Math Through the Ages, Research Paper Example

Introduction

Math education has been a part of educational systems since ancient times. Society has long held the firm belief that knowing mathematical concepts is crucial to living in society and for doing numerous jobs. Today, all developed countries extol the virtues of math education. Teaching and learning elementary math, algebra, geometry, trigonometry, measurement, data analysis, probability, and calculus helps people to be better at reasoning and problem solving. This paper investigates a wide range of topics that surround math education.

History of Mathematics

Many of the achievements of the math we know came to us from the Greeks, who gave us proofs derived from axioms. The Egyptians came up with fractions. The Babylonians developed sexagesimals (the numeral system with 60 as a base). Asian Indians produced the decimal system. Arabic speaking cultures created some algebra.

So, let us not become too Eurocentric when we scan the history of math. Babylonians were using the Pythagorean Theorem an entire millennia before he came on the scene (Struik, 1995). Numerous Babylonian clay tablets reside in museums in proof of their ancient interest in numerical solutions to equations, compound interest, and mathematical applications.

Indian mathematicians were doing work on infinitesimals in the 15^th century. Chinese math, from the Sung Dynasty during the 13^th century, held considerable influence throughout Asia. In the Americas, the Mayan culture used a complicated vigesimal system (the numeral system with 20 as a base) which no doubt found collaborations with later advances of Aztec astronomy. The Incans, with no written language, managed to use quipus (knots tied in threads) for statistical work. Studying people groups, even today, in tribal cultures, produces exciting ethnomathematical possibilities for researchers.

Teaching Math in Spanish/Teaching Math in English

Barta, Sanchez, and Barta (2009) warned against omitting indigenous cultural influences in math education, making the point that students can gain added appreciation for math if instruction comes to them in their native language. This belief extends to places, Like Guatemala, where math delivery is in Spanish rather than in the language of the Mayans. A bi-lingual educator is a bridge between struggling students and technology.

Other teachers, even those who are bilingual, find that it is best to keep side discussions in native languages, reserving English vocabulary for instructional delivery and response (Demski, 2009). The reason for this is to help students develop an academic language.

Current Issues in Math

One current debate is about the need for more materials. Textbooks alone will not suffice, nor can they assist students and teachers in meeting any more than about three quarters of state recommended standards (Witzel & Riccomini, 2007). Some state leaders, such as California Governor, Arnold Schwarzenegger, believe that textbooks need to disappear (Weekly Reader, 2010). Digital reading devices that fit into the palm of your hand can hold the same information as 100 heavy books. In addition, this appears to be a greener alternative to the production of texts, and the digitization process can update frequently, whereas texts go out of date and cannot recall easily or inexpensively. For example, when Pluto lost its planetary status, thousands of texts, which go out of date in an average of six years anyway, were supplying dated information to students throughout the country.

Another issue is about how parents react to school math expectations under No Child Left Behind and other school reforms. Remillard and Johnson

(2007) focused their work on low-income, African American reactions. They determined that standards-based math disempowered the parents in their study from assisting, at home, with school math learning.

Another contentious issue is fractions (Milford, 2008). A few math leaders think that fractions are as out of date as Roman numerals. This debate always boils down to the question, “But what about construction and cooking” (the two places where fractions appear to be used the most)?

Learning math takes work. There is no way around that. The notion that math is all fun, or should be taught that way, is a fantasy.

Current Curriculums in Math

Crosnoe, Weigle-Crumb, Field, Frank, and Muller (2008) found that girls have caught up to boys in taking challenging high school math courses but that their reasons for taking the classes are different from the boys’ reasons. Girls typically have outpaced boys in every academic indicator –except for math.

According to USA Today (2010, News, 6A), states are watering down standards. In Minnesota, a student does not have to take an exit test in order to graduate. In Arkansas and Ohio, passing grades have been set at 40% and below. In New Jersey, 15% of students receive high school diplomas even if they fail (They have to do some remedial work instead, and it is not tested). In 24 states, there is no end of course requirement for graduation. Because of these and other shortcomings in state curriculum mandates, employers are spending millions of dollars each year to teach their youngest employees the things that they should have come to them already knowing. This places the workforce at a distinct disadvantage, particularly in non-skilled and semi-skilled labor markets.

The news along these lines, however, is not all bad. In Virginia, the number of students passing the Algebra I graduation test requirement doubled  after a five-year effort targeting downward math trends.

