Introduction

Background Information

Students didn’t always take algebra I in the 8th grade. In decades past, only students that planned on going to college took algebra courses (Eddy et al., pg. 61, 2015). Since 1990, however, the percentage of students enrolled in 8th grade algebra in increased from 16% to 24%; in 2007, that number was at 31% (Loveless, 2008). Though, not every student benefit from taking algebra in 8th grade. 8th grade algebra is most difficult for economically-disadvantaged students because these students don’t have access to the educational resources they need to succeed in 8th grade algebra. Before we get to that, however, let’s look proponents’ views for having students enroll in algebra in 8th grade.

Benefits of Taking Algebra in 8th Grade

For students that are adequately prepared for 8th grade algebra, there are benefits to starting algebra in 8th grade. Algebra is considered a gatekeeper course to advanced courses in mathematics, science, engineering, and mathematics. For high-performing students taking 8th grade algebra, they are 20% more likely to take calculus in 12th grade; for students that perform in the middle, they are 10% more likely to take calculus in 12th grade (Eddy et al., 2015). These students are also more likely to complete high school and enroll and graduate college. However, for the low-performing students, they are 20% more likely to have to repeat Algebra I in the future (Eddy et al., 2015). These students are also less likely to pass geometry by 11th grade, while median- and high-performing students are more likely to do well in geometry in 11th grade(Clotfelter et al., 6). As one can see, the positive benefits only apply to students that are prepared for algebra and portraying the benefits as universal for every student is misleading.Global Competitiveness

In the large picture, why are these benefits stated above important? Besides the obvious—a high-quality education leads to a better life for everyone—it also increases the United States’ competitiveness in the global market. Knowledge of mathematics provides the foundation for careers in “commerce, industry, science, and technology” (Eddy et al., 61, 2015). Algebra instills into one to “solve problems by modeling, evaluate quantitative relationships, and express and justify generalizations (Eddy et al., 61, 2015). Again, algebra is a gatekeeper to higher mathematics. Furthermore, statistics show that the “mathematics curriculum for 13-year-old American students in the U.S. is one year behind the international community,” and it is getting difficult to find qualified applicants to fill the increasing rate of STEM jobs (Eddy et al., 61, 2015). So, the push to take algebra in middle school is also to fulfill our economic needs and remain competitive in the international market.

Closing Racial and Gender Achievement Gaps

Minority students and economically-disadvantaged students are often tracked in remedial or general math courses. These remedial and general math courses are “curricular dead-ends,” as one study describes them, because there’s no real progression in the difficulty of the mathematics topics (Loveless, 2008). Consequently, diversity in algebra courses is lacking and some students aren’t being taught the mathematics skills they need to succeed not just in algebra, but in high school, college, and career. Additionally, Students that begin algebra later than 8th or 9th grade are less likely to graduate high school and attend and complete college (Algebra for All Initiative, 2016). Instituting algebra in 8th grade gives minority and economically-disadvantaged students increases access to higher mathematics courses and increases their postsecondary opportunities. In addition, algebra in 8th grade helps close the gender gap in mathematics achievement between boys and girls; it especially helps boys because girls outperform boys in high school mathematics (Eddy et al., 19, 2015). However, for students that aren’t prepared for algebra, taking algebra in 8th grade will do more harm than good.

Arguments

Parental Income and Education Impacts Student Learning

As introduced above, the students that don’t benefit from 8th grade algebra are those that are academically unprepared, which oftentimes happen to be students of low socioeconomic status. These students don’t have the same access to high-quality education and support as their counterparts of higher socioeconomic status. 69.8% of students in the 10th percentile of 8th algebra meet the requirements to enroll in free- or reduced-lunch programs (Loveless, 2008). For some perspective, only 30.4% of students in the 10th percentile in advanced courses qualify for these lunch programs, and 36.4% of students nationwide qualify for free-or reduced-lunches (Loveless, 2008).

