Part 1: Mathematics Teacher PD: A Paradox and a Contradiction Walk into the Classroom
Part 2: Why Transformational PD Hasn’t Worked at Scale
Podcast Episode Discussing These Ideas

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In our view, most PD efforts in mathematics education have been of the transformational variety. We are not the first to notice this trend, nor the first to call for incremental approaches. Goldsmith and colleagues (2014) pointed out that, when research has looked in detail at teachers’ learning from PD, it seems to be incremental:

The studies that offer detailed accounts of teacher learning reveal that it is often incremental, nonlinear, and iterative, proceeding through repeated cycles of inquiry outside the classroom and experimentation inside the classroom (e.g., Clarke and Hollingsworth 2002; Fennema et al. 1996; Jaberg et al. 2002). Changes in teachers’ mathematical knowledge, beliefs, dispositions, and opportunities to learn from colleagues often occur in sequential increments, with small advances in any one of them depending on advances in the others (Clarke and Hollingsworth 2002; Kazemi and Franke 2004). (Goldsmith et al., 2014, p. 20)

Star (2016), though not laying out a PD approach per se, did call for a focus on small changes in instruction, emphasizing the value of a 10% improvement for 90% of teachers rather than a 90% change for 10% of teachers. Litke (2020) has been pursuing some of these ideas about instructional improvement in algebra. More recently, Cortina and colleagues (2023) found greater success in the spread of their PD efforts when they shifted to more incremental principles.

Our own project, Practice-Driven PD for math teachers, is seeking to gather evidence about the mechanisms at play with incremental PD designed around instructional nudges (hypothesized to be high-uptake practices). Here are a few reasons we think this incremental PD is worth pursuing, at least by a substantial subset of the math ed PD community, to complement (not replace) the transformational efforts.¹

1. Incremental PD closes the research/practice gap by having scholars fully embrace the realities of practitioners

The research/practice gap has been a challenge for decades. Much has been written about “bridging” the gap, or “connecting” research to practice, or “linking” research and practice. Some people have also turned it around and talked about practice-informed research. Incremental PD, instead of trying to build a bridge (even a bidirectional one), involves developers fully immersing themselves in the land of practice and working entirely within that space and its constraints. Many of the developers may have never left the realm of practice, and so this doesn’t exactly apply to them, but there are also many scholars and researchers who provide PD for mathematics teachers and for them (us), this is a key difference between incremental PD and transformational PD. Transformational PD involves important and powerful ideas from the realm of research and then attempts to bridge or connect to practice. This comes with many of the dangers we brought up in our last post. Incremental PD, on the other hand, can be based in ubiquitous practices, built with an acceptance of the constraints teachers are working under (limited time, resources, pressures), and designed to address things the teachers are asking for (Otten et al., 2022). This approach builds trust rather than separation. And we think this “practice-driven” approach goes even further than “practice-based” PD (i.e., transformational PD can be and often is “based” on practices and attempts to incorporate its instructional transformations into hands-on experiences for teachers, but our project is attempting to be fully driven not just by instructional practices but by the actual current practice of teachers).

We have come to believe that it will be easier (not easy, but easier) for people and projects from the scholarly community to adjust our mindset and orientation than it will be to change all of the constraints and systems of practice to allow for transformational research connections and impact. As many wise people have observed, it is better to focus on changing yourself and what you can control rather than wishing for others to change. And then, once we are firmly rooted within the realm of practice, we can work hard to bring about incremental change to the systems that are limiting or harmful. With incremental PD, we will be working from the inside, hand-in-hand with teachers.

To be clear, this still requires great effort from the developers. We have been actively working for several years just to develop a small set of incremental PD nudges that we hope will have high uptake, and we are drawing on decades of research and varied professional experiences to do so. Research still has an important role to play (including basic research separate from practice). And there is still an important role for big thinkers and for insightful critics who can point out the need for transformation. But while that work is going on, incremental PD can also be underway striving to make small improvements over time.

2. Incremental PD affirms what teachers are already doing and can help maintain (or improve) their confidence

Teachers in the U.S. are often enacting conventional instruction (Litke, 2020; Otten et al., 2023; Otten et al., 2024), but this should not be viewed as unfortunate or as a barrier to instructional improvement. It is simply a reality, and teachers are doing many great things within that conventional instructional model. Having respect for teachers means we acknowledge these are the forms of instruction that work for them and their students, within the constraints of the educational system. Incremental PD can be rooted in this conventional instruction, offering modest suggestions that teachers are free to try or ignore, and in this way incremental PD honors what teachers are already doing and is positioned as a sort of supportive colleague. This is in contrast to transformational PD that comes to teachers with an entirely different way to teach.²

Incremental PD can also be designed in such a way that it builds teachers’ confidence and comfort with what they are doing. In our PDPD project, the instructional nudges we have designed are based on the teachers’ own patterns of instruction. “If you use problem sets, here is a small suggestion to enhance them.” “If you have substantial amounts of student work time, here is something to keep in mind as they work.” Because the nudges are so close to teachers’ current practice, our hypothesis is that the teachers will feel confident about when and how they could try them out, and we are starting to notice confirmation of this in our preliminary data.

