Funds of Knowledge and mathematics education: a personal reflection / Fondos de Conocimiento y la educación matemática: una reflexión personal

How it started

While working on my PhD in mathematics education, I became very interested in the ideas of situated cognition (Brown et al., 1989), ethnomathematics (D’Ambrosio, 1985) and out-of-school mathematics (Carraher et al., 1985). I was very intrigued by the interplay of culture and mathematics. As I joined the University of Arizona in 1990, I wanted to pursue these interests, maybe by exploring ethnomathematics among the Indigenous groups in the Southwest. So, one day in the early nineties ¹ , I went to the Bureau of Applied Research in Anthropology (BARA) in the university because I had heard that there was a professor there who had done some work with American Indian students and mathematics. Lucky for me, this professor was in her office, and when I told her what my interests were, she said that she did not do work in mathematics but that there was a group of researchers who met regularly in some other office in BARA who may be a good fit for me. This wonderful person walked with me down the hallway, and lucky me, the Funds of Knowledge group was meeting that day: Luis Moll, Norma González, Cathy Amanti and several other project members. I joined their meeting and mostly listened, after having introduced myself. I think that some (maybe all) of them were a little puzzled by why would a mathematics educator working in the Department of Mathematics (not in the College of Education) be interested in a group that focused on language, particularly on biliteracy? I do not remember if it was at that first meeting or a later one when I met two of the teachers in the Funds of Knowledge for Teaching (FKT) project, Anna Rivera and Patricia (Pat) Rendón. At the time, they were both teaching in the same school, and as they shared their experiences with their ethnographic home visits and their interactions with students in their classrooms, the idea of developing a module around money came up. This was my first involvement in a Funds of Knowledge learning module. Both teachers, Anna and Pat, were very gracious to let me ‘play’ with them and their classes as we brainstormed how to make mathematics more visible in a learning module around money. As we debriefed the money module in some study group sessions, I remember Luis making two kinds of contributions; one was along the lines of probing our work further to maybe consider possible extensions and follow-ups. For example, in one of the classrooms, some students had become interested in the topic of ‘money, power and politics’. Luis asked how this topic had emerged and asked about the possibility of focusing on the work of this group of students. The second type of contribution that Luis made was connections to theory. He was amazing at this, as I will illustrate later.

I remember that some of our conversations centered on how to let students play with mathematics in meaningful and relevant ways, similarly to what the teachers did with language and literacy. Interviews and conversations I had with some of the teachers in the FKT project pointed to a desire to know more about ‘how the math can be explored, can be innovative; in literature we have more of an idea of how that works, we don’t have anything like that in mathematics’. The teachers wanted to ‘get out of the rut of doing math with pencil and paper and the textbook, to get the students to talk about math in cooperative groups; it’s important because sometimes other subjects are taught that way but math isn’t’.

This was something that struck a chord with me, the idea of how to develop an approach to teaching mathematics that basically reflected what they already did when teaching literacy in their classes. The meaning and sense-making that to me is at the center of a FKT approach is exactly what we need in the teaching and learning of mathematics. But there were certainly challenges in bringing this vision to life. One challenge that I have described elsewhere (Civil, 2007) was the tension between pushing for the mathematics and preserving the purity of Funds of Knowledge. This tension emerged first for me in the construction module (Sandoval-Taylor, 2005). I remember lively discussions with the teacher, Patricia Sandoval-Taylor, on possible activities that we could do in class that related to construction and were mathematically rich. In one of the meetings, I suggested an activity that would have the children (second-graders) build a chair (or some other object) for a doll or action figure. To me, this would involve proportional reasoning since the students would have to adapt a standard chair to one for their character. Granted that proportional reasoning is somewhat beyond the mathematics in second grade, but the idea was to see how the children would go about this task. But the teacher was concerned that the idea of proportional reasoning may not come out of a discussion around house construction. As she writes:

I was not sure that learning about proportion would emerge during the unit. From my experiences in my students’ community, I thought that the unit focus would more likely be on constructing buildings. . . Students could be asked, for instance, how to build an additional room on their homes. (Sandoval-Taylor, 2005, pp. 159–160)

The issue here is not that there were not mathematical-rich activities in the module, which there were. This is related to a broader question that I have raised many times, which concerns our views of what counts as mathematics. Connected questions are: What kinds of mathematics can emerge from everyday contexts? What does it take to see mathematics in everyday practices? Can students learn ‘advanced’ mathematics through everyday contexts or are they mostly using what they already know? I still, today, wonder about these questions. The construction module planted in me the seed to start exploring some of these issues. This exploration became more focused in the next couple of years as I worked with Pat Rendón on several projects with her fifth-graders, as I describe next.

