28 Jul

Okay, I am going to head over to Khan Academy and give you a blow by blow review from how user friendly it is to how well it teaches mathematics.

When I first get on the site, it clearly directs me where to go if I want to learn Algebra.   So I will click on the word Algebra.  However, after that first click, now I am bit more confused.  There is a place that says Introduction to Algebra so let’s start there.  Now I get some choices about history of Algebra and the Why’s of Algebra.  When reading another review, it commented about the lack WHY in Khan videos.  It appears that maybe they are trying to make up for some of that.  My problem is that this information needs to be integrated into each lesson not as a separate section.  It is like this is written here for an educator.  I don’t know that I see a student accessing the “Why we do things to both sides,” but let’s take a look.  After watching all these videos in this section, I give the overall videos a thumbs up!  However, the organization gets a thumbs down!  This should be considered a regular lesson for all of Khan academy for every topic.  For each topic, they should start with what they call the “WHY,”  I call it good teaching.  From there, they can move into some more procedural practice videos, and finally student practice videos.  The organization could look like this:

1. Solving One Step Equations Lesson – here would be their “Why Videos” Relating to that
2. Procedural videos for solving One Step Equations – this can be what I have traditionally seen on Khan Academy, many videos of people just solving problems
3. Practice for the student (starting with easier problems and getting more difficult)
4. NOW – Khan would move into the next developmental step
5. Solving Two Step Equations Lesson – the rest of their WHY videos here.
6. Procedural Videos for students to watch (starting with easier problems and getting more difficult)
7. Practice for student (starting with easier problems and getting more difficult)

Let’s move on and see what else Khan has to offer…

So here is where things go down hill for Khan.  They just had these nice videos that did a good example of explaining the concept of solving one and two step equations.  Following down, the next thing on that page (which seems like what I should click on since it follows those videos) is something about Yoga… I decide to skip the Yoga and click on something that has some math terms in it so I click to the third section.  Here I get a list of options of videos to watch.  Now remember, I just learned some very basic ideas of how to solve an equation using a balance scale.  After getting confused by Yoga, I see Variables Expressions and Equations.  This is sort of random lecture that doesn’t really link me into anything and makes some medium jumps and has some confusing pieces in it.  The lesson is trying to teach you to substitute in a number to a variable expression but instead of building it in a developmental approach they jump to x+y+z=5 and start letting y=2 and z=3 and solving for x.  None of it is done in an organized fashion.  Letting that go, let’s just skip to the next video, maybe it will get better…

The next one says solving inequalities and equations through substitution (I picked #3).   Well, this involves solving equations, we did some of that but we have never talked about inequalities yet….  The problem says, “If r is the number of hot dogs Joey can eat in a minute, and N is the total number of hot dogs he eats in the contest, if Joey can eat 6 4/5 hot dogs per minute, how many hot dogs does he eat in the 10 minute contest?”  They give you the equation N/10 = r.

Here is the basic explanation they give to start, “He eats N hot dogs, and the contest is 10 minutes so we divide that by 10 and we get the number of hot dogs on average he eats.  So if Joey at 6 4/5 hot dogs per minute so they are saying r is 6 4/5, so they are saying, what is N going to be?”  Hmmm… did you follow that?  Did that explanation make you UNDERSTAND anything about the problem?  Do you get it better?  If the instructor just says, well plug in r= 6 4/5 and solve for N, have you learned anything?  One suggestion he gives to solve the problem is to “just try out numbers.”  Wow, that is a great idea (sarcasm).

Summary so far:

1. You want to learn Algebra
2. Go to site and find Algebra page – easy
3. Great starter videos on how to solve one and two step equations
4. After finishing those and maybe you can solve 2x -3 = 9 (by the way, only learned how to do it with numbers that work out)
5. You see something about Yoga
6. You skip Yoga and go to the next lesson and find problems like this hot dog problem that explains nothing, makes little sense, and is totally out of place.

Let’s leave behind “Introduction to Algebra” as that is clearly too hard and see if plain old “Algebra” is easier.

