1. Georgia Performance Standards
Grades Mathematics
Day 2:
Learning to Assess and
Assessing to Learn

2. Carmen Smith Office phone: (404) 463-1746
1754 Twin Towers East, Atlanta, Georgia 30334
Office phone: (404)
Office

3. Georgia Performance Standards
Grades Mathematics
Day 2:
Learning to Assess and
Assessing to Learn

4. Group Norms and Housekeeping
Ask questions
Work toward solutions
Honor confidentiality
Meet commitments or let others know if you are struggling
Housekeeping:
Parking Lot
Phone calls
Rest rooms
Breaks
Lunch

5. Four Corners, Part 1
Choose a corner based on your confidence in understanding the GPS for K – 2 Mathematics:
Square 1 - Novice
Square 2 - Apprentice
Square 3 - Practitioner
Square 4 - Expert

6. Four Corners, Part 2 What made you choose your corner?
Discuss what you know and
what you want to know.
Be prepared to share with the group.
Have each corner share. Record on chart paper. Post chart paper in front.

7. Bloom on Mastery

8. (perhaps over 90 percent)
Most students
(perhaps over 90 percent)
CAN master
what we teach….

9. ….Our basic instructional task is to define what we mean by
mastery of a subject
and to discover
methods and materials
to help the largest proportion
of our students reach it.
Benjamin S. Bloom (1971)

10. First Grade Takes A Test by: Miriam Cohen and Ronald Himler
What do we assess?
Why do we assess?
How do we assess?

11. Table Discussion
What should we assess?
Why should we assess?
How should we assess?

12. Today’s Assessment
Develop a performance task to gather evidence of what students will know and be able to do related to the standard(s) you chose.

13. Performance Tasks & Assessments
* often occur over time
* result in a tangible product or observable performance
* encourage self-evaluation and revision
* require judgment to score
* reveal degrees of proficiency based on criteria established and made public prior to the performance
* sometimes involve students working with others

14. According to Grant Wiggins…
What is to be assessed must be clear and explicit to all students.
NO MORE SURPRISES!
Rubrics must accompany all major assignments and assessments.

15. Essential Question 1
What should we assess?

16. Geometry Map
Use math tools, colored pencils, and chart paper to design a city map (from a bird’s eye view) that meets the following requirements:
4 streets that are parallel to each other
1 avenue that is perpendicular to the 4 parallel streets
1 highway that intersects at least 2 streets but is not
perpendicular to them (intersects at an acute angle)
3 parallelogram shaped buildings, 4 square shaped buildings,
and 1 trapezoid shaped building
1 park with a 360 degree swimming pool, an equilateral triangle
sandbox, and 2 rectangle shaped basketball courts
give your city a name
label all parts of your map with original names

17. What We Should Assess What mathematics is involved in this task?
What standards/
elements are addressed?

18. Is This a Good Task? Decide whether this is or is not a good task.
Justify your answer.

19. Criteria for Good Tasks
Involves significant mathematics
Can be solved in a variety of ways
Elicits a range of responses
Requires communication
Stimulates best performance
Lends itself to a scoring rubric

20. Standards Based Education Model
GPS
Stage 1
Identify Desired Results
(Big Ideas) Enduring Understandings 
Essential Questions 
Skills and Knowledge
(one or more)
Standards
Elements
Stage 2
Determine Acceptable Evidence
(Design Balanced Assessments)
(To assess student progress toward desired results)
All above, plus
Tasks
Student Work
Teacher
Commentary
Participant’s Guide, page 8
Stage 3
Plan Learning Experiences and Instruction
(to support student success on assessments,
leading to desired results)
All above

21. The Process of Instructional Planning
Select standards from among those students need to know
Design an assessment through which students will have an opportunity to demonstrate those things
Decide what learning opportunities students will need to learn those things and plan appropriate instruction to assure that each student has adequate opportunities to learn
Use data from assessment to give feedback, reteach or move to next level
Select a topic from the curriculum
Design instructional activities
Design and give an assessment
Give grade or feedback
Move onto new topic
Standards-based Practice
Traditional Practice
The Process of Instructional Planning

22. “To begin with the end in mind
means to start with a clear understanding of your destination.
It means to know where you’re going
so that you better understand
where you are now
and so that the steps
you take are
always in the right direction.”
-- Stephen Covey

23. Converting problem situations into mathematical expressions.
Looking for Big Ideas
M4G1. Students will define and identify the characteristics of geometric figures through examination and construction.
a. Examine and compare angles in order to classify and
identify triangles by their angles.
b. Describe parallel and perpendicular lines in plane geometric
figures.
c. Examine and classify quadrilaterals (including parallelograms,
squares, rectangles, trapezoids, and rhombi).
d. Compare and contrast the relationships among quadrilaterals.
Converting problem situations into mathematical expressions.
K Standard
Share the book, The Grouchy Ladybug.

