Ms. Z

It's easy to post when your articulate, gracious, loving daughter does it for you! So surprised and honored! Get the tissue!

HAPPY TEACHER APPRECIATION WEEK!

Growing up with teachers for parents, I encountered (all too often) students who assumed teachers evaporated into thin air as soon as the classroom door shut. Only to be bewildered and horrified when they ran into us at the grocery store, proclaiming, "Ms. Zimmer, you eat Annie's microwavable pizza too?!?" While every week should be teacher appreciation week, I am glad this week is dedicated to honoring the work of our educators both in the classroom and behind the scenes.

I was fortunate enough to not realize office jobs exist until I had one sophomore year of college. I was under the impression all professionals got summers off and could be home every night to cook family dinner and help with homework. While this description makes teaching seem like a walk in the park, it is anything but easy. I am humbled every day by the patience and empathy teachers exhibit accommodating student's weaknesses and cultivating their strengths. (Patience applies to working with parents too!)

If your parent is a teacher like mine, or you have a teacher who has significantly impacted your academic experience, please take this week to APPRECIATE them and let them know that (while compensation for teachers in most countries is grossly incomparable to the amount of work they do and the positive impact they have on the community) we are grateful for their devotion to our development and contribution to our accomplishments.

— with Amy Ellen Zimmer andJeffrey Diamond.

Look for and Make Use of Structure. Play. Investigate.
We started a polar unit with this lab I made with Desmos Activity Builder.

Polar Graphing Investigation

Here are some of my student's pearls of noticing:

Just wanted to share something that pushed me outside of my comfort zone and that the kids liked too.

Here is their learnings and questions

So many things to talk about now! And because the STUDENTS want to know.

Here is a follow up I am thinking of doing.

Comparing Polar Graphs

Pretty Trippy MAN

PS The students loved the sliders! Thanks, Desmos. Now would you please get me into the kids dialogue boxes in real time?

I have been gathering evidence for my fantasy "Don't go it alone," series. We all work so hard, it is crazy that we feel so compelled to do so much ON OUR OWN. I subbed for a colleague teaching Algebra 1. She is so dang creative! Her class was working on graphing quadratics in factored form.

Unfortunately, working solo, she missed an entire page of graphing written as quadratic = 0 (instead of y = or f(x) =)

I have done this too many times myself. Would this teacher have caught her mistake if I did not happen to cover for her? Sometimes we find 'em, sometimes we don't. With 15 sections of Algebra taught at our HS, the going it alone is too common place. I believe this because I am guilty of going it alone and I know the benefits of collaboration.

Mr. H. My BTSA Participating 1st year teacher is a systematic guy. He cares so much that the students get what they need step by step. He is careful not to overwhelm them with too much information.
Here is his pool problem for our unit on solids:

My Brain exploded with extensions: Will there be 1/2 the volume if the diameter is cut in half? Are there other dimensions that use the same amount of water? What is the largest pool you can have that amount of water?

Yeah, I know that might not have been the intention in this lesson...but I loved the premise and wanted Mr. H. to give the students something to juicy to discuss and share.

I had all these cool ideas for exploring circles in Geometry. Circles are a great bridge topic between Geometry and Algebra.
I have lots of good ideas, I am just not the most organized person in the world. Lucky for me, I have colleagues that are. Here was my lesson:
Me: Multiply (x+1)^2
(x+2)^2
.
.

.
(x+12)^2 Stop when you find the pattern and just write the product.

Me: What did you notice?
How would it change if all the sums were differences?
Me: Can we work backwards? Can we find a magic number that makes a perfect square trinomial, etc...
Me: How are these equations related to the circles we have been graphing?
Me: Can you find the center and radius of this circle in standard form? x^2 + 8x +y^2 = 9?

My students were happy enough and there were "oh, I get its." We got into fractions, and even radii whose lengths were square roots.

My lovely colleague asked me how I was approaching complete the square for circles. And I shared the above. Here is how she interpreted my lesson:

To see her entire development get the file here: file

I just love how she saw the whole thing. How she was able to put the lesson into a form I could not.

I have many things I want to do with my students that I am not sure how to structure, so I shy away. The more I share with colleagues, the more we create rich and inviting experiences for the students.

Kaneka,

You are hitting me right in my gut and heart! I fear I am not smart enough to play, AND I just let my enthusiasm and age wisdom push open that door!

I am a member of MTBoS, I made myself so. That is the thing about the MTBoS, it is one of those leaps of faith. You don’t have to be the brightest, funniest, smartest, newest, greatest, rockin’-est. You just have to have FAITH that you want to be better, that there is someone to who will listen, that you have peeps that care about your mathy well-being, and your person well-being. YOU ARE SOMEBODY! And the MTBoS is here to support you. Only thing is, no one is going to beg. That is what I mean about faith. And we are patient. And we want you to be with us. There are the amazing folks who started the ball rolling, and they have HUGE hearts. Come and play! Twitter is the same way. I was so overwhelmed, I felt like I was left out of the inside of everything, and guess what, I usually am, and there is always, always, always SOMEONE who is listening and will “like” a tweet, or respond to a plea, or feel compelled to tell you about a great resource. Because that is what we do for each other.

