1. Spring Mathematics Standards Conference Elementary (K-5)
Wesley Yuu, Educational Specialist
Val Kurizaki, Resource Teacher
May 16, 2006
Dole Cannery Iwilei Ballroom

2. Desired Outcomes Participants will:
Apply understanding of taxonomic levels to analyze the alignment between assessment tasks and the HCPS III benchmarks.
Increase teacher understanding of HCPS III rubrics and how to modify them for specific assessment tasks.

3. Desired Outcomes Participants will:
Use the task-specific rubrics to analyze student work and select exemplars for each level of proficiency.
Increase teacher understanding on the use of the benchmark maps website.

4. UPDATES – Benchmark Maps
Posted on DOE website, Dec., 2005
- Labeled as drafts
- Maps were intended to be piloted and
refined over the next school year
Plans changed between 12/2005 and today
- Maps will be used by Restructuring
Providers
- State will develop Quarterly Formative
Assessments based on the maps

5. UPDATES – Benchmark Maps
THEREFORE, maps needed to be finalized.
- In April, revisions were made to the Maps
in an attempt to put forth the best
possible final draft.
Publishers of Investigations, Trailblazers, and Everyday Math given the final drafts
- Asked to provide a guide to show how
program could be used while maintaining
compliance with the Maps.

6. UPDATES – Benchmark Maps
The flash drive at every table contains the publishers’ alignments to the Maps, and also includes a blank template for you to use to align your school’s textbook to the Maps.
The final draft will replace the draft on the DOE website by the end of June.

7. UPDATES – Benchmark Maps
Formative Quarterly Assessments based on the benchmark maps will be developed for tested grade levels (schools have the option of using these or to develop their own)
The alignment between the HSA and the benchmark maps is still in discussion.

8. Training and Work Session #1
Understanding the Standards via Taxonomic Levels
What does the benchmark mean?
What is the student expected to know and be able to do?
At what taxonomic level?

9. Bloom’s Taxonomy Depth of Knowledge Marzano’s Taxonomy
Training and Work Session #1
Understanding the Standards via Taxonomic Levels
Bloom’s Taxonomy
Depth of Knowledge
Marzano’s Taxonomy
All three provide a hierarchical structure to understand different levels of cognitive demand.

10. Training and Work Session #1
Understanding the Standards via Taxonomic Levels
Marzano’s Taxonomy is used by all content areas because it addresses more than the cognitive domain…
Cognitive Domain RIGOR
Metacognitive Domain RELEVANCE
Self-System RELATIONSHIPS

11. Marzano’s Taxonomic Levels (Cognitive Domain)
Training and Work Session #1
Marzano’s Taxonomic Levels (Cognitive Domain)
Level IV
Level III
Level II
Level I
Knowledge Utilization
Analysis
Comprehension
Knowledge Retrieval
Analyze using evidence
Classify with justification
Generate/Test hypotheses
Investigate
Use ___ to determine ___
Use___ to solve
Analyze
Categorize
Classify
Compare
Create a rule
Differentiate
Find what is common among ___
Predict
Demonstrate and explain
Describe how/why
Diagram
Explain the concept
Illustrate/ describe how ___ is related to ___
Represent
Collect data
Define and find examples of
Describe different types of
Give/Provide examples
List
Name
Recall
Recognize
Select from a list

12. 3.3.1: Recall multiplication facts from 0x0 to 10x10.
Training and Work Session #1
Using Marzano’s Taxonomic Levels
3.3.1: Recall multiplication facts from 0x0 to 10x10.
What does the benchmark mean?
What is the student expected to know and be able to do?
At what taxonomic level?

13. This means that student can:
Training and Work Session #1
Using Marzano’s Taxonomic Levels
3.3.1: Recall multiplication facts from 0x0 to 10x10.
What does the benchmark mean?
What is the student expected to know and be able to do?
At what taxonomic level?
Level I (Retrieval)
This means that student can:
Use mental arithmetic to determine the results of multiplying 0x0 through 10x10

14. Training and Work Session #1
Using Marzano’s Taxonomic Levels
K.3.1: Use a variety of strategies (e.g., objects, fingers) to add and subtract single-digit whole numbers
What does the benchmark mean?
What is the student expected to know and be able to do?
At what taxonomic level?

