1. Welcome to BCIU 14 District Rollout
Day Two
Amy Martell, Intermediate Unit 17
Created by: Dan Richards & Rebecca Chadwick
Berks County Intermediate Unit

2. Let’s get our Math Brains working!
Complete Individually
Having Kittens or Security Camera
As a table, discuss.
Prepare a poster to present your solution and explanation.

3. Welcome Back! http://goo.gl/YLdcVe
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
Comments are great – if you joined the listserv you received the power point..I do not give them out on presentation days because …its like giving an answer sheet to the problem you are presenting …focus
Time in the afternoon will be devoted to the site and to setting up calendars and choosing which lesson you want to start with

4. Goals for Day 2 How does a Problem Solving FAL differ from a
Concept Development FAL?
What are the benefits to non-routine problem solving?
Develop an action plan and determine IU support.

5. Let’s Review
As a table group, put the steps of a Concept Development Lesson in the correct order.

6. 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

7. 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’ capacity to apply their mathematical thinking flexibly 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
Structured or unstructured activity possible dan meyer ted talk

8. What makes this word problem so structured ?
Organizing a Table Tennis Tournament
( print out handouts) from professional development problem solving book
This is a typical math problem it is structured because…. For example, in Organizing a table tennis tournament, students are told:
Notice the difference ( fllip page over and have the unstructured problem on the back.
How to code the players (A, B, C…).
To list all the matches that need to be played.
How to systematically organize these matches.
How to tabulate the order of play.
To remember that players cannot play on two tables at once.
It gives you the amount of players…it gives you the information to label players with letters… it gives

9. Is this better? If so, why?

10. VIDEO Lets Watch the teacher from England organize her
students for the Unstructured Tennis tournament
Found in shell site /professional development problem solving
This video was quite good – I liked how the teacher framed the lesson
I liked how she demonstrated how important it is to move around the room – one group had 3 in it and two could identify their roles and the 3rd could not – she addressed that.
She also shows how the lesson progresses from individual to partners to group of 4

11. Now it is time to look more closely at the other FAL:
Problem Solving

12. 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
Modify subsequent instruction
Problem Solving 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

13. Steps of a Problem Solving Lesson
Frame the lesson and administer the pre-lesson assessment
Analyze student responses and write feedback questions
Distribute the feedback questions and responses to the pre-lesson assessment
Students reflect individually to questions
Facilitate students working collaboratively on the problem
Facilitate whole group discussion
Students evaluate, comment, and compare sample responses
Administer the student reflection sheet
Modify subsequent instruction

14. Benefits of Problem Solving Lessons
Students are sharing ideas, communicating/explaining methods
Exposed to multiple approaches
Exposed to unique, non-routine problems
Required to analyze students’ work
Required to diagnose others’ errors and misconceptions
Required to make decisions about best method
Before showing them see if the group can make a quick list of their own…
Can you add to the list…

15. Some immediate issues that teachers raise are:
Unstructured problems are more difficult.
It is more difficult to plan a lesson with these problems.
Students may not even know how to get started on them. Will we therefore need to structure them anyway?
Students will not necessarily use what we have taught them.
If we offer help too quickly, students will simply do what we say and not think for themselves.
Students will generate a greater variety of approaches and solutions.
Students may need reassurance that it is OK to try a different approach or reach a different
conclusion.
So reactions from teachers have been….what can you say to assuage the reactions ?
Good discussion again …hearing others help answer these thoughts

16. Framing the Lesson (Concept Development or Problem Solving)
Give each student a copy of the assessment task.
It is important that, as far as possible, students are allowed to answer the questions without your assistance.
Read through the questions and try to answer them as carefully as you can.
Students should not worry too much if they cannot understand or do everything, because in the next lesson they will work on a similar task, which should help them. Explain to students that by the end of the next lesson, they should be able to answer questions such as these confidently. This is their goal.

