Mathematics education

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Overview on Degree Programs in Mathematics Education

Friday, June 9th, 2017

Are you one of those who are looking to make career as a mathematics teacher? If your answer is yes then there various options to become mathematics tutor. Either you can follow an education degree at the master’s or bachelor’s degree level and have your regular education training in math, or you may even earn a math degree at different levels and then have training with the necessary coursework. Nevertheless, if you are already a mathematics teacher and looking forward to advancing your career then selecting a degree program in mathematics can be the best option. These days many colleges and universities in the United States are offering mathematics education programs that may further help you improve your individual proficiency.

Generally, a degree program in mathematics education primarily focuses on math-specific education training along with the general education necessities that are necessary for every professional licensure. The degree programs can be broadly categorized into two sub-categories, mainly the bachelor’s and master’s degree. The bachelor’s degree in mathematics education focuses on a science prospectus along with math-focused tutor training. In addition to this, the bachelor’s degree program primarily includes learning of mathematics in different areas and provides mathematics major as a specialization. Apart from all this, the master’s degree program basically emphasizes on K-16 schools and methodology or the way students are educated in mathematics. The program can be very beneficial for you if you are a licensed teacher. Moreover, the coursework includes studies in math-centric topics and classroom administration.

If we carefully look at the employment prospects for mathematics education degree graduates, it actually seems to be very bright. Once you complete the program, you can make a career as an actuary. As an actuary, you may use your logical skills to calculate and manage risk for banking, financial services, and insurance industries. The other job profile you can look for are financial analyst and economic statisticians as well. Adding to this, in recent times a serious scarcity of math teachers exists has further created the growing demand for bright new mathematics tutors. Today as a graduate of the mathematics education degree program or being mathematics major, you can definitely pursue a great career in the education industry.

Only A Major Paradigm Shift In Societal Expectation Can Save Mathematics Education In This Country

Friday, June 2nd, 2017

A Paradigm shift is a major change from one way of thinking to another. A revolution. A metamorphosis driven by agents of change. Thomas Kuhn said “awareness is prerequisite to all acceptable changes of theory.” It would seem that the necessary awareness already exists when report after report shows the sorry state of mathematics education in this country. The recent release of Harvard’s latest report shows that the US ranks 31st of 56 countries, and only 6% of our high school students take higher level math courses. Another statistic which actually explains the other two is the fact that the failure rate of 1st year Algebra in the country is 50%, and this statistic has stayed consistent of at least four decades. How much more awareness is needed?

A major paradigm shift in something as complicated as our education system is certainly not to be taken lightly. We must first be certain that every possible attempt at positive change has been tried and shown to be a failure. Over the years, there have been at least six major philosophical changes. See my article “The Current State of Mathematics Education In This Country–Caution! You May Not Want To Know This” for a detailed explanation of those philosophical changes. That article also describes the various changes in both textbook series and educational techniques that have been tried over the past several decades. A quick look at No Child Left Behind results will show that there has been no benefit to mathematics education. An extended look at the long-term of effects of NCLB will show that, as with “New Math,” the state of mathematics education has actually made a step backward.

This simply can not be allowed to continue. We are no longer able to compete in a global market. The long-term effects of the Algebra failure rate on both society and the individual student are so harmful that it seems criminal for us to allow either to continue. And, yet, while we all agree that the consequences are bad, no one seems to be trying very hard to find solutions. The educational system for mathematics is quite literally being allowed to flounder. School districts are simply rotating though the same techniques that have failed in the past.

So where do we look for solutions to the problems of mathematics education? I believe that the wisest approach would be to look at what has been successful in the field of education and duplicate that.

It seems that nothing in the field of mathematics education has been successful, but, just the opposite is true for reading and writing education. Our very young children enter school eager for the challenge of learning to read and write, and they seem to possess an ingrained sense that they have the ability to learn. They never doubt their ability to learn. Teachers are able to hit the ground running with these students. These children with their enthusiasm, persistence, and confidence in their own abilities stay successful for many years.

