Concept development and Problem Solving

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