As colleges continue to raise the mathematics requirements for entrance, students are having an increasingly difficult time rising to the occasion. There have been many debates over when “higher” mathematics instruction should begin. “Higher” mathematics is defined as Algebra I and any other courses beyond. Some believe that it should begin in eighth grade, a year earlier than the norm, in the United States, to give students an edge on standardized tests that lead to college admission decisions. However, there seems to be a lack of data that examines the long-term effects of early access to Algebra to support the idea that the extra year really makes a difference (Silva, 1990).
The idea that Algebra I education could begin in middle school has been around for a long time. In the early 1900s the idea began to circulate to make the middle school mathematics curriculum more challenging. Some early investigations began to look into if students were capable of handling the abstract ideas of Algebra in the late middle school years. However, nothing came of these early studies. Educators continued the practice of Algebra I being taught in the ninth grade and despite the few voices of change (Taylor, 1905).
Later, in the 1990s, the educational reform movement sparked by the National Council of Teachers of Mathematics began to examine the mathematics curriculum very closely. Groups began to recognize that there was a problem within the mathematics discipline of the United State’s education system. The National Council of Teachers of Mathematics (1989) recommended increased literacy in mathematics for all students not just the academically advanced. In 1994 the National Center of Education Statistics released a report that stated that effective middle schools offer algebra for eighth grade students (NCES, 1994). These events began turning the clock of change in mathematics curriculum. A study of the TIMSS and TIMSS-R showed that the middle school math curriculum for eighth grade students in the US was comparable to the seventh grade mathematics curriculum in other countries that participated in the study. Therefore, US students were at a disadvantage by the age of 13 (Greene, Herman, & Haury, 2000). With the world’s economy becoming more interdependent and the job market more competitive we need to research what changes should be made to the middle school mathematics curriculum for the eighth grade to find a way to give US students the edge over the job market. In order for the US to stay a dominant force in worldwide trade and industry we have to give our students an edge. The US needs to put out math literate people who can perform academically in mathematics in secondary institutions to ensure that more students go on to college to pursue a more in-depth understanding of mathematics (Silva, 1990).
The purpose of this quantitative study is to examine the relationship between student achievement in mathematics, and the grade that a student completes Algebra I. Thus, the question must be asked: How taking Algebra I in the eighth grade lead to higher academic achievement and greater chance of college admission at a competitive state university? I believe that by taking Algebra I in the eighth grade students will perform better on standardized tests because they will have access to more of the mathematics curriculum. This will ensure that students can make the scores high enough to get into college. Therefore, by taking Algebra I in the eighth grade students will have greater academic success and opportunities for higher education.
Definition of Terms
Student achievement in mathematics, the independent variable, is defined as the successful mastery of key concepts from mathematics that are necessary for college. Student achievement will be measured by a students’ ACT mathematics scores.
Track will be used to mean the sequence of courses a student takes and which year they take their courses. For example, the honors track is defined as the sequence of courses where Algebra I is completed in the 8th grade and all other TOPS requirements are completed for graduation. Regular track will be defined as sequence of courses where Algebra I is completed in the 9th grade and all other TOPS requirements are completed for graduation.
There are separate theories in what year Algebra should be taken. Some people side with Piaget ( ) and say that abstract thought develops sometime after 11 or 12 therefore Pre-Algebra shouldn’t begin until 8th grade. Others argue that students actually understand how to solve problems better using Algebra (Nathan & Kodinger, 2000).
In addition, many people believe that Algebra understanding develops naturally from observations of the world around us. The basic principals of algebra are evident in our everyday lives. For example, most children can calculate how much money they need to purchase a new toy. If they have five dollars and need to have ten, they solve a basic Algebra equation: 5 + x = 10. Therefore, it is difficult to fully agree with Piaget due to the fact that young children are solving algebraic problems without even realizing it.
