By Murray Bourne, 08 Nov 2007
Algebrator's marketing claim is:
You Type in Your Homework Problem. Algebrator does the Rest!
For students, this is very appealing. They can get a good grade by copying the solutions provided by the software. And this is without having to do too much learning...
Algebrator is a similar product to Microsoft's Math 3.0, which I reviewed recently (See MS Math 3.0 Review). The intended audience is similar for the 2 products: middle/secondary school and early college math students.
So let's move on to my road-test of Algebrator.
Problem 1 - Solving an Exponential Equation
I started with a random problem and I was not very happy with the results. I entered the first line and then repeatedly hit the "Solve Step" button to obtain subsequent lines.
The second and third lines, provided by the software, are fine.
You can click on the "Explain" button to get a popup explanation of what the software has just done for you:
For the 3rd line, the explanation said:
OK, fine. But where did the 4th line [the decimal value of log2(50)] come from? No explanation is given. I feel that this step would be a key stumbling block for most students. Since there is no "log base 2" button on calculators, this step sorely needs a Change of Base explanation.
Now, most students will have no trouble solving the 4th line above:
x + 1 = 5.64385619
Not a biggie - just subtract 1 from both sides and you are done.
But let's see what Algebrator does with it.
Say, what? Why are we going into fractions and then factoring the denominator? I immediately reach for the "Explain" button and get:
I'm speechless. Why take a perfectly simple decimal and mess with it like this?
The next steps are similarly remarkable for their inanity. We immediately drop the factored denominator (why?) and go back to the 100 million format and multiply both sides.
Then we expand out the brackets.
Are you still with me on this? I was feeling very tired by this stage and we still don't have a solution. Another few lines, now:
It stopped on this last line and refused to go any further. I still could not get my nice simple decimal answer. The explanation for the second last step says:
But there was no explanation for finishing at the last step.
Notice the "Previous" and "Next" buttons? What I presume they are supposed to do is take you step-by-step through the solution. But in fact, they did not do anything at all. I had to "Close" the explanation window and then request another "Explanation" for each step. It was pretty tedious.
Problem 2 - Solving a Trinomial
Next I thought I would compare Algebrator's solution for a simple trinomial (polynomial with 3 terms) equation. This is the same one I did on Microsoft Math 3.0 and I didn't like their use of the Quadratic Formula, since factoring is a better way to attack the problem.
Algebrator does it using factoring by grouping, but in a way that I feel would confuse students. I don't believe fractions are necessary in any of the steps. From the second line, we should go to the 5th line, then the 7th.
Now to be fair, they have to write the algorithm to allow for all possibilities. When the numbers are not 'nice', all these steps may be necessary. But then again, if the numbers are not 'nice', we should be using Quadratic Formula.
One of the toolbar options is "Check Solution".
Now, this seemed like a good idea to me - let the student enter their own solution and have the system check it. From a learning point of view, this is more desirable than spoon-feeding a (convoluted) answer to the student.
However, when I entered my solution to the above problem and asked it to "check solution", this is what I got:
Hmm - time to read the instruction manual.
[When reviewing software like this, I feel that the interface should be intuitive enough that you don't need to go looking at user manuals to find out what to do. For most software, you have to reach for the manual, but that's another story.]
It turns out that:
The [Check solution] button checks whether the generated solution is correct. You are probably not going to use this button very often because, when necessary, the software incorporates the checking into the solution process (i.e. when solving a radical equation). You can use the "check solution" button when checking is not performed automatically (i.e. when solving a linear equation, or after finding the inverse of a matrix).
So it won't check the student's own work.
A bit later I noticed another button "Check Your Work". Now we are getting somewhere:
This is the feature that I expected earlier. I checked my solution and happily, it said that I was correct.
Here is a user interface issue. If the "Check Solution" button is rarely used, perhaps it should be hidden so that "Check Your Work" is more prominent.
I know that checking user input has huge challenges, but Scientific Notebook does a reasonable job of it.
Some of the "Problems" and "Formulas" (pre-built examples in Algebrator) do allow some user input.
Algebrator is not capable of doing 3-D graphs, so I could not compare it with Math 3.0's 3D capabilities.
Let's try graphing a sine curve.
I tried to type in y = sin(x), but Algebrator did not recognise it.
So I went looking for an input tool. This looked likely:
Under "log" I expected to find maybe "loge" (which is there, as "ln") but there were other (somewhat unexpected) goodies including the trigonometric functions:
After choosing "sin", I expected "sin" to appear on the workspace, but alas, no. "Sin" now appears on that toolbar (in the place of "log") and then you have to click it (again) to get "sin( )" on the work space. This is not normal Windows user-interface convention.
Anyway, it is now possible to obtain a sine graph using the "Graph" button on the toolbar:
While the axis numbering is not very attractive, at least you can read it easily at all zoom levels (unlike the Microsoft Math 3.0 experience).
Zooming is quite easy - the cursor changes to a cross (+) and you can drag over an area of interest to effect a zoom.
One problem with the zooming feature is that you can only view graphs with equal x- and y- scales. There should be a rectangular view for graphs with a small y-scale compared to the x-scale in use.
I tried the inverse of a 4x4 matrix. It uses Gauss-Jordan Elimination:
The process was quite extraordinary - after 136 steps (I counted them) we get our final answer:
(The answer is correct. 🙂 )
This is where I have a fundamental issue. It makes no sense to me for humans to churn through a process like this (or to follow through seeing what a machine is doing for us). We should use software to immediately find the final answer, and spend the time that we save talking about what a matrix is, what it can do for us, why we use them and when we use them. The steps here are not important.
If (masochistic) math teachers still get their students to do Gauss-Jordan Elimination even for 3x3 matrices, I think they are wasting everyone's time (unless the students need to know the process for programming, or something).
- You cannot highlight, delete or edit if you have made a mistake in the first line of your problem. I had to start a whole new problem and type most of it again.
- Fonts are Arial - but they should be Times New Roman for variables for better readability.
- It does not make enough use of context help (right clicking to give options, etc)
- The blue-line/red margin workspace (designed to look like a paper-based workbook) is more distracting than helpful (the math does not line up on the blue lines, as you can see from the examples on this page).
- There is no calculus facility with this software
- Font sizes are big and it is generally easy to read everything.
- There are a lot of sample problems for students to learn from - possibly better than a textbook for some of them
- User input of math expressions (like fractions, square root) is quite easy.
- The "Explain" idea is good
- There is some clever programming that has gone into Algebrator - it is not easy to cater for a huge range of possible input problems
I made the same comment in my MS Math 3.0 Review: The best learning outcome of a package like this would occur if students were required to input each step, and then get feedback on their input. What we currently have is a "teacher on the side" approach, but it comes across as a "teacher at the front doing lots of stuff that I still don't get and I am just a spectator" approach.
No, involve the student at each step with prompts and with feedback. But avoid spoon-feeding since it is too teacher-centered and transmissionist.
MS Math 3.0 has a slick interface and includes calculus abilities. It also has 3D graphing, while Algebrator does not. With MS Math 3.0 selling for under USD$20 and Algebrator at just under USD$75 (with a 'search engine special' of $50), I know which one is better value.
However, I'm not about to run out and buy either product, because I don't feel that either one hits the 'sweet spot' for mathematics education.
Disclaimer: From time to time, Agebrator advertisements appear on IntMath.com.
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