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Ensuring that Professional
Development Leads to Improved
Mathematics Teaching & Learning
Kristen Malzahn
Horizon Research, Inc.
TDG Leadership Seminar
February 2011
Purpose of Session
• Look at practice-based insights related to professional
development aimed at deepening teachers’ mathematics
content knowledge
• Think about professional development design and
implementation that is likely to lead to improved
mathematics teaching and learning
Session Design
• Share information as part of KMD dissemination
• Engage with tasks around professional
development design/implementation
• Reflect on practice-based insights from
experienced practitioners
• Consider implications for your particular context
Justifying the need for PD
• You are in charge of providing PD to
mathematics teachers in a district. The
school board asks: “Why are you providing
PD for high school teachers with college
and graduate degrees in mathematics ?
Don’t they already know the content?”
• Discuss how you would respond. (10
minutes)
Deepening Teacher Content
Knowledge
• Research has shown that contentfocused professional development is
related to changes in teaching practice
and positive results in student
achievement
• What does it mean to have professional
development that is “content-focused”?
Facets of
Teacher Content Knowledge
• Disciplinary content knowledge (DCK)
• Pedagogical content knowledge (PCK)
• Ways of knowing content (WoK)
I. Disciplinary Content Knowledge
• A. Knowledge of content at the level the
students are expected to know it
• B. Knowledge of content beyond what the
students are expected to know
– More advanced concepts
– Deeper understandings of concepts, and
connections among them
II. Pedagogical Content Knowledge
• A. Knowledge of how students think about
particular content ideas
– Initial conceptions
– Learning difficulties
– Learning progressions/trajectories
II. Pedagogical Content Knowledge
• B. Knowledge of instructional strategies for
teaching particular content ideas
– Eliciting ideas
– Challenging student thinking
– Scaffolding learning while maintaining high
cognitive demand
– Assessing student thinking/understanding
II. Pedagogical Content Knowledge
• C. Knowledge of curriculum regarding
particular content ideas
– How instructional materials develop particular
content ideas
– K-12 articulation of particular content ideas
III. Ways of Knowing Content
• A. How ideas/problems are investigated
– Conjecturing
– Designing/conducting investigations, problem
solving
– Productive habits of mind
III. Ways of Knowing Content
• B. How knowledge is established in the
discipline
– What counts as evidence
– The nature of explanation/justification in the
discipline
– The nature of working in the intellectual
community of the discipline
What does this mean for PD Design?
• They’re all important
• Research doesn’t tell us which facets
to emphasize and in what order
• We do have some guidance from
experienced practitioners
You can’t do it all
• When addressing multiple goals for
deepening teacher content knowledge
program leaders must make difficult
decisions about how deeply to pursue
each goal.
If the strategy fits
• Start by identifying a purpose, not
picking a strategy
• Select professional development
strategies based on their fit with the
content, the audience, and the intended
goals.
Using student instructional materials
Why might you use this strategy?
• Possible purposes:
– Deepen teacher content knowledge
– Help teachers understand how to use the
student instructional materials
What do we know about using
student instructional materials?
Look at it from the students’
perspective
• Experiencing the instructional materials as
their students will use them can deepen
teachers' understanding of mathematics
content.
Suggestions
• Engage teachers as learners of the
mathematics
• Learn the content at the student level
before learning how to teach that content
to students
• PD providers can model effective use of
those materials
What do we know about using
student instructional materials?
Analyze the story
• An analysis of the mathematical ideas in
student instructional materials and how
they relate to one another is helpful in
deepening teachers' pedagogical content
knowledge.
Suggestions
• This is not going through the mechanics of the materials
• Provide a conceptual frame or develop one with the
teachers
• Analyze learning progression across grade levels
• Look at the cognitive demand of the activities so
teachers can consider how modifications can affect
student learning
Example
• Brought in high school geometry text;
opened to a particular chapter and
answered the following questions: what
did the author think is the important
mathematical ideas in this chapter? What
are the author’s mathematical
expectations from students? How does the
author think about teaching and learning?
What do we know about using student
instructional materials?
Keep your eye on the prize
• Ensure that teacher concerns about
logistics and classroom management do
not get in the way of addressing
mathematics content and pedagogical
content knowledge goals.
Example
• LSC programs used tiered professional
development to address these different
needs.
What do we know about using student
instructional materials?
Consider the source
• The quality of the student instructional
materials has implications for how
teachers should engage with them in
professional development.
Suggestions
• Be aware that there is variation in quality of
instructional materials
• Help teachers see the flaws and to understand
their responsibility to provide good instruction
• Consider research on how students learn
content before analyzing the instructional
materials
What do we know about
considering student thinking?
Not any student work will do
• Selection of appropriate work samples
makes a difference in giving teachers an
opportunity to deepen their disciplinary
and pedagogical content knowledge.
Suggestion
• This is a time consuming task
• PD should be explicit about types of
understandings that are most important for
teachers to gain
What do we know about
considering student thinking?
Learn, then apply
• Teachers should first analyze a carefully
crafted set of student work before
analyzing their own students' work.
What do we know about
considering student thinking?
Focus on the positive
• Analysis of student work should include a
focus on what students understand, not
just what they do not understand.
What do we know about
considering student thinking?
Which comes first?
• Practitioners have different perspectives
on the level of teachers' content
knowledge needed prior to the analysis of
student understanding.
Simplified Logic Model for
Professional Development
Professional
Development
Teacher
Knowledge
and Skills
Teaching
Practice
Student
Outcomes
What do you do?
• Take a few minutes to reflect individually
• What is currently being done in your
school/district to help ensure that the
professional development teachers are
offered is leading to improved
mathematics teaching and learning?
Mathematics PD Vignettes
• Which one of these professional
development designs is more likely to lead
to transfer into the mathematics
classroom?
• Why?
PD strategies should be chosen:
• Consistent with the designated
purpose(s) of the PD;
• Consistent with the available
capacity;
• Consistent with the available
resources.
Engaging with practice-based insights
Read the insights and discuss as a group:
1. Which of these insights resonate with you?
2. What are the implications of these insights for
mathematics professional development in your
school/district?
3. Are there any additional insights from your own
experience that you’d like to share?
Simplified Logic Model for
Professional Development
Professional
Development
Teacher
Knowledge
and Skills
Teaching
Practice
Student
Outcomes
Final Words…
• All types of content knowledge are
important for effective mathematics
teaching
• Consider the needs of the group, your
views, time availability and capacity
In designing learning
experiences for teachers
• Consider the potential strengths and
weaknesses of each PD strategy in
relation to a particular purpose or set of
purposes.
• Design PD – and select PD providers – to
take advantage of the strengths and avoid
the likely pitfalls.
Don’t let form trump substance
•
Choose PD strategies that will help
achieve your purposes, rather than
choosing the latest strategies and
seeking purposes for them.
Be realistic
•
Choose PD strategies that fit the
resources and capacity you have (or can
develop) to provide high quality
professional development
Avoid reinventing the wheel
•
Use existing high quality professional
development materials if available.
•
TE-MAT: www.te-mat.org
Design PD to facilitate
transfer to the classroom
•
Point out connections between what
teachers are learning and what they are
expected to teach.
•
Help teachers apply what they are
learning to their classrooms, with
opportunities for practice and feedback.
Trust but verify
• Program designers need to monitor to
see if the PD is being implemented as
designed, especially during scale up.
• Collect (and use) formative evaluation
data to refine the PD plan, including
providing additional scaffolding to PD
providers.
MSP-KMD Website
http://www.mspkmd.net/