We also design the nudges to have a high likelihood of immediate success. Because of all the stress and professional intensification teachers are already experiencing, we no longer feel good about approaching them with transformational PD that might increase their frustration or make them feel that they are not living up to ideal standards for teaching. The disclaimers that “things might get a bit messier before they get better” or “this change will be very challenging, but it’s worth it” are worrisome to us. Incremental PD, on the other hand, can give teachers feelings of improvement and connection to the field but packaged in a way that is affirming of their pre-existing practice (which has developed with years and years of experience) and gives feelings of success, for teachers and for students.

We are not saying it is easy to create these tailored instructional nudges (as noted above, it’s actually quite difficult, packaging research-informed suggestions into bite-sized pieces, but it also rewarding to see uptake). It is  not easy to find the things that have both immediate success and move the instruction into a positive long-term direction, but we are saying that figuring this out is a worthwhile task for scholars and developers.

3. Incremental PD can provide suggestions a la carte, selected by teachers, not predetermined by the PD team

The version of incremental PD we’ve been investigating involves a menu of instructional suggestions, and teachers are free to pick the ones they think will be worthwhile to try. In this way, we not only build on the teachers’ existing practice but we also rely on the teachers’ wisdom to know what they can pull off successfully and what their students will respond well to. Teachers are also welcome to decline everything on the menu. Maybe they are not resonating with the particular nudges, or maybe it’s not the right time for them to make some small changes.³

To use a different metaphor, our practice-driven project is attempting to put teachers in the driver’s seat of the PD. This takes away the difficult challenge that transformational PD faces of trying to find teachers who “buy-in” and then trying to maintain a long-term relationship with those teachers. Incremental PD, in contrast, is modest and hopefully nimble enough that it can be responsive to the teachers’ requests (within reason… we do not condone fulfilling requests from teachers that would be harmful, such as asking for things that could potentially increase math anxiety or separate and marginalize students).

We want to point out that the PD is not entirely at the mercy of teachers’ preferences. If teachers are pursuing a certain goal, or want to try something new within a certain part of their practice, the developers still have the opportunity to be creative and draw upon research and the expert community as they create or formulate the instructional suggestions. Our PDPD nudges, for example, are research informed, but the actual selection and implementation of the nudges is completely driven by teachers. Nevertheless, through the careful design from the developers, there can be subtle shifts even beyond what teachers are seeking when they select a nudge. For example, if a teacher is looking for ideas to increase student engagement during in-class work time, an incremental PD effort may be able to provide suggestions that increase engagement and also set the stage for more equitable inclusion of student ideas. These ideas, by being attached to something the teacher wants to try and also connecting with a common practice, can start to take hold and then hopefully accumulate and spread.

4. Incremental PD can spread far and wide

Incremental PD can be designed around ubiquitous teaching practices and formatted in such a way that it can be taken up even within the constraints and realities of typical teachers. For precisely these reasons, we hypothesize that it can readily spread from teacher to teacher. A teacher may have personal preferences about what to try out, but the menu of options is entirely based on conventional practices recognizable to a majority of teachers and it’s likely that other teachers share similar goals (e.g., don’t we all want to increase student engagement, help promote conceptual understanding along with procedural success, and reach those students who are struggling?). The fact that the instructional suggestions are designed for immediate success also means that a teacher may be eager to share.

Focusing again on the instructional nudges from PDPD, the modest size of the nudges also make them easily shareable either as a social media post, an emailed one-page overview, or a quick conversation among colleagues. Incremental PD does not require unpacking deep ideas or engaging with challenging pedagogical skills like transformational PD does. Incremental PD can spread within minutes and other teachers can try out the suggestions in their next class period.

And the hope would be that incremental PD leads to continued changes over time, subtle enough that they can withstand changes in textbooks, administrators, or assessments. And if the changes spread and sustain, maybe in the future it sets the stage for successful transformations in practice (though this is an empirical question).

5. Incremental PD can be specifically designed to spread to teachers who are not currently served well by transformational PD

One additional point related to spread, and it’s one of our strongest motivations for trying incremental PD—as we detailed in the previous post, transformational PD is full of good ideas and has found success with some teachers in some contexts. But there are many teachers, dare we even say a majority, who are not reached by transformational PD efforts. Incremental PD is designed to be small enough, cheap enough, and shareable enough to reach this majority. Even if the instructional improvements are modest, they can still be meaningful and it is good to reach more people, especially those overlooked or excluded from the efforts of transformational PD.

