Educational Comments

Why MathMedia Educational Software Works
As the use of educational technology grows and grows and computers in the classroom (and home) become more prevalent, the need for quality, comprehensive, and relevant software becomes increasingly important. Using MathMedia computer technology in the classroom, students receive the benefits of individualized instruction on the computers in the classroom, ample math practice, immediate feedback and coaching. "On-demand" help and positive reinforcement put students in control of their own learning and help to keep them on task. Technology in the classroom supports better student interaction too, because teachers who have computers in the classroom can spend more time with students who need additional intervention. MathMedia software not only aligns with the math standards of California, Illinois, and Massachusetts but goes beyond the standards to challenge all students to "Unlock the Mystery of Math".

MathMedia understands that to integrate educational technology into the classroom, limited school resources must be used efficiently and effectively... We will work with you to achieve those goals.

Since the internet was created as the "information highway", please scroll down to read informational educational articles.
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Math Anxiety in Female Teachers
Math Anxiety in Female Teachers

www.chicagotribune.com/news/chi-teachers-math-anxiety,0,4114031.story

chicagotribune.com Study: Female teachers' math anxiety affects girl students By Kristen Mack

Tribune staff reporter

2:27 PM CST, January 25, 2010

Women teachers' anxiety about math may undermine girls' confidence in learning the subject and decrease their performance in fields that depend on a grasp of math fundamentals, such as science and engineering, research at the University of Chicago shows.

The findings are the product of a year-long study of 17 first- and second-grade teachers and 65 girls and 52 boys who were their students. The researchers found that boys' math performance was not related to their teacher's math anxiety while girls' math achievement was affected.

More than 90 percent of elementary school teachers in the country are women and they are able to get their teaching certificates with little mathematics preparation, according to the National Survey of Science and Mathematics Education.

"We are not sure whether it's something overt, whether it's non-verbal behavior or perhaps (teachers are) not spending much time on the subject," said Susan Levine, a psychology and human development professor and co-author of the study "Female Teachers' Math Anxiety Affects Girls' Math Achievement," published in the Proceedings of the National Academy of Sciences this month.

"It's not just a teacher's knowledge of the subject, but there's something about their feeling about the discipline," Levine said

Sian Beilock, a U. of C. expert on anxiety and stress as they relate to learning and performance, was lead author of the report.

To determine the impact of teachers' math anxiety on students, the team assessed teachers' feelings about the subject. Then, at both the beginning and end of the school year, the research team tested student math achievement and gender stereotypes about math.

At the beginning of the year, the students' achievement was unrelated to their teachers' level of math anxiety. By the end of the year, however, the more anxious their female teachers were about math, the more likely girls--but not boys--were to endorse the view that boys are better at math. Girls who bought into the stereotype scored six points lower in math achievement than other students.

The authors suggest that elementary teacher preparation programs be strengthened by requiring more math as well as addressing attitudes and anxiety about the subject.

kmack@tribune.com

Copyright © 2010, Chicago Tribune

<h5>Education Pick Is Called 'Down-to-Earth' Leader
<h5>Education Pick Is Called 'Down-to-Earth' Leader

By Maria Glod Washington Post Staff Writer Wednesday, December 17, 2008; A03

In seven years as chief executive of Chicago public schools, Arne Duncan has supported a range of measures to shake up the status quo in urban education, including new charter schools, performance pay and tough accountability for struggling schools.

But he has also gained a reputation for reaching out to the teachers union and the community, helping to neutralize some potential critics and win allies.

Now, Duncan will take his political skills and reform zeal from the country's third-largest school system to Washington to become the next education secretary, a post that will require him to try to bridge deep divides among education advocates, labor leaders and civil rights groups over how to fix U.S. schools.

Yesterday, President-elect Barack Obama introduced Duncan as his nominee at a news conference at a Chicago school. "When it comes to school reform, Arne is the most hands-on of hands-on practitioners," Obama said at Dodge Renaissance Academy, adding: "When faced with tough decisions, Arne doesn't blink."

With Duncan at the helm of the 408,000-student system, test scores have improved, participation in Advanced Placement classes has risen sharply and graduation rates have edged up. However, the trade publication Education Week this year reported that the city's on-time graduation rate was 51 percent for the Class of 2005, ranking it behind most of the country's 50 largest school systems.

"While there are no simple answers," Duncan said at the event, "I know from experience that when you focus on basics like reading and math, and when you embrace innovative new approaches, and when you create a professional climate to attract great teachers, you can create great schools."

Under Duncan's leadership, charter schools were expanded, and a performance-pay plan was launched with the blessing of teachers. He supports a program to bring people into teaching who have little classroom experience but strong academic backgrounds. In 2006, he called on Congress to double funding for the No Child Left Behind law.

Duncan's résumé appeals to some who identify themselves as reformers, but his calls for increased funding and his willingness to partner with teachers also win the approval of unions and school officials who think the federal government imposes too many sanctions without offering enough support.

"Duncan is someone we believe can work with everyone, and that's going to be an important part of setting a new tone to get things done in the new administration, instead of treading water," said Joe Williams, executive director of the New York-based Democrats for Education Reform.

Duncan, 44, has close ties to Obama and has helped shape his education platform. During Obama's time in Illinois, they visited schools in Chicago but also bonded over pickup basketball. (Duncan co-captained Harvard University's team and played professionally in Australia for a few years.)

Across the spectrum of education advocates, Duncan wins praise from many quarters. Education Secretary Margaret Spellings called him "a visionary leader and fellow reformer who cares deeply about students."

National Education Association President Dennis Van Roekel, head of the country's largest teachers union, noted Duncan's push for increased funding and flexibility: "For too long, federal education policy has been about teaching to the test, and Duncan could use his new position to move beyond those failed policies and provide every child with 21st-century skills."

Duncan will take over the Education Department at a pivotal time. Efforts to revamp the 2002 No Child Left Behind Law, which aims to boost achievement of children from poor families, have been on hold as Congress awaits the new president. But many educators and lawmakers from both major parties have soured on the law, which requires states to rate schools on test scores. Teachers unions and some school officials have begun to see it as too rigid and punitive.

