In which I explain our homework policy.
Did I miss any of your pressing questions? E-mail me or reply in the comments.
In which I explain our homework policy.
Did I miss any of your pressing questions? E-mail me or reply in the comments.
Time to rethink my integration of science with math. My attempts to connect proportions of the human body with measurement went down in flames in my entry last year, so I’m focusing on Systems, Order, and Organization related to sound this time.
I know sound, math, and science are all suuuuuuper tight. What I don’t know is how to adequately organize my sound unit so it includes great inquiry-based investigations. My guiding framework is an annnnncient curriculum from the National Science Resources Center (published when I was in junior high) that has such profound extension activities as the one featured below:
Ugh. Not helpful. It’s worth noting that there are a whopping two math extension activities in this entire unit.
The wise and enthusiastic Katie Weichert gave me some great ideas to chew on and think about. I wish I saw her more often. But in her absence, I had to get a move on.
So I started trolling the Internet.
This Aztec music lesson seems compelling.
I’m also interested in harmonics, but I don’t know how to build this into a full lesson. My students already use harmonic series as a procedure to line up from music class, so I wouldn’t need to go over the basic musical idea of third and fifth intervals.
THIS could be useful. It appears to be a sound generator. Could I have kids compose a song using fractions and then convert them to their frequencies? Speaking of composing music…
I imagine I could show snippets from Donald in Mathmagic Land and have students generate questions from that? Yesssssss, I could totally do that… That way the learning would be authentic and related to the curriculum we already have in place!
My only concern remains starting with a video. I want to make sure I’m looking for an introduction that inspires perplexity, not just engagement. After the 27-minute video was released in 1959, Walt Disney admitted:
“The cartoon is a good medium to stimulate interest. We have recently explained mathematics in a film and in that way excited public interest in this very important subject.”
(emphasis is my own) Now in looking at moving from merely interest to investigation…… I suppose that recording student questions will take care of that fear, right? Then having their questions shape the following lessons?
Hmmmmm. Of course, there are a wealth of videos available on sound and math, but much of the information is so complex that I can’t figure out how to simplify it.
I’m also interested in looking at the materials used in instrument strings and the number of strings included in different instruments. How do the number of notes an instrument is capable of producing related to its system? Can systems be different sizes? Is a larger system necessarily “better” or more “complete?”
Anyway. Let’s see how this goes.
The open-ended math from the Wall Street Journal a week or so ago was pretty rad. But lessons like those are admittedly woefully rare in my classroom. It’s a huge shame, right? Learning like that shouldn’t just be a once-a-month or even (eep) once-a-semester event.
So I started pondering why doesn’t math look like this in our classroom every day. I needed to keep myself real. Here’s what I came up with:
I’ve purposely chosen those phrases because I think we teachers sometimes use them as ultra-self-deprecating or unproductive language and the conversation just stops there. But I want to explain why these really are often valid concerns (or at least, valid-feeling concerns) and then focus on how I’m personally working to move past them.
Perhaps you’ve already heard me rail against people who say “I’m just not a math person” and seen me express frustration that the idea “math is sooo hard” is a bunch of bunk. That said, I’m still thoroughly unconfident in my own math abilities. I was mortified when I transposed two numbers in our soccer math. I freaked out when Mr. Brown informed me I HAVE BEEN DOING ORDER OF OPERATIONS TOTALLY WRONG. So it’s fair to say that when I deviate from our district frameworks, it’s a little stressful.
I’m moving past this excuse by being willing to really lean on my secondary-level colleagues. I love collaborating, but I don’t particularly love admitting that I need help. So this is a huge area of growth for me. Also, taking the leap to put detailed lessons online has given me a chance for feedback from folks from across the nation, like from my favorite ladies in the Midwest.
I was euphoric when our class completed its project last week. I was also exhausted. I can get sucked into manic cycles really easily. Although spinning my way into a cycle can be absolutely exhilarating. I need to be honest with my body and realize that it’s not healthy for extended periods of time.
