From: Rosantina Cavazos
Email:
Course: cd 169: Motivating Children and Adolescents in Educational Settings
College: San Jose State University
Instructor: Eugene Matusov
ClassWeb: http://www.ematusov.com/cd169
ChildrenObservations: No
Date: 24 May 1997
Time: 01:41:33
Remote Name: cust97.max17.san-francisco.ca.ms.uu.net
It is important to un-track mathematics classes in school. This is especially true for jr. high and high school. These are the critical years where students are introduced to higher mathematical concepts, such as algebra. Many of the higher paying jobs such as engineering and business demand the ability to use higher mathematics in problem solving. This is especially true for the Santa Clara Valley where many of the jobs are technical as well as business related.
Students who are put in the lower tracks are usually not taught the algebra and problem solving skills that are needed to go on to higher mathematics. Rather, they are taught basic arithmetic skills that will keep them on track to lower paying jobs. Can these students be taught higher mathematical skills? I don't thing we should ask "can they be taught?" but rather "how can they be taught?" I don't think we have a choice, since many of today's jobs require the ability for problem solving found in higher mathematics. We need to look at various methods and pick out those that are successful so we use them to educate all students in higher math. Countries like Japan consider that all students have the ability to learn mathematical concepts but some students have to work harder then others.
An alternative method to tracking is "mixed ability grouping" where students can learn in a cooperative atmosphere . The Algebra project is another method that has succeed in helping "lower ability" students succeed in Algebra
One of the main problems with tracking is that it breeds low self-esteem and lack of motivation for students in the lower tracks. If a student is going to succeed, he needs to be free of the negative feelings that being in a low-track breeds, so they don't get in the way of his success.
It is important that mathematics classes be untracked because all students need to be educated in higher mathematics for today's job market. This is especially true here in the Santa Clara Valley where so many technical as well as other high paying jobs require a college degree and a good mathematical base. For example, business and engineering both require knowledge of higher mathematics.
Student's in the lower tracks don't get exposure to higher mathematical concepts, such as algebra concepts. According to Linn, "In the 'tracked' schools of America, algebra acts as a switching station. Students who learn algebra early typically get switched into the fast track that prepares students for college and in the long run, good jobs." She goes on to say, "Students who don't learn algebra early get switched onto the slower vocational or general track. In today's high tech economy, those tracks lead mainly to low-level jobs and sometimes no job at all." (Linn 1992, p.23) So, as a result of our high tech economy, we should not be asking if we should educate "lower ability" students in higher mathematics, but rather we should be asking "how?"
In a study done by the National Assessment of Educational Progress (NAEP) The State of Mathematics Achievement, they found that in grade 12, "students in academic school programs and with plans to attend a four-year college after high school had substantially higher average mathematics achievement than students in general or vocational/technical programs or those planning to enter the work force upon high-school graduation." (Moses, 1990, p.8) That means that students in lower tracks are being denied the opportunity to learn higher mathematical concepts. Oakes gives an example of how students are divided into different levels of mathematics ability groups. The example is from Vista Junior High of a study done by Oakes of seventh-grade mathematics' classes. . Students are divided by ability into the following levels.
(I) Honors: A select group of students who have high motivation and habits of logical thought. These students have a have a good command, of addition, subtraction, multiplication , and division facts of whole numbers, decimals and fractions.
(II) Academic: Students who have many of the characteristics of Level I except in mathematical reasoning ability and attitude. But are less consistent and motivated then Level I.
(III) General: Students of average mathematical ability. They should be able to perform well as far as the basic facts of addition, subtraction, and multiplication of whole numbers.
(IV) Basic Math : Students placed in Level IV are those working below the seventh grade level in mathematics. These students cannot perform well in basic addition, subtraction, multiplication, and division facts of whole numbers.
Students are grouped in these levels according to different criteria., and most of the tracking decisions are made by teachers and counselors with no input from parents or students. As a result, the teachers and counselors may be putting a student on a life's work path that the student will have a hard time deviating from during his life-time. For that reason I don't feel a student should be put on a track. Because not only does it narrow his/her choice of careers, but when a student is placed on a lower- track the negative stigma associated with that track may cause the student to have self-esteem problems that may get in the way of the student's success.
A 1982 research analysis was done by James and Chen-Li Kulik and it "found no evidence that students learn more when grouped by ability", at lower tracks they actually learn less. (Horace1992, p.1) Can students from the lower tracks be taught the higher mathematical concepts? Countries like Japan don't question whether a student can do mathematics. They assume that all the students have the ability, just, that some have to work harder then others. You need to get rid of the idea that only talented students can succeed in mathematics. Jennififer Gutbezahl writes, "Many students in the United States believe that the only people who can succeed in a math class are those who can perform effortlessly." She goes on to explain how she told some students in introductory calculus classes that their "prior math failures were due to low effort and that increased efforts should lead to success in college." (Jennifer Gutbezahl) Students who were told this did better in calculus than students who were not told.