Obama has promised to "fix the failures" of the education law, but hammering out details will not be easy. He has pledged to improve testing and create a more nuanced way to hold schools accountable. But some of the law's advocates, including civil rights groups that applaud the spotlight on minority student performance, worry that the law could be watered down.

Duncan's challenge will be to help lawmakers and advocates reach agreement, said Michael J. Petrilli, who was associate assistant deputy secretary in the Education Department from 2001 to 2005 under President Bush and now works at the Thomas B. Fordham Foundation, an education think tank.

"This confirms what we know, that President-elect Obama has reform instincts, but he's also a diplomat and is careful to not alienate key constituencies in the Democratic Party and across the aisle," Petrilli said. "That's going to be a delicate balance -- to walk the line between the reform camp and the education establishment."

In Chicago, some Duncan-backed initiatives have met with resistance from teachers and parents. There has been some opposition to the city's move to shutter low-performing schools and reopen them with new staff.

But he is also known as an approachable, even humble, leader. In October, he choked up as he turned down an award given to him by an anti-gun group, saying too many Chicago students had been killed and he had "not earned it."

Debra Strauss, president-elect of the Illinois PTA, recalled meeting Duncan at his office to talk about how to harness the work of community organizations to engage parents and provide them with better services. She said Duncan met her at the door, shook her hand and introduced himself as Arne.

"He's sort of a roll-up-your-sleeves-and-get-down-to-work kind of individual," Strauss said. "He brings a very down-to-earth perspective."

Tom Loveless, director of the Brown Center on Education Policy at the Brookings Institution, said the choice of Duncan shows that Obama values the perspective of an on-the-ground educator.

"The message is that he wanted someone who has the respect of the field," Loveless said. "These are modest reforms, nothing way out of the mainstream, but pragmatic, and they seem to be working."

Integrating Classroom Technology into the Curriculum
Integrating Classroom Technology into the Curriculum

So, now that all this classroom technology is available, how in the world do we integrate it into our teaching methods?

Classroom technology has grown from simple calculators to entire instructional curriculum delivered by computers in the classroom. Here are a few methods from which to choose. Use this math software for the explanations and the math practice it provides. This versatile software allows the user to click and go anywhere from a menu of topics. First of all let's divide the methods into two main categories:

I. Using instructional technology in the classroom situation:

(1) In front of the class with an LCD projector

Since this software is curriculum-based, find the appropriate lesson using the computer as a tool for the introduction of the topic. Project the examples on the screen while the students actually PRACTICE at their desks. When, most of the students have given the example problem their best shot, the solution is revealed (by the teacher and the software). Discussion usually follows. This technique keeps the students actively involved in the learning process. Ideally, the homework would be the same as the classroom instruction and practice. For learning geometry, this method of instruction is very useful and timesaving because the teacher does not have to select and draw complicated time-consuming diagrams.

(2) In a "lab" setting with groups of students -- The students meet in a computer lab with 1-2 students per computer and are directed by the teacher to:

a. Work on a particular topic that is being introduced or practiced which will correlate to the homework assignment.

b. Re-enforce classroom learning by taking the included test on that topic at the computer. This is an excellent math learning tool to prepare for a classroom exam.

II. Using math tutorial software in an individual situation (1-2 students at a single computer or a student and teacher/facilitator at a single computer) where the learner:

(1) Catches up on missed material (the classroom instructor should use the included Progress forms to check off those topics a student has missed or needs extra practice on).

(2) Practices for a classroom test, studies specific topics, or takes the included test at the computer.

(3) Accelerates -- some learners like to take a peek into the future -- this is a perfect way to afford them the opportunity to do so.

(4) Is handed software along with the textbook at the beginning of the year -- the teacher then assigns sections of the software for the student to amplify and supplement the textbook material.

(5) Uses a laptop. Some schools provide each student with their own laptop at the beginning of the year and the software is loaded onto each student's laptop for use both in the classroom and at home.

(6) In remote communities such as in Alaska and other rural areas, the instructional software is very useful for distance learning programs. The student is given assignments, studies the material from the computer and is given an exam before credit is given for the course work.

(7) Instructional technology is particularly valuable if a homeschooler is absent for a long period of time. The student can keep up with the standard classroom curriculum, if he is told what to study with due dates for specific topics.

(8) Is part of an after school math tutorial program.


So, if your teaching style is to stand at the front of the class and lecture, use this classroom software as a tool for your presentations or as a private tutor for those who missed your lecture or just don't get it. If your teaching style is that the students work at the computer at their own speed while you circulate to the ones who want or need your interaction, let that be the setting for learning. And, there certainly is nothing wrong with using a combination of these methods. After school program math students benefit from the "start anywhere" and "stop anywhere" menu-driven math topics.

Let's talk about assessments provided by this comprehensive instructional classroom technology...

-- In the "Arithmetic Series", the "Basic Math Series", the "Reading and Thinking Series" and the "Algebra Series By Chapter" test answers are only available to the teacher. After the student completes the test, the computer scores the test, gives a percentage and details which responses are correct or incorrect and which topics require further study. The score sheet, evaluation of weak areas, and the test the student just completed should be printed for recording and the hard copy provides a record of the student's work. The scores are automatically recorded by the computer -- at the end of the day, week, semester, the teacher/facilitator can access the computerized record of all students who took the assessments.

-- Each topic in the "Geometry Series" and "Advanced Math Series" software concludes with a practice test that contains all the step-by-step solutions which are detailed and instructional. These tests are learning math tools. The student will know immediately if a question is correct or not and can select to view the in-depth solutions. Most of the math teaching is in the solution steps of each question. This method is perfect for review for mid-term and final exams as well as S.A.T. and A.C.T. preparation.