There are a lot of academic hardships being an economically-disadvantaged student brings. For one thing, these students’ parents are more likely to have low educational levels. Just 20.3% of students have “mothers whom graduated from college” (Loveless, 2008). For these parents, they might not be able to assist their children with their math homework, which impacts their learning and grades. Parental involvement is generally a good thing for students’ academic success; a 1997 study by the U.S. Department of Education found students whose parents were involved were “more likely to take challenging mathematics courses earlier in their academic careers” (Matthews & Farmer, 2008). Students who’re unable to get support at home might be unable to get their homework done until they go to school, assuming the teachers have time to help them. If not, it is very easy to get behind in mathematics, since it is a rigorously cumulative subject. It is important that a student is caught up on their mathematics knowledge throughout their entire academic career, not just in a single algebra course. Even if the parents knew the material, they could be working two or three jobs to support the family which leaves them little time to help their kids with homework.

Students whose parents can help them have greater opportunities for learning. Moreover, parents of low socioeconomic status probably can’t afford tutoring and learning material, such as workbooks or software programs. Students whose parents can afford tutoring and learning materials have an advantage. So, when the time comes for a student to take algebra, those with greater resources are more prepared to succeed in algebra. It is also worth noting algebra is the most-failed subject in 8th grade (Education.com, 2013).

Scarcity of Qualified Teachers and Resources in High-Poverty Schools

About 50.9% of students of low SES (socioeconomic status) attend urban schools (Loveless, 2008). 67.6% are classified as high-poverty schools, as measured by the number of students that qualify for free- or reduced-lunches (Loveless, 2018). Additionally, urban schools suffer from overcrowding; they take on 27% more 8th students than is typical (“1,012 students versus 794) (Loveless, 2018).

Being underfunded and overcrowded hinder the schools’ efforts to retain qualified teachers and learning resources. Teachers at high-poverty schools are less likely to have at least five years of experience (22.5% versus 30.3% for regular eighth-graders), less likely to have a teaching certification (74.47% versus 82.5%), and less likely to have majored in mathematics as an undergraduate (20.1% versus 26.2%). In one observational study, one inexperienced mathematics teacher often couldn’t explain the problem to his students, became frustrated frequently, and possessed poor classroom management skills (McCoy, 114, 2005). The teacher would bring in a computer tutor twice a week to have the students work on their own. The students were unfocused and were far from completing their learning goals at the end of the term.

But chaos in the classroom isn’t the only negative effect of poor teaching; it can be devastating to students’ test scores. One study in 1996 compared standardized mathematics test scores between students have had effective teachers in three consecutive years versus students that had ineffective tears for three consecutive years; the differences in test scores were more than 50 percentiles apart (Woolfolk, 7, 2013). The same study concluded that good teachers benefits low-performing students the most. The study’s authors note that good (and bad teaching) is cumulative; its effects last for years. Thus, for a rigorously cumulative subject such as math (as mentioned previously), it is of even greater importance to as many good teachers as possible.

Lacking in Basic Arithmetic Skills

To succeed in algebra, a strong foundation in arithmetic is needed. However, studies have found that that thousands of 8th grade students lack skills in arithmetic (Loveless, 2008). In an arithmetic test administered to the low-performing students in advanced courses, only 9.8% of students got the answer involving calculating a percentage correct; 37.1% got the answered a question involving rounding decimals to the nearest whole number correctly (Loveless, 2008). In a question involving operations on fractions: 42.3% students got “Item A,” the easiest, correct, and 3.4% and 6.6% respectively got “Items B and C” correct (Loveless, 2008). This lack of arithmetic knowledge is highly likely due to that economically-disadvantaged households and schools that are unable to adequately address students’ academic needs. Meanwhile, policymakers are pushing all students to take algebra in 8th grade when the curriculum should be more differentiated. Low Test Scores and Limited Postsecondary Opportunities Because of the above reasons, students of low SES don’t tend to do well in algebra. While taking Algebra I in 8th grade increases the probability of passing the course on a retake, this is at the cost of lower scores on final exams, “some scoring “37% of a standard deviation lower” (Loveless, 2008). “They are also less likely to enroll and pass Geometry and Algebra II by 11th and 12th grade, respectively” (Loveless, 2008). Low test scores are an indication that something is amiss, especially when the low-test scores are confined to some socioeconomic classes and not others. Policymakers need to understand how socioeconomic realities makes the pace of learning different for everyone.

