1. Common Core Standards mathematics
Beaver Valley Intermediate Unit; Administrator PLC
Common Core Standards mathematics
Cristine Wagner-Deitch, Barbara Lease & Corinne Murawski

2. Goals
Understand the organization of the Common Core State Standards (CCSS) as well as the rationale for their existence and use
Understand the differences between the Pennsylvania State Standards and the CCSS and the impact these differences should have on instruction and learning
Extract potential professional development strategies, resources and tools from the sessions
Create an action plan for the development of curricula that are aligned to CCSS
Develop a Professional Learning Community (PLC)
This past summer, if you recall, we were attempting to go beyond solely looking at the CCSS. We were also attempting to model some PD Strategies for you, so that you might use what you think will help you as you action plan for implementing the needed PD in your district.
We examine these goals again just to refresh your memory about where we were then. We will revisit your action plan (and your actions) later on this morning.
Right now, let’s take a look at where we are headed this morning.
Beaver Valley Intermediate Unit; Administrator PLC

3. Day 3- Overall Agenda
Updated information on Common Core State Standards and Pennsylvania
Introduction to some useful resources for moving forward in implementation of CCSS
Time for sharing and discussion
What will you do now?
Beaver Valley Intermediate Unit; Administrator PLC

4. COMMON CORE TRANSITION
October 2011
Revise Anchor/Eligible Content in Math and Reading in grades 3, 4, 5, 6, 7, 8, 11 to align to Common Core Standards
January 2012
Revise PA Academic Standards in Reading and Math to create set of PA Common Core Standards
Begin development of Common Core aligned PSSA Reading and Math tests

5. COMMON CORE TRANSITION
FEBRUARY 2012
Post PA Common Core Standards on SAS
Develop PA Common Core train the trainer modules for IU delivery to LEAs
February to May 2012
Offer CC training sessions to LEAs
February 2012 and ongoing
Align SAS resources to PA Common Core Standards

6. COMMON CORE TRANSITION
Spring 2014
PSSA tests aligned to Common Core – Gr 3-5
Spring 2015
PSSA tests aligned to Common Core – Gr 6-8

7. Keystone Exams Already aligned to Common Core
2011/ Keystone Exam hiatus based upon budgetary considerations.
2012/2013- Budget will dictate the implementation of the Keystone Exams.
Intent is to replace the Grade 11 PSSA tests with Keystone Exams subject to US Dept. of Ed approval.
Target date spring 2014.

8. CCSS Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Recall that a big part of what we did this summer in mathematics was to focus on the Standards for Mathematical Practice. They are listed here, but are also in your binder from this summer in their expanded form and are available at the corestandards.org website.
Since then, a new book has been published that has a variety of great resources referenced within. It is called… (next slide)
Beaver Valley Intermediate Unit; Administrator PLC

9. Resource for Administrators
Accessible at:
Among the new resources is a book shown here and called What Principals need to know about Teaching and Learning Mathematics. This book is not solely about CCSSM, but it is much more all-encompassing of math teaching and learning. Of course, you can purchase this publication. However, you do not need to purchase one for every administrator in your district – one per district may be enough if you are truly working as a team – because solution-tree always allow you at access some of the reproducibles online.
We are going to examine two of the reproducibles that are tied to CCSSM this morning.

10. The first of these connects instructional strategies to the Mathematical Practice.
Last summer, when we talked at length about the Mathematical Practices, you may have said to yourself, “Well, that is great that these practices will enable students to learn the content more effectively. I can definitely have people in my district learn about the practices, but I really don’t have enough information to help teachers understand how to get students to embody the practices.” So, here is one focused resource that will help you and teachers realize the connection between the research-based instructional strategies that we have been discussing in many different venues and the math practices.
(Give a minute for people to review this.)
So, we are hoping this document will help you connect things you and teachers have been reading or talking about for some time now, but you might still be thinking, “Yeah, this is fine, but I really need something a bit more akin to ‘where the rubber meets the road.’” (next slide)

11. So, here is a document (accessible online) that you might use in the classroom with teachers or as a discussion-starting within your professional learning communities.
This document ties the practices (hopefully through the use of the instructional strategies on the last handout) to classroom indicators that these practices are developing or are in place for the students doing the learning. The version I am showing you here on the screen is the one that you can download, without anything in the right-hand column. The version you have in your hand has some examples of possible look-fors that people might brainstorm as related to the particular practice on the left.

12. Additionally, if you are working with (or thinking about working with) the new PA rubrics for teacher evaluation that is based on the Danielson Model, you’ll notice connections between what is embodied in these two documents and the rubric for Domain 3, Instruction and Domain 2: Active Engagement. These Practices, Instructional Strategies and especially the Look-fors are the HOWs for Engaging students in Learning and for Using Questioning and Discussion Techniques (3b and c in the rubric)

13. Inside Mathematics Need help with the “look-fors”?
Here is a very useful website that has greatly expanded its resources since summer.
home
Show the variety of resources available at this website including:
High level tasks. Note that it has information progressing from K through 12, not just limited to one grade span.
Student work on high-level task (use a 3rd grade task – Pet shop – to show the Tools for educators tab)
Videos of classroom episodes (Classroom Video Visits tab)
When you get to the Common Core Standards tab, note the portion that talks about Classroom Observations. This can help move the conversation about Look-fors forward.
While we are on the subject or look fors….

