Student Feedback on Student Teachers

Two things happened this week that were pretty impressive to me as a mentor teacher.

#1) No tech? No big deal.

Early in the week, my projector went out.

My student teacher had planned several days' lessons around discovery with our interactive algebra tiles mat and with algebra tiles in Desmos. The plan was to start the discussions as a whole class and then allow students to do some discovery on their own using Chromebooks. Then we would allow students to justify their reasoning to the class and have some discussion on what we noticed/wondered with the structure.

That was the plan, but you know Mr. Murphy and that infamous law.

The projector would probably be out for a few days, and I knew that would throw an entire monkey wrench in everything she had planned. In previous experiences, this would have completely panicked a student teacher and they wouldn't have known what to do. Not this time.

Her reaction: No tech? No big deal.

We made use of the whiteboards in the back of the room and had students justify the factoring they did on their Chromebooks.

Shifting to a Plan B she wasn't prepared for didn't phase her a bit. She knew she could make it work, so she did.



#2) She asked students for feedback EARLY.

I don't think I've ever had a student teacher do this before, and it was really powerful for both of us to see. We started with her formal evaluation rubric that her supervisor and I will use for her two major evaluations. We reworded some of the questions into student-friendly terms, and then asked some open-ended questions.

I appreciated that she asked the tough questions that most student teachers might not want answers to yet. However, her feedback was extremely positive and the students gave her great input.

Some of the feedback:

I like how Miss Mallory...

-listens to us
-approaches us when we have questions with respect
-doesn't pressure us and expect us to do something correct immediately after learning something
-can tell when I understand or don't understand
-always wants to help
-tries to explain in a way I can understand
-walks around the room and is willing to take questions at any time
-checks on everyone throughout the class
-isn't always to herself - she walks around and is interested in our learning

This one almost made me cry:
"I like how Miss Mallory explains things in detail, it's kind of like she's following in Hedge's footsteps. I think Miss Mallory will make a great math teacher."


Next week, it would help me if Miss Mallory...

-I like how she goes around the classroom and helps me so I don't really want it to change
-would try to teach us a lesson*
-taught a lesson by herself*
-kept doing what she is doing

*This is from the class where she and I are co-teaching. She will pick that class up completely by the end of this week.

Most of the responses from students were for her to continue helping the way she is currently helping. Students have commented to me that she seems more like a "regular" teacher than a student teacher. I think a lot of that comes from the fact that she jumped in the first day and started getting to know students. She rarely (if ever) sits during class.  She also has a confidence when she talks to students, even if she's not sure what they are asking. She never calls me over to "bail her out" - she sticks with it.


For "Something Miss Mallory taught that I don't quite understand yet", she got some really specific things that students wanted to begin with next week. I appreciated that she didn't get caught up in the positive feedback, either. Her immediate focus was on improving for next week, so we spent more time discussing the feedback that was constructive.


We also talked about making this a regular weekly thing: Friday Feedback.

That first round was just a rough draft (we have a few more questions in the works for this week). For example, I want to add a section where students explain what they learned this week in their own words, and a section on "wonders" they still have.

I would also like your feedback on our questions. Is there something we didn't ask, but we should have? Is there a question that needs to be rephrased?



Up Next:
We will finish "Solving by Factoring" this week, and move into "Completing the Square".

Mentoring Through a Different Lens

I need to start this post by giving a shoutout to Tina Cardone and David Coffey for this conversation:

I think I've quoted David's reply about a dozen times whenever I think or talk about my experience with my current student teacher.  This experience is unique for me for a few reasons: (1) she knows what I'm like as a teacher when I've taught the same course half a dozen times and I have it down to a science and (2) now she's getting to experience what it's like for me to teach a course from scratch and the planning, questioning, wondering, winning, and failing that comes along with it.

