All my grade 8 & 9 students (10 students) passed the Algebra Core Regents exam. Only one student had to retake it in August and she passed with an 83%. In June she scored 53%. My two Trigonometry students passed the Regents, but only 2 out 4 students passed the Geometry Regents exams.
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On Friday my TV broke.
Kind of a bummer, but we'd had it for many years and it was time for it to go. Now we needed to get a new one, so we headed out to the store. In the process of our search, we realized that our old TV was at the extreme smaller end of the TVs they now sell, so we were going to need to buy a bigger one. We found one we liked, that was only slightly bigger than our old one. The big question, though, before we plunked down our hard-earned cash, was this: would it still fit on our entertainment center?
Our current TV was sold as a 40-inch model, and the one we liked was 43-inch. However, TVs are measured across the diagonal, not the width, so we needed to know what the actual width would be. My hubby got out a tape measure, and I got out a pencil and paper. He measured our 40-inch TV across the diagonal and found that 40 was actually just the screen size; the full diagonal with the frame was 42.5 inches. We knew the new one's frame was no larger...
As the school year ramps up again, I wanted to put out a modified version of a Memo of Understanding
http://en.wikipedia.org/wiki/Memo_of_understanding for parents and students. It seems each year in the rush to get through the first weeks of school parents and students forget the basic first good steps and then the spiral downwards occurs and then the need for obtaining a tutor and then the ‘wish for promises’ from a tutor. Pay attention to your child’s folder or agenda book. A student is generally not able to self regulate until well into high school. Some people never quite figure it out. Be the best person you can be by helping your child check for due dates, completeness, work turned in on time. Not only will this help your child learn to create and regulate a schedule, it prevents the following types of conversations I always disliked as a teacher ("Can you just give my child one big assignment to make up for the D/F so they can pass"; "I am going to talk to...
Suppose, one have two parallel lines given by the equations:
y=mx+b1 and y=mx+b2. Remember, if the lines are parallel, their slopes must be the same, so
m is the same for two lines, hence no subscript for m. How would one approach the problem of finding the distance between those lines?
First, if one draws a picture, he or she shall immediately realize that if a point is A chosen on one of the lines, with coordinates (x1, y1), and a perpendicular line is drawn from that point to the second line, the length of the segment of this new line between two parallel lines give us the sought distance. Let us denote the point of intersection of our perpendicular line with the second line as B(x2,y2).
What do we know of point A and B?
First, since A lies on the first parallel line, its coordinates must satisfy the equation for the first line, that is,
Algebra 2/Trigonometry: http://www.nysedregents.org/a2trig/home.html
Math A, Math B, Integrated Algebra, Other Math: http://www.nysedregents.org/regents_math.html
Earth Science: http://www.nysedregents.org/EarthScience/
Are you preparing for the PSAT, SAT, & ACT quantitative exams?
So are we!
My name is Paul J. and currently I have 3 students in Vero Beach, Florida who are preparing for these exams this summer. We are looking for motivated students to join us for private lessons. A limit of 5 students has been placed, so there are only 2 positions available.
Lessons will cost $30 an hour, and we plan to do 2 one hour lessons a week for 5 weeks starting in early.
Our goal is to score well enough to compete for scholarships such as Bright Futures and the National Merit Scholarship.
If you are interested, please message me on my WyzAnt Profile.
Reading Formulas can make or break how a student comprehends the formula when alone - outside the presence of the teacher, instructor, tutor, or parent.
Formula For Perimeter of Rectangle: P = 2l + 2w
How To Read: The Perimeter of a Rectangle is equal to two (2) times the Length of the longer side of the rectangle (L) plus two (2) times the Width of the shorter side of the rectangle (W).
When is reading formulas like this necessary? At three particular moments, reading this formula in this manner can be effective.
When students are initially learning what the formula means
When student are learning what it means when they should already know (remediation).
When students want to remind themselves (basics learning study skill habit)
Remember, Formulas at their introduction are complete statements or thoughts. Students cannot and will not recall complete thoughts or statements...