Conclusion and Recommendation

Conclusion

As this paper demonstrated, the lowest-performers in 8th grade algebra are often economically-disadvantaged students. Their parents and the schools they go to are also oftentimes disadvantaged as well. Parents might not have graduated college or work several jobs, making them unable to help or afford academic support outside of school for their children. The schools, which are often classified as high-poverty schools, are overcrowded and unable to keep qualified teachers. For these reasons, some students are not academically prepared for 8th grade algebra, mostly lacking the arithmetic skills needed for algebra success. This impacts their chances for taking advanced mathematics in high school, as well their chances of enrolling and graduating high school and college.

Recommendation

The fact that some students are struggling in 8th grade algebra doesn’t mean that algebra in 8th grade need be eliminated. This isn’t any either/or situation and can be fixed with the proper recommendations.

One powerful way of preparing students for 8th grade algebra is to gauge and teach the prerequisite skills needed, perhaps before they take the algebra class (Loveless, 2008). However, this is no good if students are forever trapped in taking general or remedial math courses with a watered-downed curriculum. Somehow, general and remedial education need to be reformed so that students can smoothly transfer to the regular mathematics courses. Education isn’t about who is learning the quickest, but who is learning the most at their own pace. Speed is important, but it isn’t everything. Not everyone is going to be able to take algebra in 8th grade, or calculus in 12th grade. Some would be better served taking trigonometry and calculus in college. Though, that “they can always take higher-level math courses in college” shouldn’t be used as an excuse to avoid improving the remedial/general mathematics curriculum where it needs to be improved.

Perhaps to making use of after-school programs or summer schools could be one way to facilitate the transition from remedial/general math courses to regular courses? This way, students don’t have to use up a year or two of high school to take remedial classes. The instructional design should be differentiated so that the individual student learns what they need to know and move on. This way, a student that already knows how to add fractions won’t have to stay in class while the teacher teaches it to students that don’t know how to add fractions. It also saves the student precious time in their remedial education so they can enroll in regular and advanced mathematics courses. This solution strikes a balance between speed and good learning and can probably do much to ensure that students receive the mathematics education they deserve.

References

Clotfelter, C. T., Ladd, H. F., & Vigdor, J. L. (2012). Algebra for 8th graders: Evidence on its effects from 10 north carolina districts. Cambridge: National Bureau of Economic Research, Inc. doi:http://dx.doi.org.mtrproxy.mnpals.net/10.3386/w18649

Eddy, C. M., Fuentes, S. Q., Ward, E. K., Parker, Y. A., Cooper, S., Jasper, W. A., … Wilkerson, T. W. (2015). Unifying the Algebra for All Movement. Journal of Advanced Academics, 26(1), 59-92. doi: 10.1177/1932202X14562393

Education, N. D. (2016). Algebra for All Initiative: Middle & High School Programs. New York City, New York, United States. Retrieved from http://admin.abcsignup.com/files/F474B456-0F3C-48EE-A066-0C58FCAAAC88_35/A4AMSHSOverview.pdf

Higher Math in Lower Grades: Hurting or Helping Kids? (2013, October 21). Retrieved from Education.com: https://www.education.com/magazine/article/higher-math-grades/

Loveless, T. (2008). The Misplaced Math Student: Lost in Eighth-Grade Algebra. Washington, D.C.: Brown Center on Education Policy at Brookings Institution. Retrieved from https://www.brookings.edu/wp-content/uploads/2016/06/0922_education_loveless.pdf

Matthews, S. M., & Farmer, L. J. (2008). Factors Affecting the Algebra I Achievement of Academically Talented Learners. Journal of Advanced Academics, 19(3), 472-501.

McCoy, L. P. (2005). Effects of Demographic and Personal Variables on Achievement in Eighth-Grade Algebra. Journal of Educational Research, 98(3), 131-135. doi:https://doi-org.mtrproxy.mnpals.net/10.3200/JOER.98.3.131-135

Woolfolk, A. H. (2013). Educational Psychology. Boston, Ma; Columbus, Oh; New York; Upper Saddle River, Nj; Amsterdam; Cape Town; Dubai; London; Madrid ; Milan; Munich; Paris; Montreal; Toronto; Delhi; Mexico City; Sao Paulo; Sydney; Hong Kong; Seoul; Singapore; Taipei; Tokyo: Pearson Education.

