1. Elementary PA-Math Design Collaborative Day One.
Joan Gillis, CAIU Josh Hoyt, IU 14

2. JOAN Introductions • Name
• District
• Three numbers
Inside of the card : If math were a color what color would it be – and why ?
JOAN
CAIU 15
3, 18, 26

3. Goals of Day One
How can a teacher of mathematics connect the different math practices with the content standards to guide student growth and achievement toward proficiency?
What does true formative assessment look and sound like in a classroom?
What is the Math Design Collaborative and how does it support the key elements of math instruction and formative assessment?

4. What does this remind you of…

5. Table Talk What is the purpose of starting with this video?
How is it relative to the objectives of the training?

6. Define Proficiency …
To be proficient in the Core what do students need to know how to do, mathematically?

7. 5 Essential Strands

8. conceptual understanding—comprehension of mathematical concepts, operations, and relations
procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
strategic competence—ability to formulate, represent, and solve mathematical problems
adaptive reasoning—capacity for logical thought, reflection, explanation, and justification
productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

9. As a teacher I can … conceptual understanding procedural fluency
strategic competence
adaptive reasoning
productive disposition
modeling, mapping, building vocabulary
detect errors, peer-coaching, mental math, Math 24
teaching strategies, talking about math / restating ideas
organized -logic, presenting, convince me that you’re right
CAN DO MATH ! “I can…”statements

10. Round Table :”Think and Say”
All 5 components or strands are interdependent
All 5 strands are identified as essential for all students
All 5 strands must be included in math instruction at all grade levels
The 5 strands provide a way to organize
math instruction
All strands can be matched with specific student instructional skills

11. Common Core State Standards for Mathematical Practice
Make sense of ______ and ______in solving them.
2. Reason ________ and ________.
3. Construct viable _____ and critique the _____ of others.
4. _____ with mathematics.
5. Use appropriate tools _______.
6. Attend to _______.
7. Look for and make use of _______.
8. Look for and express _____ in ______ reasoning. (

12. Common Core State 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. Illustrative Math Bill McCallum
- Practice Standards by grade levels
provides explanation, tasks, videos, and answer keys
- Content Standards by grade levels give Common Core tasks related to grade level

14. Cooperative Learning Activity
Match your puzzle-piece with other similar pieces to form a problem to solve.
As a learning group team, select a strategy to solve the problem.
Solve the problem as a team then submit a solution to the class. Your team must be able to justify the solution!!!

15. Common Core State 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. (

16. EQ 1 How can a teacher of mathematics connect the different math practices with the content standards to guide student growth and achievement toward proficiency?

17. #2 What does true formative assessment look and
#2 What does true formative assessment look and sound like in a classroom ?
Write your definition of Formative Assessment.
( individually )
(As a group) Generate a list key terms that come to mind when you think of Formative Assessment.
Share ( WHIP Strategy)
Do you want to amend your definition ?

18. The Big Idea of Assessment for Learning
Students and teachers
Using evidence of learning
To adapt teaching and learning
To meet immediate learning needs
Minute‐to‐minute and day-by-day
(Thompson & Wiliam, 2007)

19. 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

20. Types of Formative Assessment
Short-cycle
Medium-cycle
Long-cycle

21. 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

22. The Golden Rule .

23. The Five Strategies of Assessment for Learning
1. Clarifying and sharing learning intentions and criteria for success
2. Engineering effective discussions, questions and tasks that elicit evidence of learning
3. Providing feedback that moves learners forward
4. Activating students as the owners of their own learning
5. Activating students as instructional resources for one another
(Thompson & Wiliam, 2007)

24. Productive Struggle
“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.” (Shannon, 2011)

25. What does the research say about formative assessment ?
… all those activities undertaken by teachers, and by their students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet the needs.
William/Black

26. 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

27. Not All Feedback is Created Equal

28. 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.

29. #2 What does true formative assessment
look and sound like in a classroom ?

30. Prep for the first mdc lesson – have pre-assessment on tables for after lunch

31. #3 What is the Math Design Collaborative and how does it support the key elements of math instruction and formative assessment ?

32. What is MDC?
The Math Design Collaborative is a national initiative that is working to design and develop well-engineered lessons and assessment tools to support US schools in implementing the Common Core State Standards for Mathematics (CCSS).
“The materials from this project will exemplify CCSS in explicit down-to-earth performance items.”

33. 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.

34. 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.

35. Video: What is MDC?

36. 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.

37. 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.

