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The New Jersey HSPA (High School Proficiency Assessment) Test is one which all juniors in New Jersey high schools must take and pass in order to receive their diplomas. For many, this test presents a challenge as it consists of two sections, one in English, and one in math. The English section requires that students demonstrate competency in English, both from a written and comprehension perspective; and the math section requires students to demonstrate competency in four areas in high school mathematics: number sense, concepts, and applications; spatial sense and geometry; data analysis, probability, statistics, and discrete mathematics; and patterns, functions, and algebra.

Students who are above average to strong in math have really nothing to fear as the HSPA Math test should be little more than a review for them. Most students in this category find the HSPA little more than a petty annoyance. Since passing both sections of the HSPA is required to graduate, students who are weak in math view this test as a potential diploma robber. Given this fear, a parent should realize that insuring their child is properly prepared is essential. There is no greater humiliation for a high school student than to fail one or both parts of the HSPA and have to be put into a remedial course for its retaking. Such a failure not only plays with these students’ confidence levels but also robs them of time in their curriculum schedule that could be used for more enjoyable courses.

Before this untoward event happens to your child, be sure that you have a good feel for where your child is on the mathematics front. Speak with their guidance counselors and math teachers to get an idea of whether your son or daughter is in danger of failing the mathematics part of the HSPA. If you get a sense from school personnel that this is the case, remediate this situation immediately. Don’t wait even a minute. Get your child some practice exams and have them work with a competent tutor to remedy this situation. The HSPA math problems are not nearly as challenging as those of the SAT (Scholastic Aptitude Test), and therefore, by getting some extra help from a competent instructor, you can have your child on the road to a passing HSPA grade. Remember, don’t wait and start late. Get your kid the help and look forward to graduation day with a big smile.

See more at HSPA and SAT Test Preparation

Most of the mathematical concepts we encounter every day - numbers, addition, subtraction - seem so basic, so hard to avoid in discussing reality on even the most basic level, that it’s hard to imagine someone having to sit down and invent them. Who was the first person to look at two rocks and think, “Two more and I’ve got four?” The very idea almost seems absurd.

But mathematics is, in part, a language - not just a set of logical relationships and entailments that seems deeper than words, but a set of notations that allow us to discover those relationships. You can’t see that twice two makes four, until you have a symbol for “two” that your brain can operate with. And those symbols - that language - did have to develop, strange as it may seem. (Prehistoric artifacts seem to indicate that the earliest humans had only four “numbers” at their disposal “none,” “one,” “two,” and “many” - showing just how much our ability to talk about numbers depends on having the right words for them.)

We don’t know which culture was the first to develop a number system more elaborate than “one, two, lots!” A 20,000-year-old bone found near the Nile River seems to show a sequence of prime numbers - which would indicate fairly sophisticated mathematical knowledge from fairly early on. Then there was the Harappan civilization of the Indus Valley in present-day North India and Pakistan. As far as we know, these folks were the first to use decimals, among many other important concepts.

Archaeology also seems to find evidence of a sophisticated number system during the Shang Dynasty in China, 1600 years before Christ. Archaeologists often turn up new discoveries bearing on the history of human consciousness - so it’s hard to say who was the first to develop this or that idea with any certainty.

But many mathematical ideas - like many other things - begin with the Sumerians. This culture - considered by some historians the cradle of civilization - flourished near present-day southern Iraq between three and five thousand years ago, and besides contributing the world’s first known work of literature (the still-impressive tale of Gilgamesh), they developed a numerical system based on sixes. If you’ve ever wondered why an hour has sixty minutes, or a minute sixty seconds - after all, it’d be much simpler if everything went by 100 (so that our basic unit of time was made of 100 smaller units, rather than sixty seconds, sixty minutes)- it’s in part because of lingering Sumerian influence. As Sumer’s culture declined, it was absorbed into the Babylonian Empire, which also seems to have produced mathematical thought, if the handful of Babylonian mathematical writings still remaining to us provides any indication.

