Over the past couple of years, I have found myself more and more often recommending graphing calculators for Algebra 1 students. This wizard instrument, capable of far more than I myself know how to tap into, works well with my tutoring style. However, I
have seen firsthand what the consequences can be when students learn to use them without guidance. So many times, I have worked with high school upperclassmen and college students who cannot perform basic operations with fractions, graph by hand, evaluate
an expression by hand, or perform addition and subtract with positive and negative integers because they became reliant on their calculators before ever properly learning the skills. These students usually lack the time or motivation to go back and learn how
to do the skills by hand. Their courses move along rapidly and they need to spend their tutoring time keeping pace with the more advanced ideas. This is particularly unfortunate because these are the same skills they...
I recently sent this as advice to one of my clients having trouble with linear systems of inequalities. I thought I would share it here on my blog for students, parents, and tutors who have use for it.
EXPLANATION OF LINEAR SYSTEMS OF INEQUALITIES
A system with regular lines (the ones with equals signs in them that you have done before) shows the single point where the two lines cross each other on the graph. The X and Y at that point are the two numbers that make the equal sign true. For instance,
with the equations 3 = 5X +Y and 10 = 2X -Y, the answer is x = 7/13 and y = 4/13 because if you plug those numbers into both equations you get true statements, 3=3 and 10=10. The point (7/13, 4/13) is the point where the two lines cross each other. Inequalities,
where you have "less than" or "greater than" signs work the same way. But, instead of getting a point where the equations are true, you get a whole area on the graph where they are true. So,...
Psssst....parents, you have access to a free tutor and you don't even know it! As a tutor always on the lookout for more business, I am not sure I should give away this highly confidential secret, but here goes. You know your son in Prealgebra who needs
my help because he recently started getting Ds on his tests? And you know your other son, the one in Algebra II that needed tutoring to prep for finals last semester? You may not be aware of this, but son #2 knows most of the material giving son #1 problems.
Not only does son #2 have the ability to help the younger one, he would also greatly benefit from working with his dear sibling. He would stay on top of the review material he tends to relegate to the far reaches of his mind and start understanding the concepts
he knows on a deeper level that relies less on memorization. Now, let's not get carried away. I am not saying that my professional services are unnecessary for either one of them - I have a lot of expertise and experience...
Should I get a tutor? Will it help my child? These are some of the most common questions posed to tutors by parents of students struggling in school. Tutoring can be expensive and difficult to schedule so parents must decide whether the time and money will
be well spent. Instead of relying on a crystal ball, use these factors to help make the decision.
1. Does the student spend an appropriate amount of time on homework and studies?
While it can help with study skills, organization, and motivation, tutoring cannot be expected to keep the student on track unless you plan on having a session every night. If you can make sure the student puts in effort outside of tutoring, she will be more
likely benefit from it.
2. Does the student have difficulty learning from the textbook?
If this is the case, the student will probably respond to one-on-one instruction that is more personalized. A tutor will help bring the subject to life and engage the student. A good tutor will...
One day your child needs help figuring out 4 + 7 and then, seemingly overnight, is asking for help with quadratic equations. As a parent, when you decide your child’s academic struggles are out of your league and that you need to hire a tutor, it is important
to remember you still have a big effect on the outcome. Tutoring is expensive and it is in your best interest to get the most out of the process for your child. From the beginning, take an active approach to make sure the tutoring experience is a successful
1. Establish regular sessions and stick to them.
By setting up a routine, you can help your child stay ahead of trouble and stay on track. The tutor can use the textbook and class materials to work ahead when possible. This helps students develop a sense of confidence in class and gives them pre-exposure
to the material in a less demanding setting so that they can return to it in more depth the next session. Aim for once a week for elementary and junior...
As a tutor working with my students, I have encountered a recent trend in education that I call "spiraling." The idea behind this tactic is that, instead of breaking subjects and levels of work into distinct categories, the curriculum introduces students
to concepts and skills early on and then circles back to them through the years, adding more in-depth knowledge each time. For instance, instead of learning everything about quadratic equations in Algebra 2, a math student might first encounter them in a limited
basis in Pre-algebra, a little more in Algebra I, and then even more in Algebra 2. This method has obvious benefits.
First, classes can move quickly through the material because the focus is on exposure and familiarity instead of mastery. Second, studies on learning have shown that people retain information better when it is learned in spaced sessions. Third, it encourages
students to think critically and creatively about the concepts at hand. Because...
Artists recognize that different painting mediums achieve different visual effects. However, if you take a good look at a photograph, or the scenery around you, you will notice that different aspects resemble different light and color sensations. It makes
sense then that to achieve the variety we see in real pictures, we could use different mediums when we paint. I have found that if you get creative and avoid a purist standpoint, it is possible to create an impression using watercolor paints, oil paint, and
acrylic paint in the same painting.
