10
pedagogy (e.g., Boaler & Greeno, 2000; “Principles and Standards,” National Council of
Teachers of Mathematics [NCTM], 2000; Schoenfeld, 2002). But many schools that serve
students from historically marginalized groups do not offer such instruction, instead “teaching to
the test”—focusing on remediation and basic skills over conceptual learning—in an attempt to
increase student scores on state-mandated standardized assessments (e.g., Davis & Martin, 2008;
Darling-Hammond, 2010; Lipman, 2002; McNeil, 2000). While the development of basic skills
is an important aspect of mathematical learning, narrow emphasis on such skills severely curtails
students’ opportunities to learn rich mathematics.
Even in the presence of reform-based approaches, students can be differently positioned
to take advantage of rich mathematical content. For example, Lubienski (2000) has documented
differences between lower and higher SES students’ experiences with a problem-based
mathematics curriculum, finding that higher SES students were more likely to have developed
the skills and dispositions to productively engage with open-ended problems, while lower SES
students were less able to engage more conceptual problems, so that disparities in learning
remained. This disparity was most likely due to their lack of prior exposure to the kinds of
discourse patterns required in these curricula.
Lack of access for English learners
Issues of language in mathematics education hold implications for mathematics learners
both at a structural level and at the level of everyday classroom instruction. From a structural
standpoint, some argue that English fluency
4
has had an undue impact on the placement of
English learners in low-level mathematics courses (Secada, 1991, 1996). That is, by using
English fluency as a measure of mathematical competence, educators may incorrectly place a
4
We use the terms “fluency” and “proficiency” interchangeably for the purpose of this report.
11
student in a low tracked class. In some cases, the student may have already studied the content of
the class in her/his home country (Gutierrez, 2002). This problem may stem from the
assessments being used for placement, as such assessments are typically written in English.
Some scholars propose that such assessments should be coupled with other measures (e.g., oral
interviews or translated written assessments) that may afford students better opportunities to
demonstrate their mathematical knowledge (e.g., by speaking or writing in their home language)
(Moschkovich, 1999; Solano-Flores, 2010).
Aside from students’ access to advanced mathematics courses, English language barriers
are also consequential for teaching and learning in classrooms. Reforms that followed the
National Council of Teachers of Mathematics’ Standards (1989, 2000) have worked to propagate
views of mathematics learning as a social process of sense-making and classroom discourse.
Prior research has focused on English learners’ struggles in comprehending written mathematical
texts or word problems (e.g., Dale & Cuevas, 1987; Rubenstein, 1996). More recent research has
sought to move beyond emphasis on vocabulary development, instead focusing on the ways in
which students use multiple languages in oral communication with other students as they make
sense of mathematical ideas (e.g., Moschkovich, 2010).
Historically, English learners’ opportunities to learn mathematics have been limited by
English-only policies (Olsen, 1997). Numerous scholars have found that students often switch
into their dominant languages to engage with higher-level mathematical concepts (Gutstein, et
al., 1997; Khisty, 1995; Moschkovich, 1999). These findings suggest that forcing students to
communicate in English only may obstruct access to students’ full range of cognitive resources
and limit their access to rich mathematical content.
While prohibitions on classroom use of languages other than English are no longer
12
common, English learners’ opportunities to engage with rich mathematics continue to be limited
by efforts to accommodate their needs that are primarily superficial. Research shows that mere
translation of mathematical terminology from English into Spanish, for example, is insufficient
for learning (Khisty, 1995). Instead, it is optimal when English learners experience mathematical
explanations in their dominant language, a decidedly non-trivial pedagogical challenge even for
bilingual content-area teachers (Ron, 1999). Nevertheless, as Gutierrez’s (2002) study of a
school that was successful in enrolling large numbers of Latina/o students in AP Calculus shows,
it is possible to create productive learning environments even when teachers are not fluent in
students’ home languages.
Lack of access to productive math identities
From lack of rich, challenging curriculum to support to English language obstacles, we
have identified thus far a number of barriers that limit students’ opportunities to learn
mathematics. However, not all such obstacles are material in nature. Content learning is
recognized as requiring access to a vision of oneself as a future capable doer of the given
discipline (Wenger, 1998). The availability of productive math identities bears heavily on
whether and how students engage with mathematics in school (Nasir, 2002; Martin, 2000; de
Abreu, 1995; Sfard & Prusak, 2005). We conclude this section with a treatment of some of the
factors that mediate students’ access to productive identities in mathematics.
Research on stereotype threat provides evidence that stereotypes can depress the
performance in testing situations of students who perceive themselves as belonging to groups
that are the subject of negative stereotypes (Steele, 1998; Steele & Aronson, 1995). In one study
that focused on the effects of the racial narrative, “Asians are good at math,” researchers found
Dostları ilə paylaş: |