Background Information

Students didn’t always take algebra I in the 8th grade. In decades past, only students that planned on going to college took algebra courses (Eddy et al., pg. 61, 2015). Since 1990, however, the percentage of students enrolled in 8th grade algebra in increased from 16% to 24%; in 2007, that number was at 31% (Loveless, 2008). Though, not every student benefit from taking algebra in 8th grade. 8th grade algebra is most difficult for economically-disadvantaged students because these students don’t have access to the educational resources they need to succeed in 8th grade algebra. Before we get to that, however, let’s look proponents’ views for having students enroll in algebra in 8th grade.

Benefits of Taking Algebra in 8th Grade

For students that are adequately prepared for 8th grade algebra, there are benefits to starting algebra in 8th grade. Algebra is considered a gatekeeper course to advanced courses in mathematics, science, engineering, and mathematics. For high-performing students taking 8th grade algebra, they are 20% more likely to take calculus in 12th grade; for students that perform in the middle, they are 10% more likely to take calculus in 12th grade (Eddy et al., 2015). These students are also more likely to complete high school and enroll and graduate college. However, for the low-performing students, they are 20% more likely to have to repeat Algebra I in the future (Eddy et al., 2015). These students are also less likely to pass geometry by 11th grade, while median- and high-performing students are more likely to do well in geometry in 11th grade(Clotfelter et al., 6). As one can see, the positive benefits only apply to students that are prepared for algebra and portraying the benefits as universal for every student is misleading.Global Competitiveness

In the large picture, why are these benefits stated above important? Besides the obvious—a high-quality education leads to a better life for everyone—it also increases the United States’ competitiveness in the global market. Knowledge of mathematics provides the foundation for careers in “commerce, industry, science, and technology” (Eddy et al., 61, 2015). Algebra instills into one to “solve problems by modeling, evaluate quantitative relationships, and express and justify generalizations (Eddy et al., 61, 2015). Again, algebra is a gatekeeper to higher mathematics. Furthermore, statistics show that the “mathematics curriculum for 13-year-old American students in the U.S. is one year behind the international community,” and it is getting difficult to find qualified applicants to fill the increasing rate of STEM jobs (Eddy et al., 61, 2015). So, the push to take algebra in middle school is also to fulfill our economic needs and remain competitive in the international market.

Closing Racial and Gender Achievement Gaps

Minority students and economically-disadvantaged students are often tracked in remedial or general math courses. These remedial and general math courses are “curricular dead-ends,” as one study describes them, because there’s no real progression in the difficulty of the mathematics topics (Loveless, 2008). Consequently, diversity in algebra courses is lacking and some students aren’t being taught the mathematics skills they need to succeed not just in algebra, but in high school, college, and career. Additionally, Students that begin algebra later than 8th or 9th grade are less likely to graduate high school and attend and complete college (Algebra for All Initiative, 2016). Instituting algebra in 8th grade gives minority and economically-disadvantaged students increases access to higher mathematics courses and increases their postsecondary opportunities. In addition, algebra in 8th grade helps close the gender gap in mathematics achievement between boys and girls; it especially helps boys because girls outperform boys in high school mathematics (Eddy et al., 19, 2015). However, for students that aren’t prepared for algebra, taking algebra in 8th grade will do more harm than good.

Arguments

Parental Income and Education Impacts Student Learning

As introduced above, the students that don’t benefit from 8th grade algebra are those that are academically unprepared, which oftentimes happen to be students of low socioeconomic status. These students don’t have the same access to high-quality education and support as their counterparts of higher socioeconomic status. 69.8% of students in the 10th percentile of 8th algebra meet the requirements to enroll in free- or reduced-lunch programs (Loveless, 2008). For some perspective, only 30.4% of students in the 10th percentile in advanced courses qualify for these lunch programs, and 36.4% of students nationwide qualify for free-or reduced-lunches (Loveless, 2008).