The last two weeks have really helped me reflect on my previous eight or so student teachers. Maybe I haven't allowed some of my other student teachers to "peek behind the curtain" to make that planning visible. Student teachers normally spend the first two weeks watching us walk in (seemingly without prep) and teach our lessons flawlessly and effortlessly. Does that image set an unrealistic impression of the planning and preparation we did the first time we taught the course from the beginning?  Are we giving the impression that "teaching is easy and doesn't require much prep" when they see us do this? 

So I’m approaching this mentor experience from a different lens than before.  I guess you could say I’m trying to Zager-ize it as a learning opportunity for both of us: 

  

(Shoutout to Tracy for writing this book! Go buy it here.)

My wonders:

If I could put applicable tools in her hands for what she’ll need to be able to do in August, what would those tools be? What planning strategies would she need that she might not have had access to in her education courses? What does “purposeful planning for understanding” look like and how to we monitor that understanding? How do we maintain honest reflection of our teaching when they don’t? And what roadblocks do we face when planning for multiple courses?

And those are the things I keep in mind every day and in every conversation we have.  However, that takes a HUGE amount of vulnerability on the part of a mentor teacher.  Am I going to look like I don’t know what I’m doing if I honestly say, “I think I’m going to teach (insert topic) this way, but I’m not sure if this will be something they will understand in one class period because I haven’t taught this before”? 

Then again, isn’t that the type of conversations we should be having with our colleagues on social media and our school/district PLC’s? How can I expect her to take a risk and be vulnerable with her current/future colleagues if I am not willing to risk modeling it myself?

So we brainstorm together A LOT and I’m as honest as I can be. I tell her when I’m not sure how something will go over.  If I feel like something I taught didn’t go well, I ask her for her honest feedback on what I could have done differently or where we could readjust for tomorrow.  And this has worked well for us because she has become voracious for feedback on her own teaching in my classroom. She’s honest about where she feels a lesson did and didn’t go well and begins “rough draft talk” about next steps. 

My student teacher was already checking out blogs of #MTBoS before she really understood what #MTBoS was, which is a great sign.  It’s difficult for me not to overwhelm her with all the awesome in our community, but I am trying to model/introduce it a little at a time. I have been extremely impressed with our collaboration so far, and I would like to start showcasing some of our work together over the next few weeks.  She lives for feedback and suggestions, so please give her a shout in the comments of our future posts. 

Following Danielson's advice: "Find What You Love... Do More Of That..."

My last blog post was almost a year ago. If you don't remember it (or more likely didn't read it), give it a once over so the rest of this makes sense.

Danielson's words haven't just been ringing in my ears since his TMC15 keynote. They have been haunting my soul to return to my love: middle school.

This isn't going to be a well thought out blog post (sorry, not sorry) because I can't keep this a secret anymore:
I'm going back to the classroom in about a week to teach 8th grade!

This may be a surprise to a lot of people, but lemme explain:

REASON #1: The Kid.

A few weeks ago, I got a text from my 13-year old:

Don't say anything and don't ask right now, but there will be a job opening at my school and I want you to apply for it. I'll explain this afternoon.

Also, don't text me back, I'm texting from the bathroom.

[Sidenote: EW, just... EW.]

His teacher got an admin school in a neighboring state. I wondered if my kid really understood the ramifications of having his mom in the same building. The conversation on the way home that day went something like this:

Me: I would have to change your schedule so you can be in the other class with Ms. Watson.
Mike: No. I want YOU to be my teacher.
Me: Wait, WUT? You ADORE Ms. Watson.
Him: I know... I just want you as my teacher.
Me: ...are you sure you know what you're asking?
Him: Yes.
Me: ...you know I don't play in the classroom - being my kid doesn't exempt you from that
Him: I know.
Me: **still confused** so WHY would you put yourself through that?
Him: Your students have told me how awesome you are in the classroom MY WHOLE LIFE. I want to have that for myself. I want to be in YOUR class.
Me:.....
....
...
..
.

