Using Wolfram Alpha to Discover Properties of General Equation of a Conic

Today, my Pure Math 30 students, took out our department laptops and logged into Wolfram Alpha.


We were investigating the general form of an equation of a conic. Ax^2+Cy^2+Dx+Ey+F=0.
I had the students graph many different equations and observe what graph Wolfram Alpha created.


The students then had to compare the equations with their graphs and answer the following questions.

1. Describe what values you must use for A and C in order to generate a circle?
2. Describe what values you must use for A and C in order to generate an ellipse?
3. Describe what values you must use for A and C in order to generate a parabola?
4. Describe what values you must use for A and C in order to generate a hyperbola?

Wolfram Alpha made this investigation quite easy for the students. All they had to do was type the equations into Wolfram Alpha and it gave them nice, easy to read graphs.

I could have just lectured for this lesson. However, I believe that the discovery approach I used was much more powerful.

Some math teachers would say that they could have their students use their graphing calculator to do the same thing. You are right. I have had the students use a graphing calculator for this lesson before. However, I had to install a special program on the calculator for the students to complete the activity. Wolfram Alpha is accessible to all students with a computer and an Internet connection. It is a far more valuable tool than a graphing calculator. Wolfram Alpha can do so much more than a graphing calculator.

Wolfram Alpha was an awesome "TOOL" in my math classroom today.

If you have not looked at Wolfram Alpha I think every mathematics teacher should.

Assessment for Learning in Circle Geometry

I have been "dipping my toes" into the assessment for learning stream. The last couple of weeks we have been studying circle geometry in my Applied Math 20 class. The students ALWAYS struggle with this unit. It stretches their minds and really makes them use their problem solving skills. Needless to say, the students do not "like" this unit. It is hard!!!


Every semester I give a two page assignment with about 15 different circle geometry problems. In the past, I have taken this assignment in, marked it and returned it to the students. While this method gave me another mark for my mark book it really did not HELP the students to learn to solve circle geometry problems any better.

So, today, I switched things up. I gave the same assignment. However, I explained to the students that I was not taking this assignment in for marks. I explained that I wanted them to learn to solve circle geometry problems better. I asked them to solve problem #1 then bring it too me and I would mark it and discuss it with them. Then go on to problem #2 and do the same. You would have thought that the students would have grumbled that they were doing an assignment for no marks. Not one single complaint.

In this class we have had a number of discussions about how all of the work in a unit is to help them learn the material. They get the "marks" when they write their unit exam at the end of the unit. The more questions they ask and the more learning they do during the unit the better they will do on the end of unit exam.

I am struggling with the fact that I have less marks in my mark book. However, I really like the fact that my students are learning and understanding mathematics better.

Stay tuned for more adventures of the Transformed Educator!!!

Tweet Cloud

Everyone using twitter should check out Tweet Cloud

Here is a tweet cloud of my twitter posts for the past year.

Nominations for Edublog Awards 2009

My Nominations for The 2009 Edublog Awards are:

Best individual blog: Thinking in Mind - Neil Stephenson
Best individual tweeter: Dean Shareski @shareski
Best resource sharing blog: Free Technology for Teachers
Best educational use of video / visual: dy/dan - Dan Meyer
Lifetime achievement: David Warlick - 2 cents Worth

Make sure to submit your nominations for The 2009 Edublog Awards

Using Wolfram Alpha in Math Class

Yesterday we were studying Solving Systems of Equations using Elimination Method with my Pure Math 20's. We had solved a few problems together on the board. Then I said, " I want to show you Wolfram Alpha". So, I walked over to my computer, went to Wolfram Alpha and typed in the same 2 equations we had just solved. Voila!!! Here is what Wolfram Alpha spit out at us.


In less than 2 seconds we had the answer to the question. I then asked my students, "How could you use Wolfram Alpha to help you with your homework?". They thought about it for a second. One student said, "Well I can just type every question into Wolfram Alpha and get the answer. My homework would be done in 5 minutes!!" I reminded the students that Wolfram Alpha ONLY gives the answer. It DOES NOT show us all of the work to arrive at the solution.

I then talked to my students about how Wolfram Alpha let's me ask them "different" questions. Things like, "Explain what the solution (-1, 4) means in this problem." This is a much deeper question and shows their understanding of the problem.

I informed the students that I recently read that every high school student in Denmark was going to be allowed to use a computer with Internet access on ALL of their final exams. This really got the discussion going!!! We talked about how their would be NO multiple choice questions. The students would have the ability to "collaborate" during an exam. Wow!!! Different way of thinking about education.

I asked my students to imagine what it would be like if every one of them had a laptop for every class at school and how that would change the way they learned. They really started to get excited.

I informed my students that I am thinking of wheeling a cart of laptops into class and turning them loose on the students. I also informed them that I am thinking of giving them a unit exam where they all have computers and Internet access. One student said,"Please do not do that. We will have to think a lot harder on an exam like that!". She really gets it.

Yesterday's discussion really opened the doors in my mind and in my students minds about how the world we know could be very different.

Stay tuned to find out what happens!!!

Catapult Project Day 2

Today we finished off the catapult project by having each group fire their catapult from the top of a desk instead of flat along the floor. The students had to modify their original equation to factor in the height of the desk. Then they had to use their new equation to predict where a target should be placed on the floor. Part of their grade was based on how close they came to hitting a bullseye!!!

I had one group hit the bullseye dead centre. Most of the groups were within about 15 cm of the bullseye.

We ustreamed the final catapult firings so that anyone that wanted to watch was able to.

Thanks to Jared Nichol and Neil Stephenson for following along and chatting during the ustream. My students thought that was quite cool!!

I have also created an excel spreadsheet to help grade this project.

You can obtain the description of the actual project and the rubric from yesterday's post.

Catapult Project

Today my Pure Math 20 class carried out the catapult project. I have been waiting for this day for 2 weeks. Ever since I built the catapults I have been excited to see how the project would play out for a whole class. I broke my class of 30 students down into groups of 3, handed out the project to them and gave them some guiding words on collecting their data.

My first words of wisdom were practice, practice, practice the firing of the catapult before you ever collect data.

The students took my words of advice and did an awesome job of carrying out the project. Some groups even realized once they started trying to calculate the equation of the flight path of their marble that their data was not good enough. So, they redid the data collection!!! Wow, most students would have just given up.

We ran out of time to finish the project today. So tomorrow, the students will use their equations to predict where they should place a target on the floor. Then we will see how good their math calculations really are!!!! I plan to ustream the event tomorrow at approx. 10:30 a.m. mountain time. I will tweet the url for the ustream. You can follow me on twitter at kaminskiterry.

Here is a video of one group collecting data.

Check out more pictures here on flickr.

I have posted the detailed handout for the project.

I have also posted the scoring rubric I am using for the project.

I have to thank Sean Sweeney for sharing this project over at his blog. It is because of his sharing that my students are getting to enjoy a truly awesome mathematical experience. Thanks Sean.