10 January 2009

Baddie of the Month – Factoring a Quadratic with a≠1

Filed under: applets,education,math,sloodle — Tags: , , , , , — admin @ 5:13 am

Goodie: “A technique/question that can be applied in many places and teaches thinking.”

Baddie: “A technique/question that is a waste of good teaching and learning-to-think-and-do-math time.”

I am going to try to blog a baddie and a goodie per month. We shall see and of course – this is my opinion.

January 2009 Baddie of the MonthFactoring a quadratic with a≠1 “by hand”.

Okay, I can mostly understand learning to factor “by-hand”:   x²+3x+2  or   x²+x-2.  

Once you understand the principles and get the technique (my scheme), factoring a quadratic by hand with a=1 is faster than using the quadratic formula.

But, I absolutely and totally do not understand the reasoning behind other factoring-by-hand techniques!

Why not: Factoring techniques

  • serve no useful purpose – once factored, with a≠1 you must still solve the individual factors.
  • don’t always work – MOST quadratics even with a=1 and real roots CANNOT be factored by hand.
  • are hard to learn, there are many “special cases”, they take alot of time to teach, …

What to do and why: Use the quadratic formula for all your factoring needs.

  • We are going to teach them the quadratic formula anyway.
  • It always works – either we get real roots and can factor or we get non-real roots and know we cannot factor.
  • By using the quadratic formula all of the time, the connection between quadratics, roots, x-intercepts, graphs of quadratics becomes clear.
  • Repetition of a single technique is much more likely to stay in their heads.

Conclusion: Don’t teach factoring by hand except when a=1. Use the quadratic formula.

Here’s how: ax²+bx+c=a(x-x1)(x-x2) where x1=(-b+D))/2ax2=(-b-D))/2a,  D=√(b²-4ac)

(Here “by hand” means looking for the factors without a formula like when you say “The factors of 2 are 1 and 2 and oh yes, they add to 3 (first expression) or the factors of 2 are 1 and 2 and oh yes, they subtract to 1 (second expression)”.)

Related topics to come in future blogs

Please, OMG please don’t teach completing the square – an even worse waste of time than hand factoring.

Please, please don’t teach complex numbers in the same 2 month span as you teach graphing of quadratics.

20 January 2008

Sloodle Moot Itself

Filed under: moodle,SL,sloodle — Tags: , , , — admin @ 2:31 am

This will have to be a quicky – Sloodle Moot deserves more, but I haven’t time.

Talk about bad timing – installing Sloodle requires Moodle 1.6 or 1.8 . My server is just now in the process of transitioning to a different platform (I love all this geekese!), which means I can finally upgrade from Moodle 1.5. Unfortunately not in time for the Moot. So consider that I attended the Moot only knowing a bit about Second Life and an old Moodle and no real experience in Sloodle.

Here are my thoughts on the moot and the events and the presentations I attended.

1. Giannina Rossini must be comatose today as well as her fellow Sloodle Moot Supremos. I have never – ever – seen such extraordinary conference organization and in the still rather non-forgiving environment such as SL. And Gia was at every presentation (4+) and every event (2+) I attended.

2. The Sloodle Moot Auditorium

• I liked that it was walled off until the Moot opened. I am sure that this was done for the conjurers benefit, but it added to the fun of the opening.

• A small minus here – I tried practicing the teleport coordinates in the days before the Moot because I knew I would be short of time on a Saturday . It was a bit confusing to try to teleport to places I couldn’t get to.

• I rarely socialize in SL (not very good at this yet), but it was lovely to watch all the partying so thanks for all the fun lighting – the robot was cool!

3. Skylar Peck, New Nexus

• I wasn’t terribly interested in this, but it was the first event on when I got up in the morning (CET – overslept for the Jeremy Kabumpo presentation) and I liked that the voice worked.

4. Edmund Earp, Hacking Moodle

• This was absolutely the coolest presentation I attended. I was so engrossed and engaged that I totally forgot to take pictures. This presentation made the Moot for me.

• It showed a real application of sloodle, i.e. moodle and SL together – the quiz chair.

• We got to make our own and I learned not just how to do that, but also about quizzes in moodle and technical prim making stuff in SL like how to drag scripts from one prim to another.

