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 content- focused 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.

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. If the strategy fits

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.

Professional Development Teacher Knowledge and Skills Teaching Practice Student Outcomes Simplified Logic Model for Professional Development

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?

Professional Development Teacher Knowledge and Skills Teaching Practice Student Outcomes Simplified Logic Model for Professional Development

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:

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.

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