For those of us who are old enough to remember classrooms with walls, the methods we used to learn math were teacher-centered and method-based. Those who came of age before cooperative learning became prevalent in schools probably remember learning one method of solving problems and some of us may have felt the sting when we could not understand or even use that method at all.
My own encounter with The Mathematical Wall came in the second grade, when my class was learning to borrow in subtraction. I could not get the hang of it, much less make sense of the concept of borrowing anything from a number. I had only borrowed things from my older brother and it simply made no sense to me to cross off numbers in what seemed like a game of arithmetic Three-Card Monte. Panic set in and I thought I would never get past the second grade into the third. Although I was short, I envisioned a life of sitting cramped at a too-small desk until such time as those odd chicken-scratches made some sense.
Fortunately, before permanent depression set in and just in time to save me from imagining a lifetime consigned to the most elementary of work , my mother showed me an alternative method using dots instead of cross-offs and additions instead of depriving those poor numbers of their values. We both cautiously approached The Teacher and asked her if we could use this method, which made infinitely more sense to me than her game of arithmetic monopoly, She said with no hesitation yes. To this day I use that method, which has proven to be neater, faster and more accurate for me than the one I had been expected to learn.
We encounter children in our tutoring service who have experienced both an abundance of traditional uniform instructional techniques and the more free-wheeling individual-based experiential constructivism. Those who learn algorithms for multiplication and division by visual means only and without a feel for the movement of the quantities throughout the multiplication or division process are likely to be the ones who forget how to proceed over summer vacations.
Without an experientially based understanding of the process and without having the process concretized and made "solid," they are learning with only a visual memory if at all. Visual memory alone just does not do it for most of us. And yet, when children or adults are left without substantive guidance to "discover" truths and methods on their own, confusion, uncertainty and inaccuracy prevail. When it becomes more time-consuming to discover, prove and assess truths than it does to reason the logic of truths, we are engaged in a counterproductive exercise.
The general principle of constructivism, a stream of learning theory used in many classroom environments, is that we all learn differently and we all construct our knowledge bases differently. While it may have been fine for many in my class to learn to "borrow" in subtraction as a mechanical process, I needed to understand why that process worked I order to be comfortable with it. The idea that all learning is experiential is key to constructivism and it manifests itself in the math classroom in the inquiry-directed activity.
Does your childs teacher use a base of constructivism for classroom learning activities? Ask your child if s/he works in groups more than in teacher-based classroom instruction. Ask your child if s/he is asked to write procedures and definitions in math topics. Ask your child if s/he knows how to perform basic operations with whole numbers, fractions and decimals. If your childs answers indicate that groups prevail and procedures and definitions take a back seat to project-based cooperative inquiry, your child may be experiencing the constructivist method.
Under the best of circumstances, our teachers are versed in more than one method and they are blessed with the judgment to discriminate as to when to use which method. However, we are creatures of habit and large bureaucracies may dictate the method used. You owe it to yourself and to your child to determine which method is the foundation the teacher uses for instruction.
One might suppose that the world lost a highly competent jill-of-all-trades by the flexibility shown by my teacher, and yet I still do flip burgers and mop floors occasionally. The only difference between what might have been and what my reality is, is that now I can flip burgers and mop floors with a mathematical understanding of the notion of how gravity affects those burgers in their earthward descent and how my dirty floors re affected by the application of water. I never could have done it without my second-grade teachers wisdom.
