Suppose I place you at one end of a long, empty room. Your task is to get to the door at the other end of the room. Simple, right? But what if I told you that this simple task is actually mathematically impossible?
Think about it – in order to traverse the whole room, you first have to get to the halfway point, right? You'll have to travel one-half of the way there. And before you can get to that halfway point, you have to travel one-quarter of the way there (halfway
to the halfway point). And before you can get to the one-quarter point, you have to travel one-eighth of the way there (halfway to the quarter-way point). Since you have to go half of each distance before you can go the full distance, you'll never actually
get anywhere. The task requires an infinite number of steps, and you can never complete an infinite number of steps since there will always be another one. Furthermore, in order to even start your journey you would need to travel a specific distance, and...
Today, the future depends on you as much as it does on me. The future also depends on educating the masses in Science, Technology, Engineering, and Math, otherwise known as STEM. As a new tutor to WyzAnt, I hope to instill the importance of these subjects
in student's lives, as well as, the lives around them.
Besides the fact that, "the average U.S. salary is $43,460, compared with the average STEM salary of $77,880," (Careerbuilder) these subjects are interesting and applicable to topics well beyond the classroom. Success first starts with you; I am only
there to help you succeed along the way. STEM are difficult subjects. Yet when you seek out help from a tutor, like myself, you have what it takes to master them.
Please enlighten me on students looking to achieve and succeed rather than live in the past and think I can't as opposed to I can. We can take the trip to the future together, one question at a time
This week's Math Journey builds on the material in
The Function Machine. If you have not yet read that journey, I suggest you do so now.
In The Function Machine we discussed why graphing a function is possible at all on a conceptual level – essentially, since every x value of a function has a corresponding y value, we can plot those corresponding values as an ordered
pair on a coordinate plane. Plot enough pairs and a pattern begins to emerge; we join the points into a continuous line as an indication that there are actually an infinite number of pairs when you account for all real numbers as possible x values.
But plotting point after point is a tedious and time-consuming process. Wouldn't it be great if there was a quick way to tell what the graph was going to look like, and to be able to sketch it after plotting just a few carefully-chosen points?
Well, there is! Mathematicians look for an assortment of clues that help to determine the shape of a...
Vi Hart, website: vihart.com
Sal Khan, https://www.khanacademy.org/math/algebra
Mamikon Mnatsakanian, www.its.caltech.edu/.../calculus.html
This journey is heavily inspired by the youtube mathematician Vi Hart, whose videos describing mathematical concepts through doodling in a notebook were the inspiration for much of my mathematical journeys series. I'll put a link to her video on this
topic at the end of the journey, and I highly encourage everyone to go check her out.
Let's talk exponents.
But to do that, first we should talk about multiplication. Multiplication is a shortcut for adding a bunch of the same number together. If I gave you:
5 + 5 + 5 + 5 + 5 + 5 = ?
You could just add them normally, treating each of those 5's as a size-5 step along the number line. But since each of these addition steps is the same size, a faster way to figure out the result would be to determine two things: the size of the step, and how
many steps we have. Then we can multiply the size of step (in this case, 5) by the number of steps. In this case, we have a total of 6 size-5...
I am happy to announce that all my students have passed the NY State Regents examinations, except one student. The subjects varied from Algebra 1, Algebra 11/Trigonometry, English, US and Global History and Living Environment. I am so proud of them.
Most of these students are students who struggled quite a bit. It was a long journey but one I would do again.
I am very proud of them as most of them will be graduating this year. The NY State Common Core examinations are next.
I would be honored in having the opportunity of working with students and parents. The education and success of students are very important to me and I would love to do what I can to help. I am a math and education major with an Associate's of Arts and
Teaching Degree from Lee College and I am seeking a teaching career. I live in the Baytown area and I am not able to provide my own transportation due to the fact that I have a disability which prevents me from driving, so I can only rely on public transportation
and I am limited to how far I can travel. Therefor, communication is much needed. I am available until 4:30 p.m. Monday through Friday. Anyone needing a private tutor, please contact me. I would be happy to help you at any time.
In the spirit of giving, starting on 11/29/2013, I will be offering a few brainteasers/ trivia questions where the first 3 people to email me the correct answer will receive a free, one hour, tutoring session in any subject that I offer tutoring for (via
the online platform)! That's right free! Get your thinking hats on everyone!
