# Commentary

Diane’s profile is a wonderful example of how to engage students in worthwhile tasks that connect with and invite the community into the classroom by acknowledging and honoring the culture of students. She incorporated NCTM’s *Principles to Action* in that her goal is clearly focused on having students implement a geometric task that requires problem solving through its use of a quilt to

model the concepts. She supported productive struggle through suggestions or purposeful questions that helped students apply the heuristic, “Think of a simpler problem.” For example, for those having difficulty beginning the quilt pattern, she suggested that they fold the paper in four sections and work on one section at a time. Her rubric required that students’ work demonstrate the use of correct procedures for the concepts, and she elicited and used evidence of her students’ thinking to guide discussions and to incorporate it in succeeding lessons.

What makes Diane such an effective teacher of mathematics? According to the *Principles and Standards for School Mathematics* (2000):

Teachers establish and nurture an environment conducive to learning mathematics through the decisions they make, the conversations they orchestrate, and the physical setting they create. . . . In effective teaching, worthwhile mathematical tasks are used to . . . engage and challenge students intellectually. Well-chosen tasks can pique students’ curiosity and draw them into mathematics.

*(18)*

One way Diane draws her students into mathematics is to integrate mathematics into the whole curriculum. In this unit, the mathematical task combines social studies, language arts, visual arts, and research experiences for students (SMP1, 2, 4). Students created blocks for a quilt that included not only geometric concepts but also repeated patterns of the concepts (SMP8). While she gave them guidelines, students decided what the final product of their efforts will look like and whether the outcome met the high standards she *and* they had set for their work. As can be seen in this lesson, as well as in all the mathematics that she teaches, students’ communication of their mathematical ideas is paramount for Diane. “I have to be sure my students can explain their mathematics understandings both to me and to their peers. I don’t rely on classroom tests or state test scores as the only measure of whether or not a student knows the mathematical concepts” (SMP6).

Does Diane teach in a multicultural classroom? At first glance, the students in her classroom appear to have similar physical characteristics, and one could assume they are all of one culture. As Diane puts it, “It’s interesting to note that on the surface no one could have picked out the students’ background. Their culture wasn’t obvious by looking at their skin tones, hair color, speech patterns, and so forth. I was amazed at how many different nationalities are represented in my classroom.” Under the assumption that all her students were “the same,” she lumped all her students into one homogeneous group by ethnicity, then assumed common characteristics and taught accordingly. What she found when she dug a little deeper is a richness of family background that she could use in making her mathematics lessons more personal for each student’s family. What’s important in this chapter is that a group of students who, on the surface, seems to be all the same have very different ethnic origins. On the surface, Diane’s classroom could probably be considered monoethnic. However, what could be easily overlooked is that everyone belongs to more than one microculture, so even in a so-called homogeneous classroom, many cultures are still represented. Regardless of the setting, therefore, teachers should be familiar with the tenets of multicultural education as described by the National Association for Multicultural Education (2016):

Multicultural education is a philosophical concept built on the ideals of freedom, justice, equality, equity . . . It affirms our need to prepare students for their responsibilities in an interdependent world. It recognizes the role schools can play in developing the attitudes and

values necessary for a democratic society. It values cultural differences and affirms the pluralism that students, their communities, and teachers reflect . . . It helps students develop a positive self-concept by providing knowledge about the histories, cultures, and contributions of diverse groups.

*(http://www.nameorg.org/definitions_of_multicultural_e.php)*

How did Diane teach from a multicultural perspective? Not only did she reinforce mathematical concepts in this quilt unit, she also taught her students core American values: embrace of diversity, respect for ancestors, and the dignity of each person. Through this unit, Diane also gained a new appreciation for the uniqueness of each of her students. She and her students discovered commonalties about each other as well as differences about one another as they studied one another’s country of origin. According to Diane, “My students learned that many of them had similar cultural backgrounds and connected with each other through that. They also appreciated their differences. I think that, maybe for my students to appreciate the cultural differences among themselves, they first had to learn about and to value their own culture.” Since many European American students feel that they do not have a culture in the same sense as more culturally identifiable people do (Nieto, 1996), teachers must orchestrate experiences for these students to identify and to celebrate their own cultures so as to subsequently celebrate all cultures (Sharp, 1999).

Appreciation for Diane’s unit extended outside of the schools to the student’s families. Grandparents attending the students’ presentation were happy to help with stories from the old countries to incorporate in the quilt. The fact that *their* story was important to the current generation of students must have made some positive impact on their view of schooling today.