17. Gold Rush (Pre Lesson Assessment)
Before the lesson, students attempt the Gold Rush task individually. You then look at their responses and formulate questions for students to think about as they review their work.
At the start of the lesson, students reflect on their individual responses and use the questions posed to think of ways to improve their work. Next, students work collaboratively in small groups to produce, in the form of a poster, a better solution to the Gold Rush task than they did individually.
In a whole-class discussion students compare and evaluate the different methods they used.
Working in small groups, students analyze sample responses to the Gold Rush task, then, in a whole-class discussion, review the methods they have seen.
Finally, students reflect on their work.
Have individual work on it ( collect and wrtie questions)
Have partner work on it
Have table work on it for final decision

18. Analyzing Student Work
Choose 1 Misconception.
Write 1 Guiding Question.
Share Out.
Groups

19. Data Analysis – Option 1

20. Data Analysis – Option 2
What misconceptions/issues did you observe from the pre assessment class data?
What strategies did you observe your class using to solve the problem?
What needs will you address moving forward with this content or problem solving?
How will I group the students?

21. Feedback Questions
Based upon your work, I have developed some questions to help you improve your first efforts.
1. What does the rope represent, mathematically?
2. Did you create several different size plots using the same rope?
Is that enough to convince someone of your answer?
Show me how you represented this information.
3. Suppose 3/4/5/or more prospectors share land. What area of land would each prospector get? How do you know?
4. How did you organize your efforts? Can someone who did not work the problem understand what you did?
Did not need this

22. Why Ask Questions? To interest, engage, and challenge
To assess prior knowledge
To stimulate recall
To focus on important concepts
To help students extend their thinking
To promote thinking, problem solving, hypothesizing
Let’s talk about Questioning for a few minutes
(These slides were created based upon handouts from the “Improving Learning Through Questioning” module under the Professional Development tab from the Shell website:

23. Questioning Mistakes We Make
Ask irrelevant questions
Ask and answer yourself
Simplify for immediate response
Ask only capable students
Ask only closed, one-answer questions
Judge every response
Not allowing time to think
Ignore incorrect answers and move on
1. Be sure the questions have an intent to clarify or stretch thinking.
If you ask a question, expect an answer from your students.
Don’t make the questions too simplistic for the sake of brevity.
Using white boards gives you an opportunity to look for variety in answers and to call on a variety of students; not just the ones who always answer.
There are many ways to approach a problem, and in some cases, many different answers. Listen.
But don’t judge every response. You can always ask someone if they agree, why or why not.
Allow think time.
Again, use other students to provide input or feedback. This opens the door for discussion and gives all students an opportunity to rethink their response.

24. Effective Questioning
5 Characteristics of
Effective Questioning
Plan to use questions that encourage thinking and reasoning
Ask Questions in ways that include everyone
Give students time to think
Avoid judging students’ responses
Follow up students’ responses in ways that encourage deeper thinking
video
The 5 Characteristics or Principles for Effective Questioning are expounded upon of pages 4 – 6. Let’s take a look.
Share Time ----at you table
Share some of these that you feel you already use effectively.
Share some of these that you feel you need to work on to make your questioning more effective.
Does anyone want to share with the whole group?

25. Tips for Effective Questioning
Remember wait time: Provide at least three seconds of thinking time after a question and after a response
Utilize “think-pair-share.”
Ask “follow-ups” (Why? Do you agree? Can you elaborate? Can you give an example?)
Withhold judgment: Respond to student answers in a non-evaluative fashion.
Require students to defend their reasoning against different points of view.

26. Tips continued …
Ask for summary (to promote active listening) “Could you please summarize John’s point?”
Survey the class “How many people agree?” (“thumbs up, thumbs down”)
Allow for student selection: “Richard, will you please call on someone else to respond?”
Call on students randomly. Not just those with raised hands.
Play devil’s advocate

27. Collaborative Activity Preparing a Joint Solution
Review feedback questions individually and think about how you would possibly change your answers.
Discuss with your shoulder partner your strategies/methods and reasoning for solving the problem.
You and your partner will join two others to discuss and plan a presentation.
Create poster and share out.
Used chart paper
Teacher list was really thoughtful
Graph paper, scissors, string, geoboards, calculator

28. Planning a Joint Method
Take turns to explain your method and how you think your work could be improved.
Listen carefully to each other.
Ask questions if you don’t understand.
Once everyone in the group has explained their method, plan a joint method that is better than each of your separate ideas.
Make sure that everyone in the group can explain the reasons for your chosen method.
Write a brief outline of your method on one side of your sheet of paper.
Approximately 35 minutes
20 for teachers
This is similar to what we did with the Goldrush Question
This was similar to what we did ( just don’t think it should be titled “joint method”

