Discursive practices in language minority mathematics classrooms. (On-going Topics).
A survey was administered to 623 Mexican American students who attended a summer mathematics and science enrichment program at a university located on the Texas-Mexico border. The purposes of the survey were to gain an understanding of students' perception of opportunities for constructivist, classroom practices, and their feeling about how prepared they are to take advanced mathematics classes. A multivariate analysis of variance was conducted with gender, primary language, and ability as independent variables. The study found that female students with Spanish as their primary language perceived opportunities to communicate at a level nearly equal to both male and female students with English as their primary language. Low performing male students with English as their primary language reported the lowest frequency to participate in constructivist classroom activities.
There is a growing interest in the instructional practices experienced by language minority students, in particular, students with a Latino/a heritage. Moschkeovich (1999) contends that an empirical research base is needed to guide the design of classroom mathematics instruction for language minority student populations. One area of interest is the level of discourse that occurs in mathematics classrooms. Discursive practices allow teachers and students to socially construct mathematical knowledge in order to promote understanding (Atweh, Bleicher, & Cooper, 1995). Since language is viewed as a vehicle for organizing and developing reasoning, it becomes important to determine the degree to which language is used for this purpose in teaching mathematics to language minority learners (Cummins, 1984).
Both language and non-language minority students are often placed in the same classroom, especially in schools along the Texas-Mexico border. Researchers (e.g., MacGregor & Price, 1999; Mestre, 1988) have found that both monolingual and bilingual students may demonstrate poor academic performance in mathematics as a result of low levels of academic language proficiency.
Studies have examined language minority learners' understanding of word problems, comprehension of written mathematical texts, or vocabulary development (Dale & Cuevas, 1987; MacGregor & Moore, 1992; Olivares, 1996). Few studies have examined language minority secondary students' classroom experiences related to various forms of discursive practices in mathematics classrooms. In this study we sought to determine the mathematics learning opportunities as reported by language and non-language minority students. Communication is defined as discourse, both oral and written, that allows students to present ideas and completed tasks (Pirie, 1998; Sierpinska, 1998). The study sought to answer three questions:
1. What are the differences between language and non-language minority high school students' perceptions of opportunities to communicate and to use tools in mathematics classrooms?
2. What are the differences between "remedial" and "high performing" students' perceptions of opportunities to communicate and to use tools in mathematics classrooms?
3. How do language minority high school students perceive their preparation to enter a mathematics and science related career?
Teachers provide social situations where communication, as an expression of thought, takes place through discursive practices, such as whole-class discussions, small group collaborative problem solving, and written drafts (Wood, 1995). The expression of higher-order thinking is fostered through a mathematics language register, which is taught in school as a separate register where specific, and specialized vocabulary and expressions are used. Meaning for mathematical objects, such as expressions, words, formulas, and diagrams, is developed when these features become a part of discourse shared with other students (Sierpinska, 1998).
A pedagogical reform has developed in order to allow greater access for all students to mathematics learning. The reform pedagogy includes strategies such as student participation in discussions, debates, and the expression of thoughts in oral arguments. Writing is also viewed as a tool of learning and connecting ideas in the reform curriculum. Hence, a climate for discourse should be established in order to foster communication in the mathematics classroom (NCTM, 1991).
Researchers have documented that gender differences exist related to mathematics achievement (e.g., Fennema, 2000; Oakes, 1990). One factor that has contributed to the under representation of women in mathematics related fields is limited involvement in learning opportunities. This affects attitude and achievement in mathematics classes (Fennema, 2000). In particular, Catsambis (1994) found that female Hispanic students were least likely to aspire to careers in mathematics or science. Other findings indicated that female students were less likely to ask questions in class, had less confidence in their ability than male students, and that White female and Latina students had a lower self-concept of their mathematics performance (Catsambis, 1994).
The literature points out the important role that discourse plays in the development of higher order thinking. Shared knowledge, expressed during class discussions, written work, and collaborative activities, increase students' potential for learning mathematics or science concepts. With an increase in the opportunity for language minority students to gain deeper understanding of concepts through discourse, there is an increase in the potential for language minority students to enter the career pipeline in mathematics and science.
Methods and Procedures
A summer enrichment program for minority students was held at a university located on the Texas-Mexico border. The program was designed for middle and secondary school students to provide advanced academic preparation in mathematics and science for students interested in pursuing pre-engineering, science, mathematics, and technology careers. The main emphasis of the program's intent was to recruit economically disadvantaged students, with a strong desire to succeed in mathematics and science, in careers related to mathematics or science.
The sample consisted of a total of 623 middle (183) and high school (429)students from various districts in the region. The sample consisted of a predominantly Latino/a population, approximately 98%. The other 2% consisted of African American or White students. The students varied achievement levels, ranging from remedial students to high performing or on grade level students. They were also either bilingual or monolingual in either Spanish or English, and voluntarily enrolled in the summer program. There were 340 students in the analysis who reported English, as their primary language. Within this group, there were 172 males and 168 females. Two hundred eighty-two students reported Spanish as their primary language. Within this group, there were 143 males and 139 females. There were 316 low performing students and 307 high performing students as determined by their mathematics grades, 85 or above were considered high achieving students.
