CCGPS Mathematics A beginner’s guide to FALs/Classroom Challenges November 26, 2013 Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard Turtle Toms- Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Teachers tell why. 4nCE 4nCE -s -s L-s L-s 2

Does this student have: procedural skill and fluency? conceptual understanding? the ability to apply mathematics?

Does this student have: procedural skill and fluency? conceptual understanding? the ability to apply mathematics?

"If you can both listen to children and accept their answers not as things to just be judged right or wrong but as pieces of information which may reveal what the child is thinking, you will have taken a giant step toward becoming a master teacher… (not just)…a disseminator of information." -Easley & Zwoyer 5

Pause and discuss Agree/disagree with the previous statement? What do you think about this statement? What does this statement suggest about grading/assessment? 6

7 There is only one 21st century skill

Learning targets: I can explain what Formative Assessment Lessons are, and their purpose. I can describe the process of implementing a FAL. I know where to find information which will deepen my understanding of FALs and their implementation. I know and can explain the expectations of the GADOE regarding the use of FALs. 8

What is formative assessment? … all those activities undertaken by teachers, and by their students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet the needs. 9

An educational positioning system A good teacher: – Establishes where the students are in their learning – Identifies the learning destination – Carefully plans a route – Begins the learning journey – Makes regular checks on progress on the way – Makes adjustments to the course as conditions dictate

Re-teaching vs. Re-engagement Re-teachingRe-engagement Teach unit againRevisit student thinking Address missing basic skills Address conceptual understanding On the same or similar problems Examine task from different perspective Practice moreCritique student approaches Cognition lowerCognition higher

Why Now?

Collaborative learning: a research success story  Four mechanisms  Motivation: students help their peers to learn because, in well-structured cooperative learning settings, it is in their own interests to do so, and so effort is increased;  Social cohesion: students help their peers because they care about the group, again leading to increased effort;  Personalization: students learn more because more able peers can engage with the particular difficulties a student is having;  Cognitive elaboration: those who provide help in group settings are forced to think through the ideas more clearly.

What is a FAL? (short version) A classroom-ready lesson that supports formative assessment. Two types: – Concept development lesson – Problem solving lesson 14

What is a Formative Assessment Lesson? (longer version) a scripted lesson ( usually written by the Shell Center in partnership with the Gates Foundation or a Math Design Collaborative) a challenging task that is out of the ordinary and involves problem solving with "productive struggle" builds student's ability to become confident problem solvers; eliminates the "GPSing" of teaching typically used during each unit of study about half to two-thirds way through the unit uses the "5 Strategies for Effective Teaching" in order to move learning forward every day These lessons are NOT about getting to the correct answer. They are about generating thinking and discussion among students. 15

Two Kinds of FALs Concept Focused Specific content is central to the activity Generally one correct answer, but may be a variety of ways to get that answer Usually includes a small group/pairs activity that requires manipulation of mathematical information (often in the form of card sorts, etc.) Problem Solving Focused Activity draws on knowledge about a variety of content Sometimes a number of answers are plausible but must be defended Usually includes a small group/pairs activity that requires analyzing sample student work in order to look at different strategies for solving the problem at hand. Both types include both concepts and problem solving, but each puts more emphasis on one than the other.

Two kinds of FALs Concept development lessons: – Reveal prior knowledge – Develop understanding of mathematical ideas – Connect concepts to other mathematical knowledge Problem solving lessons – Assess and develop ability to apply mathematical knowledge and reasoning in flexible ways to non- routine, unstructured problems 17

Two kinds of FALs Concept development lessons: – Two-thirds of the way into a unit of study – Start of a new unit Problem solving lessons – Every month or two throughout the year 18

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How do I implement a FAL? Concept development lesson (Use the lesson guide) Before the lesson: – Pre-assessment (diagnostic) – Analyze the responses, then create questions to help students reflect on issues which surface (Common Issues in the guide) – These questions are used feedback to students 20

How do I implement a FAL? Concept development lesson: (Use the lesson guide) The lesson – a task related to the pre-assessment – Listen and question to promote deeper thinking and reflection – Timely whole class discussions- share and resolve common difficulties – Conclude by sharing different understandings and generalizing and extending what has been learned. 21