29. Evaluating Student Sample Responses
Imagine you are the teacher and have to assess the student work.
Work through a students’ solution.
Write your answers on your mini-whiteboards.
Explain your answer to the rest of the group.
Listen carefully to explanations.
Ask questions if you don't understand.
Once everyone is satisfied with the explanations, write the answers below the student’s solution.
Make sure the student who writes the answers is not the student who explained them.
Student directions
Teachers pulled up computers and did look at this …we all like the idea of error analysis
6. Work through each response using this protocol.

30. Ann’s method
What questions would you write as feedback to help Ann move forward in her thinking?
Where did you join the ropes?

31. Jake’s method

32. Kodie’s method

33. Mark’s method

35. Problem Solving FAL Alternate to Class Data Summary Spreadsheet

36. Creating Better Problems – Removing Structure - Dan Meyer
Watch and discuss the Dan Meyer video
Click on the icon to view the video.
NOTE: If you have time to extend the presentation:
A scale drawing of a very small object is larger than the object. The scale of the drawing is 2 cm:14 mm. Find the unknown measure (in cm).
width of object = 70 mm; width on drawing =  ? 
Use Dan Meyer’s problem example.
Take a drawing and scale it for a mural.
What content standard is addressed (comparing fractions, ratios, proportion, scale drawing)?
What practices standard(s) is addressed in your problem?
Take this traditional problem and change it to a problem that addresses both content and practice?
How?
Why would you want to?

37. Let’s Compare the 2 Types of Lessons Concept Development / Problem Solving
Read 2 page excerpt from “Guide”.
When do you use them?
How often do you use them?
Are grouping strategies the same?
What are the typical activities used in each?
Are the post lesson assessments the same?
When are feedback questions provided?

38. MDC and Teacher Evaluation
Focus on Domain 3 and highlight statements/areas that you feel FALs used under MDC would provide evidence to support a teacher meeting that criteria.
What did you find?

39. Pilot Comments Teacher Administrator
“With MDC lessons, I almost feel like I’m cheating the system.”
Administrator
“I did back to back observations one day with one teacher using a MDC lesson and the other teaching another typical lesson per the curriculum. The differences noticed based on the rubric were remarkable. The teacher using the MDC lesson scored significantly higher.”

40. Goals for Day 2 How does a Problem Solving FAL differ from a
Concept Development FAL?
What are the benefits to non-routine problem solving?
Develop an action plan and determine IU support.

41. Challenges and Logistics
Based on what you’ve seen in the training, discuss at your table what challenges you may face at your district.
Discuss how you might overcome them.
Share out.

42. Things to Consider Time Planning/Co-Planning Acquiring Materials
Preparing Materials
Classroom Management
Physical Structure of Classroom
Curriculum Alignment
Having a positive discussion on ways to overcome this was great and encouraging

43. Expectations for Implementation
Now to October 27
Plan and implement 1 lesson for 1 section/class.
Materials Preparation
Invite to assist with planning or observation.
Other onsite assistance as needed.
Data Chart with 15+ students.
Student Samples
Reflection Survey
On-Site Visit (structure) /

44. Sketching Out Possibilities
Review MDC lessons and district curriculum to decide what lessons would fit in the near future.
Use Calendar Planner to sketch out upcoming months
Use PA Core Alignment
Discuss with district team and/or grade level groups in and out of district.

45. Choosing Your First Lesson
Select a lesson that you will implement prior to the next group meeting.
Lesson Selection Form/Request for Materials
I originally was giving a ½ hour but they were so purposeful and so on track exploring their lessons and deliberately choosing their FAL that we went for over 45 minutes

46. Preparing for Your Lesson
Pull copy of your lesson from binder or ask to have it printed.
Read through the steps of the lesson.
Questions for me?
Complete Pre Lesson Assessment.
Complete Formative Assessment Anticipation Guide.
Determine copies needed.
Will any manipulatives assist in the lesson?

47. Workshop Evaluation Contact: Amy Martell amartell@iu17.org ©
ext 2214 (w)