A self-reported survey was designed to gauge several mathematics instructional features experienced by the students in their respective schools. The survey had four categories. These were: 1) frequency of instructional activities; 2) preparedness for careers in science, math, or engineering; 3) the role of other individuals, such as counselors, teachers, and parents; 4) frequency of the use of various tools in mathematics class, such as graphing calculators and data collection devices. The survey was pilot-tested at a middle school with 120 students.
The first section of the survey consisted of 12 items related to the frequency of various activities in mathematics classes. A Likert-type scale was used where "one" indicated never, "two" indicated that the activity was experienced a few times a year, "three" indicated that the activity was encountered every few weeks, "four" meant once a week, and "five" represented the activity was encountered in almost all lessons. The 12 items reflected discursive practices, such as "explain your thinking," share your ideas," and "work with others." Students were also asked to respond to how often they used various tools in mathematics. There were three response categories: i) not once, ii) once or twice, and iii) many times.
In regard to the students' perceptions of their preparedness, the survey consisted of six items, which included "take more advanced mathematics or science classes," "study engineering," "solve problems in mathematics or science," and "enter a job requiring mathematics or science." There were four response categories ranging from "not well prepared" to "very well prepared." The students chose from math and science teachers, counselors, family, friends, and others as choices for who influences them the most when considering a career related to mathematics or science. There were three response categories: i) not at all, ii) somewhat and iii) to a great extent.
A multivariate analysis was conducted using, gender, primary language, and achievement level as the main factors. Students' responses to survey's items were considered the dependent variables, and the analysis was partitioned into three sections: (a) mathematics classroom activities, which consisted of 12 items, (b) preparedness consisting of six items; in relation to this set of items, students were also asked who influences them the most in choosing a career in a mathematics/science related area, and (c) tools used in the mathematics classroom, which consisted of eight items.
Overall, the students, in each category, reported that "at least once a week" they explain their thinking or share ideas. The opportunity to use higher order thinking outside of the classroom, through the use of projects or investigations, occurred only "a few times a year." The students reported that every few weeks they conducted investigations in class.
In particular, female students reported being able to recognize errors more often than male students. Female students with Spanish as their primary language had greater mean ratings than any other group for items related to various communication activities, see Table 1 <http://rapidintellect.com/AEQweb/fallp.htm>.
For example, female students reported a greater mean frequency of explaining and sharing ideas and working with others than males, and female students with Spanish as their primary language had means greater than males of both categories and nearly equal to the mean of high performing, female students with English as their primary language. Although not statistically significant, male, low performing students with English as their primary language reported a lower frequency of communicating and working with others than low performing, males with Spanish as their primary language. In regard to achievement levels, high achieving students reported a greater tendency of using meta-cognitive skills while problem solving with a mean of 4.3 and a standard deviation of 1.1, and communicating their thinking than low achieving students with a mean of 3.5 and standard deviation of 1.5.
Regarding the use of tools in mathematics class, significant differences were found in each of the three factors, see Table 2 <http://rapidintellect.com/AEQweb/fallp.htm>.
The students infrequently used tools to solve mathematics problems or to collect and analyze data. However, when tools were used, female students reported a greater frequency of using calculators than male students. The use of data collection devices and sensors was almost non-existent; yet when they were used, male students reported using them more often than female students. Students with English as their primary language reported a greater frequency in the use of geometric models during instruction than those students who have Spanish as their primary language. Similarly, students with English as their primary language reported a greater frequency of using higher-order thinking skills by collecting and analyzing data. Low achieving students reported that they infrequently use either calculators or graphing calculators, and rarely collect and analyze data.
Both language groups feel equally prepared, which is somewhat to fairly well, to take advanced course in mathematics, to study engineering and enter a job requiring math or science. However, female students felt that they are "not very well prepared" to "somewhat prepared" to study engineering and "somewhat prepared" to enter a job related to mathematics while the male students felt "fairly well" prepared to do both. The low achieving students do not feel prepared at all to take advanced classes mathematics, to study engineering or enter a job that involves mathematics, nor do they feel prepared to solve problems in mathematics. Table 3 presents the main factor means and standard error for the statistically significant items. The greatest influence on the students to choose a mathematics or science related career is their family, regardless of gender, primary language, or achievement level. See issue's website <http://rapidintellect.com/AEQweb/fallp.htm>.
Discussion and Conclusion
The review of literature suggests that students should have rich opportunities to develop mathematics understanding through discourse. Although the survey was administered to a local sample of middle and high school students, the implications reach further than the study's location, which found that classroom practices that help to develop mathematics understanding occur infrequently in the classrooms in school districts along the lower Rio Grande Valley of Texas. Students reported varying levels of discursive activities. It appeared that low performing male students with English as a primary language were disenfranchised the most from classroom discourse. This group of students reported the lowest frequency of communicating mathematical ideas and using tools to solve mathematics problems, and they held the worst attitudes regarding their futures. This puts them at a greater risk of low performance. Further study is needed to examine the factors that inhibit participation in discursive practices for male students with Spanish as a primary language.