**bursts into tears**

I don't cry often, but let me assure you: I AM AN UGLY CRIER. My child has never complained or asked me for anything related to all the CRAP he's put up with during my career: long absences for conferences, crazy schedules with archery coaching, long nights locked in my office working, going off to watch games and performances of current and former students all over the place... And that's just what little I can remember.

Through all of that, he's never asked me for a single thing - until now.

REASON #2: The MTBoS.

That incredible request from my child was also paired with the overwhelming #MTBoSJealousy I've had the past 3+ years.
Do you people KNOW how difficult it is to read the AMAZING blogs you post and NOT be jealous??? Don't even get me started.

I miss the days when I could say, "I did a thing today! Here's what happened, here's what rocked and where I think I could improve. How ELSE could I improve the thing? And by the way - if you use this thing, let me know how it went!" I miss being able to write and reflect in my A.D.D. style that most people couldn't tolerate. I miss the days when I had something to contribute to #MTBoS instead of feeling like a thief.

REASON #3: The School.

I cannot say enough about the leadership and the faculty of this school. I can't enter the building without feeling an energy and positivity about learning that is hard to describe. I feel the need to obnoxiously high five each teacher and student when I visit the campus. The teachers have always made me excited to bring them new ideas because of their passion for teaching their students. I am completely honored to have the opportunity to work with and learn from one of the best math PLC's I've ever seen AND I get to teach next door to the incredible Cononiah Watson!! (Most of you have seen her around #msmathchat.) I also get to work for an administrator whose vision for students and learning aligns 100% with my own. He will push me to be a better teacher than I ever knew I could be, but that comes with a huge amount of trust and support for my vision to make mathematics accessible for EVERY STUDENT.


REASON #4: ME.
TEACHING MIDDLE SCHOOL ROCKS. I miss the middle school classroom more than I have words to express. Maybe it's the age, maybe it's my humor, maybe it's the height similarity... But I love middle school kids. As a math coach, each day I have the opportunity to work with kids is a fantastic day for me. It's what I love and what I truly feel I'm meant to do.

Did I mention I get to coach MathCounts AND archery again??? **SWOON**



So that's my news.

I'm excited, I'm extremely happy, and I can't wait to share what happens in this room with you...

Once Mr. Bunnell gives me the keys, haha.

A Different Type of "Notice" and "Wonder"

As I was walking down a middle school hallway yesterday, I glanced up and noticed some hand drawn pictures of student faces with the phrase "I wonder..." at the beginning of each one. I noticed statements like:

--"I wonder how many stars there are in the night sky."
--"I wonder if horses were ever used for something else."
--"I wonder what New York looks like from the air."
--"I wonder who is leading rushing in the NFL."
--"I wonder how many hairs are on my head."

I was excited at first, thinking this assignment was from a math class where students were asked something like, "What have you always wondered that might be number/math/geometry related?"

When I noticed the next set of pictures, however, I stopped in my tracks and my heart sank as I read:

--"I wonder why I'm here."

--"I wonder if I will ever have love."

--"I wonder who I am."

--"I wonder what I'm going to do without my mom."

--"I wonder if there's really truly any good in this world."

As I noticed this shift in responses, I began to wonder: what conversations happened AFTERWARDS?


Middle school is rough - probably more so than when I taught "back in the day". And I get that teaching middle school is like licorice - you either love it or you hate it. But for me... teaching middle school was incredible because of opportunities. Sometimes those opportunities were about shifting perceptions about mathematics. Sometimes those opportunities were about encouraging confidence. Sometimes those opportunities were more personal. Regardless of public opinion about standards and "new math", teaching comes down to relationships and trust.

I can't get those pictures out of my mind.


Christopher Danielson said, "Find what you love. Do more of that." during his TMC15 keynote. Yesterday was a reminder: THIS (middle school) is what I loved.

Now to do more of that.

