Academic journal article High School Journal

# Understanding the Significance of Context: A Framework to Examine Equity and Reform in Secondary Mathematics

Academic journal article High School Journal

# Understanding the Significance of Context: A Framework to Examine Equity and Reform in Secondary Mathematics

## Article excerpt

The purpose of this article is to outline a framework that can be used to examine issues of equity and mathematics reform. Adapted from an opportunity-to-learn framework proposed by Tare (2004), this model includes factors related to time, quality, and design. This framework is applied to the cases of two secondary mathematics teachers to illustrate how these factors can operate to shape teachers' implementation of reform. The differences between the two cases point to the significance of teaching context with respect to reform. The framework has equity implications insofar as the time and quality factors that constrain change appear to be more likely to impact students of color and students in high-poverty schools, thus denying them access to mathematics reform.

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Classroom A:

The students work in groups of 2 or 3 on an experiment involving linear functions. The groups investigate the relationship between the number of coffee cups and the height of a stack of the cups. As the students work, the teacher walks around the room asking questions to facilitate student conjectures. "Do you notice anything unusual here?" "What is going on here?"

Classroom B:

The teacher passes out the test prep booklets. She instructs the students to write the word "opposite" in their notes. She asks what opposite means. A student says that it means to change the sign. The teacher tells the students to write "additive inverse property" in their notes. She then instructs the students to write -3/4 in their notes and to find the opposite. A student says that the answer is 3/4. The teacher then asks about the reciprocal. She instructs the students that in order to find the reciprocal, they would take the number and "flip" it but not change the sign. The class continues as the students answer multiple choice problems and fill-in-the-blank questions from the test prep book.

The authors of the Principles and Standards for School Mathematics (PSSM) have established equity as one of the core principles of mathematics reform (National Council of Teachers of Mathematics, 2000). They argue, in particular, that ALL students should have access to the type of high quality mathematics curriculum and instruction described both in the PSSM and in previous sets of recommendations by the National Council of Teachers of Mathematics (NCTM).

```   Goals such as learning to make conjectures,
mathematical evidence, to formulate and
solve problems--even perplexing ones--and
to make sense of mathematical ideas
are not just for some group thought to be
"bright" or "mathematically able." Every
student can--and should--learn to reason
and solve problems, to make connections
across a rich web of topics and experiences,
and to communicate mathematical
ideas. (NCTM, 1991, p. 21)
```

In other words, the vision of equity articulated in the PSSM is one in which all students would have the opportunity to learn mathematics in a manner consistent with the tenets of mathematics reform (NCTM, 2000). However, evidence suggests that the vision of mathematics reform reflected in the NCTM Standards is not equitably distributed in U.S. schools. Certain students are more likely than others to have access to high-level content and reform-based mathematics pedagogy (Atweh, Bleicher, & Cooper, 1998; Johnson, 1994; Lubienski, 2002; Oakes, 1990). For example, Weiss (1994) found that teachers with high proportions of African American and Latino/a students were more likely to focus on low-level skills. Similarly, students in high-poverty classrooms are less likely to engage in problem solving or reasoning and more likely to experience curriculum and instruction focused on remediation of basic skills (Kitchen, 2003; Knapp, 1995; NCTM, 1999).

The two classes described in the preface to this article are representative of these differences in context and instructional content. …

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