Decide where you want to use water color paints and apply those first. They work great for soft background light, still water, and spaces of sky. Use the water color paints anywhere you want transparent, luminating, solid color. Look at your photograph and
identify areas where you want to create this effect and then apply water color paints there in your painting. In the painting shown here, I used them for the background light...
Have you ever been in the middle of a drawing or painting only to find you've run out of room for a head, fence, or other important part? Everything had looked nice in the drawing as you put it on paper, but suddenly, it becomes obvious that the proportions
are all wrong. The grid system can be tedious and often leaves extra pencil markings on the paper. This simple technique is a "halfway" solution that takes a little practice but can be used in any drawing or painting to get those proportions correct whether
you are working from a photograph or live landscape.
Hold your pen or pencil against the photograph lengthwise and measure how many "pencils" the major feature of the photograph is across as well as up and down. If you are drawing a live landscape, hold the pencil out in front of you at arms length and measure
in the air. Make sure that there after, you always hold it at the same distance.
Decide how many times bigger you want the figure...
In my experience, teachers often recoil at the saying, "Those who can't do, teach." Indeed, the underlying tone implies that teachers are nothing more than those people who lack the ability required for a certain field of expertise. However, I like to ignore
the intended insult and interpret the expression as a compliment and as an excellent description of an effective tutor. Every time I have struggled in an academic subject, the experience has given me insight into all the wrong twists and turns you can take
in the process of trying to unravel a maze of skills and concepts. As a tutor, this invaluable insight now lets me meet a student in the familiar depths of his confusion and travel with him out to the light of understanding. To those for whom a subject comes
naturally, this territory of incomprehension exists only in theory. Sometimes, explaining the correct approach in detail does not penetrate a tutoree's confusion. By understanding "not understanding,"...
Those dreaded midterms are looming, waiting to bring dread and frustration into the hearts of students everywhere. There's no need to be afraid of not passing. Certain study tips and techniques will help you out with any test, whether you're studying for
one of those killer exams, the ACT/SAT, a certification test for work, or need to help your seventh grader prepare for a social studies quiz. Use these tips to make studying for tests more fun, efficient, and effective.
Decide where to study for the test. If you have difficulty concentrating, pick one place as a study place and refrain from watching TV, eating, sleeping, etc in that area to train yourself to concentrate. If you can concentrate well, vary your study places.
This will increase your ability to remember the information in the test setting.
Use assigned textbook or power point material to make an "easy" outline. Don't worry about formal outlining. Just write down chapter titles, headings, and...
Multiplying monomials by polynomials in algebra can be tricky, especially when it comes to keeping negative and positive signs straight. Here are some guidelines to getting it right. The key is to do signs, then numbers, then variables.
1. Step 1
Write the monomial to the left and the polynomial in parenthesis to the right.
2. Step 2
Think about each sign before you think about multiplying the numbers. If the monomial is positive and the first term (chunk) of the polynomial is negative think "positive X negative = positive" and write the correct sign down in your answer. Write a negative
sign for a negative or a plus sign for a positive (expect for the very first chunk of your answer where no sign is needed if it is positive).
3. Step 3
Once you have determined the first sign, multiply the number in the monomial and the number in the first term (chunk) of the polynomial. Write down the answer after the sign.
4. Step 4
Many students and parents hire tutors unaware of what they should get out of the tutoring process. After finding a tutor, over the course of you or your child's first few tutoring sessions, there are key things you can evaluate that will indicate whether
the tutoring experience will be successful.
The tutor should be asking the tutoree questions and involving him or her in the session. If the student is falling behind in school due to lack of engagement on the part of his or her teacher or text, a tutor who falls into the same category will not help.
If your child is the one being tutored, don't be too obtrusive, but listen from the other room to hear if the tutor asks questions and encourages involvement from the student. Some students will initially be shy but, if you have hired a good tutor, you should
begin to hear them begin to speak up more in response to questions after a couple of tutoring sessions.
A good tutor should be able to give the student, parent,...
Because each student has a unique learning style, I try to make my tutoring sessions as individualized as possible. Most of the time, I can use my own observations and interactions to figure out what my tutorees need. However, sometimes direct student/parent
feedback is invaluable. I have found that this type of feedback not only improves tutoring sessions, it helps strengthen and maintain the line of communication between me as the tutor and the student. Here is the feedback questionnaire that I send out to students
to fill in and return. It contains separate sections for parents and students. However, adult students can fill out the whole form. If you are a tutor, feel free to adapt the form and use it however you wish in order to enhance your clients' tutoring experiences.
If you are a parent or student, look through the questions to get an idea of the types of feedback you can give the tutor with whom you work in order to maximize the benefit of your lessons.
The first thing to do when teaching a frustrated student is to listen to, and acknowledge, their frustrations. Let him or her vent a little. If you're working with young children, they probably won't even realize or communicate that they are frustrated.