One way to teach all students algebra and higher mathematics concepts is through an integrated high school mathematics curriculum. Linn states that students can be taught, not so much just algebra, but how to generalize, make-abstractions and predications, and have confidence in their own problem solving ability through a "rich complex, and untracked mathematics program."(Linn, 1992, p.24) Some ways that these students can be taught is by putting students into heterogeneous grouping where you have mixed ability in one group. This means putting low achievers with high achievers together and encouraging more "cooperative learning or "collaborative learning." This is where groups of students work in small groups and as a result the students can help each other in the learning process. By putting students into smaller groups the students can not only help each other but the teacher can see what problems a student may have in the learning of a particular concept. Also, more problem solving activities can be given to students as a group. This integrates a number of skills and enables everyone use of their particular talents. "Horace quotes a math teacher, Eliabeth Whitcom, as stating, "My goal was that all students would not only be reached, but also challenged, often beyond self-imposed limits, I also wanted them to know that true mathematics could be don at all levels. So, students can be given challenging problems that can incorporate practical living problems and figure out ways to solve them and thus learn problem solving strategies.(Ciabotti, 1992, p.2) Holly Perry, a principal of Philalphia's Academy is cited by Horace as she describes "what happened when her school decided to offer Algebra 1 to all eight graders, including a special ed teacher as part of the teaching team. 'One of our top algebra students right now is a special ed kid with a reading and math disability."' She continues, "I think it's really a matter of confidence.
There are so many levels of hurt a for youngsters who are set apart that it actually gets in the way of cognitive progress."' ( Ciabotti, 1992, p.5) . The Algebra Probject is am math-science program started by Robert Moses in Cambridge, Massachusetts. It is a program that has made "algebra available to all seventh-and eight-grade students, regardless of their prior level of skill development or academic achievement ." The philosophy is to get students to learn high school science and math courses that should get them ready for college entrance.(Moses, et al, p.2) In 1985 ability grouping was replaced with small-group instruction . Teachers and parents worked with the students and helped them in learning difficult material and to reach certain goals. Teacher worked with students in small groups and as a result they were able to work with the students on a more individual basis,, Many students become motivated such as Andrea a twelve year old who stated, 'I'm going to do four lessons a week because I want to finish such-and such by the end of the seventh grade…'" The Algebra Project has been successful and has spread to other areas.
Conclusion
It is important to teach higher mathematical concepts to all students because of the our technically based economy. If these students are to be successful in finding jobs in the current job market, they need to be prepared in order to fill the demand of jobs requiring good mathematical and problem solving concepts..
Tracking keeps students who are placed in the low-tracks from being able to take the required courses that will give them higher mathematical concepts and prepare them to go to college. Since the lower tracks tend to teach only basic concepts like multiplication and division, by untracking these students and putting them in integrated classes you are giving them an opportunity to learn problem solving skills as well as algebra and higher math concepts that will enable them to compete for better paying jobs. Cooperative learning and the Algebra project are two successful ways that students have been given the opportunity to learn these higher math concepts. Students have proven that given the opportunity they are able to learn these skills.
References
Ciabotti, Pat. Essential Schools''Universal Goals': How Can Heterogeneous Grouping Help? Horace Vol. 8, No.5 May 1992 p.1-11 http://home.aisr.brown.edu/ces/publicat/horace/v08n05.htm
Executive Summary. The State of Mathematics Achievement NAEP's 1990 Assessment of the Nation and the Trial Assessement of the States. National Center for Education Statistics, Office of Educational Research and Improvement, Educational Testing Service p. 1-21 At http://llenc.org/reform/journals/ENC2137/2137.htm
Gutbezahl, Jeniffer. Talent/Motive Disjunction: A Useful Mathematical Mythology ABSTRACT http://i.fix.org/-jennyg/articles/mtmd.abs
Linn, Eleanor. Untracking High School Mathematics Equity Coalition Vol III, No. 1, Autumn 1992 p.23-25
Mosses, Robert et al. ( 1994) The Algebra Project: Organizing in the Spirit of Ella Critical Studies in Organization and Bureucracy. Temple University Press 1994 p 497-519 http://www.cpn.org/sections/topics/y…stories-studies/algebra_poject.hjtm p. 1-34
Oakes, Jeannie . (1985) Keeping Track New Haven: Yale University Press