Joan Gillis, Capital Area Intermediate Unit What is MDC? Joan Gillis, Capital Area Intermediate Unit Dan Richards, Berks County Intermediate Unit

Goals for Session What is the Math Design Collaborative? What resources are provided? What is the structure and function for lessons provided?

Defining MDC (Mathematics Design Collaborative) Take the 5 x 7 index card on your desk and create a definition of MDC as you know it now. (sentences, bullets, etc.) It is completely fine to leave it blank. As we move through the next 2 days, please add and edit information to this card that you find important. At the end of day 2, we’ll reflect on what you’ve written.

What is MDC? MDC provides teachers with Formative Assessment Lessons (FALS)to engage students in a productive struggle that builds fluency with their procedural skills, and deepens mathematical reasoning and understanding. MDC provides resources, strategies, and professional development to assist teachers ASSESS FOR LEARNING.

The MDC project is not designed as an additional program, but rather as a process to enhance CC standards-based instruction. Achieves a balance among concepts, skills, and problem solving. Stresses rigorous concept development, presents realistic and relevant tasks, and keeps a strong emphasis on computational skills.

Video: What is MDC?

The Resources

Connecting MDC and MAP The Mathematics Assessment Project (MAP) aims to bring to life the Common Core State Standards (CCSSM) in a way that will help teachers and their students turn their aspirations for achieving them into classroom realities. The materials from this project exemplify CCSSM in explicit down-to-earth performance terms. MAP is a collaboration between the University of California, Berkeley and the MARS Shell Center team at the University of Nottingham. MARS, the Mathematics Assessment Resource Service, is an international collaboration dedicated to the improvement of assessment.

Connecting MDC and MAP MDC uses formative assessment lessons (FALs) from MAP to engage students in a productive struggle that builds fluency with their procedural skills and deepens mathematical reasoning and understanding. Students participate in both individual and group learning as teachers use FALs and questions to check for students’ math understanding and correct common misunderstandings. Rather than following predetermined steps to find an answer, students are supported to deepen their math reasoning to solve problems

MDC Spotlights SMP Making Sense of Mathematics Communicating Making connections Justifying Explaining Critiquing the reasoning of others Attending to precision Modeling with mathematics As most of you know, mathematics has 2 intertwined sets of standards; the content standards and the standards of mathematical practice. The formative assessment lessons are aligned to a content standard, but, more importantly, they spotlight and require the use of the standards of mathematical practice. If we want our students to become proficient learners of mathematics, they must be able to (see list) communicate using the language of the standards, make meaningful connections, justify their reasoning, explain, to look at another student’s work and describe what they did right, where they went wrong, how they can make it better; encourage students to be precise in description, terminology, computation and, most importantly how to use mathematics to model real-world events.

Let’s get our Math Brains working! Complete the “Counting Trees” task as a sample of the kind of problems you would see in a MDC lesson. Discuss how this type of problem could be used to meet the 8 SMPs.

In General, What are “FALs”? Formative Assessment LESSONS Well-engineered to uncover misconceptions Complete Teacher resources Scripted Aligned to CCSS These Formative Assessment Lessons (also called Classroom Challenges) are very well engineered to uncover misconceptions students have about specific content; help students correct these misconceptions, and support teachers in using researched-based strategies and tools that have been deemed “best practices”. All lessons are aligned to the CCSS with a real focus on the standards of mathematical practice. 3/28/2011

Two Types of FALs Concept Development Lessons are meant to first reveal students’ prior knowledge, then develop students’ understanding of important mathematical ideas, connecting concepts to other mathematical knowledge. Problem Solving Lessons are meant to assess, then develop, students’ ability to apply their mathematical knowledge and reasoning in flexibly ways to non-routine, unstructured problems – within mathematics and with real world applications.

Concept Development Lesson Frame the lesson and administer the pre-lesson assessment Analyze student responses and write feedback questions Introduce the lesson with whole class discussion Facilitate the collaborative activity Facilitate sharing and whole group discussion Distribute feedback questions and administer the post-lesson assessment Analyze growth across the pre- and post-lesson assessments Modify subsequent instruction

Teach ------ approximately 2/3 of unit The Process – CD Lesson Teach ------ approximately 2/3 of unit FAL Teach ------ remaining 1/3 with modifications of instruction to clear up identified misconceptions

Problem Solving Lesson Frame the lesson and administer the pre-lesson assessment Analyze student responses and write feedback questions Distribute the feedback questions and responses to the pre-lesson assessment Facilitate students working collaboratively on the problem Facilitate whole group discussion Administer the student reflection sheet Analyze growth across the pre-lesson assessment and the student reflection sheet Modify subsequent instruction

Pre-Lesson Assessment What do students know? What are the misconceptions? Where are the gaps in understanding? How will I group students in order to support mathematical discourse? How can I analyze this now and later to show growth?

Purpose of Analyzing Student Work To group students Homogeneously in Concept Development Lessons Heterogeneously in Problem Solving Lessons To create feedback questions Guiding students toward a deeper understanding Moving students forward To prepare for the lesson Knowing what to listen for as students are working What to address during the plenary (to revisit)

Grouping For concept development lessons For problem solving lessons Homogeneous grouping Partners for maximum interaction For problem solving lessons Heterogeneous grouping According to different approaches to the problem providing students with multiple representations Groups of 2 are recommended but logistics sometimes create other scenarios.

Why are FALs useful? Translate the vision of CCSS into classroom practice Enable teachers to assess student performance Assist in moving each student’s reasoning forward Provide a critical supplement to the curriculum Provides a model of best practices and engaging strategies With well-developed lessons, tasks, assessments, support student engagement, encouraging them to become more independent learners; owners of their own learning. Teachers become better teachers as they experience success in their classrooms and as students become excited about being involved in the learning process. We help teachers identify where students are, where they need to be, and the first steps in helping them in the right direction.

Why do you assess your students ? What different purposes do your assessments serve ? ( 5 – 10 ) I feel like this can be conversational ,especially if a district is aware of types of assessments. If a district is not aware of the types of assessments you could use PDESAS.org assessment tab to get more information Other option have partners or tables Create a tri-fold ..column one “Reasons why we assess” Column 2 Types of assessments ( summative, formative, diagnostic , benchmark) supply an example from your list example ( summative – unit test) Column 3 Reason or purpose of said assessment. Share out (call on #s assigned to someone)