CONCEPT DEVELOPMENT LESSONS Region 5 Mathematics Network Conference September 16, 2013

 How can I help students develop a deeper understanding of mathematics?

Formative Assessment Lessons  The Formative Assessment Lessons, also called Classroom Challenges, are of two types; those that focus on the development of conceptual understanding and those that focus on problem solving.

Why Use Classroom Challenges?  Research has shown that formative assessment, as embodied in the Classroom Challenges, is a powerful way to improve student learning and performance. This approach first allows students to demonstrate their prior understandings and abilities in employing the mathematical practices, and then involves students in resolving their own difficulties and misconceptions through structured discussion. This results in more secure long-term learning, reducing the need for re- teaching that otherwise takes so much classroom time.

Concept Development Lessons  Concept Development lessons are 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 and exploring structure.

Problem Solving Lessons  Problem Solving Classroom Challenges 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.

Why Use Classroom Challenges?  Research has shown that individual, routine practice on standard problems does little to help students deepen their understanding of mathematical concepts. Teaching becomes more effective when existing interpretations (and misinterpretations) of concepts are shared and systematically explored within the classroom.

Key Differences  Formative assessment involves a change in “classroom culture” – with teachers and students moving into rather different roles from those common in most classrooms: Students take more responsibility for, their own work. Students engage in “productive struggle” with rich challenging tasks. Resolution comes only gradually through interactions and discussion in the lesson as students gain new facets of connected understanding.

Key Differences Students study fewer tasks, but in greater depth. They are asked to draft solutions, compare their approaches to others and redraft their ideas as a result of their discussions. The teachers’ role is to prompt students to reflect and reason through their ideas. Teacher questioning is central to support students’ thinking and depth of knowledge, and student growth. The teacher’s role is not to provide answers and solutions..

Classroom Shifts  One way to shift practice, as described in the CCSS, is to begin by inserting occasional rich lessons such as Classroom Challenges.  These lessons are designed to support these shifts with specific guides for each lesson. Teachers have found the Lesson Guides helpful and supportive in their efforts to implement formative assessment lessons and the CCSS mathematical practices and to expand their pedagogy and practice.

Classroom Challenges  Classroom Challenges described here typically begin with a formative assessment task that exposes students’ existing ways of thinking.  The teacher is then offered specific suggestions on how these may be challenged and developed on through collaborative activities.  New ideas are constructed through reflective discussion.

Challenges  Each Classroom Challenge is preceded by an introductory assessment task.  The purpose of this is to discover the interpretations and understandings that students bring to this particular area of mathematical content.  This task is given to individual students a day or more before the main lesson and the information gathered from student responses are then used to plan and direct the lesson.

Your Turn  Let’s try this one!