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

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

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

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

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

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

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

Mean, Median, Mode, and Range Projector Resources

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

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.

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.

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.

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

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

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