CONCEPT DEVELOPMENT
AND PROBLEM SOLVING
Formative Assessment Lessons
Stephanie Finn, Paulding County Amy Lundy, Jones County Kami Wyse, Hall County
Formative Assessment Lessons
Concept
DevelopmentProblem
Solving
Commonalities 2/3 of the way through the unit. Pre-assessment/Post assessment Teachers give feedback to pre-assessment Students are paired based on pre-
assessment performance Not graded Accessible to ALL students Make effective use of Standards for
Mathematical Practice
Concept Development
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
Structure of Concept Development Lessons--Student
Students complete an assessment task individually
Whole class introduction Collaborative work on a substantial
activity Students share their thinking Students revisit the assessment task
Structure of Concept Development--Teacher
Planning the lesson Framing the task Analyze the pre-assessment and
offer feedback Students will be grouped based
on COMMON misconceptions Whole group introduction
Structure of Concept Development--Teacher Facilitate the task, asking questions 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?
Grouping based on…
Mistakes and misconceptions made on the pre-assessment
Look for common misconceptions This helps students get what they need
from the task
Problem Solving
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 Complete an assessment task individually
“Having Kittens” Activity Whole class introduction Reflect on feedback question individually Collaborative work with a student whose approach is
differentThe collaborative pair will work to create a third solution
that is even better Checking posters Sharing of work Review sample work Revisit the assessment task
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
Structure of Problem Solving--Teachers Facilitate collaborative work
Students are paired based on different approaches to the assessment task
Facilitate the sharing of work Whole group discussion
Sharing sample work Give the post-assessment Analyze post-assessment responses
Grouping
Students are to be grouped based on different approaches to reaching a solution
Practical Advice
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
Differences
Concept Development Problem Solving
Intended to assess and develop understanding of fundamental concepts
Feedback given after task but before post-assessment
Students are grouped based on common misconceptions from pre-assessment.
Intended to assess and develop capacity to select and deploy mathematical knowledge in non-routine context
Feedback given as part of task
Students are grouped based on different strategies.
Ability Levels and FAL’s
Personal Experiences
Personal Experiences
1st Nine Weeks 2nd Nine Weeks 3rd Nine Weeks
83% 79% 93%
Without FAL Without FAL Using FAL
Amy Lundy’s Benchmark Scores– Powerful Data Results
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