-- If the more advanced software is to be used for grading purposes, the teacher prints the test without the solutions and the students take the test on paper. After the test is graded and recorded by the teacher, the student can then go over the returned test at the computer. This eliminates the need for the teacher to explain each and every question of the test. The age-old problem of never having enough time to explain ALL the answers on each and every test! The teacher can then re-collect the tests and have a permanent hard copy record.

Since having an educational software library for the computers in the classroom is a good thing, as schools accumulate software from different sources, year after year, it is imperative that the software be catalogued, so that both teachers and students know what to choose from. Simply listing "Algebra" is not good enough. Each and every topic in that algebra program should be listed. A sheet or even a booklet listing the contents of each piece of software that the school owns is necessary if the technology is to be used.

In Conclusion
Math Teaching Methods
Integrating Math Software into the Curriculum:

(1) The teacher/facilitator introduces selected math topics by computer (via LCD projector and/or individual work stations)

(2) Or, choose to have the math students work alone at their computer workstations. At the end of the time period, the facilitator collects the competency data. This classroom technology pinpoints competency skills not mastered which must be reinforced by the student returning to the appropriate study section in the software.

(3) Reinforce computer session with printed worksheets for classwork or homework.

(4) The student practices on the same math tutorial program until a satisfactory score is received on the review sections and the test sections.
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A Complete Computer Based Math Curriculum - "From Counting to Calculus"
Technology in the Home School Curriculum
Technology in the Home School Curriculum

Technology allows education to take place anywhere, any time, and any place. Using computers to enhance the home school learning environment is beneficial and necessary. For this reason, home school learners benefit greatly from our math software product line. Some home schoolers use our math software curriculum as their only learning tool and others use it to complement textbook and classroom work. This software is excellent to learn from scratch or fill in the "gaps". Learn elementary math through high school math with this educational math software.

Adding math software to your home school curriculum will benefit both students who require an extra boost to supplement their class work at school or the student who is a full time home school student. Home school math can be very challenging to teach at home. With this software, the parent/facilitator can direct the math learning while the math software will do the teaching, offer the appropriate practice problems with systematic interactive solutions, concluding with a test, which will record strengths and weaknesses. Home schooling is what you make it - whether it is a part-time or full time endeavor. The home school curriculum needs to include a serious math curriculum so that the homeschooler will be able to compete on par or above his grade level peers. This interactive comprehensive math software will assure that the homeschooler is missing no part of the math education curriculum.

Although our mission and vision has been to accommodate school math programs, home users may purchase our software as a download here at our website.
Select your home school math curriculum from the menu buttons on the left side of this page. We encourage you to make your home schooling experience as excellent as possible using MathMedia as your home school curriculum for a quality math education. The cost of one MathMedia software program equals about one hour of professional math tutoring time and each program has hours and hours of content equivalent to weeks of classroom time.
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Why Learn Algebra?<br>A discussion of the benefits of learning algebra
Why Learn Algebra?<br>A discussion of the benefits of learning algebra

The truth is that you really do not "need" algebra unless you plan to teach it or use it in a scientific profession. But before you put away your algebra books, let me give you some good reasons "for" learning algebra.

Algebra is a very unique discipline. It is very abstract. The abstract-ness of algebra causes the brain to think in totally new patterns. That thinking process causes the brain to work, much like a muscle. The more that muscle works out, the better it performs on OTHER tasks. In simple terms, algebra builds a better brain (as do other disciplines such as learning an instrument, doing puzzles, and, yes, even some video games). When the brain is stimulated to think, the hair-like dendrites of the brain grow more extensive and more complex enabling more connections with other brain cells. We often hear that we use only a small percentage of our brain's capacity. The study of algebra is a way to increase our use of this marvelous muscle. By studying algebra, more "highways" are "built" upon which future "cargo" is transported -- cargo other than algebra.

My favorite analogy is comparing learning algebra to the construction of the railway system in the United States in the 1800's. When railroads were built, surely those men never conceived of the items that would be transported on those rails more than a hundred years later. They could not have imagined home appliances and computer equipment traveling over that railway system. But they knew that building the transportation system was important. So is it with the study of algebra -- you learn algebra by transporting numbers and variables -- later, those variables will change and you will transport something useful for your purposes.

An example in my own life is the four-year break I took from math education when I founded an activities company in Hawaii. I ran the business myself -- from creating forms, organizing activities for up to 1100 people per week, with folks going off in multiple directions for horseback riding, snorkeling, land tours, helicopter rides, deep sea fishing, windsurfing, etc, etc, etc -- busses and vans were coming and going at half hour intervals and only one person missed their ride -- out of 1100 people -- not too bad! So what's my point? I think that the ability to organize a rational procedure for handling this kind of chaos came from my algebra background. You lay out the variables, design a procedure, and follow the procedure. It is an intense form of organization.

Having said all this... I do believe after 30 years of experience with students, that learning algebra is truly not for everyone. I once had a 9th grade girl in my algebra class who, when I fretted over her disinterested attitude toward algebra, kept reassuring me that she really did not need to learn algebra for her life. Today, she is a successful TV actress and every time I see her on the tube, I say, "Charlotte, you were right!"

Which brings me to the right brain / left brain discussion. An actress, actor, or artist of any kind is a "right brain" dominated person. These people usually do not have an affinity for algebra. For the creative mind, algebra is usually quite a struggle. Those making an attempt to learn algebra bring themselves closer to understanding the mind of a "left brain" person for whom math, science, and usually, languages come easy. Much of our public school curriculum is based upon the latter -- a "classical" education rather than an artistic "romantic" education.
"Learning algebra isn't about acquiring a specific tool; it's about building up a mental muscle that will come in handy elsewhere. You don't go to the gym because you're interested in learning how to operate a StairMaster; you go to the gym because operating a StairMaster does something laudable to your body, the benefits of which you enjoy during the many hours of the week when you're not on a StairMaster." -- Steven Johnson, "Everything Bad Is Good For You"
There are other disciplines, which will help build a better brain, but curriculum designers have chosen learning algebra as a universal "brain builder" along with preparing those strong left-brain students for careers in math and science.