According to Nathan & Koedinger’s mixed methods study on teachers’ beliefs and perspectives on students mathematical development, symbol-precedence was the most commonly held theory among teachers in high schools. After a survey and interviews they found that high school teachers ranked Algebra word problems as much more difficult than arithmetic or symbol problems (equations). The teachers believed that student’s abilities to work with abstract symbols developed before their ability to solve word problems that had real world applications. This view is referred to as the symbol-precedence view. On the contrary, however, when the students were tested with their assessment they performed much better on the word problems that required the algebraic thought. This shows a discrepancy between the beliefs of the teachers and the performance of the students. Middle school teachers, however, did not rank algebra word problems as the most difficult and fairly accurately ranked the level of difficulty for their students. Since teachers are the gatekeepers for early access to Algebra this misconception causes a problem. Nathan & Koedinger, claim that textbooks that treat symbol problems as if they should be done easily, and word problems as if they are very difficult may create the problem. However, their conclusion is the symbol-precedence view does not accurately describe students’ abilities. The implications of their conclusion is that if teachers are the gatekeepers to early access to Algebra and they don’t truly understand the development of Algebra then there is a big problem with the way we determine who gets early access to Algebra.
As early as 1905 there were people questioning the year in which algebra was introduced. Claude Turner (1905) makes the claim that many of the concepts studied in the eighth grade year could be better taught using algebra. For example, he makes the point that exponents are best understood by using algebra. Understanding a cube root is best done through the use of algebra. In addition, Turner makes many good points in support of changing the year. He points out that we should wait until a student fully masters arithmetic to begin algebra instruction. He states that the student’s minds are much more mature and able to handle the more abstract concepts. Furthermore, he claims that many of the concepts could be best mastered through the use of algebra such as in the case of exponents. Also, he points out that students can become bored with eighth grade mathematics because of the lack of a challenge. While this article only offers his opinions based on events that he personally witnessed it is still helpful in identifying many positive arguments towards changing the year algebra is introduced.
People involved in mathematics curriculum development have a cyclical pattern of thought (Usiskin, 1997). In the early 1900s there was a movement toward pure mathematics. Pure mathematics could be defined as the ability to algebraically manipulate equations to solve problems. It could also be described as a “plug and chug” method. This is where when a problem is presented the student would find the correct formula and plug the data in. It is a knowledge-based assessment. According to Usiskin (1997) in the early 1930s the life-skills movement changed the perspective of educators to being more focused on applications. He claims this change came as a result of the Great Depression. Turner (1937) wrote a paper on the need for mathematical problems that can be applied to real life situations. Furthermore Usiskin continues to state that in 1957 the development of space programs increased the demand for pure mathematics again. Today we appear to be cycling back to the thought in the late 1960s where educators focused on applications again. The different patterns of thought change the way mathematics is taught in schools. If it is a time of pure mathematics, educators want students to have maximum exposure to Algebra. For example, Taylor (1905) calls for an increase in pure mathematics focus in curriculum. He also suggests beginning Algebra I instruction in the 7th or 8th grade. Currently, according to Usiskin, the push within the mathematics curriculum is for applications. Educators would want students to master applications in arithmetic before beginning algebra. Thus the year students began Algebra would be in the 9th grade. Usiskin accurately documents mathematic thought through the 1900s and discusses the implications of the changes in perspective. Furthermore, he goes on to examine the standardized test scores during the time periods. During the 1970s there was a decline in the mathematics scores on the SAT. Usiskin claims that it was due to an increase in the number of students taking the SAT and there was also a decrease in the verbal scores. He claims that the validity of statements made by educators that an applications focus has a negative impact could be questioned. Therefore, the year that algebra is offered could be questioned.
Speilhagen (2006) makes the case for the importance of all 8th grade students taking Algebra. He points out that the current trend is that only “gifted” or “honors” students are currently allowed to take Algebra in the 8th grade and that this is leaving the remaining students at a disadvantage. He also points out that US students are a year behind in mathematics. In other countries by the eighth grade Algebra instruction has already begun. Speilhagen conducted a mixed methods study where he studied the achievement gap and continued mathematics involvement of students who were allowed early access to Algebra I and those who weren’t. He used the standardized test in Algebra I (taken after the course is completed), the pre-placement test and the Stanford 9 standardized test. The findings were that the students who were allowed access to Algebra I in the 8th grade scored higher than the other group on everything except the state Algebra I standardized test. There was a significant overlap on this test. The students who took it in the 8th grade had mean score of 446.4 (SD=58.2)and the students who took it in the 9th grade had a mean score of 401.9(28.8). As Speilhagen points out the standard deviations of this data shows an overlap in the scores. The lowest scoring students from the 8th grade group scored the same as the highest scoring students in the 9th grade group. This is important to note because if there wasn’t a marked improvement by the 9th grade students waiting an extra year then they shouldn’t be denied access to the class. The author does a great job for pointing out that if the 8th grade students are doing on slightly better then it doesn’t make sense to deny all students the right to Algebra I in the 8th grade. While this study does a good job at identifying initial differences in math scores it doesn’t test further down the road. These same students scores on later standardized tests could be compared to see if there was any benefits from taking Algebra I a year earlier. In addition, the scores on standardized tests could be compared at the completion of Algebra II to see if there were any differences at that point. This study examines what happens in the short-term but not in the long-term.
