Project QUEST

1. Project QUEST Overview of Framework of Project QUEST The foundation of QUEST The importance of Progressions

2. The Instructional Core STUDENT • "You don't change performance without changing the instructional core," states Professor Richard Elmore. • "The relationship of the teacher and the student in the presence of content must be at the center of efforts to improve performance." TEACHER CONTENT

3. Students learn more when… We begin with the end in mind – the learning destination We begin with them – finding out what they know and need to learn We listen, watch, and respond thoughtfully, we have a chance to see them in ways no one else might and they have the chance to see themselves that way The best part of who they are and who they want to be is reflected in our eyes

4. CCSS PrinciplesEmphasized by Project QUEST Focus • Identifies key ideas, understandings and skills for each grade or course • Stresses deep learning, which means applying concepts and skills within the same grade or course Coherence • Articulates a progression of topics across grades and connects to other topics • Vertical growth that reflects the nature of the discipline

5. Why QUEST? It brings the Instructional Core to life! Students learn at varying rates, and if a misconception in mathematics develops early, it may be carried from year to year and obstruct a student's progress. To identify fallacies in students' preconceived ideas, "Uncovering Student Thinking in Mathematics" offers educators a powerful diagnostic technique in the form of field-tested assessment probes--brief, easily administered activities to determine students' thinking on core mathematical concepts. This resource combines standards, educational research findings, and practical craft knowledge to help teachers deliver informed instruction that strengthens all students' learning and achievement in mathematics.

6. What is QUEST? Action research cycle – professional development strategy The teacher notes, included with each probe, have been designed around the QUEST cycle Designed to question students' conceptual knowledge and reveal common understandings and misunderstandings, the probes generate targeted information for modifying mathematics instruction, allowing teachers to build on students' existing knowledge and individually address their identified difficulties. This handbook assists educators with: (1) 25 ready-to-use mathematical probes; (2) Teacher guides for implementing each probe at any grade level; and (3) Examples of typical obstacles and faulty thinking demonstrated by students.

8. What Types of Understandings and Misunderstandings Does a Mathematics Assessment Probe Uncover?

9. Process for Developing Probes Identify topic to be taught (content focus) Select the specific concepts or ideas and identify the relevant research findings (content focus) Focus on a concept or idea to address with a probe and identify related research findings. Focus on incorrect responses derived from cognitive research findings. (Student focus) Choose the type of probe format that lends itself to the situation. Develop the stem, key and distracters that match developmental level of the students (Student focus) Share with colleagues for constructive feedback, pilot with students, and modify as needed (Teacher focus)

10. Questioning for Student Understanding

11. Uncovering Understanding

17. Five Critical Features to Guide Educators Toward Effective Use of Formative Assessment Learning Progressions Learning Goals and Success Criteria Descriptive Feedback Self and Peer Assessment Collaboration

18. Progressions • A progression describes a sequence of increasing sophistication in understanding and skill • Three types of progressions that correlate with the Instructional Core • Standard Content • Learning Student • Task Teacher

19. Learning Progression –Based on research on student learning From Adding It Up: Helping Children Learn Mathematics, NRC, 2001.

20. Learning Progressions • Clearly articulate the trajectory along which students are expected to progress. • Descriptions in words and examples of what it means to move over time toward more expert understanding. • Depict successively more sophisticated ways of thinking about an idea that might reasonably follow one another as students learn. Heritage, M. Formative Assessment and Next-Generation Assessment Systems: Are We Losing an Opportunity. National Center for Research on Evaluation, Standards, and Student Testing (CRESST).

21. Learning Progressions Clearly articulate the key subconcepts or subskills that constitute progress toward the subcomponent of the standard. Developed from a strong research base about the structure of knowledge in a discipline and about how learning occurs (ideally). Heritage, M. Formative assessment: Making It Happen in the Classroom. Corwin, 2010

22. Standards Progressions:Number & Operation in Base Ten

23. Task/Curriculum Progression • A rich mathematical task can be reframed or resized to serve different mathematical goals • goals might lie in different domains • goals might lie in different levels

24. A word from Bill (McCallum) http://www.youtube.com/watch?v=a-P9KQdhE0U

25. Learning Trajectories… 3 parts of a trajectory 1. Learning goal 2. Developmental progression 3. Mathematical tasks used to promote learning “The starting point is the mathematics and thinking the student brings to the lesson, not the deficit of mathematics they do not bring. A standard defines a finish line, not the path. The path begins with the students’ prior knowledge and finishes with the “standard” knowledge. The path itself is described by learning trajectories and mathematical coherences.”

26. Five Characteristics of Learning Trajectories Learning trajectories identify a particular domain and a goal level of understanding. Learning trajectories recognize that children enter instruction with relevant yet diverse experiences that serve as effective starting points. Learning trajectories assume a progression of cognitive states that move from simple to complex. While not linear, the progression is not random, and can be sequenced and ordered as “expected tendencies” or “likely probabilities”. Adapted from Confrey, J & Maloney, S. Learning Trajectories. Presentation provided to CCSSO FAST SCASS Collaborative. 2010

27. Five Characteristics of Learning Trajectories Progress through a learning trajectory/progression assumes a well-ordered set of tasks (curriculum), instructional activities, interactions, tools, and reflection. Learning trajectories/progressions are based on synthesis of existing research, further research to complete the sequences, and a validation method based on empirical study. Adapted from Confrey, J & Maloney, S. Learning Trajectories. Presentation provided to CCSSO FAST SCASS Collaborative. 2010.

28. The goal of the progression activity Closely examine one domain of the CCSS and study it for coherence and focus Read the progression document for one domain with the purpose of deepening your understanding of the flow of the content Work toward the use of learning trajectories in lesson planning

29. Example of 6-8 team exploring the domain Expressions and Equations

30. Progressions in Action Standards Progressions • (List domains per grade level and directions to move to grade band team) • Given an envelope of standards that areassigned to a specific domain, work with a partner to use your professional judgment and arrange them on your chart paper by grade level

31. Learning Progressions Read the learning progressions handout Highlight concepts that have connections to the standard progressions Check your standard progression for alignment with the learning progressions and discuss with your team Note any changes you made

32. Check Your Work and REFLECT Use the standards document to check your arrangement and reflect on the following: Note any changes you made Summarize the mapping of progression process (be prepared to discuss whole group) Make note of at least two “ah-ha” and “oh-no” What standards for practice did you employ? Your work and the work of others will be used for a “Gallery Walk” tomorrow!

33. Please divide up by grade bands…(about 10 each) K-5 Number and Operations in Base Ten 3-5 Number and Operations – Fractions (includes grade 6 NS) 6-7 Ratio and Proportional Relationships 6-HS Statistics and Probability

34. Homework Solve the division problem using two strategies other than the conventional algorithm. Explain and represent your thinking using symbols, words, and diagrams, as appropriate for each strategy then… Read “Unpacking Division” article Use the “4 Quadrant” handout in your binder to reflect on the article – we will use this to create a “knowledge package” for division!