Mathematics Learning and Diverse Students

 

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students’ performance on open-ended problem solving tasks and their NAEP scores. Other 

studies also indicate that curricula that emphasize complex mathematical tasks are indeed 

beneficial for all students (Boaler, 2002b; Schoenfeld, 2002; Tarr et. al, 2008). 

 

Another aspect of curricula that support diverse learners is grounding mathematical ideas 

in contexts familiar to students (Boaler, 2008 Davis, West, et. al., 2007). Such contexts help 

students leverage their everyday, out-of-school experiences for in-school learning, and motivate 

students by communicating the power of mathematics in their worlds. In her seminal study 

involving two schools attempting to implement reform-based instruction, Boaler (2008) found 

greater gains in a school in which the mathematical tasks were closely tied to experiences in the 

students’ lives. Similarly, one of the central tenets of the Algebra Project (Davis, et al., 2007) 

curriculum is engaging students in shared experiences that serve to bring them into the language 

and culture of mathematics. Their work shows that such experiences help students to connect 

their own ways of reasoning and explaining to the formal structures of mathematical discourse.  

 

Likewise, the teachers at Railside devoted considerable time and energy to developing 

and enacting a curriculum that challenged students to engage with complex mathematical ideas. 

They worked together to plan activities and lessons that they called “group-worthy” -- employing 

mathematical tasks that foster deep engagement with challenging mathematical problems and 

rich mathematical discussions among students. They continually revised these lessons together, 

sharing ideas and strategies for optimal implementation, as well as analyzing failures and 

potential pitfalls. Over the course of several years, each teacher had compiled a large binder with 

these co-written and revised activities, which they used as the basis for their activities in the 

classroom. 

 

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Classroom Practices that Support Equity 

 

Equally important to the content of the curriculum are classroom practices that enable 

students to engage with the curriculum and create mathematical meaning from it. Powerful 

practices include those that foster student-centered discourse, student exploration of 

mathematical ideas, and on-going feedback (Davis, et. al., 2007; Boaler, 2002b; Fullilove & 

Treisman, 1990). Studies indicate that supporting students in working productively in small 

groups to discuss their understanding and provide help to their peers leads to increased 

performance (Webb & Farivar, 1994; Boaler & Staples, 2008; Silver & Stein, 1996; Fullilove & 

Treisman,1990).  

 

Researchers stress the importance of the role of teachers in fostering and facilitating 

productive student discourse as well as the importance of “group-worthy” tasks (Cohen & Lotan, 

1997; Boaler & Staples, 2008). Changing participation structures from lecture or teacher-

centered discourse to student-centered discourse may result in discomfort for some students and, 

if not sufficiently supported, can lead to a lack of positive results (Lubienski, 2000). However, as 

Webb and Farivar (1994) demonstrated with sixth-grade students, supporting students in learning 

how to talk with and help each other and providing sufficient feedback on individual work 

results in significant gains for Black and Latina/o students.  

 

 Issues of unequal status in classrooms can create inequitable learning in the context of 

group work (Cohen & Lotan, 1997). Cohen and Lotan (1997) have identified two practices that 

can address issues of differential status: broadening the meaning of “smart” by reorganizing 

curriculum and instruction around multiple ways of representing and interpreting mathematics, 

and assigning competence to low-status students by publicly recognizing these students’ 

mathematical ideas and contributions. Boaler and Staples (2008) studied the effects of these 

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classroom practices in mathematics classrooms at Railside High School, documenting their 

positive effects on both mathematics achievement and the development of positive mathematical 

identities. They found that the teachers at Railside regularly assigned competence to students 

who did not see themselves as “smart” in mathematics, and found ways to support those students 

in finding new ways to be smart, for instance, by asking productive questions. Railside teachers 

also developed shared ways of supporting students to talk mathematically and to work together 

on complex tasks. They found that giving students more challenging material was a critical 

aspect of supporting higher levels of achievement. 

 

Connecting to Students’ Cultural and Real-World Experiences 

 

In addition to high-quality curriculum and classroom practices that support equity, an 

important component of creating a classroom context that best supports the learning of students 

from historically marginalized groups is connecting to students’ cultural or real-world 

experiences. Learning is an inherently cultural endeavor (C. Lee, 2007; Nasir, 2011). The 

research literature in mathematics education identifies two potential ways that math classrooms 

can connect to students’ cultural worlds. The first is through activities that are “culturally 

congruent,” that is, activities and content that draw on students’ knowledge base and experiences 

outside of school. For instance, Gonzalez, Moll, and Amanti (2005) design classroom activities 

that build on expertise in Latina/o students’ homes and communities. They incorporate families 

and community members into the life of the classroom, and encourage teachers to connect with 

families to better understand and utilize the cultural funds of knowledge of students and their 

communities. Similarly, Civil (2007) and Moses & Cobb (2000) have designed mathematics 

lessons that build on the cultural knowledge of students and families, for instance by creating 

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