Conversely several studies argue that early access to the algebra curriculum increases mathematical literacy. Silva, Moses, Rivers and Johnson (1990) state that, ” communities whose members are lacking in mathematical literacy risk becoming a permanent underclass who generation after generation live on the margins of the nation’s economic and political institutions.'” This shows the extreme need to produce students who are literate in mathematics. The Algebra Project, a mathematics curricular movement, argues that the way to increase mathematical literacy is early access for all students to algebra. By allowing early access to Algebra, it opens the door to more possibilities and more opportunities in the field of mathematics (Silva, Moses, Rivers & Johnson, 1990).
However, the above studies do not examine the long-term effects of early access. Silva, Moses, Rivers and Johnson (1990) only make recommendations about changes in the role of the teacher and changes in the curriculum that need to be made so that all students can be successful. They do not make a case for what can be expected from putting all students, not just the higher achievers, in Algebra I in the 8th grade.
Smith (1996) attempts to examine long term results of early access to Algebra. He states the obvious that students in Algebra I in the 8th grade can advance higher in mathematics but also mentions that a greater percentage of students who complete Algebra I in the 8th grade choose to continue their math studies after they have fulfilled graduation requirements. Of course the more mathematics students take the more successful they will be. His conclusion is that taking Algebra I in the 8th grade may not directly make a student smarter but it does increase the likelihood of taking higher math classes thus affecting their standardized test scores. However, he does not collect standardized test data to examine. He simply looks at the tests given within the school to assess mathematical achievement.
In addition, Garret & Delaney (1988) found that students in the college track that took the higher mathematics such as Advanced Mathematics and Calculus scored on average 47 points higher than the students that did not take the higher mathematics. However, this study was done a while ago and did not separate students that had taken Algebra I early and those that did not. There could be an even more dramatic difference when only the students who achieved calculus are examined or those students that took Algebra I in the 8th grade.
The Algebra Project focuses on improving mathematical literacy for all students. The Algebra Project makes the argument that the current system of only placing “talented” students into Algebra I in the 8th grade is creating a huge gap for inner-city students or cultures that educators perceive to not be good at mathematics (Silva, Moses, Rivers & Johnson, 1990). They support their opinion with theory and research however they are lacking in exact data. They do not examine the effects of early algebra access for all beyond the initial first year performance. It is important to further investigate what if there is any change in long-term mathematical ability.
I would assign students in public schools in St. John the Baptist parish and St. Charles Parish into two different groups. The first group would be comprised of the students following the honors track. The honors track is defined as students that completed Algebra I with a C or better in the eighth grade. The second group, the regular track, would be comprised of students that completed Algebra I with a C or better in the ninth grade. Then, I would randomly choose a sample from both groups using computer generated random numbers list.
Once I have determined my sample, I would gather the data on the ACT scores for both groups. For the honors track I would gather each student’s average ACT score from their junior year Then I would determine the average score for the sample. The average score for the sample will be found by averaging each student’s average score on the ACT. From the regular tack I would do the same only I would gather the average ACT score for each student from their senior year. Then I would compare the average score from the honors track and the regular track.
I have randomly sampled thus I can perform a t-test to see if there was a association between the year algebra I was taken and the average ACT score for each track.
Lastly, I would perform the same test with the ACT scores from students in the honors track during their senior year and find the mean score and compare it to the mean score of the regular track from their senior year. This would give more information on the final outcome of early access to Algebra I.
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