At one of the meetings in BARA, I met Rosi Andrade, who at the time was a graduate student; Luis was her advisor. Rosi and I connected right away. Here is an example of how generous and supportive of new scholars Luis was: he basically told me that Rosi could be the graduate research assistant for the work that I was going to do as part of the FKT project. Just like this, as an assistant professor with no grants yet, I found myself with a colleague, Rosi, with whom to plan the work we were going to do with Pat. Rosi was very influential in pushing me towards the work on parental engagement in mathematics education that today is actually my most well-known work. But if it were not for Luis, I would not have had the incredible opportunity to have a thought partner such as Rosi.

So, Pat, Rosi and I embarked in a collaboration over two years (at a different school from the one where we worked on the money module, since Pat had changed schools). The projects in these two years allowed us to combine Rosi’s interest in children’s social worlds and Pat’s and my interest in exploring the teaching of mathematics through a Funds of Knowledge lens. I remember going with Pat on a home visit and learning about one of her students, Alberto, ² who was struggling in mathematics in the classroom. I remember how proud his mother was when she told us how successful Alberto had been in handling his own set of customers as part of his help with the family bakery business in Mexico (Civil & Andrade, 2002). This episode reminded me of the work in Brazil with street vendors and how successful they were in their computations in connection to their selling, and yet when problems that were mathematically similar were presented with pencil and paper, they were much less successful (Nunes et al., 1993). While the problems may have been mathematically similar or even, one could argue, equivalent, context plays a key role — street mathematics and school mathematics are not the same (Schliemann, 1995).

In Civil (2002), I describe some of the work we did during that time with Pat and Rosi. In particular, we engaged the children in a project in which, after having explored some mathematical games, they were to design their own game. Their games taught us a lot about their interests but also, overall, did not have a lot of mathematics. Once again, this observation reflects my own beliefs as to what I was willing to count as mathematics. To me, a key aspect of the philosophy behind Funds of Knowledge is to build on the family/community knowledge and experiences. In the work on the games module, this meant to follow students’ interests in the games they wanted to develop. But as I describe, this meant that getting to the mathematics was not easy:

Catching students using ‘mathematics in context’ is not easy. We cannot plan for this to happen. In fact, one difficulty in this approach to instruction is that, because we want to follow the students’ agenda, we find ourselves planning as we go along. Hence, we often see the missed opportunities for mathematics exploration after the fact. (Civil, 2002, p. 51)

While from my point of view the games were not as mathematical as I was hoping, they reflected what mattered to these students, whether it was sports, airplanes or their prior experience playing other games with friends or family members. One of the groups created a board game that represented the classroom. They called it Goof Off. The goal of the game was to make it to the teacher’s desk. Along the way, the players picked up cards that featured actions that could delay or advance them in their journey to the teacher’s desk. As I looked at some of my journal notes that I kept during that time, I had written:

When I asked Rebecca [the group leader] how she had come up with the idea for this game, she replied, ‘I watch the class; some of the events [in the cards] have actually taken place in this class.’ As Rosi says, this game is an ethnography of the class. This is perhaps the biggest contribution about these games: they tell us about the children in this class. (October 29, 1993)

In looking at some of the data now, more than 30 years later, I realize that a lens of Funds of Identity (Esteban-Guitart & Moll, 2014) could have been useful in making sense of the games that the students developed, since they reflected their interests as children in that moment. The games module had started with the students interviewing their parents or another significant adult in their household about games they had played as children, as a way to connect to their home family’s Funds of Knowledge. But the fact is that the games the students developed reflected their own interests, their own experiences. The game Goof Off was a window into how these students, primarily Rebecca, interpreted the day-to-day in their classroom. One approach used in the Funds of Identity work is to have the participants make a self-portrait (Esteban-Guitart & Moll, 2014). I wonder, would asking them to design a game also provide valuable information into their Funds of Identity?

A focus on mathematics

As the FKT project was ending, another opportunity to continue work along these lines came up. This led us to develop project Bridge (Linking home and school: A bridge to the many faces of mathematics). As can be inferred from the title of this project, the focus was going to be on mathematics. That is, we kept the structure of the FKT project (ethnographic training; teachers making household visits; study groups; classroom implementation). But the goal was to continue the work started in the money, construction and games modules, that is: how can we bring the mathematical Funds of Knowledge into the school mathematics classroom? Underlying this work was the eternal question of ‘What counts as mathematics?’ During the four years of this project, Luis acted as a mentor, meeting with us from time to time and offering his great theorizing skill, in particular during the writing of González et al. (2001). As in the prior Funds of Knowledge work, we collaborated with several teachers over the years. Here I briefly describe two classroom modules since they both illustrate some key issues for me in trying to bridge home and school mathematics.

