Standards: Mexican-American students' attitudes.

Abstract

Following a year-long implementation of a standards-based middle school mathematics curriculum, students were surveyed. The survey revealed that positive attitudes toward mathematics prevailed in each of the six middle schools where the program was implemented.

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Accountability in the state of Texas has been "a fact of life" for school districts in the state since the mid-eighties. At that time, students were tested for basic skills. Students are now being assessed at a higher cognitive level on the Texas Assessment of Academic Skills test. The test calls for students to respond to items that measure deeper understanding of mathematics concepts. The implication is that teachers in Texas have to teach for deeper conceptual understanding of mathematics. Standards-based curricula have the potential to offer the greatest opportunity to teach mathematics for deeper understanding (Senk & Thompson, 2003). There is general agreement that the quality of school mathematics programs must be improved to afford all students an opportunity to succeed in mathematics (Reys, Reys, Lapan, Holliday, & Wasman, 2003). The Connected Mathematics Program, a standards-based curriculum, is thought to develop student knowledge and understanding of mathematics, focusing on connections among the core ideas of mathematics, and applications outside of school (Ridgway, Zawojewski, Hoover, & Lambdin, 2003). Moreover, the curriculum is organized around interesting problem solving activities, designed to involve groups of students and encourages discourse and reflective writing about these ideas (Ridgway, et al, 2003). The curriculum incorporates practice with computation and symbolic manipulation into its units to build conceptual foundations for the skills (Ridgway, et al, 2003).

Questions remain whether a standards-based curriculum is beneficial for all students, teachers and situations (Chappell, 2003; Ridgway, et al, 2003). When examining how students interact with different curricula, it is important to examine affective factors (Chappell, 2003). Although some researchers (e.g., Garofalo, 1989; Schoenfeld, 1985; Underhill, 1988) have conducted studies on the affective domain, very few studies have been conducted with Latino(a) student populations (e.g., Telese, 1999) and there is limited research focusing on standards-based curriculum (Senk & Thompson, 2003). Research conducted with minority student populations has generally focused on cultural influences on the learning of mathematics (e.g. Khisty, 1995; McLeod, 1992; Orr, 1987). The purpose of the present study was to gain an understanding of Mexican-American students' attitudes towards mathematics after they have experienced a standards-based mathematics curriculum. The study sought answers to the following research question: What is the attitude toward mathematics of middle school, Mexican-American students upon experiencing a standards-based curriculum?

The Importance of Examining Beliefs and Attitudes

Research on the affective domain has maintained an active role in mathematics classroom research. Obviously, students have particular needs that must be met during mathematics instruction. Meeting the needs of students requires the identification of the beliefs and meanings that both the teacher and the students bring with them into the learning process (Nickson, 1992). The affective domain was considered by Koehler and Grouws (1992), who described four levels of mathematics classroom research. Level One considers work on teacher effectiveness. Level Two is more complex and involves multiple classroom observations of mathematics instruction. Level Three relates to the study of pupil characteristics, broadened to encompass attitudes as well as achievement. Finally, Level Four research is based on a strong theoretical foundation involving many factors. The mathematics classroom is an arena where students build and establish particular beliefs regarding mathematics teaching and learning, and a place where these beliefs develop gradually over time (McLeod, 1992).

Knowledge of students' attitudes may be useful when attempting to improve instructional practices and when directing efforts to promote success in other mathematics courses. A study conducted by the National Action Council for Minorities in Engineering [NACME] (1995) revealed that 60 percent of Latino students intended to drop mathematics at the first opportunity. Poor student attitudes toward mathematics can influence teachers' recommendations for students to enroll in advanced courses. The NACME (1995) study showed that only 53 percent of the students surveyed indicated that they were encouraged by their teachers to take more advanced mathematics and science. Ultimately, attitudes and beliefs toward mathematics play a critical role in future career choices (Thorndike-Christ, 1991). Thus, a lack of guidance and direction coupled with negative attitudes may further reduce high school students' enrollment in other high school mathematics classes and future career pathways in mathematics or science.