An encouraging result was that female students with Spanish as a primary language reported participating in discursive practices nearly at the same level as male and female students with English as a primary language. Taken together, female students used tools less often and felt less prepared than any other group of students to enter a math or science related career but equally prepared to take advanced courses in mathematics.
The frequency of students presenting oral reports in mathematics class was "never" to a "few times a year" regardless of gender, primary language, or ability. Although discussing current events in mathematics classes may not be directly connected to topics in the content areas, it was included in the study as a discursive practice because students would have an opportunity to exchange ideas and information. A characteristic of a constructivist classroom would include the teacher's use of primary sources of data for manipulation by students. However, the lack of activity related the discussion of current events in mathematics seems to indicate that the teachers are relying on traditional sources of instructional materials such as textbooks or handouts rather than actively involving students in data collected from primary sources.
Regardless of primary language students characterized, as low achieving did not share ideas, ask questions, work with others, or use meta-cognitive strategies as often as those students characterized as high performing. Low achieving students also felt ill prepared for a future in a mathematics related career or to take advanced courses in mathematics. This group of students, consequently, felt less prepared to take advanced courses in mathematics or to choose a career in a mathematics related field. In order to improve the mathematics understanding of the low performing group, it is important to find strategies to encourage them to do so. Classroom teachers need to facilitate greater participation of !ow achieving students by establishing an equitable classroom climate where all students feel comfortable in communicating their ideas, evaluating one another's ideas, and wherein mistakes are viewed as road markers to understanding.
In summary, Mexican-American students who reported Spanish as a primary language had a tendency to dominate the communicative practice in their mathematics classrooms. The data revealed that low performing, Mexican-American male students with English as a primary language reported the least amount of communication. This may be due to the self-reporting nature of the survey, and they may be less likely to be open about what they do in classrooms. This finding warrants further research.
It appears that high schools situated in the lower Rio Grande River Valley of South Texas have encouraged participation of Mexican-American, female high school students with Spanish as a primary language in discursive practices in their mathematics classes. This is a very positive finding. Previous researchers have found that female students are "left behind" in mathematics and science classes (e.g., Catsambis, 1994). In this study, teachers seemed to include female students in full participation in classroom discourse. In contrast, a disturbing finding was that Mexican-American male students with Spanish as a primary language appear to be withdrawn from classroom discourse. Their reported participation in mathematics and science classes was very infrequent. Efforts should be made to determine what factors are needed to improve their level of participation in classroom discourse and to find ways to include them.
Evidently, Mexican-American students with Spanish as a primary language participate more often in the academic features of discourse such as explaining one's thinking, and sharing ideas, and asking questions. The exception to this observation is the high performing students with English as a primary language who also participate at nearly the same level. This finding tends to suggest that students with English as a primary language are more reluctant to participate in classroom discussions and work with others, a finding that is opposite of what would be expected. High performing students with Spanish as a primary language may be more comfortable at explaining their thinking and sharing ideas than students who are not as fluent in Spanish. This implies that low performing students with English as a primary language are more reluctant to communicate their knowledge. The average student with English as a primary language tends to be more inhibited to participate in class discussions. Consequently, with less participation in discussions, they may not be able to develop conceptual understandings through discourse, at the same level, as students with Spanish as a primary language. It is unclear whether this finding is effected by culture or language background, but language background plays an important role in the students' participation level in classroom discourse.
This study revealed mathematics career-oriented Mexican-American students' perspectives on instructional practices, and their future aspirations to take more advanced mathematics classes. An instructional profile would include varying levels of opportunities for students to explain their thinking and sharing ideas depending on their language background. Students often work together in mathematics classes. There should be greater use of authentic tasks, where actual data collected are collected for manipulation and analysis in mathematics classes, that may help to foster greater opportunities for discursive practices.
Further study is needed to examine in more depth the reasons behind why female students with Spanish as a primary language participated in communicative practices at levels equal to the high performing English as a primary language students. Also, additional study is needed to examine the lower participation in communicative practices of male students with English as a primary language. A question that needs to be addressed is why do low ability male students with English as a primary language shy away from classroom discussions. Classroom observations would be needed to assist in answering these questions.
The research reported in this paper was funded by the National Science Foundation Grant No. HRD-9353644, Center for Research on Teaching and Learning CERTL III. The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation
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James A. Telese, The University of Texas at Brownsville, TX
Reynaldo Ramirez, Jr., The University of Texas at Brownsville, TX
James, PhD, is an Associate Professor of Secondary and Mathematics Education whose research interests include the use of performance assessments, student attitudes, and the learning of algebra. Reynaldo, PhD, is an Assistant Professor of Secondary Education and Science Education whose research interests include student attitudes, mentoring science teachers, and field experiences.