Comparing High School Mathematics Classroom Practices between Minority and Non-Minority Students

Introduction

The disturbingly low rates of math achievement by students of color (African-American, Hispanic, and American Indian) have gained increasing attention in the education community (Gutierrez, 2000).  Often the unequal performance of minority students compared to White students is described as an achievement gap (Flores, 2007). However, do we ask why this gap exists? Blanket statements about the low performance of certain groups of students in our schools without mentioning the underlying causes may reinforce prejudices and stereotypical images. A shift from looking at measures of performance outcomes to examining what students actually experience in schools should result in a very different way of describing disparities among students in schools (Flores, 2007).  In fact, recent research is based on the premise that the low performance levels seen among minorities are due primarily to environments and schooling practices that deny them equal access to mathematics learning (Martin, 2000; Silver, 1995).

In studying factors that contribute to minority students' success in mathematics, researchers have tended to focus on effective individual teachers. Ladson-Billings (1997) found that minority students benefit from pedagogies which entail treating students like they are competent, providing instructional support for them, extending students' thinking and ability beyond what they already know, focusing the classroom on instruction, and having in-depth knowledge of their students. Other researchers document that successful math teachers of minority students have been shown to encourage communication between students and teacher, have students work in groups, question content, and provide open-end problem solving connected to student realities (Gutierrez, 2000). Research has also shown that minority students are less likely to have teachers who emphasize high quality mathematics instruction or utilize the appropriate use of resources (Flores, 2007).

Purpose of Study

Although some critical elements for teaching mathematics to minority students have been identified, we are less clear on what specific practices effective teachers implement in their classroom in order to foster the success of minority students. This study will focus on the analysis of classroom practices/experiences and their connection with performance in college calculus courses. We will identify those practices with statistically significant associations with performance and compare the occurrences of these practices/experiences between minority and non-minority students. The purpose of this study is to examine which classroom practices, whether positively or negatively associated with college calculus performance, are minority students reporting experiencing in their high school mathematics courses. We look at college calculus performance because it is argued that calculus provides the foundation for understanding higher-level STEM courses; successful completion of calculus is required for success in quantitative majors (Gainen & Willemson, 1995). Seeing as minority students are underrepresented among college graduates in mathematics, science, and engineering, successful completion of the college calculus course is imperative.

Methodology

The data used in this study was drawn from the Factors Influencing College Success in Mathematics (FICSMath) project which focuses on finding evidence for the effective strategies that prepare students for college calculus success. Funded by the National Science Foundation (NSF #0813702), FICSMath is a large-scale study which surveyed a nationally representative sample of college students enrolled in introductory Calculus courses in the fall semester of 2009. The survey included questions on the students' demographics, academics, math interests, and high school math experiences. Drawing from a stratified random sample of universities nationwide, we obtained data from 10,492 students attending 336 college calculus courses at 134 institutions. The students' final course grades were reported by the professors at the end of the semester.

The key variables used in this study focused on high school mathematics classroom practices and experiences. This includes variables dealing with the pedagogy, use of technology, class and teacher interactions, use of class time, classroom environment, and the quality of the teacher. The students reported on these experiences in their most advanced mathematics course. The responses of 1461 minority students (479 African-American, 937 Hispanic, and 45 American Indian) students were compared against the responses of 9031 non-minority students. In order to identify those variables that are significantly associated with calculus performance, a multiple linear regression was ran with the key variables as predictors and the final course grade as the outcome variable while controlling for gender, race, socioeconomic status, and most advanced high school mathematics course taken. Of those variables found to be significant, we compared the responses between the minority and non-minority students.

Results

Results from the survey indicate that minority students performed significantly worse in their introductory college calculus course (p<.001). Based on a 100-point scale, minority students earned an average final grade of 75.9, while non-minority students earned an average final grade of 80.2.

The regression analysis identified fifteen predictors significantly associated with calculus performance at the α = 0.05 level. Among the significant predictors that are positively associated with college calculus performance are the extent of conceptual understanding required; the amount of emphasis placed on functions, vocabulary, and mathematical reasoning; the amount of class time spent teaching other students; the frequency of the teacher solving example problems after presenting new material; and the students' level of comfort asking questions. So, those students who report experiencing these classroom practices in their most advanced high school mathematics class are more likely to perform better in their college calculus course. Conversely, those significant predictors which are negatively associated with performance include the frequency of using a graphing calculator; the amount of emphasis placed on definitions, mathematical proofs, and memorization of formulas; the frequency of whole class discussions being held; the teacher's use of graphs, tables, and other illustrations; and the amount of class time spent preparing for standardized exams and class-related quizzes/tests. Thus, students who report experiencing these practices tend to do worse in their college calculus courses.

From the results of comparing the responses of minority and non-minority students on those variables found to be significantly associated with performance, minorities report either experiencing more of or the same as non-minorities of those classroom practices/experiences which are positively associated with performance. However, minority students are more likely to report feeling less comfortable asking questions in class. Also, minority students report experiencing more of those practices which are negatively associated with performance in their most advanced high school math class.

Conclusions

The results of this study show that minority students are under-performing their non-minority counterparts in their college calculus courses. Also, minority students are more likely to report experiencing those classroom practices which are counteractive toward success in calculus. However, for a number of the positively associated predictors, minority students are reporting about the same and in some cases more of these practices when compared to non-minority students. So, even though minority students are more likely to encounter classroom practices that lead to worse grades in calculus, they are still being exposed to those practices that should help them to succeed.

NCTM has taken the stance that all students should have equal and optimal opportunities to learn mathematics from a well-qualified teacher. This study suggests that teachers should be promoting certain practices in their classroom such as emphasizing conceptual understanding, mathematical reasoning, and peer teaching while minimizing the use of other practices such as emphasizing the memorization of formulas and spending a significant amount of class time preparing for standardized exams. The persistence of this achievement disparity calls for sustained teacher professional development that will help teachers to implement effective strategies that will enable all students to learn in a culturally complex environment. This research suggest that without such professional development, math classrooms may turn into sites of ineffective practices that will continue to hinder student learning and thus continue to perpetuate the differential achievement between minorities and non-minorities.

References

Flores, Alfinio. “Examining Disparities in Mathematics Education: Achievement Gap or Opportunity Gap?” The High School Journal, 91:29-42, 2007.

Gainen, Joanne and Eleanor Willemson. “Fostering Student Success in Quantitative Gateway Courses”. New Directions for Teaching and Learning, 61, 1995.

Gutierrez, Rochelle. “Advancing African-American and Urban Youth in Mathematics: Unpacking the Success of One Math Department”. American Journal of Education, 109: 63-111, 2000.

Ladson-Billings, Gloria. “It Just Doesn't Add Up: African-American Student Achievement in Mathematics”. Journal for Research in Mathematics Education, 28: 680-699, 1997.

Martin, Danny B. “Mathematics Success and Failure Among African-American Youth: The Role of Sociohistorical Context, Community Forces, School Influence, and Individual Agency”. Journal of Research in Science Teaching, 2000.

Silver, Edward A. “The QUASAR Project: Equity Concerns Meet Mathematics Education Reform in the Middle School”. New Directions for Equity in Mathematics Education, 1995.