Sabtu, 02 Mei 2009
Math Word Problems
Math word problems are frequently used to gauge students ability to decipher pertinent information and also to assess students' ability to use their analytical and mathematics skills to solve problems. Math word problems are often used to relate mathematics to real life situations. For instance, Physics applications, finance applications, Economics applications, surveying and other fields heavily rely on Mathematics. Consequently, word problems appear in a lot of standardized exams as well as in everyday assignments that students face. Standardized exams like the SAT test love word problems since they can be used to integrate many fields of mathematics; and they are a higher order thinking assessment tools. Teachers and math tutors need to know how help students solve seemingly complicated word problems using innovative approaches, as well as emphasis on tried and tested methods. Math word problems are frequently used in mathematics exams not only for reasons previously mentioned, but also because they are used to integrate many areas of mathematics in the same problem. An example would be a math word problem that tests a students knowledge of both Geometry and Algebra. There are many strategies that help students achieve the capability to solve word problems. While the enlisted strategies are different from topic to topic, teachers and math tutors should inform students of the importance of consistently writing down known and unknown quantities upon reading a word problem, underlining key words, and drawing charts. After doing so, students will should also review the specific topics in mathematics with which the word problem is involved. After efficient, effective and in depth assistance in the specific topic of a word problem, students will be able to complete a problem and reach a satisfying solution. To successfully teach math, its important to appeal to the learning styles of students in a way that will maximize the effectiveness of students in being able to draw out pertinent information in word problems and using their Mathematics skills to complete a solution for a word problem. Expert teachers and math tutors are also good at relating word problems to real life and often offer students many options of visualization and/or relations of a particular problem. Snowtime fun math problem (and answer!) Question: Alex and Alicia have piled up the snow in their front yard so that their children can learn some math and have some fun. They have made a conical pile of snow six feet high and eight feet across. They will let their children, Sandy and Sam, slide down the hill if the children can determine (a) the volume of the snow piled up to make the hill and (b) the angle down which they will slide from the top. Can you help Sandy and Sam to find the volume and the angle? Answer: The volume of a cone is calculated using the formula V= 1/3pi r^2(h), or 1/3 the number pi (approximately 3.14) times the radius squared times the height. Alex and Alicias snow cone is eight feet across, which means that the radius is four feet. The height is six feet. Therefore, that volume is 1/3 (3.14) (4^2) (6), 100.48, or a little over 100 cubic feet. Thats a lot of snow for parents to shovel! The angle down which they slide may be calculated by the dimensions of the triangle formed by the mound. If the height is 6 and the base of the triangle is 4, as shown above, using the Pythagorean theorem shows us that the outside(or the hypotenuse of the triangle) is the square root of the sum of the squares of 4 and 6, or the square root of 52. Using the arc sin function of 6/square root of 52, the angle is approximately 56 degrees
Math and the Arts
It's subtle, far-reaching, and coercive, and we start learning it as early as the first grade. It may not be well-supported by research, yet it defines many peoples' self-image, their college majors, and their job choices. What is it?
It's the idea that there are "math people" and "humanities people": students who "naturally" excel in math and students who "naturally" excel at the humanities, subjects such as English, visual art, history, drama, and social studies. Sometimes this idea is linked to the notion of "right-brained" and "left-brained" people-logical vs. intuitive-though brain scientists dispute this pop-psychological idea, pointing out that traits are not localized in the brain in quite this way, and that people cannot be sorted so easily. In any case, labeling students as "math and science types" or "English and history types" may teach them to ignore, and thus limit, their own abilities in other subjects. It teaches people who may be having a temporary bad experience with math to feel like they've run up against, not a momentary difficulty, but an essential truth of their own personality.
Why, then, do so many students experience math as a chore? Cambridge mathematician Timothy Gowers suggests that it's not math as such, but the standardized instruction of math class, that turns some students off. He writes in Mathematics: A Very Short Introduction: "Probably it is not so much mathematics itself that people find unappealing as the experience of mathematics lessons, because mathematics continually builds on itself, it is important to keep up when learning it." In a classroom of thirty pupils and one teacher, the instruction has to move at a certain plodding pace, which leaves some students bored and others, who are slower to grasp a concept, frustrated. "Those who are not ready to make the necessary conceptual leap when they meet one of these [new] ideas will feel insecure about all the mathematics that builds on it," Gowers writes. "Gradually they will get used to only half understanding what their mathematics teachers say, and after a few more missed leaps they will find that even half is an overestimate. Meanwhile, they will see others in their class who are keeping up with no difficulty at all. It is no wonder that mathematics lessons become, for many people, something of an ordeal."
But Gowers sees hope for such frustrated students in math tutoring: "I am convinced that any child who is given one-to-one tuition in mathematics from an early age by a good and enthusiastic teacher will grow up liking it."
For some of today's greatest scientists and mathematicians, and for some of our greatest artists, math and the arts are more like than unalike. Theoretical physicist Nick Halmagyi, writing in Seed Magazine, compares high-level physics, with its endless chalkboarding of equations, to playing jazz, a comparison that will ring true to anyone who remembers that in the middle ages, the study of music was sometimes considered a branch of mathematics. He writes: "[W]hat I've come to realize is that the best part of what I do is collaborating with remarkably creative people. Understanding the tiny tweaks and unexpected transitions in the universe's evolution requires prodigious amounts of rigor, originality, and personality. It reminds me of the ingredients for a good jazz ensemble. We improvise and strike out in different directions, following whichever note sounds most promising. Over time different voices float to the top. We hear both bravura solo performances and wrong notes. But ultimately, there comes a singular moment when the right chord of an elegant solution reveals itself, and we reach the essential resonance of our collaboration."