There are problems that society and schools share. When we see films like Stand And Deliver about successful math teachers, like Jaime Escalante (who passed away in March of 2010), we open such stories to criticism (Shouse, 1995). Most schools function as norm-generating places, not norm-changing places. The term at-risk becomes a sword with two edges. First, students are at-risk for failure. Second, schools are at-risk for dismissal if they cannot produce student academic achievement according to state requirements. School systems lose valued accreditation if they fail. Students lose the chance at life options when they fail.

The Escalante story is that of a Latino math teacher who went in to a Los Angeles at-risk, Barrio school, and produced students whose high school calculus scores were so impressive that the Educational testing Service accused them of cheating. To be fair, and to get out of the Hollywood version of Escalante’s passion for math and for students, we must admit that his teaching practices would not stand up in the public schools of today, for his efforts came to creaming off talent from the top of his school. He was not interested in teaching any student who resisted submitting to the rules of his domain. Any student who would support his judgment without question was welcome in his world of math. Any student who questioned his authority was out. That meant that someone else had to teach them. His remaining students were those who would come early, stay late, and come again on weekends and holidays. His remaining students were intellectual stars. The other math teachers in his building had only those whose lives included more than math. Therefore, it is no wonder that his best students succeeded. This criticism does not arise to take anything away from Escalante’s methods of results but merely to point out that what he did is not encouraged or allowed by many public schools today. Many of his requirements resemble those that we reserve for extra-curricular activities through schools with if you don’t come to practice, you can’t play in the game rules.

Texas High School Student Failure in Math

Devine (2007) issued an analysis of the dropout rates in Texas.

Graduation Requirements for High School Students in Math

(Education commission of the States) Right now, only one state, Texas, requires all students to complete three units of math in order to graduate. Thirteen more states will phase this in by 2015.

We have to learn from what outcomes show and not what they are supposed to show.

A typical class might show a 20% difference in ability. If you are building a rocket, you use reductionism, backward-planning logic. If you do that in education, you run into problems.

In education, a second grader may take a test in May, but the teacher does not see the results of it until August. That is the equivalent of having a 24-hour rocket service report coming out a year later. It has no usefulness.

How to Make Math Education Interesting

For years, teachers have worked to make math as fun as possible for students. There are various ways to do this. For example, some people have found that math is work and more play when combined with cross-curricular study as opposed to the investigation of math for math’s sake (Downs, 2009). History seems to be an especially logical way to combine math concepts with the social science investigation.

Some teachers have had success by using math manipulatives. Students, who are able to see the math as they work through word problems, either individually or in small groups, hold these. The use of electronic white boards also helps learners to experience math in a manner that is not so bookish.

Psychological Fear of Math

Some people have an actual, clinical diagnosis of a fear of math. This is known as “dyscalculia.” This problem affects about 2-6.5% of the population (Editors, 2003). This problem is similar to dyslexia, the difficulty with reading. Dyscalculia can be a life-long issue for those who suffer from it.

This can lead to an outright fear of math that produces a series of bad experiences for students as the make their way through schools. They lack self-confidence in this area, so their fear that they will not succeed becomes a self-fulfilling prophecy. Schools do not excuse these students from taking math, but they do work through various accommodations that attempt to lessen the trauma.

Dyscalculia students usually excel in other classes, but they struggle to do ordinary, daily activities that require math. For example, they usually cannot manage to balance a checkbook or figure out how to determine a tip at a restaurant. Along with this comes a typical inability to follow simple driving directions or read a map. They become frustrated with following a score in a ball game or keeping up with a schedule.

Some students do much better when math problems are read aloud to them or when they are asked to visualize questions. They respond well to rhymes and music that try to help them acquire skill in math. Some organizations, like Mathcounts (Editors, 2008), is an initiative that meets as clubs throughout the country to compete either through inter or intra school practices in order to build confidence in math. This has proved on a number of occasions to be helpful to students who fear, or simply do not like, math. Maybe, contemporary writers such as Berlinghoff and Gouvea (2002) are right. The more you understand the history of a mathematical concept, the more you have a deeper appreciation for it, for math really is a cultural activity if you think about it deeply.

Why College Students Need Developmental Classes in Math

It seems as if most students who go to college quickly find that they are under-prepared or the experience, academically speaking. A new study from the National Center for Education Statistics reports that only one in three students working toward a bachelor’s degree can solve math problems involving intermediate math skills (Fong, 2008). There seems to be a policy disconnect between what public high schools are doing with math and what public universities expect from students when they arrive at their doors.

It appears that students who represent the top 15% of their high school class standings are the only ones who are ready for college courses that do not require remedial, non-credit courses. Many students react with surprise when they arrive at colleges and the first thing they have to do is take placement exams. Al states have standards for the subjects they teach, but most do not talk with state colleges to see what successful high school graduates should know when they get to college.

