Tuesday, October 14, 2014

Intro to Parabolas with Algebra 1b

You know how sometimes, you have a BASIC idea for a lesson and when you teach it, it totally exceeds your expectations?!  Yeah, that was me today.  My students walked out of here knowing more about parabolas than I've seen students know after a week of drilling the facts.  The coolest part is, we haven't even TALKED about "quadratics"!  We've been working on "factoring trinomials" by grouping and honestly, they've struggled.  But that's a topic for another post...

I just think it is awesome that I hadn't even mentioned the word "quadratic" until today and they totally picked it up and ran with it, along with lots of other info.

So, here's what we did...

1) I asked the students to take out a piece of paper.  I told them that in the upcoming chapter, we'd be exploring parabolas and that we would begin by watching some carefully selected intro-videos about parabolas.  ( I chose these 4 out of a SEA of really boring, horrible videos so be careful what you show or this could derail really quickly)

2)  I asked them to watch the videos and write down 5 things that they learned or noticed about parabolas. I was a little nervous that 5 might be too many, but it totally wasn't and I think it kept them interested because they couldn't just get 3 and then zone out.

3) At the end of each video, I asked some questions that came into my mind as the video was playing - things I wanted them to notice.  If they hadn't noticed what I was asking about, my plan was to replay the video.  To my surprise, a student asked me to replay it before I even had a chance to tell them that's what we were going to do!!  Ha ha!  They were it.

Here are the videos I showed (in order):
Our BRIEF lesson
after a video on
what a focus is and
how it helps us

Great quirky intro with no talking - just music and images

Kinda slow, but good info.  Guy talking over images - ends with a video about a bridge that collapsed in the wind because of faulty engineering.  This showed that parabolas really are important...not JUST cool.  Also points out the idea of the focus point and the role it plays in engineering.

Mario Brothers - shows the stretch/shrink and y-intercept concepts

High school students' music video project - these are not my students, but I totally wish they were!  Great focus on open up vs. open down parabolas and the fact that parabolas are everywhere.  Students asked if they could do this project for a test grade.  I thought that was a bit much, but told them that if they did it by the end of the unit, it would be worth some serious extra credit on their test.  They were stoked about that.  (And again, students ASKING for work - that shows engagement, in my humble opinion)

4)  When we were done, I had each student share a fact that they had and they couldn't repeat someone else's fact.

5) I then drew a quick sketch of some basic parabolas and asked the students what the important features were.  They named every single part that I wanted them to see without any guidance from me!  They added these basic diagrams to their notes and I asked them to color code them (since I hadn't).

These things might not seem like much to you, but remember, these are "low-level" Algebra 1 students.  They've never seen this before, but they picked it right up.  It'll be so nice to move forward, teaching how to SOLVE a quadratic without having a 3-day existential conversation about zeros - what they are and why we care about them.  This group already knows what they are and they were the ones who told me they'd be important so at least half of my motivational speech is taken care of already!

I also like that we haven't talked about SOLVING a quadratic yet.  Honestly, it was because we ran out of time and needed to test before the end of the grading quarter so we just tested factoring only, but it is totally working out!  We'll do "solving" a quadratic within it's proper context now!  That'll be so much better than teaching how to solve and THEN explaining why...*sigh*

Today, life in Algebra 1b is good.

Monday, October 13, 2014

Question, question, who's got the question?

Professional's like eating broccoli, I think. It so good for me as an educator, but sometimes it's tough to chew and hard to swallow. As a reminder, my degree is in Elementary Ed, I'm certified in elementary grades, middle grades integrated curriculum, and math 9-12. I teach high school math. I love teaching and I love learning, but there are lots of times (like today) when I feel in over my head. Now this is a reflection post so please forgive me if I babble, but I desperately need to connect with you master teachers out there so please read and respond.

Today, we discussed the idea of using essential questions to direct our teaching. Like any normal human being, I googled essential questions for Alg 2 because it's the hardest course I teach. Here are some of the links I found helpful:

F(t): Essential Questions for Alg 2

Kingsley's Essential Questions

Saugus High School curriculum map for Alg 2 - extremely in depth, uses Holt curriculum

Incorporating EQs in math:

1) Focus on the strategy side of mathematics.

2) Look at the concept separately from the strategy. What are the big ideas in math? These are the grooming grounds for essential questions.

One of the challenges is that math is taught as a succession of skills. Students need to know these individual skills and there is more content than there is time. That is a reality. So how do I incorporate essential questions when I know that it means students may not memorize the algorithm for every skill and still ensure that they are ready for the next math class and the next set of skills? This is where vertical collaboration is so critical. I need to ask the next teacher what is critical for success in the next step.

The next level of consideration is that EQs can not simply be put on top of an algorithmic model of math. They are pointless in this setting and, I think, can be quite confusing and overwhelming for students. EQ discussions must occur within a setting of rich problem solving experiences. Maybe at the end of a unit, after I've taught the skills and quizzed along the way, we could have a class discussion of our EQs before the test. Could they be used to drive the review for a test?

I would also like to have at least one, if not two, EQs posted in the room, that I can refer back to, as it comes up, regularly. I will have to remember that Ss may not have the answer, that's ok. They might come up with more questions. That's great!

Now, if I do this in my classroom, I've got to think about what happens when students come to the wrong conclusion? My first response would be to give them an example to illustrate that their conclusion is incorrect. But then I wonder, do I need to know how to address every possible misconception? What do I do if I don't know how to address it? This is a scary thought process for me, but my principal, who is awesome, encouraged us with this quote on Columbus Day "You can never cross the ocean until you have the courage to lose sight of the shore."

Teaching is hard. Can I get an "Amen?"

What are your thoughts?