From the other side of the net, so to speak, some of today's most important literary artists also find essential inspiration and food for thought in mathematics. An obvious example is writer David Foster Wallace, whose massive 1995 cult classic Infinite Jest is frequently hailed as the defining novel of its generation. Wallace's fondness for-and expertise in-advanced math is well known, and reached its culmination (so far) in a 2004 book of nonfiction, Everything And More, an equation-filled, densely logical history of the idea of infinity. Artists of every stripe have grown obsessed with such mathematical condundra as the Fibonacci sequence, chaos and complexity theory, and the ideas of Kurt Godel. John Updike meditates on computer science in his 1986 novel Roger's Version, which fellow novelist Martin Amis called "a near-masterpiece"; Amis, in turn, contemplates information theory (among other things) in his 1995 comic novel The Information.
Both fields require creativity-and that's something human beings have in abundance. Great teaching-and attentive tutoring-can help ensure that that creativity isn't limited by that self-punishing idea, "I'm just not a math person"
It's the idea that there are "math people" and "humanities people": students who "naturally" excel in math and students who "naturally" excel at the humanities, subjects such as English, visual art, history, drama, and social studies. Sometimes this idea is linked to the notion of "right-brained" and "left-brained" people-logical vs. intuitive-though brain scientists dispute this pop-psychological idea, pointing out that traits are not localized in the brain in quite this way, and that people cannot be sorted so easily. In any case, labeling students as "math and science types" or "English and history types" may teach them to ignore, and thus limit, their own abilities in other subjects. It teaches people who may be having a temporary bad experience with math to feel like they've run up against, not a momentary difficulty, but an essential truth of their own personality.
Why, then, do so many students experience math as a chore? Cambridge mathematician Timothy Gowers suggests that it's not math as such, but the standardized instruction of math class, that turns some students off. He writes in Mathematics: A Very Short Introduction: "Probably it is not so much mathematics itself that people find unappealing as the experience of mathematics lessons, because mathematics continually builds on itself, it is important to keep up when learning it." In a classroom of thirty pupils and one teacher, the instruction has to move at a certain plodding pace, which leaves some students bored and others, who are slower to grasp a concept, frustrated. "Those who are not ready to make the necessary conceptual leap when they meet one of these [new] ideas will feel insecure about all the mathematics that builds on it," Gowers writes. "Gradually they will get used to only half understanding what their mathematics teachers say, and after a few more missed leaps they will find that even half is an overestimate. Meanwhile, they will see others in their class who are keeping up with no difficulty at all. It is no wonder that mathematics lessons become, for many people, something of an ordeal."
But Gowers sees hope for such frustrated students in math tutoring: "I am convinced that any child who is given one-to-one tuition in mathematics from an early age by a good and enthusiastic teacher will grow up liking it."
For some of today's greatest scientists and mathematicians, and for some of our greatest artists, math and the arts are more like than unalike. Theoretical physicist Nick Halmagyi, writing in Seed Magazine, compares high-level physics, with its endless chalkboarding of equations, to playing jazz, a comparison that will ring true to anyone who remembers that in the middle ages, the study of music was sometimes considered a branch of mathematics. He writes: "[W]hat I've come to realize is that the best part of what I do is collaborating with remarkably creative people. Understanding the tiny tweaks and unexpected transitions in the universe's evolution requires prodigious amounts of rigor, originality, and personality. It reminds me of the ingredients for a good jazz ensemble. We improvise and strike out in different directions, following whichever note sounds most promising. Over time different voices float to the top. We hear both bravura solo performances and wrong notes. But ultimately, there comes a singular moment when the right chord of an elegant solution reveals itself, and we reach the essential resonance of our collaboration."
