# Commentary

In their article describing a successful lesson on Native Americans making moccasins to develop measurement concepts, Mirich and Cavey (2015) write: “Historically there has been a cultural mismatch between the traditional school math perspective and the cultural orientations of Native American Indians. This mismatch has created a very real dilemma for many students who have been raised in a different cultural tradition” (17). Kisker et al. (2012) study on the effects of using the *Math in a Cultural Context* curriculum found that “a culturally based curriculum has the potential to narrow the academic performance gap between indigenous students and their mainstream counterparts and can improve the performance of mainstream students, too” (102). Tim’s unit aims to eliminate this gap by engaging students in activities that are relevant to their culture while promoting higher-level thinking skills.

The Center for Research on Education, Diversity and Excellence (CREDE) located at the University of California, Santa Cruz, is a research and development program focused on strategies for improving the education of diverse students who, in their quest to be successful, may face challenges stemming from language, cultural barriers, race, geographic location, or poverty. CREDE established five standards for effective pedagogy that, when appropriately adapted to diverse students’ needs, “represent recommendations on which the literature is in agreement, across all cultural, racial, and linguistic groups in the United States, all age levels, and all subject matters” (http://crede. berkeley. edu/research/crede/standards.html):

- • Joint productive activity: Teacher and students producing together
- • Language development: Developing language across the curriculum
- • Contextualization: Making meaning by connecting school to students’ lives
- • Challenging activities: Teaching complex thinking
- • Instructional conversation: Teaching through conversation

Hilberg et al.’s (2000) mathematics research on the effectiveness of instruction using these standards with American Indians shows better conceptual understanding and retention rate for those taught using the CREDE standards then for those who were not. CREDE’s third standard concurs with an overarching goal of NCTM’s (2014) Teaching Practices, which is to integrate mathematics into familiar contexts, to mesh with students’ personal styles, and to build on tasks that promote reasoning and problem solving (10). It is clear that Tim adheres to the standards of CREDE in his teaching. Desks in Tim’s classroom are arranged to accommodate conversation between him and small groups of students on a regular basis. He puts a priority on student-student interaction because, he says, “the students in my class tend to work better in small groups where there is a reliance upon each other for success.” He and his students become a learning community as they together explore the concepts and master the skills required to successfully launch their model rockets. His frequent use of questioning, restating, praising, and encouraging assists the students’ learning throughout the conversation. In addition, he promotes language development by incorporating science concepts and language arts skills into the model rocket unit. He is convinced that this unit helps his students see their learning as a “whole,” thereby finding meaning in the curriculum. In their review of research studies detailing instruction of Native American students, Hankes and Fast (2002) point out several principles that should guide mathematics instruction of Native American students. Key among these guiding recommendations is “cooperative rather than competitive instruction” (41).

Before his students embark on the job of building their rockets, Tim models for them as they watch the construction process. This observation-modeling process builds on the visual learning patterns common to Native American learners (Tharp, 1997). Mindful of his students’ preferred learning style, which he describes as “tactile/kinesthetic with an emphasis on practical uses for the material they are learning,” he designs a great number of hands-on projects (e.g., building a canoe) that tie into real-life problems (SMP1, 4, 5, 6). The assembly and launch of model rockets as the culmination of the unit not only provide motivation to learn mathematics but also connect to Tim’s students’ visual learning strengths and their need to produce demonstrable evidence of their learning. A wider context for learning mathematics is established as Tim helps his students apply their new mathematics understandings to the lumber and forestry industry, vital to the economics of their locale.

With technology as a tool, Tim engages students in tasks that incorporate algebra and trigonometry, concepts that may be deemed too advanced for fifth-graders. Calculators are used to informally verify concepts that students will later explain and, once these concepts are learned, students may then gather data and perform the calculations to reinforce the procedures if necessary. This utilization of technology to make real-life mathematics more accessible to students supports NCTM’s (2014) recommendation for taking action with technology to increase student engagement and creativity:

Teachers should continually explore mathematical tools and technologies to evaluate their potential to open students’ mathematical horizons . . . Given the accelerating ease with which technology can be used to carry out nearly any mathematical procedure that students might be asked to perform, mathematics educators may need to raise questions about the balance of procedures and conceptual knowledge required for math proficiency.

*(88)*

As recommended in NCTM’s Access and Equity Principle, Tim creates opportunities for his students to succeed in engaging with challenging tasks, and then he supports them with whatever assistance they need to meet the goals. Note that any accommodations Tim makes to ensure that his Native American students are successful are also applicable to all of his students. As Trumbull et al. (2002) point out, “It is interesting that the approaches of indigenous peoples to teaching and learning coincide with some of the most highly touted elements of research-based instruction called for by our nation’s education reformers” (8). Tim’s assessment of his students’ learning styles and his lesson designs are consistent with the recommendation of Bradley and Taylor (2002) to use hands-on experiences to build on Native American and Eskimo children’s learning preferences to develop their formal mathematics thinking.

Tim also demonstrates how to put into practice culturally sustaining/revitalizing pedagogy through the creation of a classroom community where students respect and support one another as they work on challenging problems that are directly related to their culture. He exemplifies the model of the teacher who identifies appropriate projects for students according to Reyhner et al. (2011):

Culturally appropriate education is not just a basic human right, it is also good educational practice. The best way to contextualize education is to relate what students are learning to their cultures, communities, lives and land. While students need to learn the knowledge and skills included in tribal, state and national standards, they and their teachers also need to respond to local concerns and have some choice in what type of learning projects they can become engaged in.

*(viii)*

What is evident to an observer of Tim’s teaching is his enthusiasm, his love of mathematics, his creativity, and his sense of fun. He is a powerful catalyst for the motivation, enthusiasm, and success of his students, showing them the way to aim for the stars and walking with them on the journey