1. Joan Gillis, Capital Area Intermediate Unit
Modeling: Mean, Median, Mode, & Range (Concept Development Lesson)
Joan Gillis, Capital Area Intermediate Unit
Dan Richards, Berks County Intermediate Unit

2. Formative Assessment Lessons Improving Lessons Through Questioning
MDC Training
Formative Assessment Lessons
Improving Lessons Through Questioning

3. Concept Development Lessons In a nutshell
Existing interpretations of concepts are shared and systematically explored
Formative assessment exposes students’ existing ways of thinking
New ideas are constructed through collaborative activities and through reflective discussion
Intended to assess and develop students’ understanding of fundamental concepts through activities that engage them in
Classifying and defining
Representing concepts in multiple ways
Testing and challenging common misconceptions
Exploring structure

4. Concept Development Lessons help students and teachers realize the CCSSM requirement that “Proficient students expect mathematics to make sense.”
These lessons are designed to reveal misconceptions and develop students’ conceptions of significant mathematical ideas and how these connect to their other knowledge.
Frame the lesson

5. Pre-Lesson Assessment
Take about 15 minutes to complete these questions alone.
Pull up samples of student work previously sent

6. Identifying Misconceptions
Use an Excel spreadsheet to record student misconceptions.
This spreadsheet will be used to analyze growth between pre-lesson assessment and post-lesson assessment

7. Whole Class Introduction
Slides are provided as a resource from MAP-Shell

8. Mean, Median, Mode, and Range
Projector Resources

9. Computer Games: Ratings
Imagine rating a popular computer game.
You can give the game a score of between 1 and 6.

10. Bar Chart from a Frequency Table
Mean score
Median score
Mode score
Range of scores
This is an introduction to the collaborative activity.
Be careful NOT to teach. This is a time to let students know what to expect during the collaborative activity, not reteach content.

11. 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.
Some of the statistics tables have gaps in them and one of the bar charts is blank. You will need to complete these cards.
I expect to hear from each of you during this activity. It is important to discuss what you are doing and how you are determining the match. Take turns and think out loud.
For teachers: It is not necessary for everyone to finish; not necessary to correct everyone, for all work to be correct
To extend thinking, have early finishers create another graph for B12, or for another statistic card, which will yield the same results.

12. 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.
One stays and one travels. The one who stays must be prepared to defend your matches. If there are discrepancies, discuss but don’t feel pressure to make changes. You might be correct.

13. Post Lesson Assessment
Very similar to pre-lesson assessment
Easy to compare to determine growth
Students should have copies of feedback questions
Allow about 15 minutes to complete

14. Analyzing Growth
Order; pre and post together; different colored paper makes for ease
Remember to discount mistakes if identifiable
Looking for true misconceptions or gaps in understanding
1 or X is used to denote evidence of the misconception
0 indicates student does not exhibit evidence of the misconception

15. Concept Development Lesson
Frame the lesson
Pre-lesson assessment
Analyze student responses
Write feedback questions
Introduce the lesson
Facilitate the collaborative activity
Facilitate the plenary (whole group discussion)
Distribute feedback questions
Post-lesson assessment
Analyze growth across the pre- and post-lesson assessments
Modify subsequent instruction
Framing the lesson – Micah Hoyt, East Hall HS, 1
Whole Class Introduction – Linda Phelps, Lowndes County HS, 3
Plenary Discussion – Linda Phelps, Lowndes County HS, 8
Post-lesson Assessment – Micah Hoyt, East Hall HS, 9
Pages 8 – 29: Handouts concerning Concept Development Lessons
Look at these later at your own convenience