We don’t need to spend much time with calculation. Technology can do that for us. We can use the extra time saved for engaging in ‘higher-level’ thinking. Mr. Conrad Wolfram in his TEd Education Talk makes a lot of sense in this video. But, I have my reservations but not because I’m for teaching a lot of calculations.
We also said the same during the era of calculator. Did it improve the math education of our youth? So, what makes us think it will happen in the age of Mathematica, GeoGebra, Sketchpad? There is something in our math classes or math education that’s stuck in the middle ages, that’s not keeping with time. Unless we find and address this, no amount of technology can help us.
I hope these two videos will make us think hard as well about the problems in mathematics education and how important it is to teach math in a way that they makes sense to students. Students are only able to apply their maths to the extent that they understand them.
Bring the mathematics back to physics!
This second video is an open letter to Mr. President Barack Obama. It presents a problem about Physics Education. The problem is as true in mathematics although I think for both physics and math, the problem is not just the curriculum but also in the teaching.
In the following video Mr. Khan’s gave an excellent task and solution on finding the equation of a sequence of blocks. I suggest you stop the video after the presentation of the problem. Let the students solve it first before you let Mr. Khan do the talking.
Mr Khan did give an excellent explanation especially the one about x – 1. The last solution involving the slope and equation of lines was not as clear. This is the part where your students need you. So I suggest that after viewing the video ask the students what part of the video made sense to them and which part was not very clear.
I think it would be best to ask students first about the rate at which the number of blocks is increasing rather than use the term slope. If you want to relate this to slope ask the students to plot the values in the table on a grid. You make then ask what the slope is of the line containing the points.
Additional solutions
Here are two more solutions to the problem. The first solution involve dividing then adding. This leads to a a different expression but will still simplify to 4x-3.
Dividing and putting together
The second solution involve completing the figure into rectangles for easy counting then taking away what was added. This leads directly to the simplified equation. Don’t you love it:-) I do. So please share this post to FB and Google. Thanks.
If students find Khan Academy’s math videos helpful and cool then by all means let’s use them in teaching mathematics. Just don’t let Mr Khan do all the teaching. Remember you are still the didactician.
I’ve yet to read a math educator’s blog that endorses Khan Academy materials. Well, this blog does. Yes, you read it right. This blog endorses Mr. Khan’s materials for teaching mathematics. No, not by simply viewing the video but using the Mr Khan’s lecture as the object of investigation. Let’s take the video on direct variation. In the video, Mr Khan started with “varies directly” like it’s the simplest thing in the world to understand. Mr Khan then gave the sample problem and solved it as shown in the image below. Mr. Khan’s method is deductive and he uses lecture method. Click here to view the video in YouTube then read on below to see how the same video can be used to develop the concept of direct variation with conceptual understanding by linking it to students previously learned knowledge about proportion and then as context to introduce or review the concept of function.
How to use Mr Khan’s videos in teaching math
Show the video. It’s a short one so it will be over before your class will realise it’s math.
Ask the class if they can solve the same problem without using Mr Khan’s solution. The problem is elementary school level so students can solve it using arithmetic. Since a gallon of gas costs 2.25 so all they need to do is to find how many 2.25 in 18. They can continue to add 2.25 until they get to 18; continue taking away 2.25 from 18; or just divide 18 by 2.25.
Ask for another solution. Didn’t they do ratio and proportion in 5th/6th grade? So, with a little scaffolding, students can set up 1:2.25 = n:18. I’m not a fan of product of the means is equal to the product of the extremes since it has nothing to do with proportional reasoning but I’ll allow it this time.
Ask for another solution. Again with a little scaffolding questions like “If 1 gallon costs 2.25, how much would 2 gallons cost? 3 gallons? Can you organise those data in tables? It’s important that at 4 gallons you asked the students to solve the problem. There’s no need to continue all the way to 18$. Asking students to predict will make them consider the relationship between pairs of values. This is an important habit of thinking and it is crucial to appreciating and understanding algebra.
Ask for another solution. With a little scaffolding again like “What do you notice about the values in the table? Can you imagine the arrangement of the points if you plot the values on the Cartesian plane? How will you use the graph to solve the problem?” Again there’s no need to plot the points all the way to 18. Students should think of extending the line to make the prediction.
Now, go back to Mr Khan. “Study Mr Khan’s solution. What are those x and y that he’s talking about? What does y = kx mean in relation to your graph? Where is it in your table? Anyone can explain what Mr Khan mean by varies directly?”
Assessment/ Assignment/ Further discussion: “The following are questions other students posted in Mr. Khan’s direct variation video in YouTube. How would you answer them?”
Sorry if this question seems basic, but I don’t understand how this example relates to functions…could someone please explain? Thanks!
What is K in general?
Why do we always have to set x?
The practice for this video includes inverse variations, which are not yet covered. It would be great if there was practice specifically for direct variation only. Thanks!
This style of teaching is called teaching math through problem solving. If you enjoyed Teaching Math with Mr Khan, don’t forget to subscribe to this site. I will try to develop more lessons where I will be co-teaching math with Mr Khan’s videos.