Copyright 2003-2006 Illana Weintraub for MathMedia Educational Software, Inc. www.mathmedia.com

Teaching to the Test
Teaching to the Test

Our tests are driving our teaching. This is the message from coast to coast as pressure mounts to produce results and meet the Adequate Yearly Progress requirements of the No Child Left Behind (NCLB) Act. Is this good or bad, and can a good mathematics program survive in this kind of environment?

Accountability is important in mathematics teaching. As professional mathematics educators, we must be able to demonstrate that our students are learning mathematics. Furthermore, the reporting of group data required by NCLB sheds light on gaps and problems within the mathematics program, including whether any group of students is achieving or not. Nevertheless, the kinds of tests that many states require, and the ways that many schools prepare their students for these tests, have serious limitations.

On the positive side, if a test assesses important mathematics in ways that require students to demonstrate mathematical thinking and proficiency, the test might effectively support a comprehensive mathematics program. For example, the state tests used in Connecticut and Washington call for students to complete a variety of mathematical exercises, including open-ended problems designed to require more complex thinking than what is called for in many state assessments. Students in a well-balanced mathematics program anchored in understanding, proficiency, problem solving, and mathematical thinking are likely to do well on these tests with or without special preparation strategies.

However, many state tests fall short of this ideal. Some are based solely on content that can be tested economically in a multiple-choice format, which often encourages students to try out all possible answers to a problem rather than actually solving it. Furthermore, although some state curriculum standards may include complex and high-level mathematical ideas, testing students’ understanding of these ideas is not easy. This important content may get overlooked as teachers prepare students for items that are most likely to be included on the test. We must be cautious about the decisions that we make about students on the basis of such measures. No decision about a student’s future should be based on any single measure, particularly a large-scale measure with inherent issues of context, bias, and intended purpose.

In too many schools, teachers are expected to “set aside” their mathematics program and instead prepare students for the state test. This may mean weeks or even months of missed instructional time. If preparing for the test means practicing a few items to get used to the format, it might serve students well. Too often, however, test preparation also includes learning tricks and tips that may or may not prove helpful on the test. For example, some schools use materials built on “clue words” for solving story problems or teach other tricks about what to do if presented with particular types of problems. Students memorize such phrases and words as all together, more than, and total, associating each with a particular operation. This type of practice falls apart on two levels. First, it misleads students. For any clue word or trick, most of us could create a test item for which the trick does not work. Second, the time that students spend memorizing tricks or words without understanding the related mathematics is precious time they lose from instruction that could support their mathematics learning. Students are better served by learning the concepts behind the numbers and operations so well that they carry mental pictures of what addition, subtraction, multiplication, or division mean. Recognizing a mathematical operation in the context of a problem and knowing how to perform the operation are far better preparation strategies than memorizing tricks or a list of words.

One other method of teaching to the test is periodic benchmark testing. Some school systems expect students to take tests throughout the year that are similar in format and content to the state accountability test. This can be an appropriate application of datadriven decision making. However, to be effective, any such strategy should be weighed according to cost and benefit. How much information is gained in a usable and timely manner for guiding and improving students’ learning on a day-to-day basis? And what are the costs in instructional time and teacher time for planning, administering, interpreting and reporting results, and incorporating those results into the teaching process? These questions are essential to consider in any decision about testing and preparing for tests.

The best preparation for any test is teaching a good mathematics program well to every student. Even if the accountability test is a less-than-ideal measure, a strong mathematical foundation can prepare students to perform well. The reverse is not true, however. If we focus on test preparation at the expense of longterm learning, we may see short-term gains, but students are unlikely to be able to build on their learning from year to year. And some schools that devote excessive time to test preparation at the elementary grades may actually find, a few years later, that their middle school test scores have fallen. The bottom line is that professional mathematics educators need to be skeptical consumers of test-preparation programs and materials and knowledgeable judges of quality assessment practices that support students’ learning. Most of all, professional mathematics educators need to be outspoken advocates for students, raising our voices when testing practices may not serve the best interests of students.


Geometry is Ubiquitous
Geometry is Ubiquitous

Unlike Algebra, Geometry is all around us – everywhere! It is physical. It is tangible.

Start talking about geometry to your children early – they won’t know at pre-school ages that it is called geometry when you talk about shapes – the ball is a “sphere”, the can is a “cylinder” and the label on the can (take it off and show them) is a “rectangle.” Road signs are a perfect way to practice shapes… there are triangles, squares, octagons, and kite-shapes.

Understanding geometry in our environment can grow with the child from the simple to the complex. From pointing out the ice cubes in the ice tray and shape of the tray itself to the cross-section of an ice cream cone (if the cross-section is parallel to the ground, it forms a circle, if not then an ellipse). A hands-on experiment would be to take the cone and place the circle part on a flat surface with the point straight up. If you cut straight across the cone (parallel to the surface), you have a circle similar, but smaller, to the one on the bottom. But, if you cut the cone at an angle, you have an ellipse. This works well with clay.

Geometry in nature is a whole complex body of study. An interesting form in nature is the inside of a snail’s shell or the inside of the nautilus shell from the ocean – these are actually ever smaller right triangles with each hypotenuse becoming the leg of the next right triangle. Take a look at our MathMedia logo for an example of this. Then, take a look at flowers. The petals of a daisy are radii from the center of the circle. The possibilities in nature are endless. A wonderful visual of these types of examples in nature are in the Disney video called “Donald Duck in Mathamagic Land” – a delightful addition to any video library for all ages. Every time you watch it, you will discover something new.