Babylonians, Egyptians and ancient Indians all seem to have shared at least one important discovery - the so-called Pythagorean theorem, a rule having to do with how to figure the length of the sides of certain kinds of triangles. (Clearly, this discovery was of use to the culture that built the Pyramids.) The fact that this theorem was common to all three major ancient cultures suggests the degree of traffic they may have had with each other, despite some historians’ suggestion that each culture was mainly closed-off to other places. And the fact that we know the theorem as the Pythagorean theorem - after the much-later Greek mathematician and philosopher Pythagoras - illustrates the well-known, and often-criticized, tendency of some historians to want to give the ancient Greeks credit for everything.

Not that the Greeks don’t deserve plenty. Greek mathematics grew up alongside Greek philosophy and Greek science - indeed, the three disciplines weren’t really separated; for the ancient Greeks, all the disciplines of knowledge were one thing. Thales, for example - whom you’ll often find cited as the first Western philosopher - used geometry to calculate the height of the pyramids, among other things. In any case, Greek thinkers took the young art of math to a new level of sophistication. Euclid wrote a geometry textbook so percipient as to remain useful today, Aristotle defined laws of logic, and Archimedes remains near the top of some math historians - all-time greats list. The tight relationship between math and philosophy in ancient Greek is well-expressed by the inscription found on the door of Plato’s Academy: “Let nobody ignorant of geometry enter here.”

A new school semester is quickly approaching and one thing is for certain. College students continue to struggle with their math courses. They find math a difficult subject often times having trouble with problems ranging from statistics to the metric conversion table. One way to resolve this issue is to ask for the assistance of a math tutor.

Math tutors provide a great solution to many of the troubles college students find in their courses. Difficulty with math is a major issue, especially when there is such a strong emphasis getting good grades for job placement. Math tests on metric measurements, for example, create terrible anxiety, and many students have no choice but to ask for outside help in order to gain confidence in absorbing material such as weight conversion and length conversion. Tutors develop learning problems and put together personalized instructional programs.

A tutor offers students the chance to sit and receive individualized instruction on work they may be having trouble with such as the metric conversion calculator. No student’s learning curve is the same and each has different needs. Often large classrooms can’t accommodate an individual student’s type of learning. I know many strong students who have received help from a tutor in order to pass a difficult test on length conversion and weight conversion.

Most tutors can be found simply by asking for recommendations from friends and family who may know someone who tutors. Your school most likely also can recommend a tutor as well based on the type of subject matter you need help with such as metric measurements. Most colleges actually post available tutors on their job boards. I have even seen retired or part time teachers offering tutoring as a way to make some extra money.

It is important that your tutor has professional training or enough experience in the subject matter at the level of difficulty you need to learn. If your tutor doesn’t understand some of the metric conversion table concepts, how can they properly teach it? The tutor’s job is to teach the major concepts and problem solving strategies of the specific subject matter. For younger students, helping with homework may be enough, but in most cases, a tutor that can help change the way a student approaches problems is preferable. You would like for the student to understand the concepts of a metric conversion calculator instead of just doing homework from it.

Ultimately, your tutor must refine all of your skills from test taking, studying and self-confidence. They provide a strong structure so you get the proper practice that excelling at math requires through a productive work routine. Tutoring time should be viewed as positive and supportive.

A tutor who tutors the flute, tried to tutor two tutees the flute. Said the two to the tutor, “It is harder to toot or to tutor two tutees the flute?

-Tongue twister

Math tutors toot no flutes but they do have to know how to tutor tutees in a variety of areas. The work involves diagnosing and understanding the nature of a student’s strengths and weaknesses as well as explication of sometimes complex concepts and procedures in mathematics.

Math homework made easy? There is no better way to demystify math homework than to use Math Made Easy’s tutoring services. Expert tutors work with you or your child to make short work of math homework. With the personal and private assistance of professional tutors, students have all the math homework help they need to reinforce concepts learned earlier in class and to forge ahead for the next day’s work.

Math Made Easy tutors are selected for their ability to do both of these difficult tasks with ease and with understanding. They are trained to work with students in a compassionate and caring way in order to nurture both a love for math and self-confidence in the student. Many have backgrounds in formal education and all have substantial background in mathematics as a discipline.