38. ADE/Learning Services/Nielsen

39. Classroom Challenges Formative Assessment Lessons “FALs”

40. What are “FALs” Formative Assessment Lessons are:
Complete, scripted, well-engineered lessons designed to uncover misconceptions using pre-assessments and hands-on activities.
Free Teacher Resources
Aligned to CCSS
3/28/2011

41. Formative Assessment Lessons
Purpose of FALs
Formative Assessment Lessons
To inform the teacher
To inform the students
To identify misconceptions
To provide feedback
To guide further instruction
To engage students
To encourage deeper thinking
To make sense of math

42. Two Types of FALs Classroom Challenges
Concept Development
(standard)
Problem Solving
(clusters)

43. Problem Solving Lesson
START:
Pre Assessment
Analyze student work - create questions - group students
Students reflect individually to questions
Collaborative Activity
Students evaluate, comment, compare sample responses
Whole Class Discussion
Self reflection /Review
Modify subsequent instruction
Problem Solving Lesson

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

45. Teach ------ approximately 2/3 of unit
CD Lesson The Process
Teach approximately 2/3 of unit
FAL
Teach remaining 1/3 with modifications of instruction to clear up identified misconceptions

46. Steps to Concept Focused Lesson…
OCT 2011 SESC Math Network Meeting
Students work solo on pre-assessment task.
Teacher takes up work and provides class feedback and intentional grouping of students.
Students work in collaborative groups – usually a card sort type.
Teacher facilitates groups, takes notes, asks questions to whole class or groups (engineers effective discussion)
Students revisit original task to revise.

47. 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?

48. 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 plenary (to revisit)

49. Grouping For concept development lessons For problem solving lessons
Homogeneous grouping
Partners for maximum interaction
For problem solving lessons
Thoughtful grouping
According to different approaches to the problem providing students with multiple representations

50. Why group homogenously ?
Video is from Gatefoundation.com
Video library ( 5 minutes)

53. Translating between Fractions, Decimals, and Percent's
Projector Resources
Intro is on T-5 They can follow along / or just summarize
Explain they will not have 40 minutes for the activity and that it is only a chance to sample the activity

54. Working Together 1 Take turns to:
Fill in the missing decimals and percents.
Place a number card where you think it goes on the table, from smallest on the left to largest on the right.
Explain your thinking.
The other members of your group must check and challenge your explanation if they disagree.
Continue until you have placed all the cards in order.
Check that you all agree about the order. Move any cards you need to, until everyone in the group is happy with the order.
(5 min) card A,

55. Working Together 2 Take turns to:
Match each area card to a decimals/percents card.
Create a new card or fill in spaces on cards until all the cards have a match.
Explain your thinking to your group. The other members of your group must check and challenge your explanation if they disagree.
Place your cards in order, from smallest on the left to largest on the right. Check that you all agree about the order. Move any cards you need to, until you are all happy with the order.
Simply follow the guided script for the activity.
B)Area card – this card is purposely placed in this slot most students forget the area representative.
C) Fractions
D) Scales
Point out the blank cards.
Also explain the importance of sharing ( using each other as a tool/resource)
Reflection from where they were to where they are ( pre- and post –assessment)

56. Grade Level FALS
In folders are Concept Development lessons relating to fractional concepts for grades 3 – 5
Look through the lessons and note how they build
upon grade level knowledge and implement formative
assessment
5 minutes on your own
10 minutes comparing with your table

57. #3 What is the Math Design Collaborative and how does it support the key elements of math instruction and the use of formative assessment ?
MDC provides teachers with formative assessment lessons (FALs) that have been strategically designed to provide teachers with formative assessment data and opportunities for feedback while engaging students in a productive struggle that builds procedural fluency and deepens mathematical reasoning and understanding.

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

59. 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
There are folders marked elementary mdc that will have lessons gathered with PA Core Standards listed. videos to remind you of the steps…tomorrow Day 2 you will have time to explore and choose a lesson to implement.

60. Formative Assessment Lesson Resources
(map.mathshell.org)
These lessons are geared for middle school but I honestly feel that some of these could be done by your students.
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

61.
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

62. Problem A

63. Problem A Answer

64. Problem B

65. Problem B Answer

66. Problem C

67. Problem C Answer

68. Problem D

69. Problem D Answer

70. Problem E

71. Problem E Answer

72. Problem F

73. Problem F Answer

74. Problem G

75. Problem G Answer

76. Problem H

77. Problem H Answer
6 to 7 pounds—No juice bottles 10 to 11 pounds—3 juice bottles 14 to 15 pounds—4 juice bottles

78. Problem I

79. Problem I Answer

80. Problem J

81. Problem J Answer
Link to slide