Teachers' role in high school students' mathematics achievement

Chuang Wang
cwang15@uncc.edu
University of North Carolina at Charlotte
Teresa Petty
tmpetty@uncc.edu
Adam Harbaugh
apharbau@uncc.edu

Data from 60791Grades 9-12 students in North Carolina who took Algebra II in 2006 were used to explore possible factors that impact high school students’ achievement in mathematics. Analysis of variance and hierarchical linear modeling both indicated that teacher variables (such as teacher expectations, the amount of homework assignment, and the type of calculators used in class) and student variables (such as ethnicity, social economic status, and English proficiency level) had significant relationships with the students’ performance on mathematics achievement. No significant differences, however, was found between male and female performance on this state-mandated standardized test. The misconception that male students are better than female students in mathematics was challenged. Researchers and educators were advised to look more into teacher’s expectations, homework assignment, and the use of calculators that might facilitate the learning of mathematics.

Objectives

This study was to explore possible factors that impact high school students’ achievement in mathematics. These factors include students’ family background, teacher’s expectations, homework assignment and completion, and use of technology.

Perspective or theoretical framework

Research has uncovered many factors that affect student achievement in mathematics, and in particular, student achievement on state-mandated mathematics tests. According to Bottoms and Carpenter in their study on rural schools, the teacher plays a large role in mathematics achievement. Having high expectations lets the students know that learning is the goal and all students can learn (Bottoms & Carpenter). Middle grades and high school students who report that they experience moderate to high expectations in their classes have significantly higher mathematics achievement than students who do not report this (Bottoms & Carpenter). This study did not report a significant difference between middle grades African-American and White students’ perceptions regarding the level of expectations they experience in their classes. However, eighth-graders whose parents had not gone beyond high school are more likely to find themselves in classrooms in which they experience low expectations (Bottoms & Carpenter).

Another factor affecting student achievement in mathematics is that of instructional strategy.
One method of instruction where graphing calculators are networked to a projection screen in math classes has been credited with raising standardized mathematic test scores (Cavanagh, 2006).  According to Cavanagh, both teachers and students reported benefits in using this method.

Research has shown that gender difference in favor of male students continue on standardized mathematics tests.  According to Quinn and Spencer (2001), “stereotype threat depresses females’ math performance through inferring with their ability to formulate problem-solving strategies.”  These researchers examined the performance level of females and males when completing word problems.  Word problems include many steps that can cause doubt and frustration.  Unfortunately, when doubt and frustration occur, women respond by doubting their own skills (Quinn & Spencer, 2001). In instances when problems were converted into their numerical equivalents women and men performed equally (Quinn & Spencer, 2001).

Other factors have been identified as contributors, either positive or negative, to student achievement in mathematics. The results from Meyinsse & Tashakkori’s study (1994) suggest that the composite of self-concept, post-secondary education plans, the ability to talk to counselors/teachers, student’s mathematics perceptions, and the academic climate at schools are positively related to scores earned on mathematics tests.  They also determined that performance on mathematics tests is inversely related to race, student’s perception of the curriculum, the percentage of minority students enrolled in a particular school, and student’s attitude toward mathematics.

The relationship between homework and mathematics achievement at the secondary level is not one on which all researchers have agreed. Alfie Kohn (2006) reported that homework has little to no effect on student achievement and criticized research reporting otherwise. Marzano and Pickering (2007) argued that Kohn had misinterpreted much of his reviewed research. Cooper, Robinson, and Patall (2006) provided the most recent synthesis of the research on homework concluding that homework, overall, has a positive effect on student achievement. Weems (1998) provided further evidence that homework has benefits for achievement in algebra. Weems also reported a significant difference between performance of students in college intermediate algebra courses who turned in homework and those that did not.

Methods

Traditional Analysis of Variance (ANOVA) and t-tests methods were used in comparison with the hierarchical linear modeling (HLM) method which takes into consideration of the nested nature of the data (in this case, students were nested within schools).

Data Sources

Grades 9-12 students in North Carolina who took Algebra II in 2006 were used as the target population in this study. This population consists of 64980 students from 359 schools. Among the students, 35090 (54%) were females and 29890 (46%) were males. As for ethnicity, 1619 (2.5%) were Asians, 17473 (26.9%) were African American, 2830 (4.4%) were Hispanics, 748 (1.2) were American Indians, 1192 (1.8%) were multiracial, and 41118 (63.3%) were Caucasians. As for the student’s English proficiency status, 63522 (97.8%) were considered proficient, 988 (1.5%) were considered limited, and 470 (0.7%) did not report their English proficiency status. For the sake of the convenience of data analysis, students who had missing data were also removed. This resulted in a sample size of 60791, which is 93.55% of the target population.

