Every educator in a teaching environment is bound to encounter a student or two who hates math. Reasons stem from its complexities with numbers and squiggles that give birth into formulas running across blackboards and often not fitting the allocated space. Some dread the need to commit these monstrosities to memory whereas others have no inkling on where or how to apply them to problems splashed across their work books.

To deliver effective mathematics education without causing his charges to run down the halls and scream in terror, a teacher needs to employ creative methods of teaching. Otherwise, learning processes imposed by archaic educational policies become a means to an end of completing the education cycle. Since the ability to learn evolves through the various age levels, the skill and know-how to deliver this task needs to be tailored to achieve maximum penetration. Younger students may benefit from visual representations to solve the mystery on the number of apples in Suzy’s safekeeping after a shopping trip to the store.

Adding to the ante is the infamous challenge to work out train arrival times based on given speeds and distances. By applying a range of techniques to solve the same problem, students learn the ability to look at it from various angles yet reaching similar goals. This then expands the mind to think out routes to solve life’s puzzles as part of their developmental growth.

Other than teaching the subject, professionals trained in mathematics education also gather statistics for the purpose of continual assessment. By observing how the teaching and comprehension of the subject matures through the generations, the importance of math in life becomes more apparent. Qualification in this expertise also allows the educator to branch into other career options. Research and spearheading educational policies are possible areas of advancement. Others may opt for a doctorate degree to instruct other educators at a tertiary level.

]]>The mathematics education in the whole world stands in bad need for reform. The education quality is getting worse. We expect our children to be less capable than us in mathematics due to the low quality mathematics education at the high school level. I do not blame the high school teachers and I do not think that it is their fault. This problem is due to policies and regulations which the teachers really have no hand in.

The policy making is overshadowed by the war between the advocates of traditional education and progressive education. For example the progressive educators in an attempt to improve the mathematics education they created a number of new curricula which were collectively known as New Math. This mathematics was created by university mathematicians. It was about sets, relations, and functions. The teachers were not yet prepared to teach this type of mathematics. This was because they were never given enough training on how to teach it. Besides, the teachers failed to see the importance of New Math. New Math went down quickly and failed within one decade. It left a disastrous legacy that made new proposals for major changes in school mathematics looked upon negatively and steered lots of criticism. This also made the battle between the two major parties of policy making intense.

If we look back at this experiment we see that the main reason behind this failure was because of policies and not because that the new created mathematics field was not useful or suitable. The idea was good but they failed on how to implement it. The implementation of New Math should have been gradual. It should have been accompanied by courses and workshops that teach the teachers the concepts of the subject, why it is important and how to teach it.

The good part about this experience is the coordination between university and high school. The university created New Math to be taught in school. We can learn from this experience that university can take an active role in high school education. After all students study mathematics in school in order to be able to go to university and be successful in engineering, science, or mathematics. If the school student is not well trained in the mathematics in school they will become poor university students and may drop out of university.

A good policy that the education managers could take to improve school mathematics education is to ask universities to support schools in mathematics education. I am not saying that the mathematics departments of all universities should get involved. First of all the mathematics departments’ teaching staff should vote whether they want to get involved in school education or not. Then the departments that vote for this project should ask several members of staff to be committed to it. The university usually approaches industry to solve some of their problems. They can approach schools the same way. They should thing of the school education as the industry of producing successful students which they need at university.

The first problem that will face the mathematics department is that the school teachers may feel threatened by the university staff and feel that they will be replaced. This is why the school teachers should be assured that the prime goal of the university staff is to improve them as teachers and help them do their job better.

The university can help schools in many different ways. For example they can run summer classes for teachers. These classes should go into the depth of the conceptual understanding of the high school mathematics subjects. In addition the classes should teach how the mathematics can be reflected into our real world. It should emphasize how to solve real life problems with mathematics.

Moreover, the classes should introduce the teachers to the many diverse and innovative software calculators. The teacher should learn how to use these calculators to create mathematics laboratory work. They should learn how to make mathematics projects that can be solved using software calculators.

]]>Mathematics is a very important element in the development of the value and standard of the life of the individual and society. Mathematics enters in everything from science, technology and engineering to arts and social sciences to economics and decision making.

It is very important that society constantly produces new generations of well trained mathematicians. This means that the school should increase the student’s interest and develop his skills in the subject. To achieve this goal the school should see the reasons why students fear mathematics and why many students do very poorly in the subject.

The fist reason for the difficulty of the subject for students is that mathematics is abstract. It is not tangible they can not hold it. To make them understand a pure concept at this early stage is very difficult. They need to relate it to real life problems that they face in their daily lives. This way they will be stimulated by its importance for them and will see that it is useful and fun. Moreover, the use laboratory experiments using calculators would make concepts more understandable. There are many new innovative software calculators built just for this purpose.

