Project QUEST. Overview of Framework of Project QUEST The foundation of QUEST The importance of Progressions. The Instructional Core. STUDENT. "You don't change performance without changing the instructional core," states Professor Richard Elmore .
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Overview of Framework of Project QUEST
The foundation of QUEST
The importance of Progressions
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
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.
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.
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)
Learning Goals and Success Criteria
Self and Peer Assessment
From Adding It Up: Helping Children Learn Mathematics, NRC, 2001.
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).
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
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.”
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
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.
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
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
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!
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
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!