With the school year winding down, arranging for summer break Math time starts!
1) Not practicing newly acquired math skills will allow for knowledge to erode
2) Not practicing previously acquired math skills will expedite knowledge erosion
3) Not having other non-math course work will allow for
- focusing on math remedial work, or
- getting a jump on next year’s math academic growth.
Math needs are the same per subject, whether the learning setting is for advanced placement, over-age/under-educated, middle school, high school, or Veterans. BUT, the instructional approach should be different. Differentiating the approach to each student’s situation addresses learning styles (do we not all have different learning styles, which, if catered to, maximize results?).
Also, a subtle,...
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, the answer...
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 about...
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There are several points in grade school that involve a critical shift in the thinking that is required in the school work. Parent's should be aware of these points as they navigate through the abyss of raising a school-aged child and supporting the child as he/she moves forward through the grades.
3rd Grade - The third grader is transitioning from whole number thinking into understanding the concepts of parts. They are exposed to fractions, decimals and percentages. This is a major paradigm shift. Students are also exposed to long division at this point. Supporting children in this phase requires an emphasis on helping the child conceptualize whole things being split into parts. In addition to homework support, tutoring, and supplementary work, parents should introduce cooking chores to children at this time, and make them follow a recipe that has precise measurements. Reading comprehension and writing is also an issue here...
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...
Come with me on a journey of division.
I have here a bag of M&Ms, which you and I and two of your friends want to share equally. I'm going to pour the bag out on the table and split it into four equal piles. For this example, “one bag” is our whole, and the best number to represent that whole would be the number of M&Ms in the bag. Let's say there were 32. If I split those 32 M&Ms into four equal piles and asked you how many were in one pile, you could certainly just count them. But a quicker way would be to take that 32 and divide it by the number of piles I'd made, which in this case is 4. You'd probably write that as:
32 ÷ 4 = 8
So there are 8 candies in each pile.
Seems easy enough with a large number of M&Ms, right? But what if there were less candies – what if our “whole” was less than the entire bag? Well, for a while we'd be okay – if there were 16, for example, we'd do the same thing and come up with piles of 4 instead of...
Today's post is about learning styles. One of the most important things that helps teachers provide better instruction is the knowledge of a student’s learning style. My belief is based upon the teachings of noted educational theorist, Dr. Howard Gardner. Dr. Gardner posits that there are “multiple intelligences,” that define our individual learning styles and complement each other (by working together) through our learning processes. His 1983 book, Frames of Mind, detailed his initial findings in this area.
In my educational practice, I attempt to identify my students' learning styles by doing extensive diagnostic testing in the very beginning. In my tutoring classes this may consist of having students to write a paragraph or two in the target language we are studying or work some basic math problems. Diagnostics also include inquiring about student preferences, because students generally do better in the areas that they like. After diagnostics, I set a plan that...
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...
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...
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.
Reading Formulas can make or break how a student comprehends their formula when alone - outside the presence of the teacher, instructor, tutor, or parent.
Formula for Area of Circle: A = π * r^2
Ineffective ways to read the area of a circle formula are as follows:
Area is π times the radius squared.
Area is π times the radius of the circle squared.
Area of a circle is π times the radius squared.
A equals π times r squared.
>>>> Why are these ways NOT effective ways to read this formula? <<<<<
1. Students will recall and repeat what they hear their educators say.
2. If students recall letters (A) versus words (Area of a Circle) they will not realize the connection with word problems.
3. Half way reading the formula (radius versus radius of a circle) creates empty pockets or disconnects in...
One of the reasons students of math struggle at test time is that they fail to quickly identify "problem types". Let's say you're taking an Algebra exam and you see something of the form 4x2 + 8x -5 = 18 and are required to solve it. You should either be thinking about factoring the equation or if that doesn't work easily, using the quadratic formula. Typically, once a student identifies the problem type, he or she is 80% of the way there. Then it's usually just standard arithmetic (watch your sign changes + or - ).
Solving math problems is really a process in itself and involves: assessment, identifying the problem type, looking for other complexities, i.e. there may be several steps along the way, doing the actual arithmetic and finally checking your answer for logic. Does it make sense that Fred took 16 hours to reach Chicago from New York? If it doesn't, go back and look at your problem -- you probably missed something.
Be disciplined in your approach...
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 corrected,...
I do believe that any subject can be learned if one decides that they want to learn that subject. Its been my way of thinking throughout my career. If you want to learn and have an open mind, then it can happen!
Positive thinking is what it takes to succeed in this life. Believe in yourself and it will happen!
A question that I have heard many times from my own students and others is this: "When am I ever going to use this?" In this post and future posts, I'm going to address possible answers to this question, and I'm going to also take a look at what mathematics educators could learn from the question itself.
Let's look at the answer first. When I was in school myself, the most common response given by teachers was a list of careers that might apply the principles being studied. This is the same response that I tend to hear today.
There is some value in this response for a few of the students, but the overwhelming majority of students just won't be solving for x, taking the arcsine of a number, or integrating a function as part of their jobs. Even as a total math geek, I seldom use these skills in practical ways outside my tutoring relationships.
Can we come up with something better, that will apply to every student? I say that...
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...
This is my all time favorite website for Math worksheets.
Hi all algebra students. I found a great website, algebra-class.com that has an algebra calculator that you can use to check your homework. It has been very useful in our algebra classes as a tool for homework help.
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...