With a fourth/fifth-grade teacher, Leslie Kahn, we developed the garden module (Civil, 2007; Civil & Kahn, 2001; Kahn & Civil, 2001). The idea for this module came from an extended study group meeting where we brainstormed different possible modules based on the findings from the home visits that the teachers had made. Leslie described her interest to participate in project Bridge to investigate whether ‘rigorous mathematics could be developed from household visits’. I think that Leslie’s interest allowed me to explore my tension between out-of-school knowledge and academic mathematics. I often think of this module as one in which we were able to somewhat combine the sociocultural component of an approach such as Funds of Knowledge with a more cognitive approach through task-based interviews with the students.

Another module was developed by an experienced mathematics teacher, José David Fonseca, who brought in a lot of experience and knowledge about architecture, civil engineering, construction, carpentry, house repairs, etc. He developed a mathematically rich project on the topic of ‘build your dream house’ for his middle school students. This project is described in a chapter by Ayers et al. (2001). As José David mentions in that chapter, he had taken a course on Funds of Knowledge taught by Luis and Norma. So when he joined the Bridge project, he was already familiar with the framework. There is no question in my mind that his project brought the mathematics to the forefront while building beautifully on the students’ and their parents’ knowledge of construction. Throughout the years of project Bridge, José David was also able to elicit the mathematics in the practices of a carpenter and a seamstress, among others. I, on the other hand, with my formal mathematics background, would have a much harder time seeing the mathematics in practices with which I am not familiar. So, as a teacher in Bridge asked, ‘If you have too much school mathematics, does it erase our practical mathematics?’ José David had a very strong mathematics background, but he also had a deep understanding of these practices. So, is this what we need? And if that is the case, then how feasible is it to try to bridge school mathematics and out-of-school mathematics?

These are some of the questions that I have wondered over the years. An example of this is in González et al. (2001), where we write about my experience seeing a seamstress creating a paper model of a skirt. To me, much of what the seamstress did was ‘mesmerizing and mysterious’ (González et al., 2001, p. 124). While my mother was an accomplished seamstress who made pretty much all my clothes growing up, obviously I did not learn the practice, which shows that the adults’ Funds of Knowledge are not necessarily those of the child. And my mathematics background did not seem to be of much help interpreting what the seamstress was doing. I am not going to reproduce here all the back and forth between what the seamstress did and my attempts to understand her actions from a mathematical point of view. This is all described in the article (González et al., 2001). The point of my story here is how part of this article came to be. I remember being at a restaurant in South Tucson, having lunch with Luis, Norma and Rosi. We were discussing the article we were in the process of writing, and I was telling them about what I had observed watching the seamstress. Suddenly, Luis started seeing theoretical connections in what I was saying. I do not remember exactly what he said, but I remember thinking, ‘What? How does he manage to see this (whatever the ‘this’ was) in what I said?’ I know he talked about mediation and the importance of social interaction. Basically, he was able to take what I said and give it a theoretical spin that I certainly would not have been able to give. And this would be a recurrent event whenever I met with him to talk about something I had observed. I would describe what I saw in more of a storytelling approach, and he would find connections to theory. I am quite comfortable moving from theory to practice when working with teachers, for example. What Luis did superbly well was to move from practice to theory.

My experience observing the seamstress was certainly part of my interest in understanding mathematics in everyday practices. The seamstress was part of a group of women of Mexican origin who met regularly to engage in literature discussions and in conversations about their experiences and their children’s education. Mathematics had not been part of these gatherings, but some of them expressed interest in exploring this topic further. This was the beginning of what has since been my main area of work, namely, mothers/caregivers and mathematics. While Luis was not directly involved in this part of my work, if he had not introduced me to Rosi and encouraged us to work together, I may have never entered this adventure. For several years, Rosi and I worked with a group of mothers at one of the school libraries, where we learned mathematics together (Civil & Andrade, 2002, 2003). In this last section, I describe some of my most recent work, which emerged from this collaboration.

My work with mothers and mathematics

Since the late nineties, when Rosi and I started our collaboration with a group of mothers, my work has primarily centered on working with parents (mostly mothers) and mathematics. When Rosi and I worked in the FKT project, we had conversations about our interest to do more beyond the household visits. In a sense, the household visits gave us and the teachers information from the families. But we felt a need to give back to the families, that is, to have more of a two-way exchange. We wanted to engage with the mothers in exchanges that would on one hand address their interest in learning more about their children’s school mathematics, and on the other hand our interests in learning about the mothers’ experiences and uses of mathematics in everyday life. It is through the work with a small group of mothers in the school library that the concept of parents as intellectual resources emerged (Civil & Andrade, 2003). Our collaboration with the mothers was still grounded on the concept of Funds of Knowledge, but ‘key to our approach was researching ways to promote families (parents) as intellectual resources in the academic development of their children’ (Civil & Andrade, 2003, p. 153).