The conventional system of teaching mathematics contributes significantly to the poor performance of students. This is because many teachers teach students how to implement algorithms without teaching them the idea behind the algorithms and there is no stress on the understanding of the concepts. This causes the interest level in the subject to decline and soon students develop a disassociation with the subject. To solve this problem the schools can create a mathematics society and a forum where students can communicate with each other discussing material and asking each other questions. This kind of social behavior may increase the student’s interest in the subject.

Students pass early mathematics classes and they are not really fit in the subject. This is because the exams and grading did not reflect the student’s true ability. This causes the students to have very big problems in senior mathematics classes which are dependent on the early classes. For example if we look at the early pupil stage we can imagine a pupil who does not understand the concept of divide and multiply. That is to say when should he divide and when should he multiply. Now can this pupil at a later stage know to solve a word problem? The answer is surely no. He will not know what we are talking about. We can also imagine a student who does not understand the concept of the algebraic equations. This student could not be asked to plot a graph because simply he will not have an idea about what we are speaking about. The teachers can use calculators to teach pupils the concepts of multiply and divide. They can let them experiment on their own with many numbers using the calculators. From the observations the pupils will understand the concepts of multiply and divide. Moreover, teachers could use calculators to teach students the concepts of functions and graphing. It is easy and fun using calculators.

Finally, those who are teaching mathematics may have sufficient knowledge in the subject. They usually have a mathematics degree but this is not enough. To be a teacher you certainly got to be strong in the subject but this is only one major factor in being a successful teacher. The teacher should know about education and student psychology. he should also have a strong personality and be a good leader.

]]>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.

]]>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.

]]>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.

]]>Introduction

The United States has a serious problem in mathematics education. Test results show that beginning in middle school, the United States student proficiency declines in comparison with other developed countries throughout the world to near the bottom by 12th grade [PISA]. The Workforce/Education Subcommittee of the President’s Council of Advisors on Science and Technology identified two principal reasons for this: too many math teachers are not trained in math, and too many math textbooks are inadequate [Herbold].

This article suggests a third important contributing reason: low homework emphasis. The United States lags far behind in time spent by our students on homework [TIMMS]. Thus, improving homework completion at the secondary level may be a significant opportunity for US math proficiency improvement at that level. This article suggests that new Internet math homework-help resources may be very helpful in getting more students to complete and understand their homework. As an important by-product, more class time will be available for more in-depth teaching than is currently possible. We identify some of the available resources, discuss their application and the background research that supports their use, present comments from several contributing authors, and present a case study of the use of one of the Internet resources.

Homework Not Being Done

Without homework practice, middle school or high school students cannot fully master the concepts presented in class. Homework provides an opportunity for the students to extend their understanding and directs the students to concepts that need further explanation. Homework provides an opportunity for students to make, discover, and correct mistakes so they can learn from them.

Students of teachers who emphasize the importance of homework score higher than students of teachers who do not [House]. However, teachers are finding that getting students to actually do assigned homework is increasingly difficult. Some students, and often their parents, express that homework is a useless burden. Furthermore, homework competes with TV, video games and other activities. A teacher in Northern California had this to say [Bradley]:

I am a good teacher as evidenced by my experience, by peer, student, and parent feedback, and by advanced certifications that I have earned. Yet, many of my students fail. Most of those who failed will say it was because they did not do the work.

Worked Examples

The use of worked-out examples is a standard practice in classroom lectures and textbooks. Some students understand the daily lesson after observing just a few worked-out examples. Others need more examples than can be presented during a class period or provided in a textbook section. These latter students would benefit significantly from additional worked examples, but they might not know where to find them or have the motivation to seek them out. The research described below shows that providing worked examples for actual assigned homework problems is beneficial. The websites described below allow students to view worked out solutions for their assigned homework.

Internet Resources for Math Homework Help Via Worked Examples

A website that provided math homework-help by showing tutorial (worked out) solutions for actual math textbook homework problems was first introduced in 2001 [Beall]. Other websites with the same general capabilities have since become available. Students needing assistance on assigned homework problems now can find immediate homework help using an Internet-connected computer, at websites such as http://www.aolatschool.com, http://www.encarta.com, education.yahoo.com, http://www.calc101.com, and http://www.hotmath.com. Each of these websites provides immediate tutorial explanations for math problems. Thus, teachers may assign homework problems for which there are explanations (worked solutions) available on the Internet. In the case of Encarta and Hotmath, the explanations are correlated to the actual problems assigned from popular math textbooks.