Homework is no longer a chore when Math Made Easy homework help is available. These highly trained math tutors work with students to establish a personal relationship in the privacy of the student’s home using a sophisticated yet easy-to-use computer-based method designed to give the best instructional help with the personal touch.

Eliminating the fuss and the fear of math homework by getting appropriate help with tutors gives the student the necessary confidence to face the following day’s work without concern. Math homework help may be scheduled online or via telephone and hours of service accommodate even the most difficult of schedules.

Math Made Easy students have a choice of math tutor, assuring that the student will control his/her experience. While every effort is made to keep each student with one tutor, a wide variety of staff ensures that each student will find the right math tutor, one who makes the student feel comfortable and confident learning math.

Math Made Easy has a proven track record of providing a wide range of services to an even wider range of students. Math tutors are capable of working in areas ranging from arithmetic to multivariable calculus to probability and statistics to solving complex problems involving several areas of math.

So even if Math Made Easy toots no flutes, the can toot their our own horn about the quality of their dedicated math tutors.

About Multimedia Tutorial Services, Inc.

Multimedia Tutorial Services, Inc. has key strengths in educational products, with highly skilled online math tutors to provide math help, algebra help, math homework help, geometry help, calculus help, math answers, SAT test tutoring, SAT preparation, and math answers. To date, the Company’s premier tutorial program, Math Made Easy(TM) has been purchased by more than three hundred thousand families. In addition, several thousand schools and colleges throughout the country have acquired the Math Made Easy(TM) series for their libraries and classrooms. Math Made Easy(TM) is widely recognized as one of the foremost home tutorial programs. The tutorial series has been featured on CNN, Bloomberg, ABC News Radio and other major networks.

Why anybody would want to get a bachelor degree in math is a mystery. When you think about it, when you get out of college with a bachelor degree in math, what can you possibly do with it besides teach? You’re certainly not prepared for any practical applications. Sure, you could get a job as an actuary but is that REALLY why you majored in math in the first place? Well, for those of you who still want to get a bachelor degree in math, hang onto your hats because the ride you’re in for is far from easy. What follows is pretty much what you can expect to go through.

Math is probably one of the hardest disciplines anybody could possibly want to go through. The math courses alone are so hard that no other courses are needed to make your four years of college a living nightmare. Think we’re kidding? Take a look at just the math curriculum itself and then decide if this is something that you think you can tackle with no sweat.

Your first two semesters of college math throw you right into the fire. This is where you learn Calculus. The courses are usually Calculus I and II. Calculus is probably one of the most difficult courses ever devised by man. How anybody even thought of this stuff is a puzzle. Talk about math that you’re never going to use in your life unless you become a scientist or an engineer.

Your next two semesters, or year two, give you a break from calculus. This is where you take Advanced, or Abstract Algebra. This is where you learn about matrixes and things like that. This is more math that you’re never going to use as long as you live. Engineers don’t even use most of this stuff.

Now you’ve reached year three and you’re back to Calculus again. This is where you finish up your training in Calculus with Calculus III and IV. The concepts in these courses are so abstract and so far removed from any real world math, you’d have to be a near genius to understand this stuff.

By year four, if you’re still a math major, you’re down to what they call “Independent Research” where you basically are on your own, but under the guidance of your advisor. You’ll do some kind of major paper on math principals or maybe even Newton for all you know. The good thing is, what you write on is up to you. The bad thing is it has to be approved by your advisor.

And if all of this isn’t bad enough, you’ve only taken 8 of your 32 courses. You still have 24 more courses to fill in your time with. Because you’ve chosen one of the science majors, you’re also going to have to take at least two semesters of either chemistry, physics or some other related science. Yes, we are talking about some more ridiculously hard material.

So if you really want to be a math major, just remember one thing. You will most certainly earn your bachelor degree in math. If you survive it.

The concept of one-to-one correspondence requires two skills: (1) matching pairs and (2) comparing sets. Matching places two like items together as a pair while comparing determines which set has more or less. In these projects, the key is to focus on the language, emphasizing mathematical terms.

Books to Read
The following books teach one-to-one correspondence using stories. I love the impact a story has on understanding, and these books do a great job of packaging the mathematical ideas in a way that young children can comprehend.