TV’s in a store are measured on the diagonal – the length or width are found using the Pythagorean Theorem (a2 + b2 = c2, where c is the diagonal of any right triangle). Billiards requires a keen innate sense of geometry with the angles and arcs necessary to predict and cause the balls to end up just the way you want them (also in the Donald Duck movie!). The immensely practical necessity of being able to calculate the area of the floor of room to know how much carpet to buy or the area of the walls of a room to know how much paint to buy – it’s all geometry. Want to buy an aquarium for a fish collection – what’s the volume of the tank? How should we cut the pizza, the pie, the cake – how many sectors and at what angle? How do we find the shortest distance between two points when driving – which route is the most efficient? For years I could not parallel park my car until someone told me to back in at a 45 degree angle – how about that?!? Every moment is a lesson – every place is a classroom!

Putting up a tent (which is a “triangular prism” with a rectangular base) requires poles perpendicular to the ground to hold up the front and back doors. A parallel bar holds up the ceiling of the tent. If a circular water sprinkler is placed in the center of the lawn, a circular area will be watered, but most lawns are rectangular – so, either the edges will not be watered or the sidewalk and building will be watered – this problem has obviously been pondered by the manufacturers of water sprinklers who have designed more efficient sprinklers that go back and forth to water a rectangular lawn.

Any kind of carpentry work involves geometry – it’s all about angles and levels (a tool to measure parallels to the ground) and circles with their radii and diameters. Obviously, an engineer building a bridge had better know geometry as well as an architect who uses geometry and physics to make sure the building will stand the test of time. Look up the “Transamerica” building in San Francisco and talk about the shapes used in that structure! Another industry dependent on geometry is theatre lighting which is all about angles and so important to some actors that they bring their own lighting designers with them. Geometry is also used to measure the width of a lake, to find the height of a tree, a building, or a mountain. In many situations, Algebra is used to find the answers to geometric situations. These concepts are covered in a high school geometry course.

Read any periodical and notice the geometric representation summarizing the contents of the written article. A graph is a geometric representation of data. Newspapers will use bar graphs, line graphs, picture graphs…. Lots of analytical discussion there! Election years bring out the best graphs on a daily basis -- understanding these graphs allows us to understand the issues.

In conclusion, whether we know it or not, we live our lives through a series of geometric experiences.

Copyright 2004 Illana Weintraub for MathMedia Educational Software, Inc. All rights reserved.


What is the difference between Arithmetic and Mathematics?
What is the difference between Arithmetic and Mathematics?

My favorite quick answer is…
“Arithmetic is to mathematics as spelling is to writing.”

The dictionary definitions of these two bodies of learning are:

a·rith·me·tic
(1) the branch of mathematics that deals with addition, subtraction, multiplication, and division,
(2) the use of numbers in calculations

math·e·mat·ics
(1) the study of the relationships among numbers, shapes, and quantities,
(2) it uses signs, symbols, and proofs and includes arithmetic, algebra, calculus, geometry, and trigonometry.

The most obvious difference is that arithmetic is all about numbers and mathematics is all about theory. In college, I have a vivid memory of Linus Pauling¹ delivering a guest lecture and after scrawling theoretical mathematics all over three blackboards, a student raised his hand and pointed out that 7 times 8 had been multiplied wrong in one of the earlier steps. Pauling’s answer was, “Oh, that… numbers are just placeholders for the concept.” And, he just waved away the fact that the numerical conclusion was obviously not accurate. Now, that was in the sixties before the plentiful access to calculators and computers, so his point is even more valid today. Learn the theory in mathematics and the calculators and computers will keep you accurate. That said, it is very important to stress that calculators have their place in our children’s education but not to the exclusion of their understanding the material with their own brain.

I have a friend who was a math major at Northwestern University… a real whiz at math with future plans in theoretical math…. Until, one summer when he discovered business and how well he could think on his feet. He could perform complex arithmetic in his head faster than anyone else and with his advanced problem solving abilities he had unique ways of thinking. He now owns 16 stores, has 400 employees, and travels around the world doing business in multiple languages with translators and making deals with his extraordinary ability to manipulate numbers accurately and quickly in his head. His non-dependence on calculators makes him the successful businessman that he is.

To be sure, both arithmetic and mathematics are abstract. There is a passage in “Zen and the Art of Motorcycle Maintenance”² where a father and his 9-year old son are traveling cross-country on a motorcycle and as they pass through badlands country, the father is talking about ghosts to his son. His son then asks his father if he, the father, believes in ghosts. The father answers abruptly and quickly with “Of course, not!” Then, he thinks about it and he explains to his son that maybe he DOES believe in ghosts because he believes in the number system and it is a ghost. A ghost is non-concrete, can’t be touched nor felt, no weight, no mass. What are numbers? They are symbols with meaning attached to them… and, for some, connecting the symbols with the actual counting process is very abstract. When we look at ancient Egyptian numbers, they are meaningless symbols to us unless we have taken the time to study and connect the symbol with its intended meaning. (For a good history of math website, visit http://www-history.mcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html)

And, then, there’s my own experience with arithmetic, which I could do during elementary school, not very fast, but I could always do it. I didn’t “perk up” until algebra – for me, THAT was interesting and became more and more so as my education proceeded. But, arithmetic always “haunted” me in both my personal and professional life. In my personal life, friends were always giving me the check at restaurants to add and divide evenly among us – ugh, that was tedious and they just didn’t get that numbers were not my thing. Professionally, I have stood in front of the class and made some terrible arithmetic mistakes while doing complex math equations, but thank goodness for Linus Pauling, I didn’t take those mistakes too seriously. Its difficult for people to understand that you’re a math teacher but you really don’t care too much for numbers. It’s the problem solving and theories of math that I find fascinating.

Having spent most of my life teaching high school math, it was disheartening to hear my uncle say that what I am teaching is not “real math” – his world was teaching the math of particle³ physics to advanced graduate students at Stanford University. Only a handful of people in the world understood the papers he wrote. His definition of arithmetic is that it is structured and that math is not – in his mind, counting through calculus is arithmetic. The theoretical math in his papers was gibberish to me but symbolic prose to him – the “marriage” of math and science. From his point of view, until you get to advanced physics, the math is not “real” math. Perspective is everything.

In conclusion, arithmetic uses numbers and mathematics uses variables – each discipline has its own complexities and thought processes.