Even students who may have fallen behind in math may be attracted to such websites, as they provide a new avenue for catching up. The help, via computer, with their assigned homework relieves them of the fear of peer or supervisory embarrassment. Math Teacher Jane Monson noted that more of her students are completing homework since they began using Hotmath.com because it answers the question, “What is the next step?” so that students can continue on their own. According to Math Teacher Lisa Winer, “I love that this website gives worked solutions to assigned homework, because students who want it can get instant help right away, on their own. If a student says they didn’t understand the homework, my response is that they should have logged on to get help.”

Scientific research has investigated the use of “worked out” examples in algebra, and the results show that this increases effective learning [Carroll, 1992]. A study was done in Texas: two groups of students, one of poor performers and the other of good performers, were taught together with only one difference; the poor performers were given their homework assignments with 50% of the problems accompanied by worked solutions. The good performers were given the same homework assignments without worked solutions. Interestingly, the poor performers achieved higher scores on the final exam than the original good performers. In related research, students in the worked examples group completed their work more quickly while perceiving the work as less demanding and displayed better performance on tests [Carroll, 1994]. The researchers suggest that the reduced cognitive load allows the students to process the underlying similarity of problems and integrate the methodology with existing knowledge [Grillmeyer, 2001]. They also note that less “wrong learning” results.

The availability of worked solutions also benefits advanced students. They can tackle the more challenging problems with more success and move forward with less outside help. Advanced, motivated students can work ahead in their textbook knowing that an instant tutor is available.

Homework review in class is an important part of math teaching. Teachers need their students to ask questions about processes, rules, and properties as a part of assessing both the students and their own teaching.

Yet, routine questions of interest to only a few students can be a very inefficient use of class time. According to Math Teacher Marty Atkins, “As our students have begun to use Hotmath.com ? I am beginning to get more ‘Why did they take that step?’ questions rather than ‘How do I start?’ questions.” A survey of math teachers using one of the homework-help sites concluded that about 20 minutes per class time was freed up [Grillmeyer, 2004]. According to Math Teacher Paula Evans, “We saved class time, which we immediately reallocated to activities which allowed students to develop insight about the material? We have used this time to develop in-class activities which ask students to extend their homework.”

When teachers assign homework problems with solutions available on any of the listed Internet homework help websites, their students can receive step-by-step explained solutions to their actual homework problems. Students are able to see their mistakes and learn from them, and parents are in a better position to see the methods being taught so they can amplify them as needed. Use of these sites is not simply checking or getting answers, but may be considered a directed, self-paced, tutorial experience.

Teachers justifiably want to balance the amount of available homework help so that students are certain to be challenged. Some students might mindlessly copy down solutions if they are available for every problem. The research concludes that 50% of assigned problems should have the available help. Two of the websites that provide solutions to actual textbook homework problems (Encarta and Hotmath) only explain the odd-numbered problems for which numerical answers are already available in the back of the textbook.

]]>Tests are supposed to measure the students’ abilities and potential. The student who performs well on a test is supposed to be good or talented in the subject and the student who does not do well in the test is supposed to be poor in the subject and needs extra training.

What is really happening today is that tests do not reflect the students’ abilities. This has disastrous consequences. When unqualified students go to do a mathematics degree and eventually become mathematics teachers or researchers they lead to the decline of future generations in mathematics.

What is happening in schools today is that administrators are applying pressure on teachers and the teachers pass this pressure on to the students. The teachers teach the students only to prepare them for the test. The point is not to make the students understand the concepts. After all this pressure exerted on the teacher he only cares that the students score high on the test. One of the main issues that face the teachers when they do that is that parts of the syllabus are skipped on the test and thus left out untaught by the teacher. However, though these parts that are skipped do not come in the exam they are important for understanding the other parts of the syllabus. This is enough to cripple the students’ understanding of the material. The teachers teach the students some tricks and mechanical drills that allow them to automatically solve exams without understanding.

Tests will be driving standards and curricula in the near future. This is why special attention should be given in how to design tests. In other words, there should be precise definitions of the concrete objectives of the subject and how to quantify the measure of success.

This problem has two sides. One side is the tests and this side is the dominant side due to pressures on schools to have good scores. The second side is the teachers. To drive the teachers to really get the students to understand rather than do mechanical work the exams should be designed to filter the students’ capabilities.

The test should be composed of several sections that cover all the different parts of the syllabus. Each section should contain questions that reflect the students’ abilities in using the different techniques taught. The student should know which technique suitable for which problem. The section should contain problems that examine the students’ abilities in using mathematics in solving real life problems. After all how good is mathematics if one does not know how to apply it to real life.

Part of the exam should be a project on an application of mathematics in real life. The student should use his earned mathematics skills to solve some real life problem in a project. The project should have two supervisors, one supervisor from the student’s school and one supervisor from another school. The students should be exposed to the many innovative software calculators that they can use to complete their projects.

When exams reflect the true abilities of students mathematics teachers would not concentrate on how to beat the system and would concentrate on developing the students’ abilities in the subject.