Andrew L. Profile
Area, Volume and Circumference equations:
Area of a Square
Area of a Triangle
Area of a Rectangle
Right Triangle/Pythagorean Theorem
Area of Parallelogram
Area of a Trapezoid
Area of a Circle
Circumference of a Circle
c=πd or c=2πr
Volume of a Sphere
Surface Area of a Sphere
Volume of a Cube
Volume of a Rectangular Solid
Slope of a line Equations
m is the slope
b is the y-intercept
y is a y coordinate on the graph (that coincides with the line)
x is an x coordinate on the graph (that coincides with the line)
I recently responded to a question on WyzAnt's “Answers” page from a very frustrated student asking why he should bother learning algebra. He wanted to know when he would ever need to use it in the “real world” because it was frustrating him to tears and
“I'm tired of trying to find your x algebra, and I don't care y either!!!”
Now, despite that being a pretty awesome joke, I really felt for this kid. I hear this sort of complaint a lot from students who desperately want to just throw in the towel and skip math completely. But what bothered me even more were the responses already
given by three or four other tutors. They were all valid points talking about life skills that require math, such as paying bills, applying for loans, etc., or else career fields that involve math such as computer science and physics. I hear these responses
a lot too, and what bothers me is that those answers are clearly not what this poor student needed to hear. When you're that frustrated...
While working on quadratic equations with students I have discovered a few techniques that are particularly effective. By far the most effective is to require the students to solve each one by all three methods ( factoring, completing the square and quadratic
formula ) for each and every problem rather than solving it only by the easiest way and to require the graph for each and every one. Of course, most quadratics are more easily solved by one particular method rather than the other two so I allow them to do
the easiest first and simply prove the result with the other two. This technique assures that the student can do it in each way and that they develop the skill of determining which is the “best” way for any particular problem. Another is to require students
to show each and every quadratic in both standard form ( ax^2+bx+c ) and in vertex form (a(x-h)+k). Still another is to explain and require students to be able to explain the derivation of the quadratic...
I was a fairly typical young person and, like my peers, counted down the days until summer. My mother was a math professor, so I never stopped doing math during the summer, but felt like other parts of my brain became a little mushy in the summer. Come September,
it was difficult to get back into the swing of writing papers and studying history and memorizing diagrams. I was out of practice and lost my routine. As an adult, I have almost continually taken classes, because I enjoy learning and find that from class to
class, I need to maintain a routine, i.e. a study area and a time of day that I complete my assignments. I have also found that reviewing material a week or two before the course begins helps me to start the class with more confidence and competence. I am
a big believer in confidence fueling success and I wonder if younger students practiced assignments in the week or two prior to return to school, if that confidence would help the transition to the school year...
I was excited on Tuesday, July 16th, 2013. This was my third meeting with this student and I finally had a breakthrough with him. On the first meeting it was clear that he saw Algebra I almost as a foreign language. I began with one of the test packet, and
had him do 10 questions and reviewed the questions he had done wrong. So this continued for a while, and of course sometimes he would say that he understood, but it was clear that he did not. Anyway, after reviewing the entire packet I began a teach and learn
session, in which I picked a variety of topics and had him practice various equations. After which I gave him a quiz.
He failed the quiz miserably, so of course he still did not understand. Anyway, I gave him another packet for homework. When I saw the student again, I reviewed with him, but still not much improvement, but at least he tried. I did the teach and learn session
again, of which some of the questions were from the previous session, and I gave him...
The Summer session has just begun. The stress has already begun to set in, but this week I had a break through with a few of the students. So this is my second week with a student who I am tutoring for both Algebra I and Earth Science. So far he seems stronger
in Earth Science but still needs much practice, before I can be very confident about his ability to pass the Regents exam in August. After the first session of Algebra, I walked away thinking about how am I going to get him ready by August 13th. I recommended
an additional session to the parents, but so far they have said no. I did several practice examples, and made the second session mainly a teaching and learning session. Then I ended the session with a quiz, but he failed :(.
So when I had to meet him again for Earth Science, my mind was swirling as to how I can help him, and will I at least be successful with this subject. When I checked the homework, there was a slight improvement but not enough to celebrate....
