This page serves as a sort of journal for Geoff’s doctoral program, separate from the Emergentmath blog. Here, Geoff will share thoughts and reflections on classes, insights into literature and other PhD-related musings. While you’re here, feel free to explore Geoff’s main blog, various “miniseries,” and select blog posts. Here is Geoff’s About Me page.

Week 4

Journal: “You guys are so smart.”
Research Reflection: A protocol for emerging bilingual problem solvers: a reflection on Kitchen (2014)

Monday 9/21/2020

Journal: “You guys are so smart.”

The estimable Dr. Joi Spencer, professor at San Diego University, a pillar in the field of mathematics education, joined our class this week. We’d read much of Dr. Spencer’s work. I’d seen her speak at NCTM conferences. In a couple weeks, we will be joined by Dr. Danny Martin, another absolute legend.

As I’m sitting in class listening to Dr. Spencer and engaging with the material, I’m left with an unshakable feeling: Why on earth would they be engaging our class, specifically me, in dialogue about research they’ve spent their whole life trailblazing? The clear answer is this: because they’re amazing people.

This isn’t exactly imposter syndrome. It’s more of like, when Buster Bluth sinks in his chair and sheepishly whimpers, “You guys are so smart.”

And to prove my point, my research reflection this week is based on a paper written by one of my professors.

Thursday 9/24/2020

A protocol for emerging bilingual problem solvers: a reflection on Kitchen (2014)

Of all the research I’ve read thus far in my nascent PhD career, Kitchen (2014) has the most direct, research-to-classroom application. In it, we learn about a formative assessment protocol built for English Language Learners (ELLs). The protocol is called Discursive Assessment Protocol (DAP). It emerged from the designers’ wish to see emerging bilingual students able to access the Common Core State Standards of Mathematical Practices (SMPs). It’s also an extension of other problem-solving protocols. In fact, as we go through the protocol, I bet you’ll notice some familiar elements from your favorite math protocol.. 

The protocol goes like this:

Stage 1: Read the task, or have the student read the task. After reading the task, ask for students to make an estimation for a reasonable solution. Remember: this is an interview, so it’s alright to be conversational and ensure the student understand what’s being asked.

Stage 2: The student solves the task and develops a written solution method. After this, the interviewer may examine the work and consider questions to ask the student, or potential items to clarify.

Stage 3: Students explain their solution – this is still a conversation at this point. The interviewer may ask additional questions. 

Stage 4: “The phone simulation.” Here, students have the opportunity to explain their solution again, but they may only use words, not their written work. 

Where possible, teachers should support the use of the student’s native language.  This protocol helps emerging bilinguals understand mathematics, while encouraging risk taking and awarding students agency in problem solving. 

Kitchen (2014) then describes two vignettes of the DAP in action with a pair of students. 

I quite like how the protocol incorporates multiple intelligences: students have to estimate, write, converse, and verbalize. But it’s done in a way that ought not to be tedious. The author notes that the final stage may be challenging for a large class. However, this is where a teacher may wish to have students record themselves on their devices.

Kitchen, R. (2014). Using Formative Assessment to Promote Innovative Pedagogy for ELLs: Introducing the Discursive Assessment Protocol.