1. Welcome to BCIU 14 District Rollout
Following the activator share some of the things that interested ( intrigued) you as you saw the scrolling “10 reasons for MDC”
Welcome to BCIU 14 District Rollout
Day One
Dan Richards
Rebecca Chadwick
Berks County Intermediate Unit

2. Goals for Day 1 What is the Math Design Collaborative?
How do we connect formative assessment to the MDC lessons?
What is the format and the reasoning behind the MDC lessons?
What are the resources that are being provided to help us succeed?
These are the ambitious goals of today…hopefully, we will have time at the end of the day to explore the resources and I am going to ask you to come back tomorrow with a choice of the first FAL that you would like to implement in your class room

3. Defining MDC (Mathematics Design Collaborative)
Using a 5 x 7 index card write your ideas/definition of what you believe describes the Math Design Collaborative.
As we move through the next 2 days, please add and edit information to this space .
At the end of day 2, we’ll reflect on what you’ve written.

4. What is MDC?
MDC provides teachers with Formative Assessment Lessons (FALS) to engage students in a productive struggle that builds fluency with their procedural skills, and deepens mathematical reasoning and understanding.
MDC provides resources, strategies, and professional development to assist teachers ASSESS FOR LEARNING.
I like to think of it as a framework because it truly does guide you and build a strong foundation for active engagement, formative teaching skills, and common core lessons. It is like one stop shopping…and I only wish I had this when I was starting out …instead of ending.

5. Achieves a balance among concepts, skills, and problem solving.
The MDC project is not designed as an additional program, but rather a process to enhance CC standards-based instruction.
Achieves a balance among concepts, skills, and problem solving.
Stresses rigorous concept development, presents realistic and relevant tasks, and keeps a strong emphasis on computational skills.
Biggest look for here is the adjectives…what catches your eye on this slide…pick one word…on the count of three say your word outloud…turn to your partner and tell them why you chose this word.

6. Math Design Collaborative - Teacher Benefits
MDC brings high quality instructional methods and professional development to teachers and promotes changes in teaching methods.
MDC helps teachers understand and implement the PA Core.
MDC provides teachers with created/validated lessons for middle and high school teachers to use called Formative Assessment Lessons (FALS).
Meets high standards of “Proficient” and “Distinguished” under PA Educator Effectiveness Model.

7. On your tables are samples of the Danielson Framework
On your tables are samples of the Danielson Framework. When you are looking at the components of the MDC you can clearly see as the days goes on that the MDC checks almost all of the buttons…teacher from our pilot…story
ADE/Learning Services/Nielsen

8. Distinguished Characteristics
Formative assessments are used to design future lessons.
Teacher invites students to explain content to classmates.
Students suggest other strategies.
Teacher uses student responses to deepen understanding.
Students extend discussion.
Students invite comments from classmates.
Students challenge one another’s thinking.
All students are engaged in discussion.
Students required to explain thinking.
Students have an opportunity to reflect on understanding.
Student understanding is monitored.
Students receive feedback from multiple sources.

9. Math Design Collaborative – Student Benefits
Allows students to see and talk about multiple representations of answers to the same problem. In doing so, it provides them with a different view they may have not thought of on their own.
Guides and develops them to work in teams to come up with a shared workable solution(s).
Students become risk takers persevering in problem solving to prove concepts to themselves and teammates. Strengthens 8 Mathematical Practices under PA Core.
Proven academic gains by students who have been exposed to the MDC framework.
So the teacher aspect of wanting these lessons is loud and clear…this training was full before I had a chance to exhale…but look what it can do for your students…we are asking them in the new core to be able to show more than one way to solve a problem…that does it for them. We are asking them to become 21st century learners – working collaboratively to apply math to real life situations…this does that form them. And bottom line is that it works and we have data to drive these statements.

10. MDC Spotlights Standards for Mathematical Practice
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.

11. Let’s get our Math Brains working!
Complete the “Counting Trees” problem as a sample of the kind of problems you would see within a MDC lesson.
Discuss how this type of problem could be used to meet the 8 SMPs.

