Geometry: Unit One

**So, I wrote this a few weeks ago, and just realized that it never published.  I scheduled it to publish, but it's just sitting here as a draft.  Anyway...here you go.  A follow-up of sorts to my Geometry Test post.

My first unit in Geometry is called Lines and Angles.  We are introduced to a lot of vocabulary (lines, points, planes, rays, etc) and a lot of notation.  We talk about angle relationships with parallel lines and a transversal and we calculate the midpoint and distance of segments on the coordinate plane.

Not a lot in this unit, and it's pretty straightforward (at least, I think so).  I expected test scores to be overall pretty high.

So, I've been doing some thinking about the unit, and how I could have improved test scores.

Here's the good:

• I made the students take notes.  I checked as often as I could that they were actually doing it during class.  I made it a part of their grade and allowed notes use on the quiz.

• There was a lot of chances to practice what we learned.  I gave homework nearly every class period (every other day because of our block schedule), and we also did some class work.

• Homework was (somewhat) spiraled.  I did give some homework about transversals when we were studying midpoint and distance in-class.

• I collected and graded nearly every assignment.  If I didn't check for correctness, I gave students a chance to check their own work against an answer key.

• I gave a quiz and got it back to the students in a timely manner.  I encouraged them to fix what they missed.

• I gave out a Study Guide with a list of all vocabulary and skills that would be on the test.

Here's what could have been better:

• Shorter, more focused homework along with more of an emphasis on in-class work, so I can see how they are doing right away.

• Two quizzes.  The unit was 5 weeks long.  Two quizzes would have been more appropriate.

• A review day of some sort.  

• Fixing mistakes on a quiz is assigned and not optional.  Perhaps for students who scored below a certain score.  

For the next unit, I am going to put some of these things into place.  I am going to continue to make them take notes.  I am going to give more quizzes more often, and make kids fix mistakes as an assignment.  Maybe kids who score below a 70%?  80%?   I am still debating on the review day.  I just don't like them.  I'll probably do one anyway.  

Here's to great scores next time around!  

As for these current tests, I still haven't figured out what to do.  

Tests this week and preliminary results

So, I gave a test this week.  Two, actually.  One in Algebra and one in Geometry.

In Geometry, I felt really good when I handed the test out.  I felt like I had given the kids plenty of feedback on their work, and lots of practice.  I didn't do a review day (which I dislike anyway), but I felt that we had still spent time learning and practicing what we needed to learn and practice.  I felt good about the test I wrote.  It seemed fair and that it would provide a good reflection on the students' understanding.

When I handed out the test the next day in Algebra, I didn't have the same feeling.  I'm teaching a new unit that I just created, and it's iffy.  I knew exactly what I wanted the kids to end the unit knowing and doing.  I wasn't sure about how to teach that and even less sure about how to assess that.  I wrote and gave out a test anyway.  We'll see how they do.

I paused grading the Geometry exams to write this post.  So far, scores are either really high or really low, mostly even split.  I'm not sure what to do with that. I'm not sure I'm willing to spend class time re-teaching when half of them have it, and I'm not willing to move on if half of them don't have it.   Ideally, I could re-teach half of my class, while the other half stayed home or something.  Wouldn't that be great?

I am more than a little disappointed with those Geometry scores.  Post coming soon about how class time went during this unit, and my ideas about what to change/fix/keep.  Also a post on Algebra results.

Small change with a big payoff

Alright, so I'm a little slow, but something I've realized this year is that kids don't remember what we did in class last time.  At least not without a little reminder.  I've been getting much better about building  that into the beginning of my lessons, and it is so paying off!

What I've realized is that I spend a lot of time planning and thinking about the flow of my lessons, both in each class, and from class to class.  I'm also the one teaching and the one who is already good at math.  As a result, I am hyper-aware of what happened last class period when I go into today's class period.  I've been assuming my kids are also aware of what happened.

But, they aren't.  They don't hang on my every word, they don't look forward to what new math knowledge they can get today, they don't take a moment to reflect on where we are and what we are learning before class starts.  So I have to make them pause and reflect at the beginning of class.

I've been noticing that kids seem to understand more.  I feel as though I'm able to move forward instead of spend the class time reviewing things that "they should know by now."  All because of 1-2 minutes that I take at the beginning to refresh their memories.

It can be as simple as saying and asking, "Remember last time, we were talking about parallels and transversals?  Can you look back in your notes and remind yourself what a transversal is?" "List the 5 relationships between angles we talked about."  I've mainly been calling on a few kids (randomly...I don't pick volunteers for this one!) to answer my questions, but I also have the idea of having them write it down at the beginning of today's notes.

I really like this small change, even though it makes me feel a little dense that I didn't figure it out sooner.

Math Quotes

One of my hobbies is collecting quotes.  I love it.  I even found a quote to explain why I love quotes:

"I love quotations because it is a joy to find thoughts one might have, beautifully expressed with much authority by someone recognized wiser than oneself."  -Marlene Dietrich

Here is one that is among my favorites:

"The simplest schoolboy is now familiar with truths for which Archimedes would have sacrificed his life."  Ernest Renan 

I like this quote because it reminds me about what I am teaching my kids.  I have a whole long list of facts for them to memorize, and if I wanted to, I could just spout them out and make the kids write 'em and learn 'em.  

But, the truth is, that list of facts represents years and years of real mathematics work.  Math work that is relevant and interesting, not just created to make high school kids groan.  

So, when I read this quote, it reminds me to let kids 'experience' math and come to their own understanding of why math is the way it is.   I want to let them learn from trial and error what the most efficient way to solve an equation is.  I want them to decide that arrows and tick marks and such on geometric diagrams are worth learning and using, because they make things so much easier.  I want them to decide that we need a word for "the side of the triangle that isn't next to the angle"  I want them to know that true math knowledge is hard earned, but so worth it.  I don't know if that was it's intention, but this quote reminds me of that.