I didn’t believe it at first. (well first of all, I didn’t even know that I who I was really contacting and commenting on) Then you comment and get a reply from Matt Vaundry, or Fawn, or Dan…and then we are just all the MTBoS and so what?

The best way to handle twitter is Tweetdeck. Just have a column for #MTBoS, or for #Geomchat or whatever, and that really helps limit all the middle of stuff that makes you feel, well, out of it.

I hope I have given you some ideas and made MTBoS and twitter less intimidating. I am listening and reading!

My daughter came home from London for a two week visit (She is a Junior at LSE), and asked, "What is the best lesson you've taught?" Whoa. Really? I can't say that one.thing. came. to. mind.

I don't think this is because I am a crappy teacher. I have a crappy memory. (Hitting 50 made things, oh, so much worse...) The best lessons come when you hear the students abuzz or the bursting bubbles of OH! Recently, I have had the students move from finding the center of a circle by construction to figuring out how to circumscribe a circle about three points. That got a lot of ohhs and ahhs. Especially when we talked about the extension of what that means. ALL triangles are cyclic polygons blew their minds and the students loved trying to prove or disprove the theorem. Moving on to quadrilaterals was fun too. When you see students hunkered down, and paper is flying, you know you've done a good thing.

Here's another way I know a lesson is going well, and I can thank Alex Overwijk at http://slamdunkmath.blogspot.com/, because now I know we're inspired when my students ask me, "Can we do that butts up Ms.Z?"

Here goes the debrief on Matrices:

Obviously I didn't meet my goal of blogging over time. I was so tired taking on an extra class!
We had to decide ahead of time the entire unit...news for you...it isn't exactly how I roll. I don't like sticking to an unwavering plan. As I get into something, I find new and different journeys to take as I see what is inspirational and what is not.
I opened with a classic system of two equation story problem:

I only showed the first one. This was Pre-Calculus, so I let them think they were oh, so smart.

For the second one, we laughed that anyone would besides a mom would buy a visor. I explained that my Girl rows, and rowers wear visors. (She's 5' 9'' and she is about medium for her 8 boat, you do not make fun of those girls (or boys). The students had a good time remembering how to and finding the cost of Visors, Hoodies, and T-shirts. Woot. (Even asked if they could go VNPS)

Then I let them go at the Sale question for about two minutes and called for a time out! Don't you want a faster, easier, better way????

The first day was a good review of lines in a plane, consistent, and inconsistent systems. We also got a good review of quadratic systems, how different conics interact with each other and lines.
Students were very motivated to learn about augmented matrices and Gaussian elimination. There was a lot of grumbling and I was so happy!
Next we did Gaussian-Jordan elimination. EVEN more grumbling (YAY!)
A minute or two, okay, a whole period on Matrix operations. Mind blown about lack of commutative property for multiplication, and what in the heck would an identity matrix look like? When do we know a matrix doesn't have an inverse?
Then we got to Matrix Inverses. They did not like the looks of this using Gaussian-Jordan elimination and were all over their calculators and Google looking for answers. (Yay them!)
Motivation: a very secret message I encrypted with a 3 x 3 matrix. I didn't do anything special (a = 1, b = 2, etc...) But it was enough to be thoroughly entertaining and engaging. The idea of encryption and decoding was a favorite. (I wonder if I should have started with the secret message and let them try to crack it). (It was also super fun to give the students extra credit for deciphering a code I encrypted with a 4 x 4 matrix when we found out it was senior cut day--a test day for us...Can we have extra credit Ms. Z? YOU Bet!)
Math Practices used: SMP 5: Use appropriate tools strategically. (I loved when students started Googling how to use their calculators!) SMP 2: Abstract, no duh!, SMP 6: Attend to precision. (oh boy, did we go down some rabbit holes!) SMP 6: Model with Mathematics. (So many geeks in one room thinking of encryption--so happy the Apple case and the FBI trying to subpoena Apple to break the San Bernadino shooters' phone was in the news!) SMP 7 and 8: Patterns and repeated reasoning (dear hearts, yes, you multiply AND add each row and column entry) Very satisfied with how many of the practices are utilized with Matrices.

That is where I ended. I did not go over determinants. I would love to extend next time with determinants and transformations in the plane. Also, I would do more with planes in 3D. Yeah, and how about writing a program that would decode these messages for us, all. at. once, cause doing 4 letters at time is tedious...

Anyone have any insights? Additions? Forgetaboutits?

I did make one Matrix Row Game for review. If anyone remembers who has the Row Game File, I will happily throw it in! File here:

Matrix Row Game

Next Posts: When you are brave and ask for help and How a new course was born

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