One of our new members has developed a website which he describes as follows:
Okay, I am not a math wiz (my son, who is getting an A in Geometry in 7th grade is the math wiz of the family). I am the CEO (not by choice) of a startup and the tech geek.
The product is based on a patent we filed 10 or so years ago. In that time we have built the software and tested it on over 3,000 students. The software takes a math problem type (an algorithm written in our proprietary language) applies various constraints to it and generates a unique problem (we call them probes). That is presented to the user with an open ended answer box and another box that says "show next step".
If the user can't solve the problem they can "show next step" and they will be presented with either
1) A Strategy for solving the problem
2) A Socratic question related to the problem
3) The answer to the Socratic question
4) The problem broken down (simplified by taking the next step)
An example of this would be:
Algebra & Functions: solving with functional notation f(x)
Let g(x) = x(x - 1) and g(m + 3) = 12
Where m is a positive integer.
What is m.
The brute force way to do this problem is by foiling and solving a quadratic. This is tedious and prone to carelessness, but this is the approach we will take here. There is an alternative, which is an extremely elegant method for solving this problem, and which we will allude to in the final comment.
What algebraic expression is g(m + 3) equal to?
Replace x in the expression x(x - 1) by x = m + 3
g(m + 3) = (m + 3)(m + 3 - 1)
4) Which can be reduced to:
g(m + 3) = (m + 3)(m + 2)
simplify: (m + 3)(m + 2) = 12
Foil the left side and set it equal to the right side. Subtract 12 from both sides (which sets the equation equal to zero).
m2 + 5m + 6 = 12
7) m2 + 5m - 6 = 0
How do you solve the above quadratic?
First factor the quadratic and then set each factor equal to zero
(m - 1)(m + 6) = 0
11) Setting each factor to zero:
m = 1 and m = -6
12) Therefore the only positive value and hence the solution:
m = 1
13) Final Comment
A much faster and more elegant solution is to consider the properties of consecutive integers.
Now, we have released a version of the product on-line to allow students to study the 50 most difficult problem types that are on the SAT/ACT exam. And to introduce the product and it's use we have made it available for free with certain limitations.
1) You only get 50 problem types
2) The problem types are presented to you randomly
3) We store no data on you, so you can get no reporting
4) We limit your time to 10 minutes per problem type
Clearly we think the product is useful (we have been watching it work for over 3000 students in the time we have developed it), and we want to showcase it. The product is NOT brain dead or crippled. It works just like it would if someone were paying for it (with the four limitations removed).
Okay, so I told you a bit about the product, gave an example and if an admin will PM me I will be more than happy to provide the URL and if the admin approves, I'll be happy to share the link here. In addition, I will be more than happy to answer any questions that there are (here in a public forum) as best as I can [remember I'm the tech geek (and an old fart who put the 250th computer on the ARPANet) and my partner is the math wiz who has been teaching it since the abacus was invented (also an old fart, well not that old, but older than I).
Imagine a student getting 10 minutes of free tutoring on each of 50 of the most difficult math problem type questions asked on the SAT/ACT exam.
College Entrance Exam Math Prep - Free
Imagine it no more.
I would like to thank Mark and the administrative team here for allowing me to share our work with you. If you have any questions, comments or concerns about the site, please feel free to start a thread and then PM me and I'll make sure that I follow up on it.
So, please view and beat up on College Entrance Exam Math Prep - Free
and if you want to know about us and our philosophy you can read up on us at: EduCAD Learning Solutions
And when we get the blog up and rolling, we will be sure to mention this site as a resource for those working on their SAT/ACT Math.
Again, thanks to all for the warm welcome, and I promise I will stay engaged here (well as engaged as I can based on my skills).