Spring Mathematics Standards Conference Elementary (K-5) Wesley Yuu, Educational Specialist Val Kurizaki, Resource Teacher May 16, 2006 Dole Cannery Iwilei Ballroom http://isb.k12.hi.us

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.

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.

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

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.

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.

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.

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?

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.

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

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

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?

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

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?

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>

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)

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?

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

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 = ____

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

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 (www.nctm.org) Supplemental Resources Design your own…SHARED EFFORT

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

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?

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 

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.

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

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

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?

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

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