It is 3:00 in the afternoon; a mother and her three young daughters sit at the kitchen table for a snack. They are having apple slices, cheese, and crackers. The mother, speaking Spanish, starts placing the snacks in plates for her children:

Tres cubitos de queso, tres tajadas de manzana y cinco galletas para Camila.

Lo mismo para Montse. El queso, uno, dos y tres cubitos. Las manzanas, una, dos y tres, y, por ultimo, las cinco galletas. 

Y para Natalia, como no le gustan las galletas, le damos cinco cubitos de queso y cinco tajadas de manzana.

(Three small cubes of cheese, three slices of apple and five crackers for Camila.

Montse will have the same: cheese, one, two three small cubes. The apples, one two, three slices, and finally, the five crackers.

And for Natalia, since she doesn’t like crackers, she will have five small cubes of cheese and five apple slices.)

Children's participation in everyday activities, such as the one described above, leads to the formation of a unique set of resources or funds of knowledge that will act as a foundation for their future learning (Moll et al., 1992, González et al., 2005). The types and frequencies of these activities and interactions, along with other features, such as who is involved and what languages are used, depend on a combination of family, community and cultural factors, including material and economic resources, ideas about optimal child behavior and development, beliefs about best ways to parent, among others (González, 2005; Rogoff, 2003).

Despite the many factors that impact how children participate in math-related activities, young children across the U.S. first encounter math at home as they participate in everyday experiences that encourage them to think and talk about, as well as to use numbers, shapes, sizes, patterns, and other mathematical concepts. As participation in these routines is culturally mediated, not all children's home-based math knowledge readily translates into school math learning. Oftentimes for children who come from culturally and linguistically diverse communities, their funds of knowledge differ from those traditionally drawn upon to foster learning in U.S. schools, and thus, are not anticipated nor used by teachers.

 The U.S. is one of the most ethnically diverse countries in the world, where an estimated 50% children under the age of 5 is non-White, about half of whom are of Latin American descent (Kids Count, 2017). Thus, as our society grows more culturally and linguistically diverse, it is imperative that educators of young children recognize, understand, and appreciate that mathematics is not an abstract domain learned only within the confines of preschool and schools classrooms. Mathematics is fundamentally a family, cultural, and community endeavor.  As such, mathematics learning begins in the context of the home and the community.

Therefore, teachers need to be prepared to take advantage of the resources and skills that culturally and linguistically diverse children bring from their home and communities. That is, teachers must be able to recognize and leverage children's cultural funds of knowledge as a way to make meaningful connections between home and school. In order to support effectively children’s learning, teachers must find ways to offer children these opportunities thereby ensuring their equal access to math content and learning in classrooms.

In addition, teachers need to be prepared to guide children to appreciate the contributions made by different cultures and societies to our current mathematical thinking. For instance, different cultures and nations have different ways of measuring, counting, and grouping and these could be compared. As a very concrete example, the U.S. is one of the few nations in the world that does not use the metric system!

The three projects described below can help your participants understand and build home-school connections into their mathematics teaching practice. Engaging in these projects might also help your participants uncover potential biases and incorrect assumptions they might have about children's ability to learn math, as well as their families' capacity to support them.

Cases

The case method of instruction uses realistic stories - in either video or written form - that invite problem solving. Unlike most stories, however, cases do not have an ending; instead they are open-ended and leave readers with lingering questions and dilemmas to ponder. In the case method, you can ask participants to read, interpret, and analyze realistic scenarios and grapple with the dilemmas that each situation raises.  For example, the case Daddy Says This New Math Is Crazy by Becky Smith-McCarthy (found here on page 11) highlights the tensions that arise when there is a mismatch between families and educators' conceptions of mathematics.  You can facilitate this case with participants to take families’ perspectives and brainstorm ways to manage the dilemma. Participants can also be invited to write their own cases, especially for math learning in the preschool years.  For instance, some families from Latin American backgrounds believe that the best way for young children to learn math early on is to have them memorize and do homework (i.e., math worksheets), whereas you are encouraging your participants to use manipulatives to engage children in active problem solving. Participants can write about dilemmas like this one and can think about ways to address this cultural difference while fostering and maintaining the family’s engagement in their children's early learning.

Home and community visits 

You can ask participants to act as ethnographers by visiting public spaces where families with young children interact (e.g., playgrounds, restaurants, museums, supermarkets, laundromats) across diverse communities, and capture the various ways families are naturally incorporating math into their everyday activities. Participants can reflect on the ways that the observed practices are similar and different from those they expected to find, as well as think about ways to incorporate the observed practices into the teaching and learning of children in an educational setting. For participants who have access to families, they can arrange to visit one family in their home, or accompany them on a routine community activity. In this case, you can provide participants with a semi-structured interview protocol to engage families in conversations around targeted math topics and practices. Participants can then design lessons that integrate funds of knowledge from families into their teaching practice. For example, in her project Hablemos de Matemáticas, Marta Civil works with teachers to go on household visits to learn about the Funds of Knowledge in the family with an eye on resources for their classroom teaching.

Action research projects 

Getting involved in action research offers participants the possibility to learn about their biases and assumptions that might prevent them from offering equal access to early math for all children. The goal of this project should be to enhance children’s learning through the critical analyses of participants’ assumptions about the ways young children learn math. Action research projects could involve partnering with a community agency to engage in a process of developing the project, collecting data, and analyzing the information in a way that meets the agency’s needs. You can intentionally design action research projects that require your participants to connect with family-facing organizations - like libraries, early childhood programs, or museums - to plan, implement, or evaluate their family math resources and services. In developing these projects, participants can talk with practitioners about what needs they have around implementing family math and talk with families about the types of support they want and desire. For example, in a library setting, participants might be tasked with diverse ways of integrating mathematics into ongoing story times. To do this, they might develop questions for families - individually or in groups - to understand better how families think math happens in children’s homes and communities. Librarians and participants can then analyze together these observations to get a deeper understanding of the relevance of everyday activities to the teaching and learning of mathematics (see Using Picture Books in our content modules for ideas, e.g. Using Picture Books: Counting). Ongoing reflection is an important part of this process so that participants come in as learners rather than as “experts”.  Ways you can help support this process is by asking participants to keep journals where they reflect on a periodic basis what they are learning, what they are worried about, what is interesting and exciting, what they see as their own strengths and weaknesses, and what more they need to know.  Engaging in this process not only helps participants to work with families, but also provides them with the tools and strategies they need to think critically about problems and solutions from a family-centered perspective. 

Mathematics does not only exist in schools, it also lives in the home and community at large, especially for younger children. Young children’s mathematics learning begins in the context of the home. The way families structure and include math into their daily lives is influenced by their own understanding of and beliefs about math, as well as cultural ideas about children’s learning and development. As educators of young children, it is crucial that we are ready to engage and support the development of children from diverse cultural and linguistic backgrounds. Thus, we need to be ready to recognize the math moments within families' daily life and to incorporate children’s funds of knowledge (or the knowledge that emerges from cultural practices of their families) into the classroom practices that support children’s learning.

Let’s watch a video of a mother and her daughter as they set a picnic table for a birthday party in their home. As you watch, consider the following:

• What mathematical concepts did you notice occurring through this mother-child interaction?
• What other ways do you think families naturally incorporate math in their daily lives?
• How can you incorporate the math practices and life experiences of families into your teaching practice?