From the other side of the net, so to speak, some of today's most important literary artists also find essential inspiration and food for thought in mathematics. An obvious example is writer David Foster Wallace, whose massive 1995 cult classic Infinite Jest is frequently hailed as the defining novel of its generation. Wallace's fondness for-and expertise in-advanced math is well known, and reached its culmination (so far) in a 2004 book of nonfiction, Everything And More, an equation-filled, densely logical history of the idea of infinity. Artists of every stripe have grown obsessed with such mathematical condundra as the Fibonacci sequence, chaos and complexity theory, and the ideas of Kurt Godel. John Updike meditates on computer science in his 1986 novel Roger's Version, which fellow novelist Martin Amis called "a near-masterpiece"; Amis, in turn, contemplates information theory (among other things) in his 1995 comic novel The Information.
Both fields require creativity-and that's something human beings have in abundance. Great teaching-and attentive tutoring-can help ensure that that creativity isn't limited by that self-punishing idea, "I'm just not a math person"
History of Math
If you've taken a first-year college history course-or read through a basic history textbook-you may have noticed a small gap. Its only a thousand years or so.
For a long time, the history of Western culture was told like this: around the fifth century BCE, math, philosophy and science developed, thanks to the hard work of some very smart Greeks such as Thales, Plato, Archimedes and Aristotle. Then Rome took over Greece, and Rome fell, and things went dark for a thousand years or so. Then the Renaissance came along, and thinkers like Galilei and Johannes Kepler took up where the Greeks had, in effect, left off.
Thanks to new historical research-and broader awareness of non-Western countries and of the very rich intellectual cultures being developed east of the Urals-this picture of the history of math, philosophy and science is changing, slowly. But still, teachers tend all too often to skip over one of the most interesting stories in intellectual history-the way that math and logic, including the best insights of Greek logicians, became the property of Muslim countries during the long twilight period, from Romes fall to the Renaissance, when most Europeans could no longer read Greek. Without the work of these great Muslim scholars, math today might be a very different animal. The Islamic Arab Empire, beginning in the eighth century, was a world intellectual capital, and Arabic became a language of learning to rival Latin. Some of the best mathematical reasoning in the world was done here.
We may as well start with Muhammad ibn Musa al-Hwarizmi (9th century), a Persian astronomer deeply learned in the mathematical lore of ancient India. From his name (in its Latin form) we get the word algorithm, and from one of his book titles we derive algebra. Its appropriate that he should be associated with the history of algebra-after all, his books preserved most of what the ancient world knew about algebra (as well as his own brilliant innovations), and his works helped to spread the use of Arabic numerals (the numbers we know and use today) to the West, thus making algebra a good deal more feasible. (To understand why this is important, imagine trying to do algebra problems while using Roman numerals: XIIa times XXVb equals c? No, thanks.)
Then theres Al-Karaji, who around 1000AD invented the proof by mathematical induction-one of the most basic logical maneuvers in math. Poet Omar Khayyam, writing in the twelfth century, laid the groundwork for non-Euclidean geometry. During this period, Muslim mathematicians invented spherical trigonometry, figured out how to use decimal points with Arabic numerals (though the decimal itself had long been invented by Hindu mathematicians), and developed cryptography, algebraic calculus, analytic geometry, among other things.
As important as any of these contributions, though, was the rescue of Aristotles texts from obscurity by Arab scholars. For long periods during the middle ages, Aristotle was considered by Western intellectuals as one of the worlds great thinkers-but most of them hadn't read him. The few of his works that had survived the twin falls of Greece and Rome were available in sometimes poor, or rather freehanded and inaccurate, Latin translations, and many of his most important works weren't available at all. Here and there a Greek manuscript survived, but almost nobody, at this point, could read Greek. (Widespread teaching of Greek had to wait for the Renaissance-even famously learned scholars such as the poet Petrarch struggled over it.) The same went for such seminal works as Euclid Elements, the greatest known treatise on geometry. During this long period, when it was thought that these brilliantly logical works were gone forever, Islamic scholars kept their own copies and translations. When European scholars began traveling to Spain and Sicily (then under Muslim rule) during the 12th century, these works and others were rediscovered in the West, leading to great intellectual ferment, including the theology of Thomas Aquinas-and to an understanding of logic that helped the discipline of mathematics to survive and, slowly, thrive again in the Western countries.
For a long time, the history of Western culture was told like this: around the fifth century BCE, math, philosophy and science developed, thanks to the hard work of some very smart Greeks such as Thales, Plato, Archimedes and Aristotle. Then Rome took over Greece, and Rome fell, and things went dark for a thousand years or so. Then the Renaissance came along, and thinkers like Galilei and Johannes Kepler took up where the Greeks had, in effect, left off.
