Mathematics Curriculum for a New Educational Paradigm

Mathematics Curriculum for a New Educational Paradigm

By Shahid Muhammad

Purpose

Mathematics is the mother of all sciences and is the root study of every discipline and profession. Mathematics is a universal language that is a vital study for any educational institution and curriculum. However, current statistics shows America’s educational system is in a state of emergency in the area of mathematical literacy and competency. There exist a vast array of data and statistics that bears witness to the massive mathematical illiteracy and poor performance of students in American public schools nationwide.

Out of all the negative statistics, studies and data, conducted on American students in both elementary and secondary education, those that have consistently performed below the standards have been the Black and Hispanic populations. The mathematical performance of inner city youth, particularly Black and Hispanic students are atrocious to say the least. There is no need to quote a bunch of statistics and studies, the terrible performance of Black and Hispanic youth in the areas of mathematics and science is a well-known fact in the educational arena. How do we go about making a revolutionary change in this respect? What programmatic steps must be taken to reverse this downward trend and devastating situation?

Many have studied and written articles, dissertations, and books centered on identifying the problem and proposing solutions and remedies. There are a few places I believe we must look at if we are serious about making change for the better.

To begin with, there must be a new outlook on how mathematics is taught, presented, valued, and exposed to the students. The old methodology is clearly producing illiterates and below average students in the area of mathematical performance. The teaching of mathematics, or any subject for that matter, must be upgraded and made innovated. The world we live in is constantly and rapidly evolving every millisecond to produce new advances, new technologies, new schools of thought and new ideas. Why do we expect to continue, in education, to pour new wine in an old wine bottle? The educational methodologies and strategies must evolve and transmogrify in tune and in step with the times or we will continue to produce students who are far behind the rest of the world in the area of math, science and technology.

Another area that must be upgraded, repaired, and renewed is the math curriculum that is used in both elementary and secondary. There are an enormous amount of problems with the current curriculums utilized in most public schools across the country. How do we know there are holes in the curriculums? We need only to look at the growing number of failing students in mathematics and the growing number of illiterate

high-school graduates, who are forced to take remedial and developmental math courses, that they should have mastered in high school.

There are a lot of problems with the current mathematics education of the American educational system. In the next sections of this curriculum plan, new and innovative strategies, methodologies and techniques of teaching mathematics will be presented.

Content

In this new paradigm of mathematics education I am not necessarily proposing a change in mathematical content. What I am proposing is a change in the structure of mathematical topics and in the time allotted for mastery of these topics. In a traditional school setting, elementary students spend from first grade to seventh grade mastering arithmetic. This is a travesty and a misrepresentation of the true potential of our students. It does not require nearly 6 years of a student’s educational experience to master arithmetic if that arithmetic is presented with the proper methodology to ensure mastery and competency.

An elementary student should master arithmetic by the fourth grade and began their early exposure to Algebra by the fifth grade. Curriculums should inculcate an Algebraic Thinking aspect to elementary math subjects, so that students gain early exposure to Algebra and nourish their cognition to accept the abstract nature of Algebra. Students should be exposed to Geometry earlier and to the concept of a mathematical proof. It does not make sense to wait until tenth grade for students to understand the concept of proving mathematical principles, theorems and postulates. Through early intervention, students will already have a foundational structure on which to build algebraic and geometric thinking and reasoning skills. Here is a look at how an elementary math timetable could look:

I. K thru Fourth Grades--

*** Arithmetic & Problem Solving

*** Basic Geometry & Algebraic Concepts

*** Proofs & Validation of Mathematics

II. Fifth Grade---

*** Algebra, Problem Solving & Proofs

III. Sixth Grade—

*** Geometry

IV. Seventh Grade—

*** Algebra II & Trigonometry

V. Eighth Grade—

*** PreCalculus

VI. Ninth Grade—

*** Calculus I or Statistics I

VII. Tenth Grade—

*** Calculus II or Other Advanced Math Topic

VIII. Eleventh Grade—

*** Calculus III or Advanced Math

IX. Twelfth Grade—

*** Advanced Mathematics

Calculators

There are continual debates on the use of calculators in the mathematics classroom. Some claim it makes the students totally dependent on the calculator and they never master the functions and operations on their own. Some teachers will not allow calculators in the math class. I believe this is a serious lack of understanding of the use of technology in the classroom. How many of us would go back to typing our papers on typewriters as opposed to Microsoft word or any other computer assisted word processing software. The calculator has its use and purpose in the math class. .Not only does it assist students in problem solving applications, but it can be used to enhance the teaching of mathematics. When teaching problem solving, calculators allow students to focus on the construction of the problem and on choosing the correct problem solving strategy, as opposed to getting bogged down with simple arithmetic operations that are too tedious and time consuming. Once the foundation of arithmetic has been properly taught and laid, students can utilize the calculator to help perform those tedious and time consuming functions and arithmetic operations. An accountant encounters many problems that they utilize calculators and computer software to lessen the time and difficulty of their tasks. This does not take anything away from the professional knowledge and skill an accountant must have to know what buttons to push and what to do with the solutions the calculator or computer outputs.

Teachers of mathematics should also utilize the calculator as a teaching tool. Calculators can help students in discovery of patterns, theorems involving number theory, sequences and series, problem solving applications, analyzing and verifying math rules and identifying and interpreting common errors. In addition, because of the more complex and sophisticated nature of today’s calculators, students need courses on just how to properly utilize and operate the calculator. This is a course within itself. Too many times, students have the tools of calculators and computers, but are void of the knowledge and skills needed to properly operate and work them.

