MMR Joint Display

Through the Rearview Mirror: A Concurrent Convergent Mixed Methods Autoethnography of Technology Experiences and Mathematics Teaching Practices

Sam Servellon

EDPS 936: Mixed Methods Research · Dr. Michelle Howell · University of Nebraska-Lincoln

Note: All findings presented here are projected. This display represents the anticipated structure and content of integration at the analysis phase of a proposed study that has not yet been conducted.

Table 1. Joint display of projected quantitative artifact patterns and qualitative critical incident findings from a concurrent convergent mixed methods autoethnography
Theme	Qualitative Projected Self-Interview Excerpt	Quantitative Projected Artifact Pattern Analysis	Integration Projected
Access	“I remember figuring out that not everyone in my class had a graphing calculator at home. I had just assumed they did because I did. That was probably the first time I understood that ‘being ready for math class’ wasn’t just about effort.”	Approximately 55–60% of early academic period artifacts are projected to reflect passive or consumptive technology use. Access interruptions are anticipated in roughly 30% of early academic period records.	Convergent Both strands position uneven access, rather than effort or aptitude, as the formative variable in early mathematics participation. The artifact record documents the structural reality; the narrative explains why it stuck.
Autonomy	“By high school, my mom gave me a list of things to have done by Friday at 3pm and largely left how and when up to me. When I heard what my peers’ school days actually looked like, I didn’t feel weird anymore — I felt lucky. I already knew what it felt like to be trusted with your own learning. That’s probably why I can’t stop trying to give that to my students.”	Homeschool-era artifacts are projected to reflect a substantially higher proportion of self-directed, project-based work relative to externally-structured task completion — an estimated 65–70% of documented academic artifacts from this period are anticipated to show evidence of learner-initiated inquiry, flexible pacing, or self-selected approach. This pattern is expected to contrast markedly with the artifact record from formally-structured academic contexts that follow.	Convergent with Expansion Both strands confirm that the homeschool experience established autonomy as a baseline expectation for learning rather than a privilege. The quantitative pattern documents self-direction as the structural norm of the researcher’s formative education; the qualitative strand expands this by revealing that the contrast with peers’ constrained experiences was itself a critical incident — the moment autonomy became visible as something that could be given or withheld, and therefore something worth fighting for in a classroom.
Identity in Transition	“Coming from math and science, I thought I knew how to use technology rigorously. Then I got into a classroom and realized I had no idea how to use it meaningfully — for someone else, in real time, with thirty kids who hadn’t signed up for my kind of rigor.”	Artifacts from the hard sciences phase are projected to reflect approximately 65% precision-oriented analytical technology use. Following the transition into mathematics education, pedagogically-oriented interactions are anticipated to constitute roughly 50% of documented use, suggesting integration of prior technical identity rather than replacement.	Convergent with Expansion Both strands document a shift in how technology was used across the professional transition. The qualitative strand expands the quantitative interpretation by revealing that the shift was ideological before it was behavioral — the artifact record shows that a change occurred; the narrative explains what had to be renegotiated for it to happen.
Unlearning	“You can’t teach a kid who already failed algebra the same way somebody taught them the first time and expect a different result. I had to figure out what I actually believed about who math is for. It turned out I had some things to unlearn.”	Approximately 40–45% of lesson artifacts produced following documented encounters with students retaking Algebra 1 are projected to show explicit equity framing in goals, materials, or assessment design, compared to roughly 20–25% in artifacts produced during periods without such encounters.	Convergent with Partial Divergence Both strands indicate that working with underserved learners catalyzed shifts in instructional design. The qualitative strand, however, surfaces a process the artifact record cannot capture: the unlearning that preceded the redesign. Frequency of equity-oriented artifacts is an insufficient proxy for the epistemic work that made them possible.
Equity as Practice	“There’s a difference between handing a kid a worksheet and saying ‘go catch up’ and building something with them that makes the math feel like it belongs to them. I had to stop designing for compliance and start designing for belonging.”	Periods with documented technology-integrated lesson designs are projected to show approximately 25–30% higher frequency of engagement markers in lesson artifacts — student-generated work, documented questions, collaborative outputs — compared to non-technology-integrated lessons within the same course context.	Convergent Both strands indicate that technology integration, when equity-oriented rather than remediation-oriented, is associated with increased student engagement. The qualitative strand clarifies what the quantitative pattern alone cannot: the orientation of the integration matters as much as its presence.
Reflection Through Making	“I wrote the most in the tracker when I was in the middle of building something — not when I set aside time to reflect. The tracker didn’t just record what I was doing; building it was what made me understand what I was doing.”	Approximately 70–75% of high-frequency documentation windows in the auto-ethnography tracker are projected to co-occur with periods of artifact creation or active tool engagement, compared to documentation rates during periods of passive use or reading.	Convergent and Mutually Constitutive Both strands confirm that making functions as a catalyst for reflection rather than the reverse. This convergence is the methodological core of the study: the quantitative pattern grounds the qualitative claim as methodology rather than preference, and the qualitative narrative makes the quantitative pattern interpretable as meaningful rather than incidental. Together they are the argument.