There are a lot of academic hardships being an economically-disadvantaged student brings. For one thing, these students’ parents are more likely to have low educational levels. Just 20.3% of students have “mothers whom graduated from college” (Loveless, 2008). For these parents, they might not be able to assist their children with their math homework, which impacts their learning and grades. Parental involvement is generally a good thing for students’ academic success; a 1997 study by the U.S. Department of Education found students whose parents were involved were “more likely to take challenging mathematics courses earlier in their academic careers” (Matthews & Farmer, 2008). Students who’re unable to get support at home might be unable to get their homework done until they go to school, assuming the teachers have time to help them. If not, it is very easy to get behind in mathematics, since it is a rigorously cumulative subject. It is important that a student is caught up on their mathematics knowledge throughout their entire academic career, not just in a single algebra course. Even if the parents knew the material, they could be working two or three jobs to support the family which leaves them little time to help their kids with homework.

Students whose parents can help them have greater opportunities for learning. Moreover, parents of low socioeconomic status probably can’t afford tutoring and learning material, such as workbooks or software programs. Students whose parents can afford tutoring and learning materials have an advantage. So, when the time comes for a student to take algebra, those with greater resources are more prepared to succeed in algebra. It is also worth noting algebra is the most-failed subject in 8th grade (Education.com, 2013).

Scarcity of Qualified Teachers and Resources in High-Poverty Schools

About 50.9% of students of low SES (socioeconomic status) attend urban schools (Loveless, 2008). 67.6% are classified as high-poverty schools, as measured by the number of students that qualify for free- or reduced-lunches (Loveless, 2018). Additionally, urban schools suffer from overcrowding; they take on 27% more 8th students than is typical (“1,012 students versus 794) (Loveless, 2018).

Being underfunded and overcrowded hinder the schools’ efforts to retain qualified teachers and learning resources. Teachers at high-poverty schools are less likely to have at least five years of experience (22.5% versus 30.3% for regular eighth-graders), less likely to have a teaching certification (74.47% versus 82.5%), and less likely to have majored in mathematics as an undergraduate (20.1% versus 26.2%). In one observational study, one inexperienced mathematics teacher often couldn’t explain the problem to his students, became frustrated frequently, and possessed poor classroom management skills (McCoy, 114, 2005). The teacher would bring in a computer tutor twice a week to have the students work on their own. The students were unfocused and were far from completing their learning goals at the end of the term.

But chaos in the classroom isn’t the only negative effect of poor teaching; it can be devastating to students’ test scores. One study in 1996 compared standardized mathematics test scores between students have had effective teachers in three consecutive years versus students that had ineffective tears for three consecutive years; the differences in test scores were more than 50 percentiles apart (Woolfolk, 7, 2013). The same study concluded that good teachers benefits low-performing students the most. The study’s authors note that good (and bad teaching) is cumulative; its effects last for years. Thus, for a rigorously cumulative subject such as math (as mentioned previously), it is of even greater importance to as many good teachers as possible.

Lacking in Basic Arithmetic Skills

To succeed in algebra, a strong foundation in arithmetic is needed. However, studies have found that that thousands of 8th grade students lack skills in arithmetic (Loveless, 2008). In an arithmetic test administered to the low-performing students in advanced courses, only 9.8% of students got the answer involving calculating a percentage correct; 37.1% got the answered a question involving rounding decimals to the nearest whole number correctly (Loveless, 2008). In a question involving operations on fractions: 42.3% students got “Item A,” the easiest, correct, and 3.4% and 6.6% respectively got “Items B and C” correct (Loveless, 2008). This lack of arithmetic knowledge is highly likely due to that economically-disadvantaged households and schools that are unable to adequately address students’ academic needs. Meanwhile, policymakers are pushing all students to take algebra in 8th grade when the curriculum should be more differentiated. Low Test Scores and Limited Postsecondary Opportunities Because of the above reasons, students of low SES don’t tend to do well in algebra. While taking Algebra I in 8th grade increases the probability of passing the course on a retake, this is at the cost of lower scores on final exams, “some scoring “37% of a standard deviation lower” (Loveless, 2008). “They are also less likely to enroll and pass Geometry and Algebra II by 11th and 12th grade, respectively” (Loveless, 2008). Low test scores are an indication that something is amiss, especially when the low-test scores are confined to some socioeconomic classes and not others. Policymakers need to understand how socioeconomic realities makes the pace of learning different for everyone.