Perplexed in Patterns

So much time has passed since I last blogged that I forgot my account/password. I think I tried at least 3 combinations of each before I cracked into my Blogger account. Hopefully I will do better in the future. I know I promised two blog posts tonight, but I forgot how difficult blogging is with my attention span.

Instead of conducting PD this week, I'm actually attending some professional development through the University of Mississippi's Center for Math and Science Education (@UMCMSE). I've probably mentioned how great this group is many times before. I attended their CCSS 3-5 workshop last year and fell in LOVE with elementary mathematics. What I love most about these workshops is that it doesn't rely on a whole lot of tech. It's basically, "How can we teach the standards in ways that students can make meaningful connections with stuff you probably already have in your classroom." Unfortunately, "technology" isn't standard across the state. In some schools, cell phones are banned from campus and wifi is wonky most of the time. This is also true for several schools in my district, SO going "low- or no-tech" is a challenge for me.

This week, I'm attending the 9-12 workshop on the *cough cough* Mississippi College- and Career-Readiness Standards. On day two, Dr. Julie gave us the following patterns task (adapted from College Preparatory Mathematics).

Patterns. Ok, I got this (thanks to Fawn Nguyen and Visual Patterns). So the first thing I notice is that if I moved that top block that's "hanging out" to the hole in the bottom right, I could make a rectangle. Badda bing, badda boom. I'm good.

** I should say here that I realize it asked for an equation and I created an expression... but I was all "celebratory" and stuff, and apparently the rest of the class was as well. We all did the same thing. Whoops. :)

We all went around the room and discussed how we got our expressions and there were some pretty interesting ones:

This person immediately saw the square in the center and the constant "extra" block up top. She also saw that the bottom row increased by one block for each phase and then realized it was the phase number plus an additional block.

I found this one really interesting because it's one I wouldn't have seen. This person added extra blocks to create a square. Then saw the pattern of doing that created three sets of "trains" of the same length plus the addition extra block needed to complete the square. (I am not explaining it as well as her work, haha). Still a very cool strategy.

So we all "ooooh'ed" and "ahhhh'ed" over each others strategies, how they were similar, how they were different, and how we could visualize that expression repeating for every new phase. And the question arose: "How do you know you're all correct?" The answer: "When we all expand our expressions, we get the same thing." "Oh really? What did you get?" "We got n^2 + 5n + 6."

And then Dr. Julie rocked my world.

"So we could easily see the repeated pattern of each of your expressions in the phases. Here's my question: Where do you see n^2 + 5n + 6 in each of the phases?"

Ummmmmmmm.....

But...but...but, I did the thing! AND I could justify the reasoning of the expressions created by my peers. We ALL did the thing.

No one had ever asked me to do this before. OH CRAP. My comfort zone was rocked.

Ok, wait, Hedge. You can do this.

Yes, I could find an n x n square in each of the phases with no problem. And I could even find six extra blocks. But the 5n? What would that even look like?

Not only that, but I have to make sure that the pattern is consistent (and not random) in each of the phases??? Oh LAWD. Let me channel my inner 4th grade Max Ray (reference this @ 1:56 - 2:00) and figure this out. This took a while.

(http://www.sticktwiddlers.com/wp-content/uploads/2014/11/time-passing-gif.gif)

Low and behold:

I found the n x n square, found the trains of length n on each side of the square, one additional train of length n below, and then six blocks (noted by the dots).

So you know me...

Then she gives us this:

I could do the "normal" inside my comfort zone. But this was new and initially wasn't easy for me. So instead of following directions (sorry, Dr. Julie, if you're reading this), I challenged myself to find the expanded pattern for each group.

And this is probably no big deal to most of you, but I've just never even thought to find the expanded form within the pattern before.

And I LIKE IT. :)

So here are my solutions to A and B. If you decide to do C and/or D and wanna compare, tweet me.

How Much Is A Ton Of Dollars?

NOTE: Apparently Chris Robinson already asked this question on 101qs.com and I totally missed it (or forgot).
Sorry, dude. Ma bad.