14. Common Core Look-fors If you have an iPhone or iPad
core-look-fors- mathematics/id ?mt=8
Take about 10 minutes to view and discuss this app
Good for helping to establish a collegial relationship around observations since this is not a tool for evaluation (however can tie to domain 2 and 3)
Good for peer-to-peer work. Its suggested use in the intro to the app
Good for self-evaluation to see how your own students are doing with the Practices
Show how to create a file and how to record, take pix, make notes, tie to the content standards, make a report, tie to the inside math website
After showing the app, tie back to inside math website and talk about how the resources we viewed today can be great starters for PD conversations about the math practices in particular, but about good math teaching and learning in the greater picture. (3 min for that)

15. Depth of Knowledge (DOK)

16. Depth of Knowledge (DOK)
Adapted from the model used by Norman Webb, University of Wisconsin, to align standards with assessments
Used by the Council of Chief State School Officers (CCSSO) for assessment alignment in more than ten states
Webb Model: Provides analysis of the degree of intersection of state assessments and content standards, which combines qualitative expert judgments and quantified coding and statistical analysis. The Council worked with Norman Webb in developing the model.
Webb Model
The model developed by Norman Webb from the University of Wisconsin, provides a reliable set of procedures and criteria for conducting alignment analysis studies, which combine qualitative expert judgments and quantified coding and analysis of standards and assessments. The product of the analysis is a set of statistics for each standard and grade on the degree of intersection, or alignment, between the content embedded in state content standards and the content in state assessments. The Webb model has been used in alignment studies with more than 10 states, partly through SCASS collaborative projects managed by CCSSO. The model has been used for language arts, mathematics, science, and social studies.
Following the training process, four to six reviewers, including teachers and content specialists, individually identify the content standard objectives that match each assessment item. They first determine the 'depth of knowledge' required by each objective or benchmark of the content standards being analyzed, and code each using one of four levels of knowledge: (a) recall, (b) skill/concept, (c) strategic thinking, (d) extended thinking. Operational definitions and labels vary somewhat by subject. Second, reviewers determine the objective or benchmark represented by each item or task on the state assessment being reviewed, and they rate the level of knowledge necessary for a student to successfully complete the item or task.
Norman L. Webb is a senior research scientist with the Wisconsin Center for Education Research and the National Institute for Science Education. Webb is a mathematics educator and evaluator who leads the Institute's work on strategies for evaluating reform and rethinking how we evaluate mathematics and science education, while focusing on the NSF's Mathematics and Science Partnerships. His own research has focused on assessment of students' knowledge of mathematics and the alignment of standards and assessments. Webb also directs evaluations of curriculum and professional development projects.

17. Why Depth of Knowledge?
Mechanism to ensure that the intent of the standard and the level of student demonstration required by that standard matches the assessment items (required under NCLB)
Provides cognitive processing ceiling (highest level students can be assessed) for item development

18. Webb’s Depth of Knowledge Levels
Recall and Reproduction: Level 1
Skills & Concepts: Level 2
Strategic Thinking: Level 3
Extended Thinking: Level 4
Sean Elkins

19. Recall and Reproduction: Level 1
DOK 1 requires recall of information, such as a fact, definition, term, or performance of a simple process or procedure.
Answering a Level 1 item can involve following a simple, well-known procedure or formula. Simple skills and abilities or recall characterize DOK 1.
Level 1 only requires students to demonstrate a rote response, use a well-known formula, follow a set procedure (like a recipe), or perform a clearly defined series of steps.

20. DOK Level 1 Examples
List animals that survive by eating other animals.
Locate or recall facts explicitly found in text
Describe physical features of places
Determine the perimeter or area of rectangles given a drawing or labels
Identify elements of music using musical terminology
Identify basic rules for participating in simple games and activities

21. Skills/Concepts: Level 2
DOK 2 includes the engagement of some mental processing beyond recalling or reproducing a response. Items require students to make some decisions as to how to approach the question or problem.
These actions imply more than one mental or cognitive process/step.
The content knowledge or process involved is more complex than in level 1. For example, to compare data requires first identifying characteristics of the objects or phenomenon and then grouping or ordering the objects 21

22. DOK Level 2 Examples Compare desert and tropical environments
Identify and summarize the major events, problem, solution, conflicts in literary text
Explain the cause-effect of historical events
Predict a logical outcome based on information in a reading selection
Explain how good work habits are important at home, school, and on the job.
Classify plane and three dimensional figures
Describe various styles of music
Organize, represent and compare data
Compare/contrast people, events, places, concepts