Two of Everything: A Chinese Folk Tale by Lily Toy Hong
Knots on a Counting Rope by Bill Martin Jr. and John Archambault
Seaweed Soup by Stuart J. Murphy
A Pair of Socks by Stuart J. Murphy
Missing Mittens by Stuart J. Murphy
Monster Musical Chairs by Stuart J. Murphy
Just Enough Carrots by Stuart J. Murphy
Some Things Go Together by Charlotte Zolotow

Projects to Learn Matching

Project #1
Take opportunity to point out situations where there is a matching set. Word emphasis: match, even, pair, each.

There are three cups and three straws. It is even. Three children and three cookies. It is a match! A pair of socks for your feet. One foot for each sock, and one sock for each foot.

Project #2
Provide the following items and allow the children to sort into pairs. Word emphasis: pair, match.

1 ice cube tray
2 screws
2 washers
2 electrical circuit binders
2 matching butterfly clips
2 matching hair pins
2 pennies
2 matching buttons

Project #3
Have a tea party with stuffed bears. Set one place setting for each bear. You could say, “One seat for each bear, and one bear for each seat.” Word emphasis: each.

Project #4
Serve a lunch with matching shapes to make their own snacks. I used cookie cutters to cut the bread, cheese, and lunch meat into matching shapes. I provided at least two different shapes so that they would have to find the match in order to build their sandwiches. Word emphasis: match.

Project #5
Play the memory game. Word emphasis: pair, match.

Projects to Learn Comparing

Project #1
Take opportunity to point out situations where there is not enough or there is too much to go around. Word emphasis: more, less, fewer, even.

Oops, I grabbed one straw too many. There are three cups and four straws. There are more straws than cups. We have six chairs at our table, but only four people in the family sitting at the table. That leaves two empty chairs because there are more chairs than people. Today we have company, so we have eight people and only six chairs. We have fewer chairs than people, so we will need two more chairs. Three children and four cookies. There are more cookies. If I eat one, it will be even.

Project #2
Invite the children to collect toys to put inside two hula hoops. Then count to see which hula hoop has more toys and which has fewer. Ask, “Which set of toys has more? Which set has fewer?” Word emphasis: set, more, fewer, even.

Project #3
Pour two cups of water and compare the volume. Which cup has more? Which has less? Word emphasis: more, less, even.

Project #4
Make sugar cookies and put chocolate chips on the frosting. Compare two cookies to see which has more chocolate chips. For an added lesson, determine how many chocolate chips need to be added to make them even. Word emphasis: more, fewer, even.

If a student is struggling in any mathematics subject area, it is important to find ways to help. Probability, Statistics and Calculus are areas where even normally high achievers may find themselves struggling.

Classroom instruction works well for many; however, for others, a 45-minute classroom session, surrounded by the distractions of their peers, is simply not the ideal way to learn. Even if students pay close attention in class, they are liable to miss a lesson or a portion of a lesson for any number of reasons. And since math works like a chain, with one concept leading to the next, a “missed link” causes subsequent material to stop making sense.

Probability & Statistics

Many students struggle with Probability and Statistics through no fault of their own. After all, Probability and Statistics has its own unique language and set of rules. Nonetheless, the frustration experienced by Probability and Statistics students can result in a loss of self-confidence.

If the student is struggling with Probability and Statistics, look for a comprehensive, step-by-step Probability and Statistics tutorial, an approach that simplifies complex concepts by breaking them up into smaller steps, using illustrations and providing real-life examples.

Calculus

Need help with calculus? You are not alone! Calculus is one of the most difficult subjects for many students, even those who are normally high achievers. But here’s some good news: once a student becomes familiar with the special “language” of calculus, it can become one of the easiest, and even most enjoyable, things for them to do!

Calculus is based on a special kind of logic–once it clicks in students’ heads, it becomes easy to apply to any type of problem. The trouble is, some students learn best at different paces, and in different environments, than others.