¹Nobel Prize Winner in Chemistry
²The author wrote autobiographically, wrestling with philosophical questions regarding the comparison of a romantic education and a classical education – feelings/emotions versus technology/rational thinking.
³Components of the nucleus of an atom

©2004 Illana Weintraub for MathMedia Educational Software, Inc. All rights reserved.
Creative Commons License
This work is licensed under a Creative Commons License.



<h5>Designing Schools for the Present Age:<br>Thoughts on an Editorial by Bill Gates</h5>
<h5>Designing Schools for the Present Age:<br>Thoughts on an Editorial by Bill Gates</h5>

Drs. Fernette and Brock Eide

In a recent editorial (speech), Microsoft founder Bill Gates demonstrated compellingly that our schools are failing both our children and our nation. These schools are "obsolete", because "they were designed 50 years ago to meet the needs of another age" in which "you could train an adequate work force by sending only a small fraction of students to college...." By contrast, "Today, most jobs that pay enough to support a family require some post-secondary education." As a result, "We have to do away with the outdated idea that only some students need to be ready for college...." However, our schools, as currently designed, are not capable of rising to this challenge, because "even when they work exactly as designed [they] cannot teach our kids what they need to know."

We could not agree more. We commend Mr. Gates' for his efforts on behalf of our nation's students, and for his willingness to think "outside the box" in addressing their needs. We also believe that to achieve the kinds of educational results Mr. Gates desires, our society must collectively think outside several boxes in addition to the one he has so ably described. Based on our experience as physicians specializing in helping children with learning problems, we would like to offer several observations on what children in the present age "need to know", and what current brain science suggests about the best ways to help them acquire this knowledge.

Schools Must Prepare Very Different Children For Very Different Lives

We agree with Mr. Gates that our schools should prepare most children to attend college, so they can obtain the advanced skills they need to compete in the modern workplace. However, this does not imply that all students must be prepared for precisely the same thing. When students reach college, they will not all pursue the same course of studies, nor will they all train for the same careers. Despite out-of-major requirements, each student will eventually focus on a single discipline such as engineering, mathematics, physics, art, literature, accounting, management, music, education, history, law, biology, chemistry, sociology, medicine, etc. These courses differ markedly because they are preparing students for remarkably different careers. Even within a given major, different students often have considerable freedom to choose advanced classes in areas of special expertise and interest, with particular class formats and professors that appeal to them. How do they decide which classes and courses of study to pursue? Largely on the basis of personal interests and an assessment of their individual strengths.

The broad diversity of collegiate education provides a fitting preparation for the diversity of the workplace. Mr. Gates own company, Microsoft, is a fitting example of the contemporary workplace in that it employs individuals with enormously varied skills and talents: software engineers who write code for word processing and email programs, visual artists who make designs for Xbox, specialists in sales, marketing, publicity, customer services, management, personnel, human relations, building design and maintenance, corporate governance, and on and on. Obviously, building a company with top-notch workers in each of these positions is not simply a matter of hiring generically well-educated persons then plugging them into randomly selected positions. Individuals are carefully chosen for each position based on their training and aptitude, in accordance with what each position requires. Some persons who are remarkably well suited for one position would flounder in others. Yet these differences between workers didn't just into existence when they showed up to fill out job applications, or even when they began to pursue differentiated curricula in college. The aptitudes and abilities that made them well-suited for their present adult work were present to a remarkable extent early in life, and were caused by variations in individual learning styles and favored routes of information processing and uptake.

Despite the crucial nature of these individual differences to success in college and in the workforce--and an overwhelming abundance of evidence that children differ dramatically in the ways they are best able to learn and express information--our present K-12 educational system fails almost entirely to take such differences into account. Our present system is overwhelmingly built around auditory-verbal (lecture-based) instruction and handwritten verbal communication. Yet this approach is optimal for only a minority of students. For most it is sub-optimal, and for those with primarily visual, spatial, or hand-on learning styles, and oral or visual communication preferences, it can be a disaster. In many instances, children that are actually quite brilliant can suffer chronic academic underachievement and even failure because they learn and think in ways that are not well served by their educational environment. Often these thinking and learning styles are not "impairments" or "abnormalities" in an absolute sense, but inherited learning differences that for some tasks can have tremendous benefit. Our own clinical experience is illustrative.

Because our clinic is located in Seattle we see many of the children of Mr. Gates' employees. Often the supposed "learning problems" that make them poorly suited for the overwhelmingly verbal learning environments in their schools are manifestations of precisely the same visual and spatial reasoning styles that have made their parents so successful and creative in their professional lives. Such problems are entirely unnecessary.

The Schools We Need: Teaching Each Child The Way That Child Learns Best

If our primary and secondary schools are to prepare children so they can excel in college and in the workforce, they must be restructured to reflect the same diversity of thinking and learning styles that are reflected both in the diversity of the workplace and in the college curriculum. While it is important to maintain minimum standards for communication, critical thinking, and problem solving, we must also recognize that students can perform these functions in very different ways. Our educational system must be flexible enough so that each student can pursue excellence in communication, critical thinking, and problem solving in ways that take advantage of individual strengths. More is at stake in this than simply workplace need: social justice is at issue as well. Research has consistently shown that there are variations in thinking and learning styles among different races and cultural populations, and that consistent failure to match learning preferences with appropriate teaching styles leads to predictable losses in learning achievement.

We are not advocating a system of tracking where students are shunted into strictly diverging educational pathways. Such programs close as many options as they open. Instead, we are advocating a more flexible approach to K-12 education that would allow students to pursue the core curriculum through a variety of routes that better fit and nurture their individual learning approaches. Such a curriculum would provide flexibility in both pace and approach, and would allow children to pursue their education through curricula that emphasize and expand their strengths, while helping them improve in areas of weakness. Rather than creating tracks that prevent some children from achieving basic competency in math, language, critical thinking, or problem solving, such a program would allow different students to achieve competency in these areas using learning approaches that are best suited to their individual styles of thinking and learning.

