Try looking at cartoon images and making up your own images for math concepts. This is one I chose from Microsoft Word images to illustrate the concept of 'absolute value.' If the frog jumps up to ground level one hop, or if the boy jumps down to the frog one 'frog hop,' the distance is the same.
I assert that if I plot my frog hops on a graph intersecting at zero, with minus five frog hops to the left on the horizontal line of the ground level, and Zero in the middle, and plus five frog hops to the right on the horizontal axis (called the 'x' axis),
I can intersect a cross axis and label it y. The 'y' will be up and down like the boy and the frog here. So, if I mark off five frog hops with plus signs above the zero and five frog hops below the zero on the y axis, I can show where the frog is by marking the minus one frog hop down.
But the number of frog hops up to the boy and the number of frog hops down to the frog will be a positive number. The distance is the same. This is how I visualize absolute value.
Can you do a visual for your own understanding of a mathematical concept?
Again, as I say in other columns, the SAT practice questions on the College Board site and the Princeton Review books are excellent sources for ‘target practice’ using questions (and immediate explanations and solutions) for the type of questions in your nightmares. You can learn to be friends with the monsters under your bed by getting to know them and all about what makes them tick.
One tip that I always emphasize is to study with the solutions while you do the practice tests. Do many practice tests, checking the solutions and explanations every five or six problems so you will not 'learn' incorrectly. Keep visual images in your brain of the correct form of the questions so you do not have to 'learn' how to do the questions while you are taking the test.
During the last week of study before the test, DO take a test with the same conditions and time length as the real test. Find someone to proctor for you (maybe a tutor). Take the test in a room that is not filled with distracting TVs. A public library is a good choice of place. Go over the answers, but do not panic if you are not pleased with your performance.
Your performance on the actual test will improve from what you learn by taking the timed test. Use the problem areas for information and do some strategic planning for what to do about those areas. Notice the questions that you missed that you know. There will be some of those.
From now until the time of the test I will discuss some of the reasons you miss answers that you know. By the time you take the test, you will get these correct. The first reason is something you may feel is 'overconfidence.' 'I know this one for sure.' That is not really exactly why you miss it. You are not confident enough to give the ones familiar to you just due when you miss them.
Stay confident about every question. You have a strategy for every question. If you know how to do the question, then you do the question; AND you check it, all the way through. You do not cut it short. Every question counts one point.
For example, if you are doing a sentence completion with two blanks; and you find that 'C' completes the sentence with the right connotation for the word to complete the first blank and for the word to complete the second blank, you mark 'C' on your answer sheet; then you notice why A is not correct, why B is not correct AND why D is not correct.
Questions with two blanks to fill in are based upon the 'best' answer, and they often have two words that fit logically with a word such as 'yet' within the sentence making a contrast necessary. You know how to do this type of question. You know that the last answer is to leave it as it is (maybe), and you know that C fits.
- You quickly note the reason that it is 'best.'
- You check each other combination and note reason to eliminate.*
- You make sure you marked the correct number with a dot.
- You move to the next question quickly and follow the same procedure. You do NOT skip around.
What if you would like to rid yourself of these concerns once and for all? How about starting an SAT book club and beginning with the ‘Big Help, No Sweat, and No Fear Math Book’?
Within a couple of hours’ time on your own, reap amazing benefits from this Sparks Notes publication—also published by Barnes and Noble. Why gather a book club? Why read this at all? Used copies are available from Amazon.com and from Barnes and Noble on-line. You can order new copies from other bookstores for $7.95 plus tax, new. But I even got a used copy along with another order on-line and did not have to pay shipping fees. (Plan a book order with the group or with your family.)Read!)
Your points on standardized tests multiply exponentially when you begin to understand some building block ways to study. You are actually building the skills that the standardized tests are measuring, and you are having fun at the same time. I’m not kidding. Games, book clubs, spelling bees, movies, practice tests together—all of these strategies are fun!
If you wonder how some parents, grandparents, and guardians can afford to pay thousands (and thousands and thousands) of dollars a year to send their children to private school, do you ever wonder why they send their children to private school? If you live in a family that would never send a child ‘away’ to school (like mine), have you ever considered some of the benefits of a boarding school experience?
Now, I did go away to college. I went to the college of my choice, the University of Georgia; and I lived on the campus in Athens, Georgia. I still remember this time of my life as being as good as I ever imagined it would be. I was living only about an hour away from my parents, and I was college age by then. I could drive. But I did not have a car. My cousin went to college at the same time, and she had a Mustang. We traveled together. That is probably why I drive a Mustang today. I connect the car with good times!