In the 2000s, I developed a research agenda that looked at issues such as immigrant parents’ perceptions about the teaching and learning of mathematics (Civil & Planas, 2010), parents as adult learners (Díez-Palomar et al., 2011), mothers’ and children’s interactions in mathematics (Civil & Quintos, 2022). For example, building on the concept of parents as intellectual resources, in a large project on parental engagement in mathematics education, we had teams of parents and teachers/school administrators facilitating mathematics workshops for the community at large. When I first suggested this idea as we were working on the proposal, some colleagues pushed back, questioning whether the parents would be effective facilitators and know enough mathematics. Luckily, we went ahead with the idea, and I have to say that some of the best workshops were the ones facilitated by a team composed of mothers only. They knew their community and they knew how to connect with it. As for the mathematics, they participated in professional development alongside teachers to prepare for the workshops, and they contributed valuable insights that often combined their own Funds of Knowledge with their experiences with the mathematics in the modules they were going to facilitate. This is not to say power issues were not present (Civil & Bernier, 2006).

This work continues today in my most recent projects, focusing on bringing teachers and parents together in a more deliberate way, in part to address the power issues I just mentioned. Both teachers and parents learn about the concept of Funds of Knowledge and the teachers are still encouraged to conduct some home visits, while the parents are invited to visit a mathematics class. We have refined the approach to bringing parents and teachers together through the use of Funds of Knowledge–based mathematical tasks that prioritize community knowledge, hence helping provide a more balanced experience that does not privilege school mathematics (Quintos et al., 2024; Varley Gutiérrez et al., 2024).

The work with parents and mathematics was one of the pillars of the NSF-funded CEMELA (Center for the Mathematics Education of Latinos) (2004–12). CEMELA brought faculty and fellows (graduate students and post-docs) from four different universities: University of Arizona, University of California, Santa Cruz, University of Illinois, Chicago, and University of New Mexico. Luis was a Co-Principal Investigator for the Center and, as such, he taught a short course on sociocultural theory in January 2006, as part of the first CEMELA School. I reached out to some of the CEMELA fellows to ask them about their memories of their interactions with Luis. I am closing this piece with their recollections.

From Javier Díez Palomar (University of Barcelona). Javi was a Fulbright postdoc at the University of Arizona:

As a Fulbright postdoctoral researcher at CEMELA, I remember participating in a course led by Luis as part of the doctoral program at LRC. This weekly course focused on sociocultural topics and learning. I clearly recall Luis explaining the influence of research based on Vygotsky’s work in the United States. One aspect that particularly stood out to me was his tendency to occasionally incorporate Spanish words into his speech, especially when joking. However, what impressed me most was the substantial number of articles and book chapters assigned for each session. Coming from an academic background where such extensive reading was uncommon in doctoral courses, I found this approach both surprising and intellectually enriching. It allowed me to engage more deeply with sociocultural theories in education than I had previously anticipated. (Email, 30 March 2025)

From Maura Varley Gutiérrez (University of Arizona). Maura was a CEMELA graduate student at the University of Arizona:

My first formal introduction to Funds of Knowledge was with Dr Luis Moll in a course he taught for CEMELA fellows in 2006. I had come straight from the classroom, and it was the first time in graduate school that I felt heard as a former classroom teacher — I taught in a small community school in Washington, DC, and the school was founded on the idea of the historically resilient community being the basis for curriculum. I still remember the video that Dr Moll showed as an example of Funds of Knowledge, of a father teaching his child how to weld to create a metal barbecue; I could envision the many applications for curriculum grounded in community knowledge and the power of this theory to transform education. The work Luis and colleagues have done to connect Funds of Knowledge to classroom and community learning settings still grounds the work I do every day as a teacher educator. (Email, 3 April 2025)

From William (Bill) Zahner (San Diego State University). Bill was a CEMELA graduate student at the University of California, Santa Cruz:

I recall that Luis was a gracious host — he welcomed us to Tucson, gamely answered naive questions from those of us who were new to educational research and pointed out landmarks from the windows of the convention rooms at UofA (e.g., Mount Lemmon) while we were on break. What I recall mostly is the feeling of warm welcome and support. (Email, 24 March 2025)

I think we can all relate to the warm welcoming and supportive attitude, the being heard and the sense of humor, traits that were so characteristic of Luis.