With this in mind, the first obvious question is why do our children excel in reading and writing? Answer? Societal expectation. There has always been a “given assumption” or “generalized understanding” that parents–even the extended family unit–have a role to play in preparing pre-school aged children to enter elementary school ready to read and write. Every mother, father, sibling, aunt, uncle, cousin, grandmother, grandfather, and even neighbors take an active interest and role as babies learn to make sounds, say words, crawl, walk, and talk. Babies are incredibly persistent at each of these very difficult tasks because every person in their small universe is quite literally cheering them on. We encourage their every attempt and we reinforce their successes at the same time that we encourage them to “try again” when they fall down. The word “failure” is non-existent at this stage of their little lives.

As the child grows the family unit plays an equal role in language development. Everyone reads to the child and encourages new vocabulary words and correct grammar begins to be evident; and all the while the child is surrounded with reinforcement and encouragement. In some homes, children actually start to read before they enter school. In most homes the necessary preparatory skills for reading are in place for the day school starts. The same has been happening with writings skills. Children are prepared with the alphabet, letter sounds, and letter shapes. They are ready to go to school to learn to read and write. They are filled with excitement. We have filled our children with so much encouragement and reinforcement that they never doubt their own ability to learn to read and write. They know they can learn because we taught them so.

Are the same things happening for mathematics? NO! At most, parents work with their children on counting without realizing that counting is actually a language skill not a math skill. Learning to say “one, two, three, four, five” is the same skill as learning to say “a, b, c, d, e.” Should we be angry with parents for not doing with math what they so wonderfully accomplish with reading and writing. Again, NO! There is no societal expectation for parents to work with anything math related.

The next obvious question then becomes why not? Why does society think that not having parents lay the foundation for math success is desirable? The blame for this can be placed squarely on Jean Piaget (1896-1980). Piaget was a biologist who studied molluscs, but eventually moved into the study of childhood development. He divided a child’s cognitive development into stages based on age. His proclamations that preschool children were capable of learning language and that children were not capable of abstract thought until age 11 have driven the course of education since the early 1970’s. Parents work with preschool children on language because Piaget said they should. And nothing is done with abstract mathematics until almost the teen years because of Piaget. Over the years, we have come to learn that many of his original assumptions were incorrect and that much of his research was flawed. And yet we hang onto those “proclamations” as if they were handed down from God himself. Piaget was wrong! And because of this, the field of mathematics education has been suffering and our children have been failing.

Is it possible for us to change this current state of affairs? I tend to be an optimist and look at things from a positive viewpoint, so, yes, I believed this can be changed. But the change needs to start immediately and it quite literally needs to involve everyone in this society. It will require government support, a great deal of financial investment, and many years to complete.

There are two pieces of research data which do give us hope. The first research result we have known for over 50 years: babies are actually born with an innate number sense the same way they are born with an innate language sense. This doesn’t mean that babies are born knowing how to count any more than they know how to speak English. But they are able from birth to distinguish between one, two, and many. This is a survival issue. And their number sense is active during the preschool years.

The other significant piece of research has come from the brain studies being conducted now that we have technology allowing us to actually study how the brain learns. Eric Jensen has been one of the most recognized names in the area of interpreting brain research data and then applying that information into useful form for the classroom. David Sousa’s book “How the Brain Learns Mathematics” and John Medina’s books “brain rules” and “brain rules for BABY” should become required reading for parents. Why? Because we have learned that the critical or primary period for learning logic and establishing the foundation for arithmetic is–are you sitting down?–ages 1 to 4! Is it any wonder that our children are failing mathematics in large numbers when we in education are totally missing the foundation forming years?

So many wasted years and so many wasted minds. Remember the commercial that said “the mind is a terrible thing to waste?” Yet, for several decades now, we have done exactly that. In trying to find the solution for our Algebra mess, we have repeated philosophy mistakes, we have thrown out textbooks by the millions (billions?), and in the end, we always blame teachers. No Child Left Behind is closing schools and running our best teachers out of the profession. All for the wrong reasons. We have been looking in the wrong places and at the wrong things.

The solution to the problems with mathematics education is not in WHAT we do. It is WHEN we do it.

I hope that you are beginning to see the paradigm shift that needs to happen. We need a major shift in societal expectation to include both language and mathematics in those preschool years. We need families doing for math what they have always done for language. That foundation in math is every bit as important as it is for language. Our children need to be constantly reinforced and encouraged and praised for their persistence for math as much as for language. And maybe most important is that our children need a self concept that says “I am smart enough and I can learn this.” They must never doubt their own ability to learn.