6. Incremental PD is stealthy enough to avoid major backlash

As we noted before, transformational PD and transformational efforts at mathematics education reform in general have triggered many backlashes. These are not just the large-scale backlashes like with school boards and state education agencies, although those are formidable. There are also countless small-scale backlashes that teachers have to face from students, parents, and the community. Incremental PD, on the other hand, by focusing on modest changes in instruction and by latching onto conventional practices (but with subtle improvements), can be stealthy enough to avoid or at least minimize a backlash. Students, parents, community members, and even school administrators are largely accustomed to conventional instruction, and they are probably okay with slight improvements to that instruction, especially if their known and trusted teacher is the one choosing to implement the improvements (not forced by an elite university or “expert”). In fact, they will probably applaud and support gradual improvement. In this way, incremental PD can work its way into classroom practice with support and good will rather than direct challenges.

This can actually position the teacher as a leader and an innovator, but in a way that does not ruffle too many feathers. We acknowledge that some feathers need to be ruffled, and some conventional systems need to be challenged, but that does not mean that teachers need to be placed in the center of a firestorm within their school or their community. Or at least teachers should be given the choice. Some may be well suited for transformational work and may be ready and willing to weather the storm, and we agree that teachers, being essential people on the inside of the educational system, can do this work. But many teachers may not want to take on all the burdens and stresses that come with visible transformations, and for them incremental PD may be a productive option. Given the century (and more) of past failures from transformational efforts, at least in mathematics education, we think there are several reasons to at least give incremental PD a try.⁴

A Concluding Comment on Incrementalism and Equity

In progressive and revolutionary discourse, incrementalism is often seen as insufficient for meeting the moment. With the depth of the inequities and injustices that people have identified within the education system, a broad transformation is necessary. From this point of view, people could critique incremental PD for focusing on the status quo and catering to it.

This is a fair point, but we do not believe it as a surrender to or an acceptance of current unjust patterns. We just want to consider incremental PD as a strategy for increasing our likelihood of making change. Rather than going big over and over again, but only finding pockets of success, we want to put our efforts into instructional improvements that have high uptake and a decent chance of spreading. It goes back to Star’s point about making 10% improvement (which seems modest) but for 90% of teachers (so the ambition is shifted over to the reach, not the profundity of the change itself). When considering equity in mathematics education, it seems especially important to seek effective strategies for change, or at least strategies that will complement the transformational work that others are already pursuing.

We take seriously the critical calls for immediate transformation in mathematics education, thinking especially about the systematic factors such as curriculum, assessment, labeling, tracking, and such (not individual teachers). But needing immediate transformation and achieving immediate transformation are two different things. We feel many efforts by math ed scholars have focused on the “transformation” part of “immediate transformation.” Perhaps incremental PD could be a worthwhile endeavor focusing on the “immediate” part. If students are being harmed and groups are being disempowered and excluded by mathematics instruction, then we need to find changes that can be taken up in the short term and can be spread widely to mathematics teachers, especially those teachers who are in typical contexts and using conventional instruction.

–Samuel Otten, Zandra de Araujo, Amber G. Candela, & F. Paul Wonsavage

Suggested citation:
Otten, S., de Araujo, Z., Candela, A. G., & Wonsavage, F. P. (2024, June 13). Why incremental PD is worth trying. Practice-Driven PD. https://practicedrivenpd.com/2024/06/13/why-incremental-pd-is-worth-trying/