12. MDC Spotlights Standards for Mathematical Practice
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.

13. Video: What is MDC?
We created a series fof videos and actually intend to add at least 3 more videos to the series. This is the first video that defines MDC
( think of your definition builder !)

14. A Quick Look at Formative Assessment
“Five Key Strategies”
Split article by sections at your table and read.
List one key phrase from each section
What did the Introduction and Conclusion say?
Share Out

15. Formative Assessment and Collaboration?
Quick Survey

16. So How Do We Do This ? In order to build a comprehensive framework for
formative assessment what do you need to keep in the forefront of your mind?
So How Do We Do This ?
Establishing where learners are in their
learning
2. Establishing where they are going
3. Establishing how to get there
Dylan Wiliam

17. The 5 Strategies of Assessment for Learning
Clarifying and sharing learning intentions and criteria for success
Engineering effective discussions, questions and learning tasks that elicit evidence of learning
Providing feedback that moves learners forward
Activating students as the owners of their own learning
Activating students as instructional resources for one another
Of these which number do you feel is a pivotal point ( quick talk at tables … hold up fingers to show which you feel is most important
yes, #3 if feedback is occurring the others will fall into place …. The important part above #3 the developing of high level questions you want answered and the clarification of your own goals for your students.
The important part about below #3 is that you put the ball back in the students’ court. The teacher also needs to set aside time for students to read, respond to, and act on on the feedback.

18. The five key ingredients are designed to ensure that students are engaged in a productive struggle with mathematics rather than on the receiving end of a lecture. Dr. Ann Shannon
This slide was revised from Leslie Texas’s presentation for SREB.

19. What does the research say about formative assessment ?
Read article and share out.
So how do you do this
Using the NCTM Articles -
Options : Jigsaw ( number 1 – 5 ) and share at your table
“Golden Word “ highlight and share out most important details
Tables create most important facts/AH-HA do a gallery walk or numbered head “share out

20. Video: Effect Size
Let’s listen to Geoff Petty’s explanation of effect size in reference to John Hattie’s research on effect size

21. John Hattie’s Effect Size
Influence
Effect Size
Source of Influence
Feedback
1.13
Teacher
Student's prior cognitive ability
1.04
Student
Instructional quality
1.00
Direct instruction
.82
Acceleration
.72
Remediation/feedback
.65
Student's disposition to learn
.61
Class environment
.56
Challenge of Goals
.52
Peer tutoring
.50
Mastery learning
To emphasize the importance of feedback during the formative phase of learning.
Click on link that will take you to the video explanation of the “effect size “ and then come back to the slide to talk

22. Research Shows Students benefit most from feedback that:
Focuses on the task, not grades or scores.
Is detailed rather than general.
Explains why something is right or wrong.
Is related to objectives.
Makes clear what has been achieved and what has
not.
Suggests what the students may do next.
Offers specific strategies for improvement.
Nothing Shell Laboratories creates and publishes is done without research and supporting data. Many of the lessons that we have used over the past 3 years have been in Alpha version. Data were collected concerning results from pre and post assessments to determine if the lesson was doing as intended; helping students make connections and better understand the mathematics. In each lesson, you will read HOW to enact the lesson and WHY it should be done this particular way. It is because of the research that Shell has created this order, sequence, etc. So, as we learn how to use these lessons in our classroom I encourage you to not make any changes to the lesson, at least not for the first 2 or 3 lessons you choose. After you have done as intended, you might want to do a little editing, but keep in mind that these lessons have gone through several hands, several edits, and have the research to support the reasons why.

23. Types of Formative Assessment
Short-cycle
Medium-cycle
Long-cycle
Use research article from NCTM in drop box (facts to add ) to support definition and understanding
Research to clarify the impact on Foramtive Assesment is by Wiliam and Thompson ( 2007)
Least effective is the long cycle that goes across the \marking periods – benchmark testing /interim tests
Medium are within and between units ( 1 to 4 weeks.)–cycle lessons
Short with in and between lessons and are day – by day …minute by minute
Medium and Short have a large effect size and
Conclusion --- In order to create a truly balanced assessment system that will propel student learning forward, we need to use formative assessments that are short, medium and long-cycle.