15. Using Marzano’s Taxonomic Levels
Training and Work Session #1
Using Marzano’s Taxonomic Levels
K.3.1: Use a variety of strategies (e.g., objects, fingers) to add and subtract single-digit whole numbers
What does the benchmark mean?
What is the student expected to know and be able to do?
At what taxonomic level?
Level II (Comprehension)
This means that student can:
Show how to add/subtract single-digit numbers in several different ways <list different strategies>

16. Access the document: HCPS3.Math.BenchmarkMeanings.Elem
Training and Work Session #1
Group Task
Access the document: HCPS3.Math.BenchmarkMeanings.Elem
Work as a table to complete the right column for the grade level benchmarks assigned to your table
Each table will save a compiled file onto the flash drive (add grade-level to the suffix of the file name)

17. Training and Work Session #1
Individual Reflection
How did understanding the taxonomic demand of the benchmark help to understand the intention of the benchmark?
How important is it to dialogue with others about the meaning of the benchmarks?

18. Training and Work Session #2
Evaluating Assessment Tasks
Does the task align to the targeted benchmark?
At the appropriate taxonomic level?

19. Evaluating Assessment Tasks
Training and Work Session #2
Evaluating Assessment Tasks
4.3.3: Use a variety of strategies to add and subtract fractions with like and unlike denominators
Does the task align to the targeted benchmark?
At the appropriate taxonomic level?
Solve the following:
1. 1/3 + 1/4 = ____
2. 1/8 + 1/2 + 3/8 = ____

20. Training and Work Session #2
Group Task
Evaluate the assessment tasks that were brought today (revise if necessary)
Access the document: MathUnit.PlanningMatrix
Fill in Box 1 and 2a for each set of tasks.
If time permits, develop tasks for other benchmarks in your grade level
Save all files onto the flash drive

21. Identifying Assessment Tasks at School
Training and Work Session #2
Identifying Assessment Tasks at School
Chapter Tests (modifications may be necessary)
Question Banks accompanying textbook
Websites (
Supplemental Resources
Design your own…SHARED EFFORT

22. Training and Work Session #3
Developing and Using Task-Specific Rubrics
How can the HCPS III rubric be tweaked for a specific task?

23. The 8 Types of HCPS III Rubrics
Training and Work Session #3
The 8 Types of HCPS III Rubrics
Read handout for descriptions and examples of the eight types of rubrics.
(bright orange handout: HCPS III generic rubrics)
Identify the rubric type for each of the given rubrics.
Could another type of rubric be appropriate for the benchmark?

24. Training and Work Session #3
Example
MA.4.2.1
Describe situations involving addition and subtraction of fractions and decimals
Rubric
Advanced
Proficient
Partially
Novice
Describe situations involving addition and subtraction of fractions and decimals, with accuracy 
Describe situations involving addition and subtraction of fractions and decimals, with no significant errors 
Describe situations involving addition and subtraction of fractions and decimals, with a few significant errors 
Have difficulty describing situations involving addition and subtraction of fractions and decimals 

25. Example Create a story problem that can be solved by adding 3/4 + 1/3.
Training and Work Session #3
Example
TASK
Create a story problem that can be solved by adding 3/4 + 1/3.
Task-Specific Rubric
Advanced
Proficient
Partially
Novice
The story problem can be solved by adding 3/4 + 1/3, AND the use of fractions in the problem is appropriate
The story problem can be solved by adding 3/4 + 1/3. 
The story problem appropriately involves the fractions 3/4 and 1/3, but addition is not involved; OR addition is involved, but not with the given fractions.
The story problem does not involve the correct operation; and the given fractions were not used appropriately.

26. Group Task Access the documents that you developed prior to lunch.
Training and Work Session #3
Group Task
Access the documents that you developed prior to lunch.
You already filled in Box 1 and 2a for each set of tasks; now fill in Box 2b.
Save all files onto the flash drive

27. Training and Work Session #3
Group Task
For each task that has a set of student work, identify one exemplar for each of the four ratings (Advanced, Proficient, Partially Proficient, Novice)
Attach post-it notes to the exemplar and write a commentary to explain how the work exemplifies the rating that it represents

28. Training and Work Session #3
Individual Reflection
How did understanding the taxonomic demand of the benchmark help to identify/develop an appropriate assessment task?
How important is it to dialogue with others when identifying exemplars?

29. Putting it all together…
(brown handout: “Standards-Based Implementation Model”)
Today’s outcomes focused on the first two steps in the Standards-Based Implementation Planning Model…
Identifying the targets (relevant benchmarks)
Determine acceptable evidence and criteria

30. The Standards-Based Implementation Model involves…
Putting it all together…
(brown handout: “Standards-Based Implementation Model”)
The Standards-Based Implementation Model involves…
Broadcasting targets and outcomes
Providing multiple learning experiences and feedback to achieve the targets
Assessing achievement of the targets
Reporting current levels of achievement and other factors to others