I can tell you that the children in boarding schools do get homesick, and they would like to be closer to their parents and siblings much of the time. However, the private schools where children attend school when their parents pay large sums of money for their children’s education and care are nothing like those awful boarding schools in novels (unless maybe you include A Separate Peace). The school where I worked has beautiful grounds, including a river, and some private schools have swimming pools, tennis courts, and horses. All of them have dining rooms. Most of them have drama facilities and productions, sports teams, and lounges with widescreen TVs.
None of this meant much to my student who missed being home in his native island country, but he was glad when he got his diploma (and so was his family). Too, we read many books in that class! He and I read The Hobbit aloud. He has many talents and abilities. Private school with individual instruction or private tutoring uncovered all of his strengths for his own benefit.
The reason parents, grandparents, guardians, and/or mentors are able to talk the students into going to private school (and into going back the next year and the next!) is because the private schools are, in general, more relaxing, individualized places to be than public schools. As an individual student, parent, grandparent, guardian, teacher, or tutor, however, you can take some of the strategies from these expensive environs and make your own version. There are ways to take advantage of flexible programs close to universities, cities, and rural areas. Students develop talents while horseback riding, gardening, and dancing.
How do the private school teachers manage students who have severe problems and issues to make significant progress in short periods of time? It is true that private school programs often turn conditions around for a student to reach individual goals within weeks, months, and high school years. Can you aspire to do the same without all those resources?
If you do not have the money, the scholarship, or the inclination to find out for yourself by attending private school, visit with me here. Begin to notice what you would like to know and where you do want to be.
For example, one of the advantages I mentioned earlier is the one-on-one attention. On this website, I am addressing my reader in this 'one-on-one' conversational style. When you read, you are 'listening' to the author. The more you find the books and articles to satisfy your interests and curiosity, the more listening and reading will be a normal way for you to learn. Meanwhile, you can find an attentive mentor in a number of places. Due you your interests, you may need more than one. Be open to the search for mentors and guides. Some day you may be one yourself!
Another pleasant part of education can be your surroundings. If you must be in a tight spot somewhere, can you spend some time outside? Is there a swing? One of the least expensive and most useful items of furniture I have ever had was a redwood picnic table. If weather is too unpredictable for outdoor work, can you find a place for a picnic table and the benches? The table top provides sturdy, wide study and project area. If not, what about a smooth board that you can take to a chair with arms. When I was a child, my father would sit in an upholstered chair and put a smooth board across the arms where he would write his engineering papers and draw his diagrams.
Throughout my tutoring, columns, and books, I say again and again that there is nothing like individual tutoring. What I do not say every time is that you may be that tutor--even for yourself. I am. You can extend the dynamics by tutoring someone else or forming a book reading partnership.
But if you need to have a tutor, and you do not have a way to be with a mentor right now, stay with me here. Reading is the way to tutor yourself right through every standardized test, every scholarship application, every diploma, every certification...everything you desire.
I will help you. You are not alone.
The secret is in individual attention, especially in individual attention to designing study according to your personal interests and strengths, while using what we know about learning styles and the brain to develop our different types of intelligence. Even in private school, the one-on-one tutoring is the strongest element for an individual student.
3 again:
- Building vocabulary is one fast, sure, efficient code-building method to increase points on standardized tests.
- Reading with guidance and groups is another way.
- Understanding the reasoning behind the specific standardized test is another way to add points.
When you understand the purpose, you predict with more precision. Prediction is a heavy aspect to reading comprehension. Reading comprehension ability will achieve points for you on standardized tests even when you are reading in unfamiliar subject matter.
Here is how to read--faster than I can write it down or say it in words--to show you what happens in the brain while reading something you 'know' ahead of time on a test. You can see from this how much easier this is with every word you know and with every concept you know.
Hopefully, you will also see how learning reading comprehension skills, including root words and patterns, can help you to answer questions on an aptitude test (such as the Scholastic Aptitude Test, SAT), even when the question does not look familiar to you.
Example:
The following three sentences are from the No Sweat No Fear Math Book. These sentences are on page 108. I am a good reader. I took graduate courses in reading:-) But when I look at these three sentences, I don't 'see' anything on the 'blackboard' or the 'movie screen' of my mind.
I need an image somewhere! I take a pen and jot something down.
