Situated Learning and Authenticity

As I continue to think about pedagogy as part of my participation in the Cluster Pedagogy Learning Community, I want to revisit the one of the math ed articles that I think most about. I share it partly because it terrifies me. Reflecting on this article made me realize that an individual can be a dedicated, well-intentioned teacher who implements high-quality practices and who still has little influence on how/if a student uses the content from the class. The article in question is a 1985 investigation into the mathematics used by Brazilian children as they worked as street vendors as compared to the mathematics they used in the classroom, entitled Mathematics in the Streets and in Schools. Check out the article here.

Summary of the Article

In this study, Carraher, Carraher, and Schliemann sought to understand the mathematical thinking of 5 Brazilian children. They first performed informal tests, visiting the children in a street market and posing a series of questions that required the children to perform computations related to their work. We’re talking, “I want 3 coconuts and pay with a $20, how much change should I get?” types of questions. Each child answered at least 7 questions (the child who answered the most did 19). Among all 5, only 1 computational error was made on a single question. Their performance was almost perfect. 

The researchers then changed the setting for a more formal test. The exact same questions that the children had already answered correctly were used in this formal test. They were either posed as traditional word problems (“Maria bought 3 coconuts. If each coconut cost…”), or as basic problems without context (maybe something like 20-3×4, if 4 was the cost of a coconut). Performance on the word problems was still high, though not nearly as accurate as the informal test in the streets. The context-free performance tanked. It wasn’t good at all. The researchers also found that children tried to use completely different strategies in those different settings. Reminder: these were the exact same set of children.

The authors used the results to specifically question the practice of teaching children algorithms and rules in school and then expecting them to use those tools in their day-to-day lives. This won’t surprise anyone who has really thought about their mental computation strategies. I know that I often use different strategies depending on the situation. I rarely try to perform a standard algorithm in my head.

For me, this implication is powerful, but feels very specific to mathematics education. An overarching implication that this article highlights is how interwoven learning is with the context in which things are learned. Do children fail to use school-learned algorithms in their day-to-day lives because those algorithms were taught without context (I’m sure that’s part of it), or do children do school math at school and use other strategies that have been developed in other contexts outside of school? This question haunts me. The fact that children used completely different strategies in the different settings suggests that something as seemingly objective as mathematics may still be context driven. The reason that this scares me is that even when school mathematics improves (and it has, though rote memorization activities still abound), school math might continue be the knowledge and skills that one uses in school, with little impact on how an individual uses the mathematics in outside of school. 

Now, I think we have plenty of evidence that transfer does, in fact, exist and that things are not so bleak. This study considered a very small sample. This article, however, serves as a regular reminder to me that I need to be thinking about how closely the context of the learning matches with the contexts in which I hope the learning can be utilized. It’s this article that keeps me thinking about the authenticity of the learning experience.

Implications for CPLC

I teach people who want to be elementary school teachers. They spend a lot of time studying pedagogy and specific teaching practices. I often wonder, “What if my students develop a nice knowledge base, with associated practices, that their brain decides to label University Pedagogy? And then they go into the field and work with practicing teachers and develop a whole new knowledge base and practices that their brains label as School Pedagogy?” Which pedagogy will they use (spoiler: it’s the one they used in the setting that most closely matches where they will use it)? It could (and should) be argued that as long as the University Pedagogy matches the School Pedagogy then transfer will surely happen. That’s great, but perfect alignment between those settings serves more to reinforce the status quo than it does to push thinking in different directions. I want to equip my students with the knowledge they need not only to work within the system, but to challenge it when necessary.

What is the utility of a teacher preparation program if practicing teachers learn most of their best stuff outside of their program? I don’t think I’m off the rails here. Do you know how many practicing teachers, myself included, who rave about how much they learn and grow in their first couple of years teaching? That’s not a bad thing, of course, as learning should be continual. I worry, however, about how much of their university learning experience never actually makes it into their day-to-day practice. Just like the Brazilian street merchants, they’ve developed their own strategies that work just fine for them in the context in which they need them.

So what advice can I give to the CPLC cadre as I reflect on this piece (and bemoan all of the things the piece reminds me that I could be doing better…)? I think as we consider the three pedagogical approaches we’re investigating, we can find not only an opportunity to improve our practices generally, but also to implement practices that encourage greater transfer. Again, we could improve our courses tremendously, but if we do so in a way that is heavily context dependent then students will develop a wonderful knowledge base that becomes almost inaccessible outside of the university setting.


The value that I see in interdisciplinarity is the opportunity it provides educators to reflect on their discipline. I find that the deep specialization that one experiences while pursuing a doctoral degree can have the potential to shut a person off from broader contexts in which a discipline exists. I, for example, identify heavily as an elementary mathematics educator. I could happily lose myself in issues directly related to the teaching and learning of mathematics. In seeking to improve my courses I might use the best resources from national organizations and plan a series of related experiences that would result in students who were were-versed in all things math education. 

