Mathematics, Collaborative Learning in

Principles for Equitable Mathematics Teaching

In reviewing the literature on equitable mathematics teaching, this entry distills the lessons into the following four principles that support the goals of effective collaborative learning.

• 1.
  Learning is not the same as achievement. Students' mathematical competence is often conflated with their level of achievement, which is typically signaled by the mathematics class that they are in. Although learning and achievement are related, they are not the same. Learning happens when students deepen and extend their knowledge of mathematical ideas. Achievement reflects how they are progressing in school. Most educators recognize the imperfect correlation: Some students progress without understanding, whereas other students understand without progressing. Nonetheless, students and teachers often respond to learning and achievement as the same thing, with negative consequences for student participation and students' academic identities.
• 2.
  Achievement gaps often reflect gaps in opportunities to learn. Although enrollment in advanced mathematics classes has increased overall because of changing graduation requirements, many low-income students and students from historically disenfranchised racial and ethnic groups continue to opt out of advanced mathematics. Different educational outcomes manifest themselves as disparate levels of achievement on standardized tests, but this focus on individual student achievement erases the radically different opportunities for mathematical learning that exist within and across schools that provide a critical context for these demographic patterns.
• 3.
  All students can be pushed to learn mathematics more deeply. Opportunity gaps exist for students across the achievement spectrum. Although the social and economic consequences are greatest for low-achieving students, opportunity gaps affect all students. Middle-achieving students may simply get by in mathematics class without learning much, missing the chance to develop their own intellectual powers and foreclosing future educational opportunities. Even high-achieving students need a better mathematics education. High-achieving students are often raced through the curriculum, often pushed past the rich connections that engage them in the subject or offer some of the affective pleasure that might spur them on to study it at higher levels. A key characteristic of equitable classrooms is that all students are supported to participate substantially in each phase of instruction, although not necessarily in the same ways. In equitable classrooms, all students have opportunities to learn meaningful mathematics, no matter their prior achievement.
• 4.
  Students need to see themselves in mathematics. In general, children do not see themselves as mathematicians in the same way they might see themselves in more expressive subjects like art or literature. Consequently, adolescents' emergent identities typically do not adhere to mathematics in the same way they might to these other content areas.

For students whose home culture or language differs from the school culture, the problem of alienation from mathematics is often exacerbated. Even something as simple as the way a question is phrased or singling out a student for praise may go against the grain of that student's home culture. When students do not see themselves in what they are learning, finding meaning in school activities is harder.

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