Project QUEST
Overview of Framework of Project
QUEST
The foundation of QUEST
The importance of Progressions
The Instructional Core
STUDENT
TEACHER
CONTENT
 "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."
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
CCSS Principles Emphasized 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
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.
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.
Questioning Student
Understanding of a
Learning Target
Teaching
Implications
Seeking Links to
Cognitive Research
Uncovering Student
Understanding
Examining Student
Work
What Types of Understandings and
Misunderstandings Does a Mathematics
Assessment Probe Uncover?
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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)
Questioning for Student Understanding
Uncovering Understanding
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
Progressions
 A progression describes a
sequence of increasing
sophistication in
understanding and skill
 Three types of progressions
that correlate with the
Instructional Core
Standard
Task
Learning
 Standard
 Learning
 Task
Content
Student
Teacher
Learning Progression –
Based on research on student learning
From Adding It Up: Helping Children Learn Mathematics, NRC, 2001.
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).
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
Standards Progressions:
Number & Operation in Base Ten
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
A word from Bill (McCallum)
Learning
Task
http://www.youtube.com/watch?v=a-P9KQdhE0U
Standard
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.”
Five Characteristics of Learning Trajectories
1.
Learning trajectories identify a particular domain and a goal
level of understanding.
2. Learning trajectories recognize that children enter instruction
with relevant yet diverse experiences that serve as effective
starting points.
3. 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
Five Characteristics of Learning Trajectories
4. Progress through a learning trajectory/progression
assumes a well-ordered set of tasks (curriculum),
instructional activities, interactions, tools, and reflection.
5. 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.
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
Example of 6-8 team exploring the
domain Expressions and Equations
Progressions in Action
Standards Progressions
 (List domains per grade
level and directions to
move to grade band team)
 Given an envelope of
standards that are assigned
to a specific domain, work
with a partner to use your
professional judgment and
arrange them on your chart
paper by grade level
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
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!
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
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!