We choose linear equations, the first choice, and what is a variable, that sounds nice and basic.  Here we go, this is a much better place to start.  The lessons here so far have been basic and sequential.  A few minor problems are noted.  For example, when teaching how to plug in to evaluate an expression:  4n^1 + 2n^0.  (Carrot here means raised to the power of).  When “teaching” that anything to the first power is equal to itself, the instructor used a variable as their example x^1=x, this is teaching at a more abstract level rather than showing things such as 4^1 = 4 and 7^1 = 7 which is concrete and more easily grasped by the beginning student who just learned about x’s 5 minutes ago.

They begin to substitute in numbers with 2 variables and include positive and negative numbers.  In their example, they end up with -10 – 15.  They write the answer is -25.  The very first comment shows the lack of a strong teacher in these videos.  The first comment says, “why is -10-15 = -25, I think it should be 5.”  She continues to say, “Wouldn’t it have be -10–15 to get -25.”  Good teachers already know the mistakes that students will make and include this information into their lectures.  If I were to make this video, I would always quickly reteach older concepts whenever possible.  In this case, I would remind students that when dealing with positive and negative numbers and subtraction, you always want to do “switch change.”  Change the minus to a + and the sign of the number after that to its opposite.  -10-15 = -10 + -15, this makes seeing the -25 much easier for students.

Going back to their user interface.  One comment asked about practice problems.  The answer was that the lessons with the stars are the practice problems.  Having this written somewhere on the site would be helpful as it wasn’t clear to me either until I read the comment feedback.  On the practice problems, I do like the hint buttons and that you can ask for several hints if you get stuck.  However, I don’t like that the practice problems are not developmental.  The ideal situation would for them to start off easy and after you get 2 easy ones right in a row without hints, you get harder problems, and so on.

In the next unit, they talk about solving inequalities.  I don’t like the use of the words, “swap the inequalities.”  Most math teachers refer to it as flipping it.  The second thing is that their first introductory problem is -.5x < 7.5.  Their first step is to multiply by -2.  Again, “magic” math!  Most kids at this point CANNOT make the leap to seeing -.5 is =-1/2 and using its inverse.  Two seems like an odd number to throw into a problem with 5’s and 7.5’s.  Don’t start with something like that when the point you are trying to make is about flipping inequality signs, why muddy the water with something so confusing as -.5 and its inverse being -2.  He also immediately introduces the idea of how to graph inequalities on a number line and use interval notation.  He just sort of does it, no explanation of the number line and a quick explanation of the interval notation.  After years and years of experience with students, I know that kids can’t just hear that or view it at that speed with such little discussion and explanation and understand the concept.  There needs to be a whole lesson just on graphing inequalities (when to use open and closed circles and why) and writing interval notation, not an after thought in this lesson.  This is also another issue with Kahn.  Some areas they go so slow and other areas that need to go slow, they whip through it so fast.  It is like they have never worked with real students of various levels before.

We are at the point where big leaps are being made in Algebra.  I was pleased with the intro to solving equations videos.  I liked the discussion about what a variable and overall most of the plugging in to equations by substitution wasn’t too bad but now that we are getting into the meat of Algebra, we will start losing students.

At this point, I randomly picked another topic to see how it was done.  I picked completing the square.  If you read the comments you get the full the picture:

1. I don’t understand why c=22
2. I can’t see how this video has anything to do with practice
3. Is this Algebra 1?
4. I still don’t get how to do this?  Why is the FOIL method on the right?
5. I don’t get that pattern about (x+a), my teacher showed us a different way

The teacher goes through a symbolic proof.  Although this is nice for Algebra teachers, be real, the majority of kids don’t get this at this level.  What you need to do for kids is provide a written set of steps, let them know where it is used, why it is important, and situations of application.

Overall, there are some decent videos but the entire system needs an overhaul.  Here are my recommendations.

1. Someone who is a very strong math educator and who really knows how to teach well should go through each video and make suggestions for change.
2. The organization needs updating for ease of use.
3. A developmental approach needs to be used for both problems in lessons and practice.
4. Teachers should not rely on this for their lessons as it stands, the lessons are not strong enough and it is missing the benefits of dynamic teaching.

Written by:  Lynne Gregorio, Ph.D. Mathematics Education