Thanks to new historical research-and broader awareness of non-Western countries and of the very rich intellectual cultures being developed east of the Urals-this picture of the history of math, philosophy and science is changing, slowly. But still, teachers tend all too often to skip over one of the most interesting stories in intellectual history-the way that math and logic, including the best insights of Greek logicians, became the property of Muslim countries during the long twilight period, from Romes fall to the Renaissance, when most Europeans could no longer read Greek. Without the work of these great Muslim scholars, math today might be a very different animal. The Islamic Arab Empire, beginning in the eighth century, was a world intellectual capital, and Arabic became a language of learning to rival Latin. Some of the best mathematical reasoning in the world was done here.
We may as well start with Muhammad ibn Musa al-Hwarizmi (9th century), a Persian astronomer deeply learned in the mathematical lore of ancient India. From his name (in its Latin form) we get the word algorithm, and from one of his book titles we derive algebra. Its appropriate that he should be associated with the history of algebra-after all, his books preserved most of what the ancient world knew about algebra (as well as his own brilliant innovations), and his works helped to spread the use of Arabic numerals (the numbers we know and use today) to the West, thus making algebra a good deal more feasible. (To understand why this is important, imagine trying to do algebra problems while using Roman numerals: XIIa times XXVb equals c? No, thanks.)
Then theres Al-Karaji, who around 1000AD invented the proof by mathematical induction-one of the most basic logical maneuvers in math. Poet Omar Khayyam, writing in the twelfth century, laid the groundwork for non-Euclidean geometry. During this period, Muslim mathematicians invented spherical trigonometry, figured out how to use decimal points with Arabic numerals (though the decimal itself had long been invented by Hindu mathematicians), and developed cryptography, algebraic calculus, analytic geometry, among other things.
As important as any of these contributions, though, was the rescue of Aristotles texts from obscurity by Arab scholars. For long periods during the middle ages, Aristotle was considered by Western intellectuals as one of the worlds great thinkers-but most of them hadn't read him. The few of his works that had survived the twin falls of Greece and Rome were available in sometimes poor, or rather freehanded and inaccurate, Latin translations, and many of his most important works weren't available at all. Here and there a Greek manuscript survived, but almost nobody, at this point, could read Greek. (Widespread teaching of Greek had to wait for the Renaissance-even famously learned scholars such as the poet Petrarch struggled over it.) The same went for such seminal works as Euclid Elements, the greatest known treatise on geometry. During this long period, when it was thought that these brilliantly logical works were gone forever, Islamic scholars kept their own copies and translations. When European scholars began traveling to Spain and Sicily (then under Muslim rule) during the 12th century, these works and others were rediscovered in the West, leading to great intellectual ferment, including the theology of Thomas Aquinas-and to an understanding of logic that helped the discipline of mathematics to survive and, slowly, thrive again in the Western countries.
math easy
Dont worry about your difficulties with math, Albert Einstein is said to have told a schoolgirl who wrote to him to lament her lack of success in the subject-"Mine," he wrote, "are still greater." Like many of Einstein off-the-cuff remarks, this one contains a profound truth. Math is the sort of subject that increases in complexity the more you understand it; as the diameter of your knowledge grows, so does the circumference of your ignorance.
Some educators see this expanding difficulty as a hurdle to overcome, but in fact, its exactly the quality that causes many young people to fall in love with math. After all, a young football players love of the game often increases in proportion to the toughness of the competition; and video game fans actively seek out greater difficulty-the only game they wont play is the one that fails to increase in difficulty with each level cleared. The fact is that children love to solve problems; the problem-and opportunity-lies in the fact that schools often fail to tap into this intellectual curiosity, and sometimes even stultify it.
Why, then, do so many students experience math as a chore? Cambridge mathematician Timothy Gowers suggests one possible answer in his Mathematics: A Very Short Introduction, in answering the question "Why do so many people positively dislike mathematics." He writes: "Probably it is not so much mathematics itself that people find unappealing as the experience of mathematics lessons, because mathematics continually builds on itself, it is important to keep up when learning it." (His comment will ring true to anyone who remembers endless third-grade drills on the multiplication tables.) Standardized instruction and memorization of these details has to move at a certain plodding pace, which leaves some students bored and others, who are slower to grasp a concept, frustrated. "Those who are not ready to make the necessary conceptual leap when they meet one of these [new] ideas will feel insecure about all the mathematics that builds on it," Gowers writes. "Gradually they will get used to only half understanding what their mathematics teachers say, and after a few more missed leaps they will find that even half is an overestimate. Meanwhile, they will see others in their class who are keeping up with no difficulty at all. It is no wonder that mathematics lessons become, for many people, something of an ordeal."