Geometry

Many students struggle with geometry. Geometric shapes don’t translate very well on a blackboard. Students need a much more visual imagination to understand concepts such as: points and lines; angles; parallel lines; analytic geometry; the coordinate plane; distance; midpoints; slope; equations of lines; deduction and formal proofs; polygons; introduction to triangles; angles of a triangle; right triangles pythagorean theorem; congruent triangles; similar triangles; quadrilaterals: trapezoids, parallelograms, rectangles, rhombuses, squares; perimeters and areascircles; lines associate with circles: radius, diameter, chord, tangent, secant; the equation of a circle; angles associated with a circle; area and circumference! Nonetheless, geometry is an essential component of a good education.

Tutorial programs and tutors can help a student grasp difficult mathematical concepts and excel in his or her math class. Find a math tutor who can offer a comprehensive tutorial program and cement challenging math concepts through repetition. Hundreds of interactive exercises are available by tutors to ensure that the student masters all the formulas and concepts of the review. Tutors can also assist with recommending and providing good math workbooks. Such workbooks provide additional practice and exercises and students can eventually work through and solve problems on their own.

The knowledge and sense of achievement that a tutoring program can bring to the student will pay big dividends for years to come. Not only will it help earn a good grade in Probability and Statistics or Calculus, but it will also lay a critical foundation for future success, including help with college admissions exams.

“Numbers are the highest degree of knowledge. It is knowledge itself.” -Plato

As the quote elucidates, knowledge sits on the shoulders of numbers. Whenever I encounter a quote like this, particularly when the source is as renowned as that of the likes of Plato, I sit back and muse smugly that I hit the nail on the head many years ago when I realized that numbers were indeed the highest degree of knowledge. Extrapolating from this realization, we can say with certainty then that learning to work with numbers as through math tricks and such-that is, getting an inner feel for all their intricacies and richness-will produce extraordinary results in the education of any man, woman, or child.

During my first year of college, my fortuitous stumbling in pre-calculus actually led me to the transcendent awareness that mathematics paved a road to a higher-indeed spiritual-realm. Because I was determined to maintain my “A” average, I forced myself to open my arms to this subject and to study it feverishly. Having secured the “A” grade in pre-calculus, I plunged headlong into calculus. Similar experiences with calculus reinforced my belief that math and numbers were the key to all higher learning and our connection to the divine. Indeed many of the quotes from famous mathematicians embrace the idea that math touches upon this very sphere of existence.

So how do we use this knowledge about numbers and mathematics to our benefit? Simply, we probe the world of numbers and operations involving them. To make matters more fun, we learn math tricks which sharpen our math skills and give us a sense of power over these curious and ever mind-bending creatures.  By learning how to better deal with numbers and their associated arithmetic properties, we forge a tunnel that leads to the very essence of nature: mathematics and science, two inter-related disciplines that can only be understood through numbers and their properties.

By studying and learning the inter-relationships among arithmetic and algebraic properties like the Associative, Commutative and Distributive laws, we become better connected to numbers and consequently see evidence of such laws working in nature.  Learning about special sequences like the Fibonacci only requires a basic understanding of numbers; but then, one learns that this very sequence of numbers is used as a stock trading tool by professionals to make millions of dollars!

When one delves into numerical operations, he comes to share the sense of enlightenment and empowerment that comes with a mastery over numbers. And as though this were not enough, the extra dividend of learning math tricks and mastering numbers is that educational success overall is sure to follow, besides possibly making a killing in the stock market! Now what could be a better road map to success in school and life than this?

Basic facts are key to a student’s success in math. Basic facts are simple mathematic equations like eight times seven or forty two divided by six, similar to knowing common words in language or reading notes in music. They are essential skills used for every concept in math. Only about one third of students achieve the needed level of proficiency in with basic facts school. Another third will get most of them, but will fumble through the tougher ones resorting to time consuming techniques like to counting fingers. The remaining third will be hopelessly lost. You will see this in almost any classroom you walk into. These skills are as important as learning to dribble and shoot in basketball. They are simply skills a child needs to succeed in math.

As a general rule when asked a multiplication question students that can answer within three seconds will do well at math and those that answer in less than one second will do excellent at math. They must be able to do this for every basic fact for addition, subtraction, multiplication and division. As well, a student must be able to answer the fact whether it is written with numbers (written on the board), given verbally (asked by the teacher) or represented symbolically (shown blocks representing numbers). Although this seems particular, imagine listening to someone sing “Oh Canada” only knowing most of the words.