The obvious mandate of community colleges is to take in all students who make application to them, even the ones who are not prepared academically in one or more academic areas. The mistake that is made by these schools is that they allow concurrent enrollment between remedial and regular classes. This does not lead to a very successful outcome for those who are not ready for regular classes, as evidenced by their high school transcripts and their community college placement instruments (Hagan, 2004). The thought arises that a policy shift should be enacted in these schools. Students should be required to complete remedial classes before they are allowed to begin their regular classes that are required for graduation or certificate.

Conclusion

Starr (1997) reported from one of the most comprehensive math studies ever conducted, some 15 years ago, that showed United States fourth graders doing above average in math, while United states eighth graders were doing a little below average in math, while United States twelve graders were among the worst in the world in math. Why the sharp decline?

Some say that United State students are too bound to television screens. Others say that there is too little homework. Still more point to rampant poverty as the root cause. A few even mention things like poor teacher training and lack of student motivation. Since Starr’s report, we might speculate as to the relationship between teen texting, on-line chatting and math success.

Most any teacher will tell you that students must approach learning with enthusiasm. How to get them enthused is the matter of contention. Basics, along with challenges, problems that need to be solved and real world applications of subjects are used by most for varying levels of success.

Matching the learning style of a learner with the presentation of classroom material is key to tapping some magical, mystical, neurological place inside a student’s mind. This approach should allow for more openness from the student to accept mathematical lessons that they need in order to grow and develop their minds for their adult lives and careers. Children come with special intelligences. As hard as it is for teachers to do, they must find ways to know their students –how they think and how they react most favorably –to all of the multiple paths for learning. Does a math student do better with rote memory or hands-on projects, for instance?

By middle school, students should have grasped firmly mathematical foundations that are secure enough for them to expand their work in algebra and geometry. State and local standards need to be raised instead of lowered when it comes to math expectations. Student performance needs to be measured in ways that verify that standards have been met. Curriculums should encourage students to do more (especially in twelve grade) instead of less. Math teachers need specialized training, and they need to teach in the fields where they have received instruction themselves. The idea that high level math courses are only for those who aspire to careers in engineering and the like needs to be replaced with an attitude that calculus is good for all students who wish to grow intellectually.

It is not America’s methods for teaching math that need to be improved. It is the repetition of undemanding curriculums that need to be reappraised. One observer has said that United States school mathematics is “unfocused…a mile wide and an inch deep” (Starr, 1997, p. 1). Our students deserve to have the best math education in the world, and our country should insist that our children rise to the highest of expectations in this regard.

References

Barta, J., Sanchez, L., & Barta, J. (2009). Differences between Spanish (Mexican)/English (USA) teaching of math in the milpa. Teaching Children Mathematics, 16(2), 90-97.

Berlinghoff, W., & Gouvea, F. (2002). Maths Through the Ages- A Gentle History for Teachers and Others. Farmington, ME: Oxton House Publishers.

Crosnoe, R., & Riegle-Crumb, C., Field, S., Frank, K., & Muller, C. (2008). Peer group contexts of girls’ and boys’ academic experiences. Child Development, 79(1), 139-155.

Demski, J. (2009). Learning to speak math. T H E Journal, 36(8).

Editors. (2003). ‘Dyscalculia’ adds up to everyday problems. USA Today, 21 Jan Editors. (2008). Kids plus math clubs minus fear equals skill and confidence. USA Today, 02 Jan

Editors (2009). Textbook toss-up. Weekly Reader, 109(1).

Editors. (2010). To boost graduation rates, states water down standards. USA Today, 01 Feb

Illich, P., Hagan, P., & MeCallister, L. (2004). Performance in college-level  courses among students concurrently enrolled in remedial courses: Policy implications. Community College Journal of Research & Practice, 28(5), 435-453.

Fong, A.. (2008). Examining the links between mathematics and remedial courses in Nevada public colleges and universities. National Center for Education Statistics: Issues and Answers Report, REL2008058.

Milford, J. (2008). Should fractions be consigned to dustbin of math history? USA Today, 24 Jan

Seife, C. (2003). How a scribe learned math, ca. 1800 B.C. Science, 299(5607)

Shouse, R. (1995). Beyond legend: Stand and deliver as a study in school organizational culture. Mathematics Teaching, 153(8).

Starr, L. (1997). Math wars! Education World, 27 Apr.

Struik, D. (1995). Multiculturalism and the history of mathematics. Monthly Review, 46(10)

Witzel, B., Riccomini, P. (2007). Optimizing math curriculum to meet the learning needs of students. Preventing School Failure, 52(1), 13-18.