I rarely watch TV these days, but today I heard this commercial while watching a recording of Perception ("Silence" episode):


"If you had a dollar for every dollar car insurance companies say they'll save you by switching, you'd have like a ton of dollars."

Oh really? Interesting.

We all know this is my brain:

Because of that, questions start randomly popping in my head:

1. Which ton (short, long, metric)?
2. How much does a dollar weigh?
3. How much would a million dollars weigh?
4. Geico claims to save me 15% or more, so how much would that weigh?
5. How many car insurance companies are out there claiming they'll save me money? And at what rate?
6. ...How much does my insurance cost since I got a speeding ticket?
7. What's the value of a ton of dollars?
8. Are they exaggerating?

It reminded me of the Carnival Cruise commercial that advertised "...in any one moment, there are over a million ways to have fun".


A million is a lot. How would you quantify that? You're on a boat (I'M ON A BOAT!) with a limited amount of space and, while I know there are fun things to do, are there really a million ways?

Let's call this the lesson I always wish I'd written. Show students several advertisements that sound too good to be true and then get them to figure out how to prove or disprove the claim. Then have students put together some type of undercover news report (or Weekend Update "REALLY" skit) to pretty much call them out on it and let the mathematics back it up.


Back to having a "ton of dollars" (and what the value is), that's becoming an interesting task for me (now that Perception is over and I can focus). The question of "How Much Is a Ton of Dollars" seems so much like a Robert Kaplinsky question that I had to go look at his lesson page a few times to see if he'd already done it. I love Robert's work, so this lesson would be along the lines of the amazing work he's done (and that I've used from 5th grade to adults).


With my imaginary students, I would take the "be less helpful" path of making them figure out what they would need to answer the question, "How much is a ton of dollars?" I'd want them to start by estimating (shoutout to Andrew Stadel) the value of a ton of dollars, and have them write those estimations down and commit to a value. If I had a classroom (did I mention I miss teaching?), they'd write their estimate on a Post-It note (their name on the back), and then plot their estimates on a data wall (dry erase board with a blank number line at the bottom - this board would ONLY exist for plotting data, no announcements, etc.). I'd like to see the range of estimates and have some really good "notice" conversation about their estimations. At this point, my students would be in groups with the goal in mind of finding the value of a ton of dollars. I wouldn't want to tell them what to do first because I'd want them to figure it out.

Weight would be a great discussion to have with students once they started realizing in the research that there are three types of measurement for a ton:

Weight of a dollar is pretty easy to find from any search engine, but I would like to encourage my students to find the legitimate primary source of information (not to take the word of Wikipedia or random resources). Depending on the age group, they might know about the Treasury Dept:

There are about 453.592 grams in a pound, so I would hope to hear students recognize that a pound of dollars is worth between $453 and $454. If there are 2204 pounds in a metric ton, then "a ton of dollars" would roughly be worth between $998,412 and $1,000,616. That's A LOTTA dollars.

Back to the original Esurance claim:
"If you had a dollar for every dollar car insurance companies say they'll save you by switching, you'd have like a ton of dollars."

So basically:
"If you had a dollar for every dollar car insurance companies say they'll save you by switching, you'd have around...

That still seems like a lot of money and makes Esurance's claim kind of fishy.

Hmmm... So let's think about this. Here's the claim from Geico:

So Geico is one company offering to save me 15%. Let's say I didn't get a ticket (I WISH) and my car insurance is about $150/month. I could save about $22.50 by switching to Geico. But that's a single car insurance company. How many companies offering $22.50 each would I have to talk to before I was offered "like a TON of dollars"?

