Well I did it! I published and defended my dissertation. My committee was so wonderful and supportive and they urged me to publish my findings in other places. So here we go!

I know that a dissertation may seem like a small project to seasoned researchers, but for me it was a very impactful experience. I am very passionate about the topic of mathematical discourse and how it plays a part in shaping student math identities, and if facilitated well, allows every student to become part of the math conversation.

If you know me, you know that I think in pictures both when solving math problems and when synthesizing information or thinking about big ideas. So below I will include some visuals that will hopefully make a lengthy study feel digestible and meaningful.

Rationale

Discourse is the container for many of the NCTM 8 effective teaching practices and is why it was used to measure successful implementation of Problem Based Learning.

Many teachers struggle to move from direct or explicit instruction to a problem-based instructional approach. If we understand more about what teacher actions support the facilitation of math discourse, it could provide support for teachers who are hesitant to shift their practice. The findings could also support teachers in facilitating discourse in their classrooms.

Synthesis of Reviewed Literature

• Inquiry and Problem-Based Instruction lead to increased student achievement. Gives ALL students the opportunity to participate in high quality, grade level math while building conceptual understanding and procedural fluency.
• Universal Design for Learning is a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities, asset-based approach. UDL is designed to target the how, what, and why of learning.
• Teacher implementation is at the forefront of this study. Teacher content knowledge, efficacy, and beliefs about teaching mathematics play a large role in teacher practice.
• Coaching assignments vary by type, location, and focus.
• Math discourse supports collectivist culture, helps build and maintain classroom community, is the measuring stick for successful PrBL implementation.

A case study was chosen for the research design because the study attempted to:

• Search for meaning and understanding
• Positioned the researcher as the primary instrument of data collection and analysis
• Employed an inductive investigative strategy
• Produces product that is richly descriptive

Themes and Findings

So Now What? How Do We Set Up a Discourse Rich Environment?

Below you will find strategies teachers used that contributed to setting up a discourse rich environment. I think this is a very clear illustration of when explicit instruction should be used in math class. Students need to be explicitly taught certain routines and procedures for engaging in productive discussions, providing feedback, and engaging with content. So to say there is no explicit teaching in a problem-based classroom is inaccurate. Great teachers know when to leverage explicit teaching and when guided inquiry is the best approach. Anyone reading this knows my thoughts on guided inquiry – that it should be the primary method of instruction and explicit instruction should be woven in as needed for examples like some of those provided below.

I believe that the findings from the study could support teachers in the following ways:

Interesting next steps for research studies could include:

If you’d like to read the entire dissertation, please email me and I’ll be happy to share:)