Results

Question 1: What student background information impact their achievement in statewide mandated test in mathematics?

Significant differences were noted among the following groups: Asian (M = 71.46, SD = 11.47), Caucasians (M = 68.74, SD = 10.05), Multi-racial (M = 65.96, SD = 10.29), Hispanic (M = 64.87, SD = 9.68) and American Indians (M = 63.91, SD = 8.95), and African Americans (M = 60.85, SD = 8.98). For lunch status, significant differences were also noted among full-price lunch (M = 67.67, SD = 10.45), reduced-price lunch (M = 64.34, SD = 9.54), and free lunch students (M = 62.15, SD = 9.23). Non-LEP students (M = 66.44, SD = 10.40) had significantly higher grades than LEP students (M = 62.12, SD = 9.91).

Question 2: What is teacher’s role in facilitating students’ academic achievement in mathematics?

Significant differences were noted between students who have homework but do not do it (M = 64.02, SD = 10.72) and students whose teachers never assigned homework (M = 58.66, SD = 9.79). Teacher’s homework assignment measured by the number of hours required to complete was a significant indicator of students’ mathematics achievement, F (5, 60699) = 428.10, p < .001, partial ç2 = .03. The more homework teachers assigned to students, the better these students did in this mathematics test. The type of homework assignment was also found to be a significant indicator. Students who have homework assignment to solve problems in textbook (M = 66.87, SD = 10.12) did better than those who did not have such homework assignment (M = 62.39, SD = 10.34), t (60727) = 33.41, d = 0.45. Students who were assigned to work on worksheets (M = 67.23, SD = 10.36) did better than those who did not have such homework assignment (M = 63.20, SD = 9.98), t (60727) = 39.55, d = 0.40. Similarly, students who were assigned homework to read outside textbook (M = 64.85, SD = 10.16), to research in the library or on the internet (M = 67.73, SD = 10.85), and to write essay or lab reports (M = 67.79, SD = 10.85) also did better than those who did not have such homework assignments, but the effect size were small.

In addition, the type of calculators used most often in the class also played an important role in the students’ achievement in mathematics. Those who often used graphing calculators (M = 66.88, SD = 10.33) did better than those who often used scientific calculators (M = 61.42, SD = 9.58). Those who often used scientific calculators did better than whose who often used fraction (M = 58.44, SD = 8.93) or simple 4-function calculators (M = 58.33, SD = 9.88).

Furthermore, teacher’s anticipated grade for the students was also found to be positively related to these students performance on this state-mandated mathematics test. Students who were anticipated to get an A for the mathematics course (M = 76.55, SD = 9.04) did better than those who were anticipated to get a B (M = 69.43, SD = 8.66). Similar patterns were found for students who were anticipated to get a C (M = 64.18, SD = 8.43), D (M = 60.52, SD = 7.94), or F (M = 56.55, SD = 7.76) for the mathematics course.

References

Bottoms, G. & Carpenter, K. Factors affecting mathematics achievement for students in rural schools.  Southern Regional Education Board, 03V04.

Cavanagh, S. (2006, November 15). Technology helps teachers hone in on student needs. Education Week, 26(12), 10-11.

Cooper, H., Robinson, J. C., & Patall, E. A. (2006). Does homework improve academic achievement? A synthesis of research. Review of Educational Research, 76, 1-62.

Kohn, A. (2006, September). Abusing research: The study of homework and other examples. Phi Delta Kappan, 8-22.

Marzano, R. J., & Pickering, D. J. (2007). The case for and against homework. Educational Leadership, 64(6), 74-79.

Meyinsse, J., & Tashakkori, A. (1994). Analysis of eighth graders' performance on standardized mathematics tests. (ERIC Document Reproduction Service No. ED390676)

Quinn, D., & Spencer, S. (2001). The interference of stereotype threat with
women's generation of mathematical problem-solving strategies. Journal of
Social Issues, 57(1), 55-71.

Weems, G. (1998). The impact of homework collection on performance in intermediate algebra. Research and Teaching in Developmental Education, 15(1), 21-26.