# Commentary

Now a secondary math teacher, Bob Moses had taught mathematics to his children at home to supplement the mathematics they had in school. In 1982, his daughter’s teacher, Mary Lou Mehrling, invited him to work with students on algebra in the eighth-grade classroom in the Open Program at Martin Luther King School in Cambridge, Massachusetts. Students in the Open Program were not expected to be high achievers in mathematics. However, Moses was successful in producing students from that program to qualify for honors geometry. In subsequent years, the group studying algebra grew but still focused on academically talented students. Academically talented African American males, in particular, felt uncomfortable joining the group because they would be separated from their friends who were on other math tracks. As a parent-organizer, Moses decided to take action. He drew on his background as a civil rights organizer in Mississippi in the 1960s to make the learning of algebra more than a curriculum issue; it became a broader political issue.

Moses began a dialogue with parents, teachers, and administrators in the Open Program. Eventually, consensus was reached that each student in the Open Program could achieve math literacy. The results of this change in philosophy included changes in the content and methods of teaching math, classroom involvement of parents and their participation in workshops on student achievement and self-esteem, emphasis on students’ self-motivation to succeed, the recruitment of African American college graduates to serve as role models and tutors, and the birth of the Algebra Project (Moses et al., 1989). As a philosophy, the Algebra Project contributes to mathematics and science literacy, which is a prerequisite for employment and citizenship. Three broad goals are addressed: to develop mathematically literate and motivated students who will master the college preparatory mathematics necessary for careers in which they will need mathematics; to produce teachers who create learning environments in which students connect real-life experiences to their construction of mathematics knowledge; and to build a community of nurturing support for students.

As a curriculum, the Algebra Project Transition Curriculum follows a five-step curricular process. First, the program uses physical events from students’ everyday experiences that are the links between the physical world and the abstractions of mathematics. Next, students make a pictorial rep- resentation/model of physical events. Next, students use their own intuitive language to talk/write about the events, followed by the teacher using regimented English sentences to guide students from their intuitive language responses into equations to represent the physical events. Last, students begin by developing their own symbols and then are introduced to standard symbols (Silva et al., 1990).

The experiential learning of the Algebra Project Transition Curriculum helps students to create the conceptual language of mathematics, honors how students think and their experiences, emphasizes group work and cooperation, and assists students to clarify and organize their thinking as they present their math understanding to their peers (Checkley and Moses, 2001). It also emphasizes efficacy and the belief that confidence and effective effort are alternatives to an ability model of learning (Moses et al., 1989). Confidence is a strong predictor of mathematical course taking and has a significant, positive correlation with mathematics achievement (Reyes, 1984). According to Sparer (2016):

The program works by using math to generate a space where teachers can collaborate with parents and students to create a safer environment with room for students to grow. What many people don’t understand is that without The Algebra Project, learning math, an opportunity many kids dread, isn’t even a right, it’s a privilege many minority students won’t even get.

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Lynne is not only an exemplary teacher but also a developer and a champion of the Algebra Project in the Cambridge area. The lesson profiled in this chapter exemplifies the philosophy and pedagogy of the Algebra Project in several ways: It connects to the students’ real-world experience of the Chinese zodiac; in it are multiple opportunities for the students to articulate their understanding through both action and language; in the group setting, students acting as a community of learners negotiate mathematical meaning; and the lesson uses meaningful games to establish mathematical patterns and rules.

What can educators who are not teaching the Algebra Project Transition Curriculum learn from Lynne’s approach? Does her approach address what experts suggest are effective strategies for teaching mathematics to African American learners? Ladson-Billings (2014) writes that the development of her pedagogical theory called culturally relevant pedagogy (CRP), which grew from a focus on how to increase the learning of African Americans, was likely to apply to all students. In her earlier work, Ladson-Billings (1998) noted that the hallmarks of CRP included student-posed and teacher-posed problems; students treated as competent; high expectations set by the teacher; use of prior knowledge as a bridge to new learning; the extension of students’ thinking beyond what they already know; and strong interpersonal relationships of teachers with students. Lynne’s lesson integrates the CRP strategies of cultural competence through its use of the Chinese zodiac not as a mere picture or as a quick introduction to get to the algorithms but as an important tool to uncover important patterns that lead to the algorithms (SMP4). According to Crombie (2013), via its embodiment in the Winding Game, the zodiac encourages students to behave as mathematicians as they use it to make and record observations followed by making predictions and using it again to determine whether the predictions are true or not (SMP1, 2, 3, 6, 8).

In accordance with the Equity Principle and Teaching Practices of NCTM’s *Principles to Action *(2014), Lynne communicates high expectations for her students and provides quality experiences for them to excel in a very supportive classroom environment. Walker and McCoy (1997) emphasize the link between the teacher’s personal interaction with the students and their desire to perform well in the class. Mathematically successful students in their study reported that the positive encouragement given to them by teachers and parents helped them to realize the importance of mathematics and motivated them to take more mathematics courses. On the other hand, Walker and McCoy caution that the teacher of mathematics “must realize that his or her classroom environment may be damaging to the confidence of African American students” (79). In her article on experiences that influenced the racial and mathematical identities of high-achieving black college students in mathematics and engineering, McGhee (2015) describes components of a framework for the development of mathematical identities of black students based on what she calls a fragile and robust mathematical identity:

In this framework, the term fragile is defined as the delicate and vulnerable relationship between Black students’ mathematics success and the persistent racialization they endure in their discipline. The term robust is defined as the strength and agency that students develop in spite of their racialization to maintain self-motivated mathematics success. The three components of fragile and robust mathematical identity are (a) central motivations to succeed in mathematics, (b) the use of coping strategies in response to students’ racialized mathematical experiences, and (c) dispositions associated with one’s successful outcomes in mathematics. During specific time periods, mathematical identities are either mostly fragile or mostly robust, and those labels became useful in unpacking the actions and motivations behind the mathematical experiences.

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A question McGhee (2015) poses for research and reflection at the end of the article is: *How might mathematics teachers work within the three components to assist black students in developing a robust mathematical identity*? Lynne’s profile demonstrates some concrete answers to this question because the Algebra Project’s approaches to problem solving (collaborative work in a welcoming environment, situations relevant to her students’ interests, student-directed discussions, real-life activities, multisolution problems) preserve students’ self-efficacy and build a firm foundation for their future success in algebra. These approaches align with the recommendations of Smith et al. (2000) who report that with the least academically prepared students, “open-ended problems rooted in concrete, real-life settings worked best” (92). Equally critical is that the unit focuses on important mathematical goals.

In her article on effective teaching practices, Tolle (2015) writes, “Good instructional packages need solid mathematical goals” (619). Reflective questions that are critical to helping Tolle improve her own practice for engaging students are: “What is the mathematical goal of that activity? Yes, it engages students, but is it intellectually engaging, and what mathematics should the students learn by the end of the activity? What mathematics should we hear students discussing and see them doing as we watch and listen to them? Are they intellectually and mathematically engaged in the activity?” (619-620). For this unit, the mathematical experiences, students’ participation, and Lynne’s attention to students’ disposition all model McGhee’s (2015) and Tolle’s (2015) recommendations for helping students develop a robust mathematical identity.