The school administration should help in this by giving teachers strong support by letting them attend training classes in mathematics and teaching psychology.

]]>Over the years, it has been acceptable to say or tell someone that you can’t do math. The society welcomes it and in many homes today, the saying still goes on. Imagine for example here in the United Kingdom, English is what we speak and you would surely expect everyone you meet in the street or in the office to know the language. It will come as a surprise to you if you happen to ask for direction in the middle of Oxford street London and only to be told ‘sorry, I can’t speak English.’

The role of every parent in children mathematics education is huge. In my professional duty, I do communicate with parents on a regular basis. Personally it does not surprise me when people say that they can’t do math but what worries me is the legacy the impact of the phrase ‘can’t do math’ will have on their children and there after.

Mathematics is a broad subject. Its beauty overlaps in many other subjects and most practically in our daily business activities. This message really needs to be drilled down to the minds of your children. Now, you can promote mathematics in your home by applying the following strategies.

(1) Using your shopping receipts.

After shopping, throwing away the receipt is not helpful by any means particularly with young children at home. Pass the shopping receipts to them and ask them to re-calculate the totals including the deductions. Take away calculator from them and ask to see the working out. This is a good way to set homework for your own children. By doing the long list of calculation, your children will be mapping their minds to helping their parents against over-payment without realising they are practising accounting and computation.

(2) Using the telephone bill.

Please be cautious here. Ideally your children would not interfere with your telephone numbers but, if that is not the case, then block the numbers by crossing them off or doing photocopies. Again, the mathematics to be tapped is huge. Accuracy is number one. Place values and working with decimals are difficult topics with young students, but you see, your children can consolidate on these by working on your telephone bill. Again take away all calculators. The role of every parent in children mathematics education has to be something to be proud of.

(3) Using Gas bills and Electricity bills.

Do the same here. This requires a little bit of high level maths but let them do it. If they can do it once, they will not ask for your help next time round. There is lots of mathematics to be learned from these bills. Skills in conversion is needed, percentages, ratio, meter reading and value added tax calculations are all part of everyday mathematics. By engaging your children to the family mathematics, you are technically equipping them with life essential skills.

The added bonus is that your children will be aware of ways to reduce cost by using less water, switching off lights when not in use, saving food rather than throwing them all away in the bin and guess what, you will be helping them to become more energy efficient thereby saving the environment.

]]>Many students start to feel the crunch in the later years of high or secondary school. Many find the subject so intimidating that they feel unable or unwilling to progress any further. At least some of this difficulty can be attributed to the prevalent methods of instruction and attitudes that’s practiced in most schools today.

More so than for any other academic subject, more emphasis should be placed on ‘training’ rather on ‘teaching’. In this regard, maths is more like music or sport – a skill that’s developed through action than study, although reading, watching and listening has its place. The long term objective of training is to develop an ability to analyze and learn independently. With the right tools and attitudes, students will learn to overcome obstacles and difficulties in the learning process.

Although students may have memorized numerous formulas and results, many do not quite understand what their implications are. Rote repetition is good practice, but it isn’t a substitute for critical thinking. In traditional classrooms across the world, teachers simply repeat the main results in textbooks, assign exercises, then expect students to figure out the rest.

Of course, self-discovery is an important aspect of learning, but perhaps more attention should be given to skills development and problem-solving techniques, so that students will be better-able to solve problems independently. These may include standard algebraic tricks, experimentation, using visual and graphical methods. More time should be spent on how to interpret expressions and equations and how to read and write mathematics in a clear, concise manner.

Once students have developed thinking skills and problem-solving techniques, they will also be able to pick up new topics and concepts with relative ease. These are the keys to developing confidence and enthusiasm. Many students at schools today have not been specifically trained and assessed in this regard. As a result, their self-confidence is low and mathematics becomes frustrating.

It’s productivity that really counts, not just the absolute number of hours spent on study. Here I define productivity as the student’s ability to absorb new topics and ideas, It’s hard to see how large classrooms could possibly offer high productivity to students, especially when it comes to maths.

Each student has their strengths and weaknesses, so imposing a ‘one-size-fits-all’ approach is ineffective. Regardless of whether students have mastered a skill or not, the classroom lesson continues on, leaving some students in the dark. At the same time, students with more gifted abilities would not have the opportunity to reach their full potential.

Individualized and tailored tuition is a direct and targeted approach that helps to bridge any gaps in the student’s understanding of the subject. By identifying specific areas of weaknesses, relevant drills and exercises can be prescribed to address any deficiencies and problems.

Preparation for existing standardized international examinations (GCSE, A-Levels, IB, SAT) can be accomplished in one year, instead of the two years practiced in many schools today. With personalized attention, productivity increases significantly so ideas can be communicated and absorbed more efficiently.

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