24. 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
NCTM brief supports slides on research
FALS fall in the medium cycle type

25. So in summary, What are “FALs”?
Formative Assessment LESSONS
Also referred to as “Classroom Challenges” on website
Well-engineered to uncover misconceptions
Complete
Teacher resources
Scripted
Aligned to CCSS
These Formative Assessment Lessons (also called Classroom Challenges) are very well engineered to uncover misconceptions students have about specific content; help students correct these misconceptions, and support teachers in using researched-based strategies and tools that have been deemed “best practices”. All lessons are aligned to the CCSS with a real focus on the standards of mathematical practice.
3/28/2011

26. Two Types of FALS Problem-Solving Concept- Development Think Standard
Think Cluster
I like the idea that this slide can connect you with content. When you are going thru a unit and you want to make sure they are grasping a specific skill you would use a concept development lesson. These lessons help a teachers formatively identify the skills they understand and the skills they are weaker in it will focus her attention on the remaining part of a unit.
A problem solving is more encompassing – it is used at the end of a unit or at a chosen time by a teacher to formatively assess whether students have retained a learned skill and can apply it to an everyday situation.

27. Two Types of FALs
Concept Development Lessons are meant to first reveal students’ prior knowledge, then develop students’ understanding of important mathematical ideas, connecting concepts to other mathematical knowledge.
Problem Solving Lessons are meant to assess, then develop, students’ ability to apply their mathematical knowledge and reasoning in flexibly ways to non-routine, unstructured problems – within mathematics and with real world applications.
Take time to read the descriptions and see what conclusions
Note key words

28. Concept Development Lesson
START:
Pre Assessment
Analyze student work - create questions - group students
Whole Class Introduction
Collaborative Activity
Whole class discussion
Post Assessment
Analyze student work for growth
Modify subsequent instruction
Concept Development Lesson
The Concept Development lesson is structured in the following way:
It occurs about 2/3 of the way through a unit
Before the lesson, students work individually on an pre-assessment designed to reveal their current understanding and difficulties.
You then review their responses and create questions for students to consider when improving their work.
After a whole-class introduction, students work collaboratively on a card matching activity.
Towards the end of the lesson there is a whole-class discussion.
In a follow-up lesson, students work alone on a post assessment similar to the introductory assessment

29. MDC in the Classroom

30. Concept Development Lesson
Frame the lesson and administer the pre-lesson assessment
Analyze student responses and write feedback questions
Introduce the lesson with whole class discussion
Facilitate the collaborative activity
Facilitate sharing and whole group discussion
Distribute feedback questions and administer the post-lesson assessment
Analyze growth across the pre- and post-lesson assessments
Modify subsequent instruction
Lets discuss these steps because each one is equally important but separate in the sequence

31. Teach ------ about 2/3 of the way into a unit
The Process – CD Lesson
Teach about 2/3 of the way into a unit
FAL
Teach remaining 1/3 with modifications of instruction to clear up identified misconceptions
I like the fact that this does occur after the lesson has begun…again, it is not taking away from your curriculum but in a way it is helping to identify perhaps a weakness in curriculum. Giving you a heads up to prevent a gap in learning. For the student, I like it because it should provide the student with some evidence of learning …it isn’t like the student is taking the pre-assessment from the start where he/she may not have any prior knowledge to work from.

32. Pre-Lesson Assessment
What do students know?
What are the misconceptions? (vs mistakes)
Where are the gaps in understanding?
How will I group students in order to support mathematical discourse?
How can I analyze this now and later to show growth?
This goes back to the Comprehensive Formative Assessment..giving you knowledge /evidence of what your students know.
Looking at their work and knowing if it is a misconception (or is it a mistake – to be easily taken care of by the student