Infinity is a term with which most people are familiar, but few truly understand. Infinity is not an actual value, like the number 3 -- it is an abstract concept. In math terms, it is used as a "limit", where a value can approach infinity by getting continuously
larger, but it will never actually get there. Consider the act of cutting a pizza into slices. You can cut it in half, then cut those halves in half, then cut those halves in half, etc. As the slices get smaller, the number of slices gets larger; therefore,
as the size of each slice approaches zero, the number of slices approaches infinity. Again, in math terms, this means that as x approaches zero, the value of 1/x approaches infinity. Some go so far as to say that 1/0 equals infinity, but this would not be
entirely correct; nothing can actually "equal" infinity, since it isn't a value, but an abstract limit that can only be "approached".
Here's another example. You are standing...
When I was studying to be a teacher, one of the classes I had to take was Literacy in Secondary Education. Since the word
literacy is associated to reading and writing by most, it would strike many as a surprise that Math teachers have to take courses on literacy. However, literacy is the most practical and crucial aspect of ANY academic discipline, simply because it
involves the ability to read and write in said subject. For mathematics, it could not be anymore important. If you cannot understand the words that I am using, then it is almost as if we were communicating to each other in different languages.
So whatever subject you are studying, I suggest you learn its vocabulary.
As the helpful tutor that I am, I will share a list of vocabulary terms that was distributed in my literacy class to all of you so that you can check your own vocabulary. Keep in mind that this is considered to be the Mathematics vocab that one should know
by the time they finish high school...
Hello Miss Gil, I received a 96% in Global History. I was so excited to hear these words from my student! At first she did not want to be tutored. Her father dropped her off at the Library. So I told her that if she did the practice test, and did well, she
would never have to see me again. Well, she scored a 58%, and there were so many events and topics that she did not know.
We scheduled 3 additional three hour sessions. By the last session, her essays had improved and her overall score was an 83%. I told her that I believe that she can score as much as a 95% on the Regents Exam. She laughed and said "Yeah right". Well she scored
a 96% and I am very proud of her.
Humans have a tremendous capacity to learn and adapt. However, we consistently build barriers that hinder our natural ability to change and grow. Many people, regardless of age, perceive themselves as not being talented enough to excel at math and science.
They view math and science as the realms in which only scientists, engineers, mathematicians, and geniuses truly soar.
Nothing could be further than the truth. Sure, possessing a natural affinity towards these subjects helps. Yet, a supposed lack of talent does not prevent you from learning. The path may be more arduous. The journey may be longer. Nevertheless, you possess
within you the fire to endure. Willpower, dedication, self belief, and an open mind can compensate for any lack of ability.
Bruce Lee was a legendary martial artist, actor, and philosopher who continues to inspire millions with the sheer intensity which he pursued his endeavors. Frail, sickly, and small as a child, Bruce Lee overcame many physical...
Before I go run a marathon, play with my family at the pool, ride a roller coaster, head to the beach, or eat some serious amounts of ice cream, I will look back on the successful school year I have had.
I got to tutor over 15 students in Middle School, High School, SAT, and College Math...and even Chemistry! I watched GPAs rise for everybody-some were happy just to pass that College Math course to graduate, others enjoyed their hard earned As that were
brought up from the D level. I must say, that things did get crazy with exams at the end of the year, but it all worked out amidst our busy-ness.
My tutoring schedule is light for the summer, and I am hoping nobody waits until December exams to contact me! I want things to be done the right way...after all of the swimming, adventure, and ice cream, of course! :)
Now that students, teachers, parents and tutors have had a chance to catch their breath from final exams, it's time to make use of the weeks we have before school starts back. Consider all that could be accomplished in the next few weeks:
Areas of math that students NEVER REALLY GRASPED could be fully explained. This could be
elementary skills like adding fractions, middle school topics like systems of equations, or
high school areas like sequences and series.
Students could have a TREMENDOUS HEAD STARTon topics that will be covered in the first few weeks of school. Imagine your son or daughter being able to raise their hand to answer a question in the first week of school because they had worked
several problems just like the ones that the teacher is demonstrating.
ENORMOUS PROGRESS could be made in the area of preparation for the standardized tests (PSAT, SAT, ACT and more) that are so important to getting into a great college.