Selection of References Informing Our Views
Cortina, J. L., & Višňovská, J. (2023). Designing instructional resources to support teaching. In T. Lamberg & D. Moss (Eds.), Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 15-26). Reno, NV: University of Nevada. http://www.pmena.org/pmenaproceedings/PMENA%2045%202023%20Proceedings%20Vol%201.pdf 
Desimone, L. M. (2011). A primer on effective professional development. Phi Delta Kappan, 92(6), 68-71. https://journals.sagepub.com/doi/full/10.1177/003172171109200616 
Goldsmith, L. T., Doerr, H. M., & Lewis, C. C. (2014). Mathematics teachers’ learning: A conceptual framework and synthesis of research. Journal of Mathematics Teacher Education, 17, 5-36. https://link.springer.com/article/10.1007/s10857-013-9245-4 
Guskey, T. R., & Yoon, K. S. (2009). What works in professional development? Phi Delta Kappan, 90, 495-500. https://journals.sagepub.com/doi/abs/10.1177/003172170909000709 
Heck, D. J., Plumley, C. L., Stylianou, D. A., Smith, A. A., & Moffett, G. (2019). Scaling up innovative learning in mathematics: Exploring the effect of different professional development approaches on teacher knowledge, beliefs, and instructional practice. Educational Studies in Mathematics, 102, 319-342. https://link.springer.com/article/10.1007/s10649-019-09895-6 
Hiebert, J., & Morris, A. K. (2012). Teaching, rather than teachers, as a path toward improving classroom instruction. Journal of Teacher Education, 63, 92-102. https://journals.sagepub.com/doi/full/10.1177/0022487111428328 
Kieran, C., Krainer, K., & Shaughnessy, J. M. (2012). Linking research to practice: Teachers as key stakeholders in mathematics education research. In M. A. (Ken) Clements et al. (Eds.) Third international handbook of mathematics education (pp. 361-392). Springer New York. https://link.springer.com/book/10.1007/978-1-4614-4684-2  
Koichu, B., Sánchez Aguilar, M., & Misfeldt, M. (2021). Implementation and implementability of mathematics education research. ZDM Mathematics Education, 53(5). https://link.springer.com/journal/11858/volumes-and-issues/53-5 
Litke, E. G. (2020). Instructional practice in algebra: Building from existing practices to inform an incremental improvement approach. Teaching and Teacher Education, 91. https://doi.org/10.1016/j.tate.2020.103030 
Otten, S., de Araujo, Z., Candela, A. G., Vahle, C., Stewart, M. E. N., Wonsavage, F. P., & Baah, F. (2022). Incremental change as an alternative to ambitious professional development. In A. Lischka & J. F. Strayer (Eds.), Proceedings of the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Nashville, TN: PME-NA. https://drive.google.com/file/d/1u75KDk47pH5IqLguQMBvbkI9ej0oLsjC/view 
Otten, S., de Araujo, Z., Wang, Z., & Ellis, R. L. (2023). When whole-class discourse predicts poor learning outcomes: An examination of 47 secondary algebra classes. In T. Lamberg & D. Moss (Eds.), Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 1007-1011). Reno, NV: University of Nevada. https://drive.google.com/file/d/1R4eWG8S73_qmS9Lh_QrUU7VqGkEQwOTG/view?usp=sharing 
Star, J. R. (2016). Improve math teaching with incremental improvements. Phi Delta Kappan, 97(7), 58-62. https://kappanonline.org/star-improve-math-teaching-incremental-improvements/ 
Valoyes-Chávez, L. (2019). On the making of a new mathematics teacher: Professional development, subjectivation, and resistance to change. Educational Studies in Mathematics, 100, 177-191. https://www.jstor.org/stable/45184687 
Wilkie, K. J. (2019). The challenge of changing teaching: Investigating the interplay of external and internal influences during professional learning with secondary mathematics teachers. Journal of Mathematics Teacher Education,22(1), 95-124. https://link.springer.com/article/10.1007/s10857-017-9376-0

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1. In these blog posts we are primarily focused on PD aimed at changes to instruction. There are certainly other types of PD for teachers, such as those addressing knowledge, beliefs, cultural awareness, etc. Although Goldsmith et al. (2014) noted that teachers’ identity knowledge and beliefs also develop via incremental changes, we have been working specifically on incremental changes in the actual instructional practices teachers enact. And like Hiebert and Morris (2012), we do find it valuable to focus on teaching rather than the teachers in and of themselves. ↩︎
2. Some people may accuse us of simply taking the easier path. This is a fair point. But it might also be effective for making change, or at least complementary to transformational PD. It is noble to pursue hard things, but if you want a lot of human beings to do something—if you want to promote spread, particularly spread to the places currently missed by transformational PD—then make it easy and modest. ↩︎
3. Although the incremental PD that we are envisioning involves modest suggestions for teachers, it’s worth noting that “modest” is relative to the teacher. We have seen in our work with teachers that modest (in the sense of easy to take up and try) often means an instructional suggestion that is quickly comprehensible and one they can implement in class with little preparation needed. But there are certainly teachers who are ready for ambitious changes in their instruction or who are happy to do some preparation for a new instructional activity, and for those teachers who are ready for it, incremental PD might mean some fairly ambitious suggestions. In other words, “modest” does not mean low-level or basic, it just means within reach for that particular teacher. We are formulating this as the notion of “high-uptake practices,” defined relative to each teacher. ↩︎
4. Although we think incremental PD is worth a try, and we are in the midst of a multi-year project doing just that, we are nevertheless very open to evidence that we might be wrong. If there’s evidence that certain transformational PD can reach the masses, then we should go for it. As we’ve said multiple times, transformation is certainly needed. Moreover, if there’s evidence that incremental PD does more harm than good (e.g., entrenching people in less-than-ideal instruction rather than moving them toward a place where they can then make larger changes), then we will change tactics or abandon our approach. We are seeking effective strategies for supporting teachers and improving instruction and we are willing to follow the results rather than a predetermined vision of what needs to happen, and we hope that other scholars are similarly committed. We are also bolstered by the widely positive feedback we’ve been receiving from teachers and school administrators since we’ve taken this incremental approach. ↩︎