Some students, for example, are much better at processing verbal information through reading than through listening. For others the opposite is true. Some children find that they can listen better when they take notes. Others find it impossible to take notes and listen at the same time. Some students prefer visual or hands-on presentations of information to purely language-based instruction. Other students benefit little from visual or spatial sources of information. Similar differences are seen with math, where some students solve math problems using primarily verbal approaches, others with visual approaches, and others using spatial approaches. While all students need to achieve basic competency in these subjects, there is no reason to believe that all children will find their needs optimally or even adequately met using a single educational approach. This is true not only at the middle and high school levels, where differentiated curricula are used to some extent, but from the earliest days of school.

Many common educational practices and assumptions need to be reexamined if our schools are to better prepare students for college and an increasingly competitive workforce. Three seem especially ripe for reevaluation:

· The notion that all students should master a core body of information at the same rates and in the same ways, using identical educational materials and informational pathways. Basic skills can be acquired in many ways, and each child's instruction should be tailored to his or her optimal learning style.

· The notion that students are best educated in age-based cohorts. The rates at which children develop vary as greatly as their learning styles, and clustering by age makes no more sense than clustering by height or weight. The whole notion of grade-levels is equally questionable. There is no reason to assume that each year every child should make identical progress in all subject areas, nor is there any justification to prevent a child from making progress in one subject (e.g., math) because he is having difficulty in another (e.g., reading). Flexible, modular instruction could eliminate this problem.

· The notion that lecture-based classroom instruction should be the primary--even a major--route of learning for all students is unsupported by data on children's learning styles. For enormous numbers of children lecture time is not only a waste but a strong provoker of misbehavior and dissatisfaction of school.

K-12 education must be updated to take into account the variations in thinking and learning styles that are reflected in the diversity of the workplace and the post-secondary educational environment. It must incorporate the kind of flexibility of emphasis and approach that is found in college, so that students can pursue knowledge in ways that are best suited to their individual thinking and learning styles. To make these changes, we must leave behind the arrangements of an earlier era that employ antiquated technologies and ideas to meet obsolete goals. As Mr. Gates has clearly demonstrated, the needs of our students and the requirements of the workforce have changed greatly. It is now time to use our modern technological resources and more precise knowledge of the ways children think and learn to create a flexible, individualized, and rigorous education that will meet the needs of our students and our society both now and in the years to come.
Drs. Fernette and Brock Eide
Location:Edmonds, WA
Drs. Fernette and Brock Eide are physician-parents with a national referral practice for children with learning difficulties. They are strong advocates for neurologically-based approaches to learning and learning differences.
Their sister website is: http://www.neurolearning.com and their book on Neurolearning.
technology in the classroom Bill Gates explains designing schools learning styles

Test Anxiety
Test Anxiety

Generally, we all experience some level of nervousness or tension before tests or other important events in our lives. A little nervousness can actually help motivate us; however, too much of it can become a problem — especially if it interferes with our ability to prepare for and perform on tests.

Dealing with Anxiety The first step is to distinguish between two types of anxiety. If your anxiety is a direct result of lack of preparation, consider it a normal, rational reaction. However, if you are adequately prepared but still panic, "blank out", and/or overreact, your reaction is not rational. While both of these anxieties may be considered normal (anyone can have them) it is certainly helpful to know how to overcome their effects.

Preparation Can Help Preparation is the best way to minimize rationale anxiety. Consider the following:

Avoid "cramming" for a test. Trying to master a semester’s worth of material the day before the test is a poor way to learn and can easily produce anxiety. This is not the time to try to learn a great deal of material.

Combine all the information you have been presented throughout the semester and work on mastering the main concepts of the course.

When studying for the test, ask yourself what questions may be asked and try to answer them by integrating ideas from lectures, notes, texts, and supplementary readings.

If you are unable to cover all the material given throughout the semester, select important portions that you can cover well. Set a goal of presenting your knowledge of this information on the test.

Changing Your Attitude Improving your perspective of the test-taking experience can actually help you enjoy studying and may improve your performance. Don’t overplay the importance of the grade — it is not a reflection of your self-worth nor does it predict your future success. Try the following:

Remember that the most reasonable expectation is to try to show as much of what you know as you can.

Remind yourself that a test is only a test — there will be others.

Avoid thinking of yourself in irrational, all-or-nothing terms.

Reward yourself after the test — take in a movie, go out to eat, or visit with friends.

Don’t Forget the Basics Students preparing for tests often neglect basic biological, emotional, and social needs. To do your best, you must attend to these needs. Think of yourself as a total person — not just a test taker. Remember to:

Continue the habits of good nutrition and exercise. Continue your recreational pursuits and social activities — all contribute to your emotional and physical well-being.

Follow a moderate pace when studying; vary your work when possible and take breaks when needed.

Get plenty of sleep the night before the test — when you are overly tired you will not function at your absolute best.

Once you feel you are adequately prepared for the test, do something relaxing.

The Day of the Test To be able to do your best on the day of the test we suggest the following:

Begin your day with a moderate breakfast and avoid coffee if you are prone to "caffeine jitters." Even people who usually manage caffeine well may feel light-headed and jittery when indulging on the day of a test.

Try to do something relaxing the hour before the test — last minute cramming will cloud your mastering of the overall concepts of the course.

Plan to arrive at the test location early — this will allow you to relax and to select a seat located away from doors, windows, and other distractions.

Avoid classmates who generate anxiety and tend to upset your stability.

If waiting for the test to begin causes anxiety, distract yourself by reading a magazine or newspaper.

During the Test: Basic Strategies Before you begin answering the questions on the test, take a few minutes and do the following:

First review the entire test; then read the directions twice. Try to think of the test as an opportunity to show the professor what you know; then begin to organize your time efficiently. Work on the easiest portions of the test first.