A wise man once told me: "You can continue to beat your head against that rock, but you will not chip the rock, your head (on the other hand) will be deformed." I guess I should have seen it coming, my being summarily fired from a tutoring job - The parent (in this case the mother) demanding extra "busy-work" for her son between sessions, the lack of discipline, on the student's part (especially his inability to do homework or speak to his subject teacher) and his continual lack of attention during sessions. The call came, "You are not coming here anymore, Billy Ben (not his real name) ONLY got an 81 on his Geometry test. We want top performance, 95 or better, YOU failed." Did I tell you that this student, previous to my seeing him, was working on a solid average of 40? So, it was over. Had I failed? I'm not so sure. First, I didn't take HIS test, and second, knowing the student as I did, I actually thought that an 81 was pretty good and we might have...
I have been working with a few students who are ready to learn math much, MUCH faster than allowed by the traditional classroom model in which math is taught over 6 to 8 years. Based on this experience I believe that many students as young as 4th grade and as old as 8th grade (when starting in the program) can master math in 2 years from simple addition through the first semester of Calculus, with Arithmetic, Algebra 1, Geometry, Algebra 2, Precalculus, Probability, Statistics, and Trigonometry in between.
This is significantly faster than the traditional approach and is enabled by a combination of one-on-one teaching and coaching and a variety of media that I assign to students to complete in between our sessions. This is a "leveraged blended learning" approach that makes use of online software, selected games, and selected videos with guided notes that I have created that ensure that students pick up the key points of the videos, and which we discuss later. The result...
Occasionally, parents demand “worksheets”. I have a tepid reaction to that request. First, I personally believe that a tutor is not meant to be a “worksheet provider”. Sometimes parents want their child to be “drilled” into learning. Those parents may feel that the only way to acquire skills and/or knowledge is to force it into their child’s psyche by repetitious action – worksheets. Most parents do recognize that a tutor has excelled in a particular area of study, but some still trust education to the worksheet. A thesaurus lists as synonyms for “tutor” the words: coach, educator, guide, mentor, and instructor. (Nothing about “worksheet provider”!) Nevertheless, parents still get “hung-up” on worksheets, and demand “lots of them”. From a purely educational stance, worksheets can be used only one way. Worksheets are generally considered to be convergent materials by professional educators.Worksheets lead students to believe that there is only a single correct way to use them, and worksheets...
I hear a lot about math teachers from my students, and while every teacher is unique, some comments are repeated over and over. By far the most common one I hear is that their teacher didn't really explain something, or was incapable of elaborating when questioned and simply repeated the same lecture again. As a tutor, my first priority is to make sure the student understands the material, and if they're still confused, to find another way to explain it so that it makes sense. In order to do that, I need to have a thorough understanding of the concepts myself, so that I am not simply reading from a textbook but actually explaining a concept. In my years of tutoring math, I've developed a point of view and approach to math that I refer to as “teaching the concept, not the algorithm.”
An algorithm is a step-by-step procedure for calculation. The term is used in math and computer science, but the concept of an algorithm is universal. I could tell you that I have an algorithm...
Here are 48 of my favorite math words in 12 groups of 4. Each group has words in it that can be thought of at the same time or are a tool for doing math.
What are your favorite math words? If you aren't sure, search for "mathematical words" and pick a few.
Proof of the Assertion that Any Three Non-Collinear Points Determine Exactly One Circle
This is an interesting problem in geometry, for a couple of reasons. First, you can apply some earlier, basic geometry principles; and secondly, you can choose two different strategies for solving the problem.
The basic geometry underlying: any three non-collinear points determine a plane, somewhere in 3D space. Once that has been done, imagine that the plane has been rotated into the x-y plane, which will make the problem much easier to solve!
The two strategies for solution are: (Proof A) actually solve to find the circle. This is equivalent to finding the center of the circle (finding the equation of the circle is simple from there). But, you actually have to do some math to get this! If, while doing this, there is no possibility to obtain other values for the coordinates of the center of the circle, you have proved the assertion as well as obtained a method (and perhaps...
Mathematics is the only language shared by all human beings regardless of culture, religion, or gender.