23. Strategic Thinking: Level 3
DOK 3 requires deep understanding as exhibited through planning, using evidence, and more demanding cognitive reasoning. The cognitive demands at Level 3 are complex and abstract.
An assessment item that has more than one possible answer and requires students to justify the response they give would most likely be a Level 3.
The complexity does not result only from the fact that there could be multiple answers, a possibility for both Levels 1 and 2, but because the multi-step task requires In most instances, requiring students to explain their thinking is at Level 3; requiring a very simple explanation or a word or two should be at Level 2. 23

24. DOK Level 3 Examples
Compare consumer actions and analyze how these actions impact the environment
Analyze or evaluate the effectiveness of literary elements (e.g. characterization, setting, point of view, conflict and resolution, plot structures)
Solve a multiple-step problem and provide support with a mathematical explanation that justifies the answer
Explain, generalize, or connect ideas using supporting evidence from the text or from other sources

25. DOK Level 3 Examples Develop a scientific model for a complex idea
Propose and evaluate solutions for an economic problem
Explain, generalize or connect ideas, using supporting evidence from a text or source
Create a dance that represents the characteristics of a culture

26. Extended Thinking: Level 4
DOK 4 requires high cognitive demand and is very complex. Students are expected to make connections-relate ideas within the content or among content areas—and have to select or devise one approach among many alternatives on how the situation can be solved.
Due to the complexity of cognitive demand, DOK 4 often requires an extended period of time.
Many on-demand assessment instruments will not include any assessment activities that could be classified as Level 4. However, standards, goals, and objectives can be stated in such a way as to expect students to perform extended thinking. “Develop generalizations of the results obtained and the strategies used and apply them to new problem situations,” is an example of a Grade 8 objective that is a Level 4. The extended time period is not a distinguishing factor if the required work is only repetitive and does not require applying significant conceptual understanding and higher-order thinking.  

27. However, extended time alone is not the distinguishing factor.
Task
Thinking
Collecting data samples over several months
Recall
Organizing the data in a chart
Skills/
concepts
Using this chart to make and justify predictions
Strategic
Developing a generalized model from this data and applying it to a new situation
Extending
Many on-demand assessment instruments will not include any assessment activities that could be classified as Level 4. However, standards, goals, and objectives can be stated in such a way as to expect students to perform extended thinking. “Develop generalizations of the results obtained and the strategies used and apply them to new problem situations,” is an example of a Grade 8 objective that is a Level 4. The extended time period is not a distinguishing factor if the required work is only repetitive and does not require applying significant conceptual understanding and higher-order thinking.  
is a task. exemplifies a. results in an increase to. would represent a.

28. Extended Reasoning/Thinking Examples: Level 4
Gather, analyze, organize, and interpret information from multiple (print and non print) sources to draft a reasoned report
Analyzing author’s craft (e.g., style, bias, literary techniques, point of view)
Create an exercise plan applying the “FITT (Frequency, Intensity, Time, Type) Principle”

29. Extended Reasoning/Thinking Examples: Level 4
Analyze and explain multiple perspectives or issues within or across time periods, events, or cultures
Specify a problem, identify solution paths, solve the problem, and report the results
Write and produce an original play

30. The Depth of Knowledge is NOT determined by the verb, but the context in which the verb is used and the depth of thinking required.

31. Same verb—three DOK levels
DOK 3- Describe a model that you might use to represent the relationships that exist within the rock cycle. (requires deep understanding of rock cycle and a determination of how best to represent it)
DOK 2- Describe the difference between metamorphic and igneous rocks. (requires cognitive processing to determine the differences in the two rock types)
DOK 1- Describe three characteristics of metamorphic rocks. (simple recall)
Same verb—three DOK levels

32. DOK levels can be cumulative
An item/standard written to DOK 3 often contains DOK 1 and DOK 2 level demands.

33. Remember…
• Depth of Knowledge (DOK) is a scale of cognitive demand.
• DOK requires looking at the assessment item/standard-not student work-in order to determine the level. DOK is about the item/standard-not the student.
• The context of the assessment item/standard must be considered to determine the DOK-not just a look at what verb was chosen.

34. Old Boxes People are the next step
If people just swap out the old standards and put the new CCSS in the old boxes
into old systems and procedures
into the old relationships
Into old instructional materials formats
Into old assessment tools,
Then nothing will change…
But we are the key to major change over the next 3 to 4 years. We CAN create new boxes in our field. In order to do that we must open our minds to possibilities and NOT attempt to put these new State Standards into the old boxes. We must look forward towards the potential of what can be. If we truly want to serve our children well in the future, we must change the way we “do school” and CCSS are a big part of that.
In order to start creating these new boxes and filling them, one of the first, most logical steps for us to take is to look deeply at the standards for practice in math and ELA. <<next slide>>
Beaver Valley Intermediate Unit; Administrator PLC