Standards-based mathematics curriculum designed to develop understanding should be made approachable for all students. This brings into play the notion of equity. Does teaching for understanding benefit particular students? There is a danger that if equity concerns are not addressed, then group differences may be exacerbated (Secada & Williams-Berman, 1999). Thus, a standards-based mathematics program offers the potential for students to experience a contextually based curriculum that offers an opportunity to learn concepts and develop favorable attitudes. Chappell (2003) urged that researchers should begin to examine attitudes as students (i.e., middle school students) interact with different curricula. The purpose of this study was to examine middle school students' attitudes toward mathematics following their participation in a standards-based curriculum.

Methodology

Participants

Participants consisted of sixth grade students in a large school district in deep South Texas located along the Rio Grande river, which had six middle schools. There was a total of 1,193 sixth-grade students who completed the surveys. There were 599 female students and 569 male students, 25 students failed to report their gender. The ethnic break down consisted of 957 Mexican-Americans, 50 European-Americans, 25 Asian-Americans, and 128 students who indicated "other" as a choice for ethnicity. School A had 284 students, Schools B had 231, School C - 222, School D - 98, School E - 148 and School F had 207 students while three students failed to report what school they attended.

Background of the Schools

The district's mathematics curriculum coordinator provided background information related to the schools. In School D, one teacher used the curriculum 100 percent of the time while other teachers used the curriculum in an "on-off" fashion. The coordinator reported that this school struggled with its achievement test scores.

School E was the school with the greatest percentage of students from low socioeconomic families (SES). Many students come from poverty-stricken homes in the "colonias." Colonias are unincorporated, underdeveloped settlements along the Texas-Mexican border. Colonias typically lack water, sewer systems, electrical services and safe, sanitary housing; however, this does not stop the thousands of residents who dream of owning a home and purchasing land in these underdeveloped settlements. At this school, again one teacher used the curriculum exclusively while three used it most of the time to develop questioning skills. The other teachers used the Connected Mathematics curriculum three days and on the other two days used a different program or they presented Connected Mathematics on a two-day basis, and for three days used another curriculum.

School F was a school where all the teachers taught using the Connected Mathematics Program. One teacher struggled with the curriculum. Teachers felt that there was not enough "content" in Connected Mathematics. The teachers at this school did not attend the 90 hours of training provided by the district.

School C had 50 percent of its students who were from upper SES families. There was a high rate of parental involvement. It was reported that the parents did not have a favorable view of the curriculum. One teacher used the curriculum 75 percent of the time. Two teachers in the school needed a lot of support to implement the curriculum due to their poor mathematics background. Two other teachers had a science background. Two teachers were trained in the beginning but there was a lack of coherence, and these two teachers had negative comments concerning the program. Eighteen months later, these same two teachers expressed their pleasure with the program and acknowledged that they had struggled with the shift from the traditional pedagogy they had experienced as students and in which they had been trained previously.

School B had a low rate of implementation of the curriculum. The teachers maintained a classroom environment where the desks were in straight rows. The teachers were authoritarian in the presentation of mathematics concepts, and they were not comfortable with the mathematics in the Connected Mathematics Program. There was a preponderance of direct instruction in this school. There was a high rate of teacher absences. Also, there was a lack of administrative support.

School A had a strong administration and supported the use of the Connected Mathematics Program. There was support for teacher training. At this school, questioning skills rapidly developed. The teachers developed lesson plans together and met to reflect on the lesson presentations. There were a few teachers who struggled with the program. The mathematics teachers were involved in professional development in mathematics content.