Therefore, the first thing to do is say "you're very frustrated with learning ________ aren't you?" If you are in a group situation, take the student aside to talk to him or her about it so he or she doesn't become embarrassed.
One of the best things you can do when teaching frustrated students is to watch them one-on-one in academic action and observe every little detail when they think, write, and speak. Often, students are lacking very particular, previous basic skills. By watching
them work, you can identify where they are going wrong and notice common patterns. For instance, I have tutored many algebra students whose frustration stemmed from an inability to deal with negative numbers. Once this problem was...
As a private tutor, I've had many parents resort to hiring me as an "enforcer of homework time." In other words, a stranger that holds power over a reluctant student and has the paid time to watch over his or her shoulder. Getting kids to do homework can
be one of the most frustrating tasks parents face. When kids don't get their homework done, they end up lacking basic conceptual understanding, and report card grades begin to slide downhill. To prevent your kid's academic struggles from escalating, it might
be time to put some new tactics into practice. If you are faced with a kid that isn't doing his or her homework, try keeping these things in mind.
Don't let kids get too tired before they start their homework. I've seen many kids struggle to keep their eyes open following after-school activities. When tired, kids cannot concentrate, have a difficult time following directions, and cannot learn new concepts.
Keep activities parred down to what...
Completing the square is one of the most frustrating and easily forgettable algebraic processes. The quadratic formula is complex but straightforward and easy to use once memorized, so why even bother using "completing the square" to find the solutions
to a quadratic equation? Besides the obvious answer that the teacher is probably requiring it, completing the square is useful for other things in algebra such as putting a parabola in vertex form or writing the equation of an eclipse or hyperbola. Therefore,
it is good to practice these steps.
Make sure the leading coefficient is 1. This is the number in front of the X squared. If it isn't 1, divide everything in the problem by the leading coefficient. For instance, if you have 3 X squared, divide everything by 3. If you get fractions, don't panic!
You will just have to take your time to work with fractions through the problem.
Move the constant (the plain number...
French grammar can be tricky. To form the future tense (not the simple future tense learned later) in French, it is important to know that the irregular French verb "aller" literally means "to go," but it is also used for forming the future tense. In
fact, we use a form of "to go" for the future tense in English as well. One would say "I am going to swim." To form the future tense in French, you need two verbs side by side.
Write in the French subject (the name of the person OR thing that will be doing the action or a subject pronoun such as "je" or "ils.")
Conjugate the French verb "aller" in terms of who will be doing the action. This is the "future" part of the two verbs. For instance if it is one girl, you would use "va" and if it were a group that included yourself, you would use "allons," the nous
form. Place the form...
Graphs are a staple part of any science or social science class because they help interpret information and relationships between an independent variable and a dependent variable. In fact, knowing how to label a graph is so crucial for college and future
careers that it often crops up on standardized tests such as the SAT or ACT. By learning how to correctly label a graph, you can avoid losing points on assignments and develop problem solving skills that will be useful for a long time to come.
Begin by labeling the bottom and side (the axes or variables) of your graph. To do this, you have to know that the independent variable goes on the bottom and that the dependent variable goes on the side. The bottom variable or independent variable is like
the x axis in algebra. This is the "input" or the thing that the experimenter is changing. So, think about the information. It is often easier to figure out the dependent variable first.Which variable "depends"...
"Veni, Vidi, Vici!" is probably the most famous Latin expression. It has come to represent victory ever since Caesar himself first boasted with it. What most people don't know is that this phrase would have actually been pronounced "Wenee Weedee Weekee."
Doesn't sound so tough that way does it? Ancient Latin is pronounced differently from both our English interpretations and Medieval Latin. For instance, many people are surprised to learn that Mel Gibson's "The Passion of the Christ" was filmed completely
wrong with Ancient Romans speaking Latin that wouldn't exist until hundreds of years later! Learning how to pronounce Ancient Latin from a textbook or other source can be difficult. Here are some tips to keep from making the mistakes when it comes to pronouncing
In Ancient Latin, pronounce "c"s hard like our English "k"s and do not make the "s" sound. For example, "Cicero"...
Whenever I ask someone about their favorite teacher or tutor from the past, the description always involves an engaging character who knew how to draw students into the material by asking questions. Indeed, asking questions is one of the most essential tutoring
tools. Now, I must explain that by asking questions I don’t mean the “what is the answer to this?” type of question.
Instead, good questions might encourage students to relate concepts to ones they might already know. For instance, if a student is struggling with a Spanish vocabulary word, you might ask “Does this word look like any English words you know?” or “Does this
word feel like it is positive sounding or negative sounding?” Asking questions is a great way to create mental paths that teach students, not only what the right answer is, but different ways that he or she can try to reach it in the future. By the time you
start talking about the solution, the student has several links to it lingering in...