When I write, I IMMEDIATELY understand the three sentences by making the pattern I am always
What I plan to do: Follow the directions of the three sentences to see if I can make the two fractions that I already know are equal follow these directions to 'prove' they are equivalent.
Notice that to jot down two fractions to test this, I managed to recognize the meaning of the following words:
'cross-multiplication'
'fraction'
'equivalent' (hint: equi = equal)
'product' (answer in a multiplication problem...talk about words used in different ways!)
'numerator' (top part of a fraction...I know this because of the 'd' in the 'down' part of a fraction)
'denominator' ('down' part --bottom part of a fraction)
'vice versa' (turned around the other way)
All that list up there--Look! Those are the words I noticed when I glanced at the three sentences.
Here are the three sentences:
Read this out loud or read it 'out loud' in your head:
We already talked about using cross-multiplication to check whether two fractions are equivalent. (Multiply the numerator of the first fraction by the denominator of the second and vice versa, and then compare the two products. If the cross-multiplication products are equivalent, then the fractions are equivalent.I teach gifted students in English and challenged students in reading. I am not bragging. I am trying to tell you that this is difficult for me to read, and it is not on a high reading level. So this is what I do, and this is what I would do if I were working this as a problem on a test. Do this with me! I pick up a pen and write –making a drawing of a sample of the images I know from the words.
Important point: If I AM taking a test and this is really mysterious, I will mark the best answer to whatever question is posed with a dot to mark the place and move on to something more familiar. Every question counts a point. What I am trying to convey here, however, is that I can use strategies to 'attack' this quickly. These sentences are familiar to me. I understand them.
Even so, they are a transition from what my mind usually processes. I am an English teacher, yet I teach science, math, social studies, and other categories of studies more than the average teacher (or student) because I am a tutor for exceptional children and for students taking standardized tests.
What I want to show you is how I have learned to use my left and right brain in a balance. These are learned strategies. My original talents and interests were focused in the literary areas. I know you can do this transition because I do it all the time. There is pleasure in it because you actually feel your mind shift into noticing certain things.
What do I know? I know what “cross multiplication” means. I know what a fraction is. I know the denominator is the number on the bottom of the fraction (‘d’ for down) and the numerator is the number on the top of the fraction (the ‘other’ one from the ‘down’ one).
I know that ‘product’ in mathematics is a term that is different from the meaning of product in a supermarket. What is ‘product’ in mathematics? It is the answer when you multiply!
I know that equivalent is a word that has ‘equal’ in it. I am just going to consider it as ‘equal’ or =.
So when I look at this paragraph, I jot down two fractions that I, personally, know ARE equal:
4/8 and 1/2
I try out doing what this paragraph says to do.
You will notice that I am a “wordy” person.
What can I do to use only numbers and symbols here?
Here is something very useful and quick for me.
Maybe I can look at this paragraph that is unfamiliar to me and transform it into something I can recognize how to check something!
I know that 4/8 is equal to 1/2 so can I use this in the pattern of that unfamiliar paragraph? Let’s see.
All of those words and here is what I jot down: 4/8 = 1/2
Multiply the numerator of the first fraction by the denominator of the second and vice versa (the other way around) and
compare the two products (answers).
If they are equivalent (equal =),
then the fractions are equivalent.
4 x 2 = 8 (numerator of the first fraction times the denominator of the second)
Other way around:
1 x 8 (numerator of the second fraction times the denominator of the first fraction) equals = 8
The fractions are equivalent.
Okay, by plugging in two fractions I KNOW are equivalent, I see that I can prove whether two fractions are equivalent by cross multiplying. If I can write this out neatly, I can remember a way to prove whether two fractions are equal (or 'equivalent').
Hmm.
This is on page 108 of the No Sweat No Fear Math Book ...The book has a little story line that should yield some vocabulary words, too.
The purpose of the Scholastic Aptitude Test (SAT) is to measure your aptitude. The definition of aptitude is so close to the definition of intelligence quotient or ‘IQ’ that students (and parents and even educators) begin to imagine that this is a set number that can be measured. The fact is: You have some control, possibly a wide margin of control, over this number.
You remember my general theory is: You are the star of your own story. Nobody else is the judge of your aptitude, your potential. In my opinion, your aptitude may be one of the MAIN areas under your personal control, along with your spirit and soul. Do not give someone else the right to judge your intelligence to any extent that affects your personal opinion of yourself. Take control of the reins yourself and use these standardized tests as part of your portfolio of self-inventory, just one more part of metacognition, knowing what you know.