Conclusion and Recommendation

Conclusion

As this paper demonstrated, the lowest-performers in 8th grade algebra are often economically-disadvantaged students. Their parents and the schools they go to are also oftentimes disadvantaged as well. Parents might not have graduated college or work several jobs, making them unable to help or afford academic support outside of school for their children. The schools, which are often classified as high-poverty schools, are overcrowded and unable to keep qualified teachers. For these reasons, some students are not academically prepared for 8th grade algebra, mostly lacking the arithmetic skills needed for algebra success. This impacts their chances for taking advanced mathematics in high school, as well their chances of enrolling and graduating high school and college.

Recommendation

The fact that some students are struggling in 8th grade algebra doesn’t mean that algebra in 8th grade need be eliminated. This isn’t any either/or situation and can be fixed with the proper recommendations.

One powerful way of preparing students for 8th grade algebra is to gauge and teach the prerequisite skills needed, perhaps before they take the algebra class (Loveless, 2008). However, this is no good if students are forever trapped in taking general or remedial math courses with a watered-downed curriculum. Somehow, general and remedial education need to be reformed so that students can smoothly transfer to the regular mathematics courses. Education isn’t about who is learning the quickest, but who is learning the most at their own pace. Speed is important, but it isn’t everything. Not everyone is going to be able to take algebra in 8th grade, or calculus in 12th grade. Some would be better served taking trigonometry and calculus in college. Though, that “they can always take higher-level math courses in college” shouldn’t be used as an excuse to avoid improving the remedial/general mathematics curriculum where it needs to be improved.

Perhaps to making use of after-school programs or summer schools could be one way to facilitate the transition from remedial/general math courses to regular courses? This way, students don’t have to use up a year or two of high school to take remedial classes. The instructional design should be differentiated so that the individual student learns what they need to know and move on. This way, a student that already knows how to add fractions won’t have to stay in class while the teacher teaches it to students that don’t know how to add fractions. It also saves the student precious time in their remedial education so they can enroll in regular and advanced mathematics courses. This solution strikes a balance between speed and good learning and can probably do much to ensure that students receive the mathematics education they deserve.

References

Clotfelter, C. T., Ladd, H. F., & Vigdor, J. L. (2012). Algebra for 8th graders: Evidence on its effects from 10 north carolina districts. Cambridge: National Bureau of Economic Research, Inc. doi:http://dx.doi.org.mtrproxy.mnpals.net/10.3386/w18649

Eddy, C. M., Fuentes, S. Q., Ward, E. K., Parker, Y. A., Cooper, S., Jasper, W. A., … Wilkerson, T. W. (2015). Unifying the Algebra for All Movement. Journal of Advanced Academics, 26(1), 59-92. doi: 10.1177/1932202X14562393

Education, N. D. (2016). Algebra for All Initiative: Middle & High School Programs. New York City, New York, United States. Retrieved from http://admin.abcsignup.com/files/F474B456-0F3C-48EE-A066-0C58FCAAAC88_35/A4AMSHSOverview.pdf

Higher Math in Lower Grades: Hurting or Helping Kids? (2013, October 21). Retrieved from Education.com: https://www.education.com/magazine/article/higher-math-grades/

Loveless, T. (2008). The Misplaced Math Student: Lost in Eighth-Grade Algebra. Washington, D.C.: Brown Center on Education Policy at Brookings Institution. Retrieved from https://www.brookings.edu/wp-content/uploads/2016/06/0922_education_loveless.pdf

Matthews, S. M., & Farmer, L. J. (2008). Factors Affecting the Algebra I Achievement of Academically Talented Learners. Journal of Advanced Academics, 19(3), 472-501.

McCoy, L. P. (2005). Effects of Demographic and Personal Variables on Achievement in Eighth-Grade Algebra. Journal of Educational Research, 98(3), 131-135. doi:https://doi-org.mtrproxy.mnpals.net/10.3200/JOER.98.3.131-135

Woolfolk, A. H. (2013). Educational Psychology. Boston, Ma; Columbus, Oh; New York; Upper Saddle River, Nj; Amsterdam; Cape Town; Dubai; London; Madrid ; Milan; Munich; Paris; Montreal; Toronto; Delhi; Mexico City; Sao Paulo; Sydney; Hong Kong; Seoul; Singapore; Taipei; Tokyo: Pearson Education.