How do I implement a FAL? Concept development lesson: (Use the lesson guide) After the lesson – Post-assessment (similar or identical to pre- assessment) to demonstrate learning from engaging in the lesson 22

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How do I implement a FAL? Problem solving lesson (Use the lesson guide) Before the lesson (one or two days in advance): – Assign the task for students to complete individually (takes 10 to 15 minutes) – Assess the responses to the task, noting approaches and difficulties – Create questions (Common Issues in the guide) 24

How do I implement a FAL? Problem solving lesson (Use the lesson guide) The lesson : – Students individually review their own solutions in light of the questions raised by the teacher – Compare and build on strategies in small groups – Observe the groups, looking for different approaches and supporting problem solving through questioning – Whole class discussion- groups share strategies – Groups discuss, analyze, and critique sample work 25

How do I implement a FAL? Problem solving lesson (Use the lesson guide) After the lesson : – Students individually review their own solutions and improve upon them – Compare and build on strategies in small groups – Observe the groups, looking for different approaches and supporting problem solving through questioning – Whole class discussion- groups share strategies – Groups discuss, analyze, and critique sample work 26

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Provide feedback that moves learning on Key idea: feedback should: – Cause thinking – Provide guidance on how to improve Comment-only grading Focused grading Explicit reference to mark-schemes/rubrics Suggestions on how to improve: – Not giving complete solutions Re-timing assessment: – E.g., three-fourths-of-the-way-through-a-unit test

Five Effective Strategies for Formative Assessment 1.Clarify, share, and understand goals for learning and criteria for success. 2. Engineer effective classroom discussions, questions, activities, and tasks that elicit evidence of students’ learning. 3.Provide feedback that moves learning forward. 4.Activate students as owners of their own learning. 5.Activate students as learning resources for one another.

What would students need to know to get started on this problem? Consider background knowledge, choose carefully based on where students are…a little above where they are now Is there more than one way to approach the problem? Make sure the task is OPEN and has multiple possible solution strategies… How do I introduce the problem? Frame the task What should I do after introducing the problem? Stay quiet, answer questions with questions which move the learning forward…

Supportive accountability What is needed from teachers: A commitment to: The continual improvement of practice Focus on those things that make a difference to students What is needed from leaders: A commitment to engineer effective learning environments for teachers by: Creating expectations for continually improving practice Keeping the focus on the things that make a difference to students Providing the time, space, dispensation, and support for innovation Supporting risk-taking 41

Resources Suggested placement in GADOE frameworks? Links on K-5 wiki: 5.wikispaces.com/K- 5+Formative+Assessment+Lessons+%28FALs%29http://ccgpsmathematicsk- 5.wikispaces.com/K- 5+Formative+Assessment+Lessons+%28FALs% wiki: 8.wikispaces.com/Assessment+Resourceshttp://ccgpsmathematics6- 8.wikispaces.com/Assessment+Resources HS wiki: 10.wikispaces.com/Assessment+Resourceshttps://ccgpsmathematics9- 10.wikispaces.com/Assessment+Resources 42

Mathematics Assessment Project – Designed and developed well-engineered assessment tools (FALs) to support US schools in implementing the Common Core State Standards for Mathematics (CCSS). – Funding is provided by the Bill and Melinda Gates Foundation through the University of California, Berkeley. KDE mathematics specialists are developing FALs for grades K-5

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Expectations Try a FAL If possible, try the FAL collaboratively with your colleagues. Think about how what you learn by implementing FALs can shape your instructional approach to other tasks in a unit. Think about how the use of FALs can shape the manner in which you provide feedback to students There is no mandate from the DOE that you will use FALs, but we hope you decide to! 45

We need to create time and space for teachers to reflect on their practice in a structured way, and to learn from mistakes. Bransford, Brown & Cocking (1999) “Always make new mistakes.” Esther Dyson “Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.” Beckett (1984) 46

Learning targets: I can explain what Formative Assessment Lessons are, and their purpose. I can describe the process of implementing a FAL. I know where to find information which will deepen my understanding of FALs and their implementation. I know and can explain the expectations of the GADOE regarding the use of FALs. 47

Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the K-5 Mathematics listserve. Follow on Twitter! Brooke Kline Lead Program Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. James Pratt Secondary Specialist Turtle Toms Program Specialist (K-5)