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.

Revisiting 2 Metaphors for Learning

Setting the Stage

I have been privileged to join a large group of faculty and staff at Plymouth State University in the Cluster Pedagogy Learning Community (CPLC). The aim of this learning community is to support instructors as they seek to improve student learning. We are considering learning through specific learning theories (constructivism and connectivism), through three broad pedagogical approaches (interdisciplinarity, project-based learning, and open education), as well as our general education program’s outcomes, or Habits of Mind (Purposeful Communication, Problem Solving, Integrated Perspective, and Self-Regulated Learning).

As part of my participation in this learning community, I read an interview with Cathy Davidson, author of The New Education. After outlining the failure of both edtech and a skills-centric approach to saving higher education, she noted the need for higher education to emphasize “learning how to learn”. This focus, she argues, is necessary for preparing students for a world in flux. Adaptation and flexibility, persistence and problem solving become critical traits in a world that changes so rapidly.

In considering my participation in the CPLC and some of my initial reading, I have found myself revisiting papers and studies that have been critical to my learning and development as a mathematics educator. I keep finding myself thinking about how those same articles, which helped me so much in mathematics education, might inform my work in higher education. One of the first papers I want to revisit is Anna Sfard’s amazing discussion of different ways in which we conceptualize learning. It’s a pretty heavy read, but definitely worth it if you have some time to dig deep. My intent is not to summarize the entire paper, but simply to introduce main ideas that could help us as we continue to rethink how we approach curriculum in higher education.

The two metaphors that Sfard discusses are the acquisition metaphor and the participation metaphor. She makes the argument that, at least in mathematics education, both perspectives on learning are necessary. 

The Acquisition Metaphor

This metaphor captures common Western views on learning and knowledge. In this metaphor, knowledge is a cognitive construct that one can obtain and possess. When we “learn something” we have somehow captured it and sufficiently trapped it in our brains. Now, a whole variety of learning theories discuss different mechanisms for how we come to possess that knowledge. Some view the learner as a passive recipient while others view the learner as an active co-constructor of the knowledge. Behaviorists and constructivists differ greatly in how they define learning, but both view knowledge as a cognitive construct that one must acquire. 

We see this tradition all over higher education. Colleges, departments, and programs are often created around the shared “stuff” that students are expected to learn (read: acquire). Course numbers often have a specific discipline code, categorizing the type of stuff one is to acquire in that course. Many professional preparation programs have culminating exams to ensure that graduates have sufficiently procured the necessary knowledge to be trusted in that field. Higher education (and education more generally) is not struggling to leverage this particular metaphor. One of the primary reasons I share this article and discuss its implications is because it’s very easy to get excited about a particular learning theory without understanding its inherent connection with a learning theory one is trying to shed. I have seen this in mathematics education. In moving away from behaviorism and toward constructivism and social constructivism we have made amazing strides and breathed new life into the discipline. I have seen engaging curriculum and improved assessments. If we make similar changes in higher ed, I have no doubt that student experiences and learning will improve. What will not change, however, is the baggage that comes by overemphasizing any learning theory that rests wholly within the acquisition metaphor.

One of the clearest problems with an acquisition perspective on learning is that when we treat knowledge as a commodity that one can obtain (again, Sfard outlines this well), it becomes easy to separate the “haves” from the “have-nots”. In education, those who have successfully obtained more knowledge than another is worthy of accolades, honors courses, and/or scholarships. Those who have obtained less are identified as in need of remediation, intervention, or is at risk of severance. Unspoken hierarchies develop. Traditional power structures are reinforced. Deficit perspectives abound. The long-term impacts of sole focus on knowledge acquisition, even when fueled by student-centered learning theories, are ultimately harmful for so many of our students.

Participation Metaphor

As a worthwhile counterpoint to the acquisition metaphor, the participation metaphor provides a vastly different conceptualization of knowledge. In this metaphor, knowledge is not the possession of facts, but rather, the ability to engage within a specific community and to contribute to an activity in a relevant way. Knowing is replaced by doing, and the role of context and community are highlighted. Now, this is far more than listing skills one should possess (there’s that acquisition language again). Knowledge is manifest through authentically belonging. For more detailed information, it’s worth checking out socio-cultural learning theories, especially as they highlight notions such as situated cognition and cognitive apprenticeship (thanks Brown, Collins, and Duguid), and communities of practice (Lave and Wenger). 

There is something liberating about the participation metaphor. Regardless of the learning theory that guides me, I could never possibly facilitate the learning of everything my students would need to know in order to be successful in their field. I cannot adequately distill a list of topics and skills students need to acquire and then cover it in a series of courses. When I stop putting pressure on myself to ensure that my students’ heads are crammed full with all the important stuff from my field, then my focus changes. It’s not that my job gets easier, but I can at least avoid all the pedagogical pitfalls of trying to cover everything.

So, before I launch into how my focus changes, let me pose a few questions. How might your practice change if your end goal was to prepare students to find a place in which they can work with others and make meaningful contributions? What types of learning experiences would you value? What would you, as an educator, need to understand about the communities your students intend to join? What communities might you seek to join? 

