001).
Ontario's Standards Pg

15. Holistic Rubric Holistic Scale pg.2, 4, 6, 8, 21
This rubric is holistic because it is used once to determine one single score. It is definitely a summative test. POINT OUT THAT RUBRICS CAN BE IN A TABLE FORMAT OR JUST A SCALE. POINT OUT THE DIFFERENCE BETWEEN ANALYTICAL AND HOLISTIC RUBRICS USING HOLISTIC SCALE LINK PG 2 AND 3!
Holistic Scale pg.2, 4, 6, 8, 21
DOROTHY IS RUNNING FOR PRESIDENT pg 11-13

16. List

17. Authentic Tasks
Rubrics really help place a grade on authentic assessment—portfolios, journals, performance tasks, etc. This rubric has each step listed.

18. Kid Friendly Analytic Rubric
Uses “kid talk,” easy for students to use. If you are working in elementary schools, it is important to have students comfortable with the rubrics. This is more easily done with ‘kid friendly’ rubrics.
From Constructive Assessment in Mathematics: How to Get It Going in Your District (Anderson n.d.

19. Other Kid Friendly Rubrics
I like the visual levels. Also on the bottom has a “grow” or something to work on & a “glow” or something that the student did really well on. Again, could have double points available for organization, grammar, requirements, and mechanics, but still give some points for effort.

20. Self-Assessment Rubric
Rubrics really are a great tool for students to assess themselves. This rubric has levels by words or proficiency, not #s.

21. 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.
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.

23. Very basic scale for math
Very basic scale for math. Some teachers suggest having more points for understanding and planning a solution (0,3,6) and less for getting an answer (0,1,3)

24. Annotated Holistic Rubric
(Base-ten block task on decimals.)
An annotated rubric is a good idea when you need to justify a score for placement in different programs or tracts. Very helpful for lower grade CBMs.
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

25. Rubrics Can Be Used for Anything:
I like the idea of having a rubric on the wall for what is expected. Have some symbols (not necessarily these). As you are walking around while students are working, you could point to a symbol to let them know how they are doing.

26. Might look at another one on a website.

27. 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.
Rubrics help assess things that a standardized test cannot. It also makes grading tasks and applications more easily.

28. 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.
Rubrics can help teachers differentiate both instruction and assessment for their students.
Rubrics can improve student performance, as well as monitor it, by making teachers’ expectations clear and by showing students how to meet these expectations. The result is often marked improvements in the quality of student work and in learning. Thus, the most common argument for using rubrics is they help define “quality.” Understanding Rubrics by Heidi Goodrich Andrade

29. What to Include in a Rubric (3)
“Rubrics should be based developed based on what you are looking for in your class.” (Charlesworth, 2005, Experiences in Math, pg. 46)
Take categories from key steps, items that should always be in a problem/graph, neatness, or CORE standards.
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.
This is really basically for analytical rubrics. Holistic rubrics generally have only one category. There are more detailed steps also. This is broken down to the very basics. A more detailed step is included at the end of the slide.

31. Level 4—Above expectations, outstanding.
Levels of Success
Level 4—Above expectations, outstanding.
Level 3—Meets expectations, acceptable.
Level 2—Needs revision or more work.
Level 1—Shows need for reteaching.
There is some debate at how many levels should be used. Most researchers said use an even amount levels. Even numbers give students credit for “in-between” work. 4 works great for math. You can decide what you want to use.

32. 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.
For example, if you are trying to see who needs additional instruction, you don’t have to give a grade to the rubric. However, if you are grading a final project, you would translate the rubric to a score though.

33. “Anchor Papers” “Dorothy” Anchor Papers pg. 14-26
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.
WHAT GRADE LEVEL (IF ANY) DOESN’T NEED TO SEE EXAMPLES OF DIFFERENT LEVELS? Could even show a variety of these are papers of what I expect with younger grades. Make sure that you have a variety to encourage creativity.
“Dorothy” Anchor Papers pg

34. Along with a rubric, anchor papers should be shown
Along with a rubric, anchor papers should be shown. It would be helpful to have annotation to describe why a specific anchor paper is in the certain category.

35. Four for 6 cents Two for 4 cents
Let’s 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.
Four for 6 cents
Two for 4 cents
NEED: NUMBERS.
(Mathematics Assessment, 2005, pg )

36. Before Beginning to Score a Rubric Indentify:
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 known—students may or may not take this into account)
What specifics, if any, you would add to the rubric(s).
We are looking at their understanding and planning at this time. Maybe we have talked about comparing and want students to compare the two possibilities (you may need to reword problem to let students know that is expected).

37. Idea for Scoring
Have a rubric attached to each assignment. If you use the rubric enough, you could have a stamp with your categories made.