Well, if a ton of dollars is about $1,000,000 and each company can save me roughly $22.50, then that would be approximately 44,444 car insurance companies offering to save me money. WOW. Is that even possible? Are there seriously over 40,000 different car insurance companies in the U.S.? Hmmmm. That makes me wonder, "How many different car insurance companies are in the U.S.?" The first thing I found in my research was information from Wikipedia. I can't use that because I told my imaginary students they couldn't use Wikipedia as a source, hahaha. Then I found some information from "LoveToKnow" which promises to be "advice I can trust". Ummmm...NO. Without links to primary evidence from a legitimate source, I'm not going to trust you because you told me I could.

I did some IRS digging wondering if I could get a list of car insurance companies (because they'd have to have a tax ID number, right?). But maybe I have to pay for that information like they did in "Gone in 60 seconds" when they were trying to track down the cars ("$5.00 a car, 20 cars, would you like a calculator?"). I guess this is where I'm currently stuck. Hmmmm. Any ideas?

In any case, I don't know exactly where this lesson would fit. It might be a good application problem for 5.MD.1 (and could also tie in 5.NBT.7 if we round to the hundredths place). Or maybe this would be a good 1st day problem for 6th or 7th grade just for students to work on Math Practices 1, 3 and 6. I dunno. I didn't really set out to write this post as a lesson, but it kinda turned out that way. If it helps, great.

If not....

Mario's Parabola... Or is it? (with Update)

Most of the time my A.D.D. is a huge pain, but tonight it actually gave me a cool idea. Well, sorta cool. Maybe not cool at all. I dunno - you make the call after you read this and let me know if I'm way off base.

BACKGROUND:
I'd shown a Dan Meyer video today (short and sweet video here). As usual, I didn't close out the tab after I showed it (yes, Joelle, I know I have a problem). Tonight, I started to use that tab to search for something else, but a video on the side caught my eye:

Parabolas in Mario?!!
**watch it**


I thought, "Hmmmm... I see a some errors in there. I wonder what the reasons were? Is it a true misconception or is it lack of drawing capability? Do they think some of these statements are truly correct? Did they verify it mathematically on paper and can't draw to match?? WHAAAAAAT happened???"

**I'm telling you, A.D.D. run amuck - I can get quite dramatic**

Anyway, I started to dismiss the video and get back to what I SHOULD be working on, but I accidentally scrolled in the wrong direction. I saw this comment:

...hold the phone. This could get interesting.

The conversation continued:

My brain starts screaming "Math Practices THREE, FOUR, and FIVE!! HELLOOOOOO???"

So, because I have three more workshops to prep for this week, I'd like to leave these little "idea nuggets" with you:

Idea #1: Mathematically critique the video

Show the video to your students and ask them if the video is mathematically sound.

"Hey guys - watch this video I found this weekend. Does anything weird stick out to you? What questions do you have when you watch this? Is there anything we can use to verify or critique the mathematical statements made in the video?"

Idea #2: Verify your side and critique the reasoning in an epic math battle

Show the conversation to your students and ask them to prove who is right.

"Hey guys - so I found this video over the weekend that you gotta watch. But THEN... oh, this is REALLY REALLY good... THEN, they get into this "math war" in the comments. Who do you agree with? James Bond people on this side of the room... T.O.D. people on this side of the room. You guys need to use some type of mathematical tool to (a) verify that your guy is mathematically correct and (b) prove why the other guy is mathematically WRONG. Choose your side aaaaaaaannnnd.... GO! "

I'd love to find the time to take screen shots of that video, load it into Desmos and actually determine the answers to those questions, but you know what I would love even more?

...watching students jump at the opportunity to do it.


IMPORTANT NOTE:
Within the verification, I would expect students to do it in a "constructive" way. I don't want to encourage "math burns" in the classroom - that will destroy the collaborative culture that we work very hard to build inside the classroom. I think this would be a great opportunity to talk about ways to "critique the reasoning of others" without being a total jerk face.


UPDATE:
You cannot imagine the appreciation that warmed my cynical old lady heart when I saw this tweet from Desmos the day after this blog posted:



You can click on the tweet to take you to Parabola Mario.

Desmos, thank you. <3