Instrument

The questionnaire consisted of 25 items adapted from the Fourth National Assessment of Educational Progress (Dossey, Mullis, Linquist, & Chambers, 1988) that focused on two areas: i) student attitudes and beliefs toward mathematics were addressed in items one through 10, and ii) the classroom activities experienced by the students were probed in items 11 through 25. The attitude and belief items included statements that were considered by the researcher to be favorable attitudes toward mathematics, such as "Math is interesting," and "Math is fun." The students responded to the first ten attitude/belief items using a Likert-scale from one to five where a one represented that the student strongly disagreed and a five represented that the student strongly agreed with the statement. The next 15 items were statements that described classroom activities associated with traditional and non-traditional activities. This paper will report on only the attitude related in each items. An exploratory factor analysis, using a principal component analysis was conducted on two hypothesized factors: i) positive attitude toward mathematics, and ii) negative attitude toward mathematics. This was followed by a Promax rotation on all the items to determine latent structure. Cronbach Alpha coefficients were produced for the entire survey and attitude items. The data were analyzed using the statistical package SAS (1990) program, including the exploratory factor analysis. Descriptive and inferential tests such as two-and three-way ANOVAs were conducted for the main factors Gender, Ethnicity, and School.

Results

Cronbach alpha coefficients indicated that the factorial reliability was adequate for the hypothesized categories of Positive Attitude Toward mathematics, 0.73, and rather low Negative Attitude with 0.34. The students definitely agreed that mathematics is useful and knowing why an answer is correct is important in mathematics. They held a rule-oriented view of mathematics. A contradiction was evident by the means associated with items nine and 10. Although the students' attitudes about mathematics consisted of recognizing the importance of mathematics and its usefulness in daily life, they were uncertain whether they would like to have a job that uses mathematics.

The students' neutrality on several of the attitude items indicated their indifference to the subject. However, a positive result may be seen for some of the students who felt that memorizing is not important. This implies that they should understand concepts and procedures rather than memorizing them. It appeared that the students had a tendency to lean toward the idea that the process of guessing may be helpful when solving problems. Statistical significance was tested using a three-way ANOVA, Gender x Ethnicity x School, with the dependent variables, Positive Attitude, and Negative Attitude. There were no statistical differences for the main effect, Gender with, Positive or Negative attitudes, indicating that both genders held a similar degree of positive attitude toward mathematics with an F-value of 0.59 with 1 and 1,089 degrees of freedom, and a partial eta-square of 0.001. The result was similar for Negative attitudes, with an F-value of 0.62 and with 1 and 1,089 degrees of freedom, having an eta-square of 0.001. Each ethnicity category held similar attitudes and perceptions of mathematics. For the main effect, School, the results indicated no differences in attitudes either positive or negative toward mathematics.

Each of the six middle schools reported improved means for the state's student performance index, Texas Learning Index (TLI), from the year 2002, prior to implementing the curriculum to the year 2003. School E, where the implementation was extensive and had the greatest percentage of low socioeconomic students had a mean TLI of 100. School F had the most extensive implementation also had a mean TLI of 100.

Conclusion

The study's results indicated that the middle school students' attitudes toward mathematics were similar in each school, and that both female and male middle school students held the same view whether a positive or negative view toward mathematics. It appears that the use of a standards-based curriculum, in this case, the Connected Mathematics Program had minimal impact on attitudes. The degree to which the program was implemented varied from school to school. Consequently, the attitude of students toward mathematics was generally favorable regardless of the program they experienced. This is a positive finding in that the students see mathematics in a favorable light even though they do not want to pursue a job that uses mathematics. Student achievement prior to the study was relatively good. However, following the implementation of CMP in each school, regardless of the extent to which it was reported to have been implemented, achievement gains were made in each school. School E had greatest number of low SES students and made a significant improvement in achievement scores. This finding indicates that the CMP program may be beneficial in improving the mathematical understanding of low income and minority students. Although the study did not include classroom observations, and the findings are based on student self-reports, the results are favorable toward the use of CMP in middle school classrooms. A teacher who did not care for the program in the beginning, eventually saw how powerful the program is in developing mathematical understanding. The survey was sufficient to gauge attitudes. The results of this study lends support for the use of CMP in schools to help foster favorable attitudes toward mathematics and improving mathematical understanding.

References

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James A. Telese, University of Texas, Brownsville

James Telese is an Associate Professor of Secondary and Mathematics Education