Spring Mathematics Standards Conference

Elementary (K-5)Wesley Yuu, Educational SpecialistVal Kurizaki, Resource Teacher

May 16, 2006Dole 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?

Understanding the Standards via Taxonomic Levels

Bloom’s Taxonomy Depth of Knowledge Marzano’s Taxonomy

Training and Work Session #1

All three provide a hierarchical structure to understand different levels

of cognitive demand.

Understanding the Standards via Taxonomic Levels

Cognitive Domain RIGOR

Metacognitive Domain RELEVANCE

Self-SystemRELATIONSHIPS

Training and Work Session #1

Marzano’s Taxonomy is used by all content areas because it addresses more than the cognitive domain…

Marzano’s Taxonomic Levels (Cognitive Domain)

Level IV Level III Level II Level IKnowledge Utilization

Analysis ComprehensionKnowledge 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

Training and Work Session #1

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

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?

Using Marzano’s Taxonomic Levels

Training and Work Session #1

3.3.1: Recall multiplication facts from 0x0 to 10x10.

Level I (Retrieval)

This means that student can:

Use mental arithmetic to determine the results of multiplying 0x0 through 10x10

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

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

Level II (Comprehension)

This means that student can:Show how to add/subtract single-digit numbers in several different ways <list different strategies>

K.3.1: Use a variety of strategies (e.g., objects, fingers) to add and subtract single-digit whole numbers

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)

Group Task

Training and Work Session #1

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?

Individual Reflection

Training and Work Session #1

Training and Work Session #2

Evaluating Assessment Tasks

Does the task align to the targeted benchmark?

At the appropriate taxonomic level?

Evaluating Assessment TasksTraining and Work Session #2

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 = ____

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

Group Task

Training and Work Session #2

Chapter Tests (modifications may be necessary)

Question Banks accompanying textbook Websites (www.nctm.org) Supplemental Resources Design your own…SHARED EFFORT

Identifying Assessment Tasks at School

Training and Work Session #2

Training and Work Session #3

Developing and Using Task-Specific Rubrics

How can the HCPS III rubric be tweaked for a specific task?

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?

The 8 Types of HCPS III Rubrics

Training and Work Session #3

Example

Training and Work Session #3

MA.4.2.1Describe situations involving addition and

subtraction of fractions and decimals

Rubric

Advanced ProficientPartially

ProficientNovice

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

Training and Work Session #3

TASKCreate a story problem that can be solved by

adding 3/4 + 1/3.

Task-Specific Rubric

Advanced ProficientPartially

ProficientNovice

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.

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

Group Task

Training and Work Session #3

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

Group Task

Training and Work Session #3

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?

Individual Reflection

Training and Work Session #3

(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

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

Putting it all together…