But then one of those students might come back and say something like, “I feel really ready to teach an amazing unit that helps children to develop meaning around fractions, but do you have any ideas on how to support a child who has experienced trauma?” My discipline exists in a complex context and those who research in my discipline are not the sole arbiters on all things that impact our discipline. An elementary school teacher would be well-served by becoming trauma informed, and a mathematics educator may not be the right person to offer that support. Embracing interdisciplinarity is not about mastering everything that could be important to my students, but rather, seeking to understand the complexities of the contexts in which the learning is supposed to serve the students. Once I contemplate those contexts, I feel the need to reach out to others, who have different areas of expertise, to ensure that my students are learning everything that they should. 

I was in a recent unconference session at a CPLC meeting in which we were discussing ungrading (part of our goal, of course, was to see how many words we could put the prefix unin front of). One of the participants discussed the difficulty of implementing ungrading approaches due to the amount of content that his students just needed to know. We all nodded our heads because we have all felt the pressure of making sure our students leave our programs with specific content that’s just essential in our field. Interdisciplinarity helps us to think about (rethink?) the primacy of content within our disciplines. 

I won’t argue that content knowledge is unimportant. I believe, however, that too often we ignore how we expect students to use that content knowledge. As an example, I think it’s pretty important that teachers can discuss, in depth, the ins and outs of rubrics. That is content knowledge that matters to a teacher. This is content that I have studied and thought a lot about. I do not, however, walk over to a colleague’s office, peek my head in the door and say, “So, a single point mastery rubric lacks some of the development that supports objective evaluation of student work, but they’re far superior than traditional rubrics for providing formative feedback,” and then give my colleague a high-five and leave. That’s not how that content knowledge is used. Being able to simply rattle off a statement like that isn’t evidence that I implement high quality assessment practices. Possessing knowledge is great, but knowing how and when to use it is even more important. Interdisciplinarity can be an invaluable approach to reflect honestly about the contexts in which our disciplines exist. Authentic learning experiences that lack interdisciplinarity are probably not as authentic as we think, and thus, will be unlikely to support transfer. 

Open Education

Open education has interesting potential, but it’s impact on transfer seems entirely dependent on how it is used. Approaching open education with a desire to increase the authenticity of the learning experience can do far more than simply dedicating oneself to utilizing open education (see my last post about metaphors for learning and epistemologies). In your discipline, how do people find information? What do they do if they face a situation that doesn’t conform to the norm? How do they use the information they find? Are there common mechanisms for sharing information that they can contribute to? 

As I’ve written previously, my use of OER and open pedagogy comes from a desire to engage preservice teachers with dynamic sources that most closely align with how teachers, especially early career teachers, seek out knowledge. I want my students to feel empowered to contribute their experiences to the broader knowledge base. Open education has helped me think through some of these issues. Again, careful reflection on the contexts in which I hope my students will utilize their learning has helped me to see benefit to open education. While there are many great reasons to dedicate oneself to open ed, the potential for improving transfer should be part of the consideration.

Project-Based Learning

One of the primary benefits of exploring project-based learning (PBL) is its potential to connect the learners to meaningful issues in the community. Even better, PBL can connect students directly to the community. As such, it is in a wonderful position to improve instruction in a way that encourages authentic experiences. Not surprisingly, authenticity is considered one of the essential design elements of a gold standard PBL. As such, this approach seems to be a natural fit for those concerned with the potential of the learning experiences to support knowledge that transfers. I won’t ramble about this approach. Good PBL focuses on authenticity in ways that other approaches might inadvertently sidestep. It’s hard to do PBL without dedicating oneself to issues of transfer.

We’re Doing That

It’s easy to assume that transfer happens whenever good teaching happens. Any shift away from traditional lecturing is assumed to lead not only to improved learning, but transfer. I mentioned the wrestles I’ve had with transfer and authenticity at one of our first CPLC meetings with a few colleagues (it was a short conversation) and their reply was, “Oh yeah, we’re doing that. We do case studies and simulations and stuff like that.” The reply caught me off guard. This topic, which feels so daunting to me, was so easy dismissed. Granted, I probably failed to communicate my thinking clearly, but still. I was coming at this from the position of trying to increase and improve field hours in my program and moving my courses off campus and into local schools. I think case studies and simulations can be amazing, but they also don’t seem to capture the complexity of transfer. Transfer is tricky. It’s not automatic. Even when we improve learning, we may not improve transfer. One of the things that this article reminds me of is that if I think I’m doing authenticity well, it’s probably still worth taking more time and seeking to understand the contexts in which the learning is to be used, especially as those contexts change and our understanding about those contexts change.