38. Let’s Practice Scoring a Holistic Rubric4
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.
Might have cards 0, 1, 2. Or 1, 2, 3, 4. (Write “general consensus” on board.)
(Mathematics Assessment, 2005, pg.120)

39. Let’s Practice Scoring an Analytic Rubric
(Mathematics Assessment, 2005, pg.121, adapted)
Understanding the Problem
Complete misunderstanding of the problem. 3
Part of the problem misunderstood or misinterpreted. 6
Complete understanding of the problem.
Planning a Solution
No attempt or totally inappropriate plan.
Partially correct plan based on part of the problem being interpreted correctly.
Plan could have led (or did lead) to a correct solution if implemented properly.
Getting an Answer
No answer or wrong answer based on inappropriate plan. 1
Copying error; computational error; partial answer for a problem with multiple answers.
Correct answer and correct label for the answer.
Understanding the Problem & Planning a Solution are weighted more than getting an answer.

40. Holistic Scores & Comments Analytic Score & Comments
Student
Holistic Scores & Comments
Analytic Score & Comments
Jeanette
2—Substantially accomplishes the task, recognizes getting more for amount of money, communication missing.
Understanding –3 (no price comparing
Planning—0 (reasoning missing)
Answer—3
Martha
4—Fully accomplishes the task; shows a grasp of the concept, communication clear.
Understanding—6
Planning—6
Correct Answer—3
Michael
3—Partial understanding of purpose of task, understood central idea. (Michael includes extra info that 4 is more than 2, does not explain.)
Understanding—3
Planning—3
Mashonna
1—Shows little or no progress, doesn’t seem to be getting it. Needs reteaching.
Understanding—0
Planning—0
Answer—3 (No reasoning given)
How close were we? What could eliminate any variables? What do you think are the strengths and weaknesses of each rubric? How could you use the results? ALL THE STUDENTS GOT THE ANSWER CORRECT. IF WE WERE CHECKING BY TRADITIONAL METHODS RIGHT/WRONG, WHAT INFORMATION WOULD WE LEARN FROM THIS PROBLEM?
(Mathematics Assessment, 2005, pg.129, adapted)

41. Use a variety of expectations already in place to create a rubric.
Designing a Rubric
Rubric
Levels of Success
Criteria
Checklist
Objectives
Some teachers view rubrics as hard to put together. Use expectations you always have to develop your levels of success to develop a rubric. Remember, you can reuse these, so the time it takes is well worth the effort.
Use a variety of expectations already in place to create a rubric.

42. Criteria vs. Rubrics Describes intent of standard.
Similar to learning objective.
More detailed.
Tells levels of success. (MAIN DIFFERENCE!)
Easy to turn criteria into a rubric

43. Example: “A Story of Students and Criteria” (Mathematics Assessment, 2005, pg.130) This teacher had students come up with the criteria for good work and super work. They made the criteria into a checklist. It would be easy to take the criteria and checklist and make a rubric.

44. Example: “A Story of Students and Criteria” (Mathematics Assessment, 2005, pg.130) This teacher had students come up with the criteria for good work and super work. They made the criteria into a checklist. It would be easy to take the criteria and checklist and make a rubric.

45. It would be easy to take the criteria and checklist and make a rubric.

46. 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
A title.
Labels on both axis.
Be accurate.
Be neat and readable.
Other ____________
Adjust these to your discussion.
This is your criteria!
Next, determine levels of success.

47. TITLE LABELS ACCURACY NEATNESS3
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.
The graph does not have a title
The graph is not labeled.
The data is missing.
The graph cannot be read.
Rubric from Reading “Seven Practices for Effective Learning”

48. Keys to Design a Rubric
Decide the type of rubric. (chart, scale, list, etc.)
Determine what you would like to see in the task. These will be your categories.
Next you need to determine the quality levels acceptable ….. How many levels?

49. Determining Levels of Success
Identify the key mathematical elements that determine whether a paper is acceptable (4) or unacceptable (1).
Identify specific differences between a paper that is barely unacceptable (2) and one that is clearly unacceptable (1).
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 21st Century: Methods and Activities for Grades 6-12)

50. Rubric Websites
x.php?screen=CustomizeTemplate &bank_rubric_id=25&section_id= 7&
b_tools/rubrics/homework/
htm

51. Let’s Practice Developing Our Own Rubrics ….
Take the remainder of the time (__ minutes) to discover some of these sites.
Need: Computer Lab!

52. Step by Step Help in Designing a Rubric
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 don’t 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.
This gives a more detailed information how to design a rubric. (EXTRA INFORMATION)

53. Step by Step Help in Designing a Rubric Cont.
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.

54. Summary of Steps

55. Example Upper Elementary Math
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.
This is an example of a teacher who used these steps to design a rubric.

56. Mr. Harris’s Rubric http://pareonline.net/getvn.asp?v=7&n=25
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.