• BTW – Don’t rotate and object that you plan for people to sit on. I sat on my rotated cone with my head in the sand :)

5. Pedro McMillan, Moodle-SL Interactions

• This was a very fine presentation – I loved the pipelines and how the lit up when you were presenting; please tell us how to do this!

• I don’t know alot of technical stuff, so I didn’t really understand exactly how the flow works, but it was so well presented that I got a good idea of what flows in what order between SL and Moodle – so well worth my attention.

• I must remember to write and ask which flows are for course setup, which for teacher and which for student?

6. Esme Qunhua, Discussion

• I tried and tried to find this in some astro place – the teleport coordinates just wouldn’t work. Then I saw the location had been changed, but by the time I got there, it must have been over. (I was dumb and did not download the updated schedule – basically because I had been given the (old) schedule on a SL notecard and put it into Word which was easy for me to look at and on Sloodle it was only available in xls or pdf – picky me).

7. Jeremy Braver, Educational Games

• This was great fun and the presenter is a whiz at engaging the audience but (a) I didn’t really see how it fit into the Sloodle environment and (b) was dissappointed when I found out the game will be for sale. (I live in a country where even a $10 game is alot of money.)

8. Buddy Sproket, Scripting

• Firstly, this was a very interesting presentation. I liked all the applications; I must admit I didn’t see how they function in Sloodle, but it was information I wanted, it was well presented so that I could follow most of it and I love Buddy’s hair.

• Secondly, I must apologize to Buddy and all of those present – I didn’t realize that my scripts from making prims in the back part of the sandbox would come into the chat window. I thought it would be like Edmund’s quiz chair demo and I am VERY hands-on so I wanted to try as I watched. So please forgive me.

• I have to admit that as we went from scripts in SL to php I got kind of lost. I couldn’t follow how the script in the prim and the php on a server were connected. It is entirely probable that I was not the intended audience profile :) . But I learned alot and saw possibilities so I am very glad I attended!

Oh my gosh – I did not realize that I had actually gone to so many presentations!

Still, I wish I could have gotten to more events.

I had a wonderful time, learned alot and my thanks to all the SUPREMOS and presenters!


16 January 2008

Sloodle – Second Life and Moodle

Filed under: moodle,SL,sloodle — admin @ 7:32 am

Yesterday I attended a sloodle mini-conference. What’s that you say?

Cool beans my friends - and hence I will go to Sloodle Moot starting January 18!

I admit, I wasn’t expecting much. But I enjoy Second Life and I use Moodle in my teaching so off to the mini-conference I went.

Here is what happened …

  • I was at home in my jammies (it went from 12 – 1:30AM CET) in a village in FYR Macedonia, sipping tea (and then the caffeine was duly processed and I was also able to take – hmmm – what is the current euphemism – ah yes – a comfort break).
  • I was present in Second Life in all my 3D glory as Janita Collins (my SL avatar) in the ISTE island auditorium and
    • I was chatting with my co-participants as we arrived and being introduced to new persons, and then
    • I was sitting in a comfy chair, listening to the speakers (yes audio and at a level I could control!), watching a powerpoint presentation, and then
    • I was raising my hand, asking questions and having them answered in real time and then
    • I was picking up virtual handouts, and then
    • I was applauding and waving goodbye at the end.

A actual (better than RL-real life) conference! I was amazed. This is my third SL presentation and SL is really coming along. The audio worked, the powerpoint pages focused in real time, the ISTE auditorium is really cool. The handout boxes worked. Just in SL, I was impressed.

But wait – there’s more …

  • At the same time we were “at” the SL conference, we were Moodling. That is, we had our browsers open and were attending the Moodle course for this mini-conference. So I could
    • study the conference materials
    • look up words that I didn’t know in a online glossary
    • review a powerpoint slide that had gone off the SL screen
    • taking part in a real-time blog with the same participants
    • and all this without anybody seeing that I wasn’t actually riveted to the speaker (oh sorry, I am always getting in trouble for this at a RL conference!)

I didn’t understand it all – but what I saw was actual potential for actual use. My kind of technology in education.

Now, I am truly looking forward to the Sloodle Moot!

My thanks for great presentation to: Gia and Buddy and KJ and see you soon!


My thanks to Esme Qunhua and Entropy Hax for the wonderful SL tours from SLolar -> Gia ->Sloodle -> SloodleMoot!

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