As I have reflected on the participation metaphor, there are a few changes I’ve tried to make. I’ve focused more on the authenticity of student experiences, access to generative resources, and identity development. I won’t go into detail about each as each deserves, and will probably receive its own post, but I will give a brief overview as that will help illustrate the benefit of thinking through both metaphors. As I imagined my students becoming meaningful participants in their various communities, I worried about the alignment between the university classroom experience and the elementary school experience (the setting for which I prepare my students). What will happen if students get out in the field and come across messages from practicing teachers that directly contradict what they learned in my courses? Would that be an indication that my courses were out of touch? I’m certainly willing to entertain that possibility. Would they view that as a flaw in the practices of their colleagues? Either approach could be detrimental as it acts as an obstacle to joining their community. This raised a whole host of other questions. Is my job simply to maintain the status quo in education so that the preservice teachers I teach can move seamlessly into the workforce? If I do challenge the status quo, how can I do it in such a way that my students do not find themselves ostracized for not fitting a desired mold? The answer, for me, was to seek out ways to join my students in the field by moving my courses off site. Not only would this give my students a more authentic experience, but it would also help me to better understand the issues that different communities are wrestling with. I started the process of trying to join the very communities my students might later join. By serving within those communities together, we gained a stronger collective sense of how to navigate, challenge, and support the broader system. 

Moving courses off site was a great start, but I still worried about how well-connected their university experiences were with the realities of communities they sought to join. I thought back to my time as an elementary school teacher and remembered that though I kept all of my textbooks from my own program, they all sat on a shelf behind my desk, collecting dust. I never looked back to my university resources. I looked forward to new resources or used resources that other teachers were using. My textbooks felt like a remnant of my past. Growth came not from rereading a textbook, but from finding new resources to bring to bear. The more I reflected on this, the more I knew that utilizing open educational resources (OER) would be critical for my students’ ability to engage in their respective communities in meaningful ways. Using OER wasn’t simply about ditching a textbook or saving money (though both of those things were fun). It was about connecting students to resources that grow and get updated. It felt more authentic for teachers in the field (target community) to read blogs and access Twitter. I wanted my students to view learning as dynamic and ongoing, and a textbook seemed too static. Funny thing though, if I’m completely honest I would tell you that the textbooks I ditched were better than the OER with which I’ve replaced them. At least from an acquisition perspective. They contained all the information I’d hope the students would come to possess, packaged nicely with illustrations. The fact that students barely read/understood/applied the chapters in the text speaks volumes for not relying solely on an acquisition perspective. 

Why Both Metaphors

I have some more examples, but I’ll save those for a later post. At this point, some of you still reading (I applaud your persistence), may wonder why we need that acquisition perspective at all. I mean, if the participation metaphor led to strong pedagogical changes, why not kick that acquisition metaphor to the curb? Permanently. I understand the desire. I think I’m a better educator when I focus on the participation metaphor. 

At the crux of the matter, however, is transfer. Sfard explains how learning theories that emphasize the situated nature of learning and the importance of interacting within a specific community fail to explain how individuals are able to carry knowledge or tools from one situation/community to another. The best explanation for that transfer is to view knowledge as a cognitive construct that one can possess and take into different scenarios. The fact that transfer exists tends to weaken the supremacy of the participation metaphor. I should note that I think we assume transfer happens far more that it actually does, but again, that’s a post for another day. I see this transfer happening at 2 levels.

At a more superficial level, when university students learn the basic ideas and buzzwords of a particular community, it gives them a sense of legitimacy that invites some degree of participation within that community. Possessing the right knowledge can give someone a foot in the door. At a deeper level, if there are core concepts that one needs to have acquired in order to thrive within a particular community, it would behoove us to identify what those are and to ensure that they are, in fact, acquired. We have some great research, for example, that suggests that mathematics teachers who have a deep and interconnected knowledge of mathematics turn out to be better mathematics teachers. The acquisition metaphor is helpful in that regard. It’s important to note, however, that a deep and interconnected knowledge of mathematics alone will not make someone a good math teacher. That knowledge will not be enough to ensure that colleagues want to interact with that individual and support and/or learn from that individual. Here’s where looking at things from a participation metaphor could be powerful. The overall experience of university students would be enhanced if faculty and staff considered goals using both the acquisition and the participation metaphors.

How Does this Connect to the CPLC?

One of the main reasons I wanted to write this piece and to reflect on this particular article is that I see so much of the participation metaphor already shining through in the goals of the CPLC. PSU’s Gen Ed outcomes, the Habits of Mind, are written in a way that really supports both metaphors. I am a big believer, however, that when educators are explicitly thoughtful regarding their ontology and epistemology then they can be more purposeful in the pedagogical decisions they make. In our work we can easily bat around a number of good ideas or… *sigh*… best practices (you know, because we’ve definitely identified all the best ones). People may make changes to a course because someone keyed them in on this really cool thing they’re doing. Educators are amazing at recognizing good pedagogy and trying it out. The problem with that approach is that when those choices lack a firm anchor (as a clear epistemology provides), then educators find themselves vulnerable to getting swept up in the next fad. Strong pedagogical practices bear fruit only as they are thought about, implemented, revised, shared, tailored to a new group, and revised some more. The fad approach leads to the premature abandoning of amazing ideas that just hadn’t developed yet. Talk of theory, though not sexy, helps to keep us grounded. I am so excited to work with colleagues across disciplines to improve our work. As we do so, I’m happy to be the person sitting off to the side who periodically shouts out, “Let’s not forget the theory that drives us!”

I have found great traction as I have reflected on the differences between the acquisition and participation metaphors. I am confident that those delineations can be powerful for others engaged in this same work.

If you have the time, go back and read that source article.