Ethan Smith

Discursive Drift in the Enactment of Small Group Elementary Mathematical Writing Tasks In this paper, we investigate the ways in which informative/explanatory and argumentative genres of mathematical writing (MW)—or an instructional focus in line with the goals of these types of MW—a...

This article was a lot of fun to create with my STaR collaborator Bea, and I hope that you all can find something meaningful to take away from it, too! DM me for a copy or access the article at doi.org/10.1080/1947...

Finally, MW genres may be positioned to promote inclusive language. It may stand that, since you are being asked to explain ideas or construct arguments, you may also be situated as having a more active role in the activity of mathematics compared to just rehashing procedures

The fact we saw so much drift also reinforces the importance of looking at teachers' setup AND enactment of tasks. Teachers may need support maintaining the focus of their tasks past setup. BUT, drift may also be GOOD at times (e.g., drifting from explanations to argumentation).

What are some implications? Well, teachers would engage in some informative/argumentative tasks, but often with just spoken expectations. Considering how spoken discourse can support mathematical writing and vice versa could be a productive approach to increasing teachers' MW use

We found that teachers tended to maintain their linguistic choices that they started with, but also we saw that most of our inclusive language drifts happened when teachers (re)focused students on informative or argumentative goals of the tasks.

But did the expectations "drift" at all? Yes! About 60% (20) of our coded lessons showed a drift in the discursive focus of the task. We actually saw a lot of drift toward informative/argumentative foci when a task started as procedural, for instance!

But when we ALSO include how teachers (re)focused students on tasks throughout the groupwork, the picture is more complicated. There's a lot more informative or argumentative focus (but still a lot of exclusive language with procedural writing expectations)

When we JUST looked at how teachers initially setup tasks during groupwork, we saw a lot of exclusive language, and a lot of focus on procedures. Most inclusive framing happened with (relatively few) informative or argumentative tasks.

What did we find? First, a lot of writing students were being asked to do during these tasks was procedural rather than mathematical writing. Many expectations were also ambiguous about whether students were to produce written work, or primarily engage in spoken discourse

I think that inclusive language matters because it positions the subject as an active participant in a creative process of “doing” mathematics (math=alive!), where exclusive language frames the subject as executing a defined set of actions to reach a predetermined conclusion.

I'm particularly interested in the framing aspect. Inclusive versus exclusive language entails linguistic choices such as interrogatives vs imperatives, pronouns ("we" versus "you"), and hedging language for inclusive ("how might we").

Flowchart of the coding processes for this study.

For initial task setup and then implementation, we considered the genre of task (symbolic/procedural, informative/explanatory, or argumentative), the expectations for student participation (writing, speaking, ambiguous), and whether teachers used inclusive or exclusive framing...

We look at the extent that teachers' discourse includes inclusive language when framing different genres of symbolic or mathematical writing (MW) tasks, and how the focus of that discourse drifts over the enactment of the tasks during small group work...

The abstract of the article, Discursive Drift in the Enactment of Small Group Elementary Mathematical Writing Tasks

#mathedresearch #mtbos I'm excited to share a new article from me and Bea Ellis, titled Discursive Drift in the Enactment of Small Group Elementary Mathematical Writing Tasks, out now in Investigations in Mathematics Learning! doi.org/10.1080/1947...

In sum, CRMT cannot be achieved strictly through standardized curricula. But these materials ARE the framework for millions of students' experiences w/ math in the US, and warrant scrutiny. This analysis suggests urgency + paths toward greater attention to CRMT in such materials. (8/8)

We recognize the present political climate is explicitly hostile toward equity & cultural responsiveness. This sort of investigation not only calls attention to the current desultory approach to CRMT in curricula, but also provides tools for stakeholders to advocate for CRMT. (7/8)

To be clear, CRMT requires RESPONSIVENESS to a particular set of students, so standardized curriculum materials inherently require adaptation and to be balanced with other instructional resources and supports. But this is NOT an excuse for curricula to ignore attention to CRMT. (6/8)

What does this tell us? Well...these materials are presenting SOME opportunities to attend to culturally responsive math teaching (CRMT), but their sporadic and siloed attention toward CRM suggests the need to adapt and supplement such materials to support CRMT. (5/8)

There was greater attention toward promoting high cognitive demand, but CRM aspects such as disrupting status issues or using math to address social issues was pretty much nonexistent in the analyzed materials. (4/8)

What did we find? Well...these curricula provide only brief attention toward culturally responsive mathematics (CRM), but there ARE differences across curricula. Perhaps unsurprisingly, curricula attend more to the dominant dimensions of equity than the critical dimensions. (3/8)

We analyzed the middle school materials of six different widely adopted math curricula, considering how the materials present opportunities to attend to Zavala and Aguirre's CRMT2 framework. (2/8)

#mathedresearch #mtbos I am excited to share the newly published article I cowrote with Riley Stone and Raisa Ebner, titled "Culturally Responsive Mathematics and Curriculum Materials: Present Realities and Imagined Futures." You can view the article here: mdpi.com/2227-7102/15... (1/8)

However, coaching is also social in nature--coaches are not merely vessels for implementing district policies. These findings also show the value in considering the perceptions of different participants in school policy. Teacher and coach perceptions of their shared work matters!

We discuss how this shows that coaches can play a positive role in fostering positive perceptions of district PL+curricula, but they also act as "cheerleaders" of these policies, with higher perceptions of their quality compared to their teachers.

What might be going on here? A few ideas: (1) coaches may be focusing on the curriculum BECAUSE their teachers are not (yet) bought into the materials. (2) Teachers may have lower perceptions BECAUSE they have engaged deeply with the curriculum - they know its strengths + flaws.

Interestingly we found that coaches who used curriculum materials MORE in their coaching worked with teachers who reported the PL+curriculum to be of LOWER quality. You might think greater focus leads to greater teacher buy-in/agreement, but we did not find this to be the case.

We also found that teachers who reported higher coach quality--both expertise and affective quality (e.g., “My coach is respectful and collegial”) also had higher perceptions of PL+curriculum quality. Perceptions of coaching quality matter!

However, teachers who had an instructional coach had stronger perceptions about the quality of their PL and curriculum. So coaching--or districts that use coaching and other supports--seemed to strengthen teachers' perceptions of PL and curriculum quality.

We found that coaches had more positive views about the quality of district-mandated PL and curriculum materials compared to teachers. True for specificity, consistency, buy-in, institutional authority. So coaches view PL+curriculum in meaningfully dift ways than their teachers

Coach and teacher alignment in the context of educational change - Journal of Educational Change Professional learning (PL) programs increasingly rely on the expertise of instructional coaches in supporting teacher learning and instructional change. To continue to improve the use of coaching as a...

New #mathedresearch article alert! We investigated middle school math teacher+coach perceptions about quality of professional learning and the curriculum materials embedded in that PL, and considered coaching approaches that may have influenced teachers’ perceptions. doi.org/10.1007/s108...