The trouble with learning basic facts is that most students are only taught one way to memorize them. Many teachers use the default method of rote memorization typified by the posting of the multiplication tables and routine time tests often called “Mad Minutes”. Although occasionally a teacher will use an alternative to this approach, the result is inevitable. Only one way to learn the facts is presented and only one third of the kids in a classroom will learn them.

Although the lack of basic skills will not be obvious to the teacher, parents or even the child, there will be signs. Since these students will focus a large amount of unnecessary time on computing the basic facts they often miss the other concepts taught in a lesson. Although children can fake their way through many math lessons, low scores, disruptive behaviour and a genuine dislike for math are often the results. If the source of this destructive trend goes unchecked, the student will continue to suffer down the road.

The solution in most cases is simply time. Being aware of this situation is a huge step for many parents and teachers. By taking the time and patience to do a thorough job of teaching the basic facts is one of the greatest gifts you can give a student. Offering options for learning the information like using flash cards, card games, posters or manipulatives will give more opportunities for success. Every minute of practice will improve the skill and confidence of a learner. There are many learning styles and ways of categorizing and approaching these styles. Thorough teaching and testing is crucial. If a student cannot add nine and seven easily, algebra is going to be a nightmare.

There are also alternatives that go outside the normal field of thinking. Using mnemonic devices (memory techniques) specific to math can allow students to learn the math facts in hours instead of months or years. This method is not easily accepted by adults as it breaks tradition on is different from how they were taught, but it does work. I’ve personally seen it work with hundreds of students with amazing results.

This article hopefully gave you some insight into the mind of a struggling math student, the numbers to reassure you that you are not alone and some optimism that there are solutions out there.

You know who those students are. No matter what you do as a teacher, they just **** math. Perhaps there is a simple concept they never picked up in the earlier grades, or maybe they just don’t care for numbers. You can make the class as exciting as possible, but some children are just more interested in other subjects. One way to motivate those students who really would rather be in another class is with computerized math games.

Math games do not replace the need for a teacher. There is nothing that educational software can teach in math that can be taught without a teacher. Math is one of those subjects that really requires an instructor. However, math games can be used to reinforce and reward in the math classroom.

Imagine if you are teaching junior high math and realize that some of your students do not know how to add and subtract. If you have to take valuable class time to teach these basic elementary math skills, the rest of your students will suffer. However, if this student group is not able to do simple addition or subtraction, they are going to struggle all year. One way to encourage them to practice in a fun, competitive way without detracting from the overall class is to allow them to play math games. Maybe time can be set aside regularly and designated as free time. Students who need to reinforce skills can get extra math practice and students already at grade level can start homework or be challenged at a higher level. Teachers can set up the math games so that they focus on areas that need reinforcement. You can make random groups and rotate them so all of your students get a chance to play during the week. This way, certain students are not identified and all students receive important practice.

One benefit of math games that is often overlooked is the fact that the students are working independently. Sometimes those students who struggle in subjects, especially math, are embarrassed about their difficulties. If you were to play a group practice game or ask them to answer questions orally, they might be too embarrassed to try their best. On the computer, however, these students are not faced with their peers. They can progress through the math games at their own level, gaining valuable practice each day.

As you are shopping for math games, you need to realize that there is a wide range of products available. You will still be able to find traditional math games. These are the games where students practice their basic facts with arcade-like programming. But, math games are no longer only the arcade-style games you may remember. You can find software that contains your students’ favorite cartoon or movie characters. As they move through the levels they must answer math questions to proceed. Tracking student’s progress and the cability to personalize lessons to the student’s ability are features of some math game software. Students advance levels once they’ve reached competency on skills being worked on. Some math games have features that encourage and build analytical skills, problem approach, logic and systematic thinking. While your students may not realize this is math, you know that these thinking skills are essential to finding success in the subject. You can even purchase mystery programs where the students act as detectives solving “math mysteries.”

Whatever program you decide to use in your math classroom, be sure to set aside time when the students can play math games. Interactive math games are one way to introduce and reinforce math concepts with an entertaining medium. With math games, math can become a little bit more fun for everyone.