Pi is still approximately 3.14159... regardless of what country you are in. Adding up the cost of a basket full of groceries involves the same math process regardless of whether the total is expressed in dollars, rubles, or yen. With this universal language, all of us, no matter what our unit of exchange, are likely to arrive at math results the same way. Very few people, if any, are literate in all the world's tongues—English, Chinese, Arabic, Bengali, and so on. But virtually all of us possess the ability to be "literate" in the shared language of math. This math literacy is called numeracy, and it is this shared language of numbers that connects us with people across continents and through time.
With this language we can explain the mysteries of the universe or the secrets of DNA. We can understand the forces of planetary motion, discover cures for catastrophic...
In high school geometry, we learned of the perfect right triangle. Both sides and the hypotenuse are integers (whole numbers). The perfect right triangle shown was 3, 4, 5. (3 sq + 4 sq = 9 + 16 = 25 = 5 sq). I wondered if there were others.
Years later, I seriously searched for other perfect right triangles. I began with a list of the squares of whole numbers and the difference between one square and the next (the "delta").
Discovery #1: The series of deltas = the series of odd numbers. I looked for deltas which are squares. Since the series of deltas is the series of odd numbers, the square of every odd number is the difference between two squares.
Discovery #2: Every odd number 3 and above is the side of a right triangle. Implication of Discovery # 2: Since there is an infinite number of odd numbers, there is an infinite number of perfect right triangles. Next, a formula for finding the other sides and hypotenuse of a right triangle was worked...
Several of my current Geometry students have commented on this very distinction. This has prompted me to offer a few possible reasons.
First, Geometry requires a heavy reliance on explanations and justifications (particularly of the formal two-column proof variety) that involve stepwise, deductive reasoning. For many, this is their first exposure to this type of thought process, basically absent in Algebra 1.
Second, a large part of Geometry involves 2-d and 3-d visualization abilities and the differences in appearance between shapes even when they are not positioned upright. Still further, for a number of students, distinguishing the characteristic properties amongst the different shapes becomes a new challenge.
Third, in many cases Geometry entails the ability to form conjectures about observed properties of shapes, lines, line segments and angles even before the facts have been clearly established and stated...
Although I enjoy geometric constructions, as in solving geometric problems with the equivalent of a string, I find that many students have little to no interest in them. I particularly like learning about how ancient cultures such as the Egyptians used them to design Pyramids where the error in the corners are about 1/300 of one degree, much more accurate than can be seen and even more accurate than almost all houses built today. Although learning about their history is interesting there is not a lot of places to apply this knowledge in the modern world, i've solved some problems in surveying with geometric constructions but there are always more advanced CAD methods which can also do the trick; which is why I was happy to find Euclid The Game.
This is a straightforward game that applies all the basic principles of geometric constructions into a fun little game. Although it doesn't require the attention to detail the Egyptians would have...
The majority of the students that I have often have the same problem -- they aren't grasping the information fast enough or they aren't really able to follow the lessons a teacher gives.
Sometimes, teachers aren't adaptive to every learning style for each student in their classroom. However, know that each student has the capability to learn math on their own. It is just necessary to have key characteristics to make it successful.
Every math student should have:
open communication between themselves and their teacher (inside and outside the classroom)
Always try to study outside of your home or dorm room. In our minds, those are places that we relax at and it can be difficult to turn your mind off from the distractions to study. Public libraries, universities, coffee shops, and bookstores are the way to go. Some...
As you may know, I am a big fan of the well-known author and brain specialist, Dr. Daniel Amen. He mentions in several of his books that Physical Exercise is good for the brain. I have read of research studies that showed a clear correlation between IMPROVEMENT in students' test scores in math and science, and their level of physical activity (for example, when math class followed PE class, the students had significantly higher scores). Maybe we should schedule PE before all math classes in our schools. What do you think about that idea?
This morning I read an online article on the myhealthnewsdaily site, entitled "6 Foods That Are Good for Your Brain," and another article about how Physical Exercise helps maintain healthy brain in older adults too. The second article, "For a Healthy Brain, Physical Exercise Trumps Mental Workout" was found under Yahoo News.
The remainder of this note is quoted from that article:
Regular physical exercise appears to...