The how to make this happen is the topic of another article, but we can all begin right now by spreading the word. Everyone in society needs to understand that they are an essential part of creating the foundation for a successful future in mathematics for our pre-school children. Again, the solution to the problems with mathematics education is not in WHAT we do. It is WHEN we do it. Spread the word. Time is critical.

The Current State of Mathematics Education In This Country – Caution! You May Not Want To Know This

Thursday, May 25th, 2017

You probably already know that the current state of mathematics education in this country is very bad. What you may not know is exactly how bad. Harvard recently released to the news media the results of a study about mathematics. Their findings: (1) the US currently ranks 31st out of 56 countries, and (2) only 6% of our high school students take higher level math courses. Another statistic you may not have heard (except from me) is that the failure rate for first year Algebra students is a deplorable 50%. That statistic has direct bearing on the Harvard results; and, as if these statistics aren’t bad enough, you need to understand that the 50% failure rate was true in 1972 when I started teaching and it is still true today. Doesn’t this just make you want to shout “Why isn’t anyone doing anything about this?”

In reality, mathematics educators, education specialists (seems like an oxymoron, doesn’t it?), and universities have been trying for over 40 years to make positive changes. During my lifetime I have experienced, to varying degrees, at least six different methodological changes. (1) I grew up using the “skill and drill” of the old days. This method produced temporarily strong basic skills but very weak application or understanding; and without the latter, the former fades quickly. (2) In 1972, I started teaching just after the pendulum swing to “New Math.” All math books started with a chapter on set theory, out went rote memory, and in came understanding. In theory, if students understood the why of mathematics, then they would create the skills on their own. Of course, none of that happened, and mathematical understanding actually decreased. It is now universally agreed upon that “New Math” was a miserable failure. Fortunately for me, I was raising a family during most of those years and didn’t have to teach it very long; but I often wish that we could apologize to the students of the 70’s and early 80’s. “New Math” caused you more harm than good. That shouldn’t have happened.

Since the final death of “New Math” in the early 80’s, there has been no overriding mathematical philosophy for the country. Instead, different states–even individual school districts–have been searching for that perfect solution. (3) Some school districts returned to “skill and drill” by adopting the Saxon method. Of course, the problems that existed with “skill and drill” the first time still existed. Returning to a method that was unsuccessful before is not logical. Math people should know better. (4) In 1983, the University of Chicago conducted a great deal of research into why Algebra students were failing in large numbers. Then they created an entirely different approach to teaching mathematics. In 1988, I was very fortunate to have been working in Colorado Springs when my district (Air Academy School District #20) adopted the UCSMP (University of Chicago School Mathematics Project) textbook series. UCSMP was truly revolutionary and inspired. To learn more about how it came to be and how it was different, read my article “Frustrated With Everyday Mathematics/UCSMP? Why Is It So Different?” For the first time ever I saw large numbers of students improve both their basic skills and their understanding of mathematics. UCSMP continues to this day in various parts of the country, although the extreme difference in approach coupled with the fact that our society is now highly mobile have caused major difficulties, especially for parents. For UCSMP to have a positive impact on the country, it would have to be adopted by all schools. And we all know that will never happen.

Two other approaches bouncing around the country are (5) Project-based and (6) Activity-based programs. Project-based programs give classes a “situation” and that situation is worked on for weeks or months. The Pit and the Pendulum is the project I have heard the most about. This approach works well with certain students, but you haven’t read anything about startling success because that hasn’t happened. Activity-based programs are similar to project-based programs except for length of time spent on the activity. The activities might last a day or a week, and then change to another activity. In both of these methods, the math skills are taught as they are encountered in the situation. Classroom management issues arise with both of these methods. And, again, you aren’t hearing shouts of joy over the positive benefits to mathematical understanding.

In addition to the philosophical changes, there have been many smaller changes in teaching techniques and classroom changes. Some still exist in some places, but most have been replaced with the newest and improved techniques. Cooperative learning was all the rage for a time and it is still a useful technique. I have lost count of how many of these teaching fads have come and gone over the past 40 years. You will notice, however, that the failure rate remains unchanged. So where are things now? Floundering. While school districts and states are bouncing around trying to find that magical solution, No Child Left Behind is slowly but surely destroying what little enthusiasm for learning still exists. No Child Left Behind may very well be the final death knell for mathematics education in this country.