But Gowers sees hope for even the most frustrated student, writing, "I am convinced that any child who is given one-to-one tuition in mathematics from an early age by a good and enthusiastic teacher will grow up liking it."
Gowers remark suggests a few possible directions for school districts and state legislatures concerned by recent declines in math scores. Smaller classrooms, more individualized instruction, and greater access to math tutoring and afterschool homework-help programs for poorer children all may help. If students can work at math in the way that they work at other, more pleasurable problem-solving tasks-moving at the pace that comfortable to them, so that they aren't inhibited by frustration, fear of failure, and invidious comparison to faster-moving classmates-they may find themselves taking satisfaction in their own intellectual attainments, enjoying the intrinsic incentives that make scholarly success its own reward for top students.
Gowers mention of "one-to-one tuition" may also help to explain the explosive growth of math tutoring services over the past decade. Tamar Lewin, in a November 2006 New York Times story, writes that in Washington State alone, "residents spent $149 million on tutoring and other education support services in 2004, more than three times the $44 million they spent 10 years earlier." In a state where many parents hope to see their children grow up to work for such local giants as Microsoft or Boeing, math instruction is especially important.
Math Made Easy provides Math help for Algebra help, Geometry help, math homework help using math online tutorial services and math tutorial cd so you can watch your math scores soar.
Some educators see this expanding difficulty as a hurdle to overcome, but in fact, its exactly the quality that causes many young people to fall in love with math. After all, a young football players love of the game often increases in proportion to the toughness of the competition; and video game fans actively seek out greater difficulty-the only game they wont play is the one that fails to increase in difficulty with each level cleared. The fact is that children love to solve problems; the problem-and opportunity-lies in the fact that schools often fail to tap into this intellectual curiosity, and sometimes even stultify it.
Why, then, do so many students experience math as a chore? Cambridge mathematician Timothy Gowers suggests one possible answer in his Mathematics: A Very Short Introduction, in answering the question "Why do so many people positively dislike mathematics." He writes: "Probably it is not so much mathematics itself that people find unappealing as the experience of mathematics lessons, because mathematics continually builds on itself, it is important to keep up when learning it." (His comment will ring true to anyone who remembers endless third-grade drills on the multiplication tables.) Standardized instruction and memorization of these details has to move at a certain plodding pace, which leaves some students bored and others, who are slower to grasp a concept, frustrated. "Those who are not ready to make the necessary conceptual leap when they meet one of these [new] ideas will feel insecure about all the mathematics that builds on it," Gowers writes. "Gradually they will get used to only half understanding what their mathematics teachers say, and after a few more missed leaps they will find that even half is an overestimate. Meanwhile, they will see others in their class who are keeping up with no difficulty at all. It is no wonder that mathematics lessons become, for many people, something of an ordeal."
But Gowers sees hope for even the most frustrated student, writing, "I am convinced that any child who is given one-to-one tuition in mathematics from an early age by a good and enthusiastic teacher will grow up liking it."
Gowers remark suggests a few possible directions for school districts and state legislatures concerned by recent declines in math scores. Smaller classrooms, more individualized instruction, and greater access to math tutoring and afterschool homework-help programs for poorer children all may help. If students can work at math in the way that they work at other, more pleasurable problem-solving tasks-moving at the pace that comfortable to them, so that they aren't inhibited by frustration, fear of failure, and invidious comparison to faster-moving classmates-they may find themselves taking satisfaction in their own intellectual attainments, enjoying the intrinsic incentives that make scholarly success its own reward for top students.
Gowers mention of "one-to-one tuition" may also help to explain the explosive growth of math tutoring services over the past decade. Tamar Lewin, in a November 2006 New York Times story, writes that in Washington State alone, "residents spent $149 million on tutoring and other education support services in 2004, more than three times the $44 million they spent 10 years earlier." In a state where many parents hope to see their children grow up to work for such local giants as Microsoft or Boeing, math instruction is especially important.
Math Made Easy provides Math help for Algebra help, Geometry help, math homework help using math online tutorial services and math tutorial cd so you can watch your math scores soar.
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