24. From Understandings to Questions
“Students will define and identify the characteristics of geometric figures through examination and construction.”
Why is it important to be able to identify and define these characteristics?
How can I represent this knowledge through authentic application?

25. Skills and Knowledge KNOWLEDGE (declarative) SKILLS (procedural) Facts
Concepts
Generalizations
Rules, Laws, Procedures
Skills
Procedures
Processes A P L I C
A T I O N
Participant’s Guide, page 13
KNOWLEDGE
(declarative)
SKILLS
(procedural)

26. Skills and Knowledge 1) Angle (two rays that share an endpoint)
2) Equilateral Triangle (a triangle with all sides the same length)
3) Intersect (to meet or cross)
4) Parallel (always the same distance apart)
5) Parallelogram (a quadrilateral with two pairs of parallel and congruent sides)
6) Perpendicular (forming right angles)
7) Quadrilateral (a four-sided polygon)
8) Trapezoid (a quadrilateral with exactly two parallel sides)

27. Concept
Development
Abstract
Semi-
Abstract
Semi-
Concrete
Concrete

28. Multiple Representations
Pictures
Tables
Words
Symbols
Graphs
Demonstrate activities that can be used to support the given standard:
Arrays (Pictures)
Collections (Words)
Repeated Addition (Symbols)
Multiplication Table (Tables)
Function/ Input-Output Chart (Graphs)

29. Essential Question 2
Why should we assess?

30. is to prove achievement, and the purpose of formative assessment
summative assessment
is to prove achievement,
and the purpose of
formative assessment
is to improve achievement.”
--Pratt, 1980

31. My Perfect Saturday
Create a circle graph that represents all 24 hours of your “Perfect Saturday”
Activities should be clearly labeled and represented on your circle graph
Put all “like” activities together. For examples: all meals should be in one fractional part of the circle
Give your graph a title
Be prepared to share

32. Graph of the Perfect Saturday
Complete the task.
Identify the standards addressed by this assignment.
Specify the criteria of the assignment.

33. Perfect Saturday Graph
What could you learn about students based on their performance on this task?

34. Accountability The purpose of the Georgia Testing Program is to
measure the level of student achievement of the standards
identify students failing to achieve mastery of content
provide teachers with diagnostic information
assist school systems in identifying strengths and weaknesses in order to establish priorities in planning educational programs.

35. Testing
CRCT Information

36. Essential Question 3
How should we assess?

37. Visualize Tyler’s bike ride as you listen to this story.
Long Bike Ride
Visualize Tyler’s bike ride as you listen to this story.
Tyler left his house and rode his bike
4 7/8 miles south to his friend Matt’s
house. They then rode their bikes
3 ½ miles west to the park. At the park
there was a wonderful water fountain that
they played in and rested for awhile.
When they felt refreshed they rode their
bikes 3 ¼ miles north to the soccer fields
and played with some friends from
school. When they left the soccer field
how many miles do they have to ride their
bikes east and then north (following the
main roads) to get back to Tyler’s house?

38. Long Bike Ride Use the information in the problem to find the answer
Draw a diagram on your chart paper to represent the data
All work must be shown
You may work individually
or with a partner

39. How We Should Assess Which standard(s) does this task assess?
What are the desired results?
How does this task assess the desired results?

40. Matching Assessments with Standards
ASSESSMENT FORMAT
ACHIEVEMENT TARGET
Selected Response
Constructed Response
Performance Tasks
Informal Assessment
Knowledge/
Informational
Skills/Process
Thinking and Reasoning
Communication
Other:
Can assess mastery of specific elements of content knowledge
Short answers allow students to apply content knowledge
Not a good choice for this target; other options preferred
Teacher can ask questions, evaluate answers, and infer mastery; but this may not be time-efficient
Can assess application of some patterns of reasoning
Can observe and evaluate skills as they are being performed
Strong match when skill is oral communication
Written descriptions of complex problem solutions can provide insight into reasoning proficiency.
Can watch students solve some problems or examine some products and infer reasoning proficiency
Can ask students to “think aloud” or can ask follow-up questions to probe reasoning
Can observe and evaluate oral & written communication portions of performance tasks.
Strong match with some communication skills, especially oral communication
Can assess under-standing of the steps of a process, but not a good choice for evaluating most skills
Not a good choice for this target; other options preferred.
-Adapted from Marzano and Stiggins

41. Types of Classroom Assessment
Selected Response
Constructed
Response
Performance Assessment
Informal Assessment
Multiple Choice
True-False
Matching
Fill-in-the-blank (words, phrases)
Essay
Short answer (sentences, paragraphs)
Diagram
Web
Concept Map
Flowchart
Graph
Table
Matrix
Illustration
Presentation
Movement
Science lab
Athletic skill
Dramatization
Enactment
Project
Debate
Model
Exhibition
Recital
Oral questioning
Observation
Interview
Conference
Process description
Checklist
Rating scale
Journal sharing
Thinking aloud a process
Student self-assessment
Peer review

42. Group Activity Choose one of the four assessment formats.
Read the information provided about the format.
Get a piece of chart paper and marker.
Use a Standard and element to compose an example of an assessment item using the format. Write it on the chart.
Record the advantages and limitations of the item.
Report your example and ideas to the whole group.

