### Concept development and Problem Solving

```Formative Assessment Lessons
Stephanie Finn, Paulding County
 Amy Lundy, Jones County
 Kami Wyse, Hall County
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Commonalities
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2/3 of the way through the unit.
Pre-assessment/Post assessment
Teachers give feedback to pre-assessment
Students are paired based on preassessment performance
Accessible to ALL students
Make effective use of Standards for
Mathematical Practice
Concept Development
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Concept Development lessons are
intended to assess and develop a
students’ understanding of fundamental
concepts through activities that engage
them in classifying and defining,
representing concepts in multiple ways,
testing and challenging
misconceptions and exploring
structure.
Genres of Concept Development
Lessons
Classifying mathematical objects
 Interpreting multiple representations
 Evaluating mathematical statements
 Exploring the structure of problems
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Structure of Concept
Development Lessons--Student
individually
 Whole class introduction
 Collaborative work on a substantial
activity
 Students share their thinking
 Students revisit the assessment task
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Structure of Concept
Development--Teacher
 Planning
the lesson
 Analyze the pre-assessment and
offer feedback
 Students will be grouped based
on COMMON misconceptions
 Whole group introduction
Structure of Concept
Development--Teacher
 Facilitate
 Facilitate the sharing of work
 Whole group discussion
 Give feedback questions
 Post-Assessment
 Analyze post-assessment
Mistakes and Misconceptions
Why do students make mistakes in
mathematics?
 What different types of mistakes are
there? What causes these mistakes?
 How do you respond to each different
type of mistake? Why?
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Grouping based on…
the pre-assessment
 Look for common misconceptions
 This helps students get what they need
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Problem Solving
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Problem Solving FALs are intended to
assess and develop students’ capacity
to select and deploy their mathematical
knowledge in non-routine contexts and
typically involve students in comparing
and critiquing alternative approaches
to solving a problem.
Structure of Problem Solving
Lessons--Students
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 “Having Kittens” Activity
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Whole class introduction
Reflect on feedback question individually
Collaborative work with a student whose
approach is different
 The collaborative pair will work to create a third
solution that is even better
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Checking posters
Sharing of work
Review sample work
Structure of Problem Solving-Teachers
Planning & Preparation Framing the task
 Analyze the pre-assessment and give feedback
 Whole class introduction
 Analyze student work
 Allow students to
reflect on feedback
questions and improve
their own work
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Structure of Problem Solving-Teachers
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Facilitate collaborative work
 Students are paired based on different
Facilitate the sharing of work
 Whole group discussion
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 Sharing sample work
Give the post-assessment
 Analyze post-assessment responses
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Grouping
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Students are to be grouped based on
different approaches to reaching a
solution
Allow students time to understand and
engage with the problem
 Offer strategic rather than technical hints
 Encourage students to consider
alternate methods and approaches
 Encourage explanation
 Model thinking and powerful methods
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Differences
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Intended to assess and
develop understanding of
fundamental concepts
Feedback given after
Students are grouped
based on common
misconceptions from preassessment.
Concept Development
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Intended to assess and
develop capacity to
select and deploy
mathematical knowledge
in non-routine context
Feedback given as part
Students are grouped
based on different
strategies.
Problem Solving
Ability Levels and FAL’s
Personal Experiences
Personal Experiences
Amy Lundy’s Benchmark Scores–
Powerful Data Results
1st Nine Weeks
2nd Nine Weeks
3rd Nine Weeks
83%
79%
93%
Without FAL
Without FAL
Using FAL
```