1. Assessing students using the KCASM/CCSSM
Minute-by-minute
Day-by-day
Katrina Slone, KDE Regional Math Consultant – KVEC
Debbie Waggoner, KDE Regional Math Consultant - CKEC
Kentucky Council of Teachers of Mathematics
Bowling Green, KY October 8th, 2011

3. Today’s Targets I can define formative assessment.
I can describe examples of formative assessments.
I can classify formative assessments by their types.
I can explain why each type of formative assessment is critical to both assessment and further learning.

4. Diagram #1
Listen to the following directions. Without talking to anyone, sharing work with anyone
or asking any questions, draw the figure described.

5. Diagram #2
Listen to the following directions and draw the figure described.

6. List 3 examples of formative assessment….

7. Formative Assessment
Some things you may have identified as Formative Assessments and are now using:
Exit Slips entrance slips bell ringers
Thumbs up/down
Common Assessments
Are these really Formative Assessments?
Answer: It depends!

8. Formative assessment can and should be done BY STUDENTS as well as by teachers.
The key to improvement is
how students and teachers
use
assessment information.
The key to formative assessment—the use of the information to move students forward—has not changed.

9. Formative Assessment Evidence of Learning
Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes.
KDE, 2010

14. Student Responses to Discuss
Describe the problem solving approach the student used.
You might, for example:
Describe the way the student has colored the pattern of tiles.
Describe what the student did to calculate a sequence of numbers.
2. Explain what the student needs to do to complete his or her solution.

15. Leon’s method

16. Gianna’s method

17. Ava’s method

18. Is this task a formative assessment?
Is this task a formative assessment?

19. http://www. insidemathematics. org/index

25. Formative Assessment
Review the NCTM Research Brief : What does research Say the Benefits of Formative Assessment Are?
Long-cycle
Medium-cycle
Short-cycle

26. Typology of Kinds of Formative Assessment
Type
Focus
Length
Long-cycle
Across marking periods, quarters, semesters, years
4 weeks to 1 year
Medium-cycle
Within and between instructional units
1 to 4 weeks
Short-cycle
day-by-day
minute-by-
minute
Within and between lessons
24-48 hours
5 seconds to 2 hours

28. Why Now?

29. Lack of Engagement in Math
Lack of student engagement in learning is the greatest problem in many math classrooms.
The Mathematics Practice Standards present a way to leverage discourse.
Formative assessment or Assessment for Learning as learning activity for teachers and students.

30. Traditionally Teachers Choose One
of Three Options
1. Go back and re-teach the topic with the entire class.
2. Identify the students needing remediation and find some time/opportunity to re-teach the topic while the rest of the class continues on.
3. Feeling the pressure of the over packed curriculum the teacher ventures on to the next topic.

31. Re-teaching vs. Re-engagement
Teach unit again
Revisit student thinking
Address missing basic skills
Address conceptual understanding
On the same or similar problems
Examine task from different perspective
Practice more
Critique student approaches
Cognition lower
Cognition higher

32. Generalizing Patterns: Table Tiles
Projector Resources

33. How does the Table Tiles task require this kind of thinking?

34. How does the Table Tiles task require this kind of thinking?

35. How does the Table Tiles task require this kind of thinking?

36. CCSSM/KCASM ~ Content Cluster
CLUSTER: Building a function that models a relationship between two quantities
CCSSM/KCASM ~ Content Cluster

37. CLUSTER: Building a function that models a relationship between two quantities
Knowledge Targets
Reasoning Targets
Performance Skills Targets
Product Targets
Define “explicit function” and “recursive process”.
Write a function that describes a relationship between two quantities by determining an explicit expression, a recursive process, or steps for calculation from a context.
Combine two functions using the operations of addition, subtraction, multiplication, and division
Evaluate the domain of the combined function.
Given a real-world situation or mathematical problem:
-build standard functions to represent relevant relationships/ quantities,
-determine which arithmetic operation should be performed to build the appropriate combined function, and
-relate the combined function to the context of the problem
Identify arithmetic and geometric patterns in given sequences.
Generate arithmetic and geometric sequences from recursive and explicit formulas.
Given an arithmetic or geometric sequence in recursive form, translate into the explicit formula.
Given an arithmetic or geometric sequence as an explicit formula, translate into the recursive form.
Use given and constructed arithmetic and geometric sequences, expressed both recursively and with explicit formulas, to model real-life situations.
Determine the recursive rule given arithmetic and geometric sequences.
Determine the explicit formula given arithmetic and geometric sequences.
Justify the translation between the recursive form & explicit formula for arithmetic and geometric sequences.

38. Assessing the Targets
Target
Formative Assessment
Define “explicit function” and “recursive process”.
Determine the recursive rule given arithmetic and geometric sequences.
Identify arithmetic and geometric patterns in given sequences.
Evaluate the domain of the combined function
Exit Slip: Define explicit function.
Entrance Slip: Find the recursive rule for this sequence.
Thumbs UP if you think this is an arithmetic pattern for this this sequence. Thumps DOWN if you think it is a geometric pattern.
Evaluate the domain of this combined function on your white board.
Possible student work (even faked?)

39. So…Do these assess the standard?
Can you convict students guilty of achieving the standard based on each piece of information about the targets?

40. Standard Cake
Ingredients/cake analogy to targets/standards

41. CCSSM/ KCASM Learning
“I thought that if I taught them all the bits, [students] could put them together.” FAL Trial Teacher
Explain acronym KCASM
CASL helped us to take apart the standards into the bits necessary to teach and learn them. Short-cycle FA helps us to know if students get the bits. Medium-cycle FA, in the guise of FALs, help us to know if they can put the bits together to really understand and utilize the standard.
Deconstruction was like sand-blasting to see each part: each skill & concept students need to build on..,
Now we need students to make a Mosaiac seeing how the targets & standards fit together to make clusters & BIG IDEAS in mathematics…

42. Linking to Research: The QUASAR Project
Low-Level Tasks
memorization
procedures without connections to meaning (e.g., Martha’s Carpeting Task)
High-Level Tasks
procedures with connections to meaning
doing mathematics
(e.g., The Fencing Task)

43. Research – based Conclusions
Not all tasks are created equal -- they provided different opportunities for students to learn mathematics.
High level tasks are the most difficult to carry out in a consistent manner.
Engagement in cognitively challenging mathematical tasks leads to the greatest learning gains for students.
Professional development is needed to help teachers build the capacity to enact high level tasks in ways that maintain the rigor of the task.
Based on QUASAR & TIMSS Video Study

45. From Smarter Balance

46. Formative Assessment Lessons, or Mathematics FALs, are based on the research about formative assessment and about implementing high level tasks

47. Today’s Targets I can define formative assessment.
I can describe examples of formative assessments.
I can classify formative assessments by their types.
I can explain why each type of formative assessment is critical to both assessment and further learning.

48. How Can We Support You? Katrina Slone
KVEC Regional Mathematics Content Specialist
Kentucky Department of Education
Office of Next Generation Learners
Debbie Waggoner
CKEC Regional Mathematics Content Specialist
Kentucky Department of Education
Office of Next Generation Learners
PLEASE CONTACT US FOR SUPPORT!!
Thanks for your participation today. 48