43. Whole Group Reporting Choose a recorder for each type of format.
Have each group report their examples to the recorder for each type of format.
Discuss examples, advantages and limitations.

44. Assessment vs. Grading
Student 1 receives mostly As and high Bs in the beginning; but his/her performance drops off considerably, and s/he receives an F on the final performance test.
Student 2 is erratic, receiving an equal number of As and Fs.
Student 3 is clueless at the beginning, but by the last few sessions, s/he catches on and performs flawlessly on the final performance. His/her grades are, in order from the first test to the last, F, F, F, F, C, B, A, A, A.

45. WHICH STUDENT DO YOU WANT TO PACK YOUR PARACHUTE? WHY?

46. Assessing for Learning vs Grading
Continuous process
Provides feedback to improve student achievement
May be formative or summative
Provides a means of collecting evidence of student mastery of the standards
Provides a photo album of student progress through which student growth can be observed
Grading
A means of assigning numerical or alphabetical grade to a student’s work to inform students, parents and other stakeholders
May be formative or summative
Provides an attempt to quantitatively describe student achievement
Provides a snapshot of student progress

47. Putting It Into Practice
Analyze the four pieces of student work to this task using the steps for “Analyzing Student Work”.

48. Analyzing Student Work
Complete the assignment or task.
Identify the standards addressed by this assignment.
Specify the criteria of the assignment.

49. Analyzing Student Work
Generate a rough rubric or scoring guide based on the standards addressed and the criteria for this assignment.
Score the work or provide feedback on the work, using the rubric/scoring guide.
Plan a strategy for improving student performance based on the work.

50. Multiple Representations
Pictures
Tables
Words
Symbols
Graphs
Demonstrate activities that can be used to support the given standard:
Arrays (Pictures)
Collections (Words)
Repeated Addition (Symbols)
Multiplication Table (Tables)
Function/ Input-Output Chart (Graphs)

51. A rubric is a set of rules that:
Shows levels of quality
Communicates standards
Tells students expectations for assessment task
Is NOT a checklist (yes or no answers)
Includes dimensions (criteria), indicators and a rating scale.

52. Advantages of Using a Rubric
Lowers students’ anxiety about what is expected of them
Provides specific feedback about the quality of their work
Provides a way to communicate expectations and progress
Ensures all student work is judged by the same standard
Disengages the “halo” effect and its reverse
Leads students toward quality work.

53. Basic Rubric Template Scale Criteria Indicator Indicator Indicator

54. Ugly Rubrics
Too wordy so that no one can understand, let alone use them for a fair grade
Checklists – Have it, don’t have it
Judge the wrong thing so student can just jump through hoops to get a good grade.

55. Pretty Rubrics Are tools
Show level of quality of a performance or task
Communicate standards clearly and specifically
Are given to students to set expectations
Show what to avoid and addresses misconceptions
Are consistent and reliable
Use content that matches standards and instructional emphasis

56. Small group discussion: What has to happen?
If you know what a student must understand, how do you check to see if that student understands?
What evidence will you use to evaluate the level of understanding?
What will you do in your classroom based on the evidence you collect?

57. Geometry Map
Create a rubric to assess the Geometry Map task as a culminating task for the unit on angles, lines, and geometric plane figures.

58. Put that Rubric to Use
Now to try your hand at assessing student work. You are to choose two of the “works” posted around the room and assess this work using the rubric that you have created.

59. Teacher Commentary
Now think about how you would give commentary to the two works that you assessed.
Be sure that the commentary addresses both successes and growth opportunities.
Has the standards that this work addresses been mastered? How do you know?

60. Self-Assessment
Setting a Goal

61. Field Assignment Redeliver Day 2.
Use what you have learned today to create an assessment you will use with your students. Collect work samples to share with the group.
Bring a copy of the assessment and student work samples of your task to Day 3.
Bring resources to help you plan for instruction.

62. Days of Training Implementation Year One Implementation Year Two
Day One: Standards, Content, and Curriculum Mapping
Day Two:  Assessment
Days Three and Four: Classroom Implementation
Implementation Year Two
Day Five: Differentiation
Day Six: Examining Student Work
Day Seven: On-line Survey
We don’t have to do it all today!

63. Carmen H. Smith Office phone: (404) 463-1746
1754 Twin Towers East, Atlanta, Georgia 30334
Office phone: (404)
Office