Computers

Any mathematics curriculum that does not inculcate and integrate the application of computer technology into the classroom is outdated and unproductive. There exist a wealth of information and educational opportunities available to students via the internet and computer applications. Students are very familiar with the internet, but mainly for entertainment purposes. However, every subject taught in elementary and secondary can be enhanced and edified by the proper integration and utilization of computers and the internet in the classroom.

There exist a vast array of internet websites dedicated to mathematical research, mathematical discussions, mathematical studies and projects, as well as mathematical fun and excitement. Each teacher should make themselves familiar with as many websites on mathematics as possible. Students can access these websites for outside learning, exploration and enrichment. Many sites contain activities, projects, exploratory problems, puzzles, games and brain teasers. All of these help to enhance the student’s exposure, appreciation and motivation toward mathematics. The computer also can be used as a means for students to present classroom projects, to learn mathematics via educational software and multimedia presentations, and as a resource bank for the edification of their mathematical knowledge. Teachers can utilize the computer as a means of teaching mathematical concepts like matrices, spreadsheets, statistics and conversion and scale relationships.

The computer also serves as a wonderful means of communicating with parents. Teachers can set up websites for the class and keep parents informed on up-coming events, student progress, classroom rules and procedures and school functions. Teachers can utilize their email to stay in touch with parents and students.

Multi-Faceted Approach

One area that bears witness to the declining affairs of the public schools in the area of mathematics education is in the student’s performance on standardized tests. Due to the over-emphasis placed on test scores, school districts are running around attempting to do all they can to raise test scores. Funding and other political madness has caused test scores to be the focal point of all educational pursuits and the purpose and rationale for education has been placed on the back burner. Standardized test are necessary but should not be the end all in evaluating schools and student’s mastery of subjects.

In the area of mathematics, one common problem that explains the rationale for declining test scores amongst Black and Hispanic students in particular, is the inconsistency of what students see in class throughout the year versus what is seen on the standardized tests. Too many times teachers are teaching math in a one-dimensional framework that is based on solving rote memory or simple comprehension facts versus raising the student’s cognition to encompass the multi-faceted nature of mathematical knowledge. Mathematics is not one-dimensional in its nature. There are various components and branches that make up the enormous definition of mathematics.

True mathematical literacy and competency involves learning mathematics through a multi-dimensional approach. Students of mathematics must be able to evolve through a wide range of steps and levels to eventual mastery. In mathematics, you have problem solving, knowledge, comprehension, applications, validation, spatial visualization, pattern discovery, number theory, critical thinking and reasoning, compare and contrast, relationships and logical thinking. These are just a few of the many branches that compose the science of mathematics. But the problem lies in the curriculum and textbook arrangements of most inner city public schools that rely heavily on the simple levels of mathematical understanding that force students in a box and stagnates their ability to see math in various situations and complexities.

Teachers will teach concepts and skills to the best of their ability, but still hear complaints from students that they never learned this or that. It is not that they never learned the concepts or skills, but rather, the manner and mode in which they learned it was not flexible enough to accommodate a change in problem presentation. Teachers must incorporate mathematical learning that involves various levels of mathematical thinking and problem solving. Most educators are familiar with Bloom’s Taxonomy from our many teacher preparation classes in college. In using Bloom in our classrooms, we learn that teachers must teach the mathematics in such a manner that the learning, questioning and presentation of the math must cover all levels of learning in-order for it to be considered thoroughly taught.

If we recall, Bloom laid out seven levels of understanding and questioning. These levels are structured and formatted into the math problems we see on standardized tests. If a teacher only takes students through the first two or three levels, then the students are ill-prepared to handle questioning and problem construction on higher levels, hence the low test scores we witness each year. Here is a review of the levels, spelled out by Bloom in his learning levels:

1.  Memorization

2.  Translation

3.  Interpretation

4.  Application

5.  Analysis

6.  Synthesis

7.  Evaluation

In a sufficient and efficient mathematics curriculum, each level of Bloom’s Taxonomy, as it relates to mathematics, must be covered. It must be covered in all areas of mathematics education. Teachers must implement it in their questioning, problem construction and formulation, class and homework assignments, evaluation and assessment tools and resources, and in re-teaching and enrichment activities. This implementation and integration of Bloom will ensure the proper preparation and prerequisites are there to enable students to perform above average on standardized tests.

Integration of Culture and History

Most public schools are having problems with students being properly motivated and inspired to learn mathematics or any subject. The Black and Hispanic youth culture does not place high value on educational pursuits. Black students in particular have a very dismal level of motivation and inspiration toward education, particularly Black boys. In the areas of mathematics, most Black and Hispanic students do not possess that vibrant inspiration and desire to learn the subject. Most see it as irrelevant to their reality and goals.

One way this can be combated is with the proper inclusion and integration of the contributions of Blacks and Hispanics to the field of mathematics. The Most Honorable Elijah Muhammad represents this as a need for our students to gain a thorough knowledge of self. Most textbooks used in the inner city public school systems, lack any references to the contributions of Blacks and Hispanics to the sciences, especially mathematics. You can hardly find a Black or a Hispanic mathematician mentioned in a math textbook. What type of signal does this send to Black and Hispanic students that you are attempting to motivate to master math? If they do not see themselves accomplishing and having success in mathematics, there is no drive or positive self-esteem and self-efficacy to learn it.

This is why it is mandatory that all math curriculums include and promote the accomplishments of Blacks and Hispanics in the areas of math and science, to serve as positive encouragement and drive to push these students to meet their potential. Imagine if students knew that Blacks were the originators of mathematics. Imagine if Hispanics knew that the Mayans possessed one of the most highly sophisticated civilizations in math and science. This would fuel their desire to learn and provide them with the necessary role models to build their self-confidence in mastering math and science.