For essay questions, construct a short outline for yourself — then begin your answer with a summary sentence. This will help you avoid the rambling and repetition which can irrate the person grading the test. For short-answer questions, answer only what is asked — short and to the point. If you have difficulty with an item involving a written response, show what knowledge you can. If proper terminology evades you, show what you know with your own words.

For multiple choice questions, read all the options first, then eliminate the most obvious. Unsure of the correct response? Rely on your first impression, then move on quickly. Beware of tricky qualifying words such as "only," "always," or "most."

Do not rush through the test. Wear a watch and check it frequently as you pace yourself. If it appears you will be unable to finish the entire test, concentrate on those portions which you can answer well. Recheck your answers only if you have extra time — and only if you are not anxious.

During the Test: Anxiety Control Curb excess anxiety in any of the following ways:

Tell yourself "I can be anxious later, now is the time to take the exam."

Focus on answering the question, not on your grade or others’ performances.

Counter negative thoughts with other, more valid thoughts like, "I don’t have to be perfect."

Tense and relax muscles throughout your body; take a couple of slow deep breaths and try to maintain a positive attitude.

If allowed, get a drink or go to the bathroom.

Ask the instructor a question.

Eat something.

Break your pencil lead — then go sharpen it.

Think for a moment about the post-exam reward you promised yourself.

After the Test Whether you did well or not, be sure to follow through on the reward you promised yourself — and enjoy it! Try not to dwell on all the mistakes you might have made. Do not immediately begin studying for the next test. . . indulge in something relaxing for a little while.


Cool Art <br><h6>...where art, science and math merge...</h6>
Cool Art <br><h6>...where art, science and math merge...</h6>


Click on the icon to see more cool art!


Learning Math - Bumps in the Road

In basic math education, students struggle with fractions when they have not mastered multiplication. We all know that math is sequential and when a student has "holes" in their math education background, they must be addressed by returning to the pre-requisites... that is the ONLY way students will feel the thrill of math success. These math lessons and math activities provide the proper sequencing to learn math or review for SAT prep, ACT prep or college placement exams. From basic math help through college algebra help, our educational software is here to assist the student in learning math.

In Algebra 1, students face the challenge of factoring polynomials, only to find out that once again, multiplication skills are imperative. Yes, we have the calculator but punching in 3x4 is a major waste of time when solving complex multi-step algebra problems. The calculator is wonderful for the study of trigonometry - but it slows students down when used for simple calculations that could have been practiced and drilled with the help of math lessons and math activities software which addresses not only the concepts of basic arithmetic operations but provides ample interactive practice followed by printable worksheets for reinforcement. Other Algebra 1 topics that require a solid arithmetic and basic math background include algebraic fractions and algebraic division.

In Geometry, there are several challenges. Learning how to write a proof in geometry is usually the first hurdle. We'll show you how to do it - how to think about it so that you keep it straight in your mind and write the proofs in an orderly fashion. The next big hurdle is learning all the properties of quadrilaterals - there is a lot to learn and practicing with various types of questions and problems enhances learning. The geometry software chapter on circles seems to always be a topic where students need as much geometry help as they can get. Additionally, for some reason the S.A.T. and A.C.T. have an over abundant number of circle problems. Right triangle geometry is a necessity for solving circle problems and being successful later in trigonometry. Math vocabulary is always explained.

Algebra 2 is a "buffet" of mathematics. Every chapter is a new topic having little or nothing to do with the previous chapter's topic. Conic sections have little to do with sequences and series or logarithms. Nonetheless, Algebra 1 skills are imperative.

Trigonometry relies heavily on a strong right triangle geometry background - trig is a very interesting course because it integrates so much of the prior math learning.

And, this is just the beginning of the world of math!
A Word About MathMedia Electronic Textbooks

As ebooks become more and more popular, some districts are replacing traditional hardbound textbooks with electronic versions of the same material.

As school districts introduce eBooks into their classrooms, teachers give students traditional textbooks to keep at home, and they use electronic books at school. Students use our electronic textbooks with Windows XP, Vista or Macintosh OSX either on their own school-provided laptops or on the school desktop computers.

In some states, districts are moving away from old-fashioned textbooks entirely. School officials say eBooks have several advantages over traditional textbooks. For one, they are easier to update with new information. One of the issues surrounding textbooks is once they are published, they can't be changed. MathMedia electronic textbooks are upgraded continuously with even the slightest changes provided to our customers. Historically, we have not charged for these upgrades.

The growth of student enrollments also is easier to accommodate with self-paced instructional tutorial math software since eBooks can be uploaded to laptops quickly, instead of waiting weeks or months for a shipment of new textbooks.

Instructional math software has become an alternative to traditional textbooks as the use of electronic curriculum materials in schools gathers momentum. MathMedia began publishing electronic textbooks in 1993 with the same quality curricular content expected from a tradtional textbook. We now provide the entire interactive math curriculum in the form of elearning with our electronic textbooks. We are constantly upgrading and improving our quality math instruction as the need for eBooks grows.
This math site provides mathematics software programs which are curriculum-based math education. These educational software programs are self-paced eBooks, interactive, and instructional with math help just a click away. Each mathematics software program provides in-depth instruction for math tutoring from which students can self-teach and practice math problems with lots of understandable math help. Learning math is in the detailed explanations of this math software and in the solutions to the practice math problems! MathMedia will be your virtual math tutor as well as provide curriculum math software for teachers to follow in an organized learning system. Printable math worksheets are available for each section in the "Arithmetic Series". Comprehensive pre and post tests are available for the basic math series. Mathematics education teachers can use these programs as math lesson plans to provide a cohesive course of instruction.

With this math help software, students practice classroom math topics or prepare for the SAT or ACT by working from a menu of clickable topics, introductions, examples, interactive math problems and step-by-step math help. When the student answers incorrectly, they are provided with an explanation as to why their answer is incorrect.

At this math site you will learn how to integrate technology into the classroom using MathMedia math lessons - Learning math with math media educational software works - teachers use this mathematics software as math lesson plans to introduce topics, practice problems with the class and use the math worksheets and tests for evaluation.
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