33. Pre-Lesson Assessment (CD)
I am going to give you about 10 – minutes ( students get 15 minutes)to work on your own on this problem… Tell your students : do not worry about getting right answers ( read script from lesson)by the end of the next unit you should nbe able to answer this question with confidence !
When you finish use the formative assessment anticipation sheet to fill out areas where you feel your students would succeed and where they would need help….lets discuss what issues you see….
20 minutes Give sample packets out. Having partners look at papers and look for misconceptions – you can also identify mistakes. What questions can you create to guide their thinking ? Use post –its or write on pack if you want
Have partners do 3 pre-assessments. Using the index cards write the issues of all three pre-assessments as a list. When you hear one of the misconceptions from a group put a mark next to it…we want to see/hear the top misconceptions so we can create a data base of misconceptions so we can see how effective we have been pre- and post,.
Using doc camera…( numbers in a bowl (1,4,5 ) (4,2, 8) (1, 3,7) (3, 5,6) (7,6,2) (8,3,6)choose one more if time allows.
Just identifying where the student was having diffiuclty

34. Analyzing Student Work
Student Work Packet
Analyze 3 students
Write down at least 1 misconception.
Write down 1 question you would use to move student forward attempting to be guiding without pointing out an obvious answer.
Groups
1-2-3, 2-3-4, 4-5-6, 5-6-7, 7-8-1, 8-1-2

35. Purpose of Analyzing Student Work
To group students
Homogeneously in Concept Development Lessons
Heterogeneously in Problem Solving Lessons
To create feedback questions
Guiding students toward a deeper understanding
Moving students forward
To prepare for the lesson
Knowing what to listen for as students are working
What to address during the discussion
After this slide lets do the student samples
Assign three student pre- assessments
Discuss and show what the area is ( using the doc camera)
Who has a similar match ?

36. Analyze Pre Assessment. Prepare Feedback and Questioning.
Lets look at the common issues found in the manual…circle the ones you identified. Now look to the guided questions on the other side.
Using student samples at your table discuss and find 3 -4 main misconceptions or areas you need to keep in the forefront of your mind.
Discuss the impact identifying the misconceptions and providing questions INSTEAD of answers may have on your students

37. Data Analysis Template Listing Prominent Misconceptions

38. Data Analysis Charting Misconceptions

39. Grouping For concept development lessons For problem solving lessons
Homogeneous grouping
Partners for maximum interaction
For problem solving lessons
Heterogeneous grouping
According to different approaches to the problem providing students with multiple representations
Always try to use partners.
In problem solving the purpose is to be exposed to multiple representations so perhaps start in 2s move to 4s for sharing and preparing for whole class presentations.

40. Concept Development Lesson
START:
Pre Assessment
Analyze student work - create questions - group students
Whole Class Introduction
Collaborative Activity
Whole class discussion
Post Assessment
Analyze student work for growth
Modify subsequent instruction
Concept Development Lesson
The Concept Development lesson is structured in the following way:
It occurs about 2/3 of the way through a unit
Before the lesson, students work individually on an pre-assessment designed to reveal their current understanding and difficulties.
You then review their responses and create questions for students to consider when improving their work.
After a whole-class introduction, students work collaboratively on a card matching activity.
Towards the end of the lesson there is a whole-class discussion.
In a follow-up lesson, students work alone on a post assessment similar to the introductory assessment

41. Computer Games: Ratings
Imagine rating a popular computer game.
You can give the game a score of between 1 and 6.
Whole class introduction
Each FAL has projector resources

42. Bar Chart from a Frequency Table
Mean score
Median score
Mode score
Range of scores
Each teacher /partners have sheet to do ? Or follow along
And fill in as we go…lets fill it i( doc )

43. Whole Class Discussion
Score 1 2 3 4 5 6
Frequency 8
Mean score
Average (3.6)
Median score
Middle (4)
Mode score
Most (5)
Range of scores
H-L (5)
How many people scored ? Etc…

44. Concept Development Lesson
START:
Pre Assessment
Analyze student work - create questions - group students
Whole Class Introduction
Collaborative Activity
Whole class discussion
Post Assessment
Analyze student work for growth
Modify subsequent instruction
Concept Development Lesson
The Concept Development lesson is structured in the following way:
It occurs about 2/3 of the way through a unit
Before the lesson, students work individually on an pre-assessment designed to reveal their current understanding and difficulties.
You then review their responses and create questions for students to consider when improving their work.
After a whole-class introduction, students work collaboratively on a card matching activity.
Towards the end of the lesson there is a whole-class discussion.
In a follow-up lesson, students work alone on a post assessment similar to the introductory assessment

45. Collaborative Activity
Do the cards /match (20 min)
Collaborative Activity

46. Matching Cards
Each time you match a pair of cards, explain your thinking clearly and carefully.
Partners should either agree with the explanation or challenge it if it is unclear or incomplete.
Once agreed stick the cards onto the poster and write a justification next to the cards. (Recorder Sheet)
Some of the statistics tables have gaps in them and one of the bar charts is blank. You will need to complete these cards.
Provide “Recorder” sheet

47. Sharing Posters
One person from each group visit a different group and look carefully at their matched cards.
Check the cards and point out any cards you think are incorrect. You must give a reason why you think the card is incorrectly matched or completed, but do not make changes to the card.
Return to your original group, review your own matches and make any necessary changes using arrows to show if card needs to move.
Leave on tables…one person can leave to scout out and another person stays to defend their work..others may ask questions as they “scout” the room

48. Whole Class Discussion
Have a couple groups draw their filled in blank table from the card sort.
Which cards were the easiest to match? Why?
Which cards were difficult to match? Why?
What strategies did you use?

49. Providing Feedback as Activator
Return pre lesson assessment with questions.
Generate general list of questions to post using projector.
Staple “Suggested Questions” to pre lesson assessment.

50. Feedback Examples

51. Post-Lesson Assessment
Give student samples of post to compare with pre assessment

52. Post Lesson Analysis Look at “Post” packet.
Take a quick look at the same students you had earlier.
Compare the last problem for all.
Was progress made?

53. Change in Instruction Based on Evidence
Give view of data and growth. Explain that data sheets with excel formula is on SAS site which we will go to after our break

54. What are the resources that are being provided to help us succeed?

55. Join SAS Community PA Mathematics Design Collaborative
See “PDE SAS - PA Mathematics Design Collaborative Community” direction sheet.
Link to PDE SAS
Follow directions on sheet to take through website.
There are 8 copies on table if you are not a member
I will take those that are members and you can watch…to follow

56. Join PA-MDC Listserv
From the that you would like to use to subscribe, create a new to .
You can leave the subject line blank.
In the body of the type “sub PA-MDC”.
You will receive a confirmation . Click link within that to send request for approval.
If you want to hear what is going on through out the state or pose questions.
Distribution List of MDC Participants

57. Formative Assessment Lesson Resources
(map.mathshell.org)
The Mathematics Assessment Project (MAP) aims to bring to life the Common Core State Standards (CCSSM) in a way that will help teachers and their students turn their aspirations for achieving them into classroom realities.
The materials from this project exemplify CCSSM in explicit down-to-earth performance terms.
MAP is a collaboration between the University of California, Berkeley and the MARS Shell Center team at the University of Nottingham. MARS, the Mathematics Assessment Resource Service, is an international collaboration dedicated to the improvement of assessment.
Explore  Lessons, Tasks, Professional Development
ADE/Learning Services/Nielsen

58. MAP Website Organization
Tabs for Lessons and Tasks
Search by Grade
Organized by Problem Solving or Concept Development

59. MAP Website Organization
MDC uses formative assessment lessons (FALs) from MAP to engage students in a productive struggle that builds fluency with their procedural skills and deepens mathematical reasoning and understanding.
Students participate in both individual and group learning as teachers use FALs and questions to check for students’ math understanding and correct common misunderstandings.
Rather than following predetermined steps to find an answer, students are supported to deepen their math reasoning to solve problems

60. MAP Website Organization

61. Explore Website Refer to PA Core Alignment Guide.
Look through some lessons at your grade/course level.
What do you see that you like?
What questions do you have about the lessons?
What’s missing?

62. What still needs answered, questions from the day?
Thank you!
See you tomorrow!
If your head is spinning and you need clarification on anything covered this day please ask and we will review tomorrow
If you have no questions…then suggestions or take- aways would be appreciated