“The management is hard.” That’s what people tell me when I share our latest project. I agree, but not in the way they intended. Teachers often mean, “I’m going to have children stringing stuffed monkeys from the room if I open the lesson to exploration.” I share with my kids the explanation from Twyla Tharp’s book The Creative Habit that in order for creativity to take place, it happens within a system of order. A dance studio is essentially a bare floor and mirrors. An artist can’t create a masterpiece if she can’t dig out the right paints in her chaotic mess. And we can’t have deep, meaningful conversations about math in our lives if we’re not already solid in our class expectations.
So, the management I’m talking about isn’t the student-secretly-reading-under-the-table-instead-of-doing-math business. And it’s not because issues like that don’t exist in our classroom — the aforementioned situation actually happened last week and was dealt with swiftly. I’m talking about the mental gymnastics I put myself through as I’m wandering about the classroom facilitating conversations. Although the brain only takes up 2% of our body weight, it uses 20% of our energy, according to Bill Bryson‘s A Short History of Nearly Everything.
So I’ve gotta keep myself mentally in shape. That means reading tons of books I love even when other teachers tease me. That means blowing off grading homework for a night to paint my nails. That means making time for my physical health and not necessarily devoting hours of lesson planning each day.
Not enough hours in the day. I’m, frankly, super-pissy when I hear teachers say this, and then five minutes later I’m nodding at the truth in it. Because yes, our job is impossible and yes, there are insane demands coming at us from all angles. But I feel like you can’t automatically default to complaining about time without carefully looking at how you currently do spend your time.
For me, this has meant a intentional devotion to super-quick transition times and an up-tick in the priority I make in keeping my room clean so I don’t have to scrounge for materials. Now, my goal is shifting to providing great math instruction by still letting me be a human.
Among neuronormative folks, the general consensus is I’m an overachiever. *I* don’t feel that way, but apparently the speed with which my brain works and the resulting efficiency I have in completing mental tasks makes me one. When I think of overachievers in my mind, I definitely don’t want to be someone who spends hours constructing the perfect math centers that can only be used for a week or two. I’m certainly not that extreme, but I admit I’m still working on this. Mainly because I get sucked into interesting information online and can’t pull myself out. But limiting myself to a half-hour of prep time before class begins seems to have been a good boundary to set.
I want a system, whether it just be an internal mental process or a procedure I can use in my classroom, to ensure that I’m pursuing great math with my kids but I’m not spending hours in the staff lounge or on the Internet to do it. I suppose a time-hog that others might forgo would be the time I spend documenting my process and further questions I have through blog posts here, but the writing-about-it part is just fun.
I could continue writing, I suppose. But I’m off to redo my nails. Because I’m only going to really be a good teacher if I know when it’s time to let go.
When you take time for yourself, good things follow. In this case, it was some REALLY AWESOME MATH.
Friday morning, I missed the bus (oops) and was able to drive to work at a legal speed.
I’ve been thinking a lot about Dan Meyer commenting on how we spoon feed each step to a problem solving situation, and so today, I went out on a skinny limb and used this graphic to help us work on our measurement skills. I wasn’t sure where our work would take us, but we’re early on in the unit, so many of my students are still working to measure accurately using a ruler.
I showed them the graphic, and Samuel helped me pronounce all the players’ names. He was our resident expert. Then I opened the floor to mathematical questions.
Here’s what we brainstormed as our big questions.
Then, people started asking more “nitty-gritty” questions, which we identified as being the “questions along the way” you had to answer to get to your big ideas. We kept this poster up as we worked. I stayed near my computer so I could capture students’ comments.
“You need to know how big the field is,” Savanah spoke up. I handed her my iPad so she could find the field size. She paused. “Do I need to know like, how BIG it is or how long the sides are?” “I think you’re asking me whether you need the area or the perimeter?” “Yeah… ohhhh, I need the length of the sides.” Here’s the information she found.
After checking another site to verify the accuracy of her information, we added the dimensions of the field to the poster. (Yes, I know I could have taken a screen shot of the iPad, and I did, but I couldn’t get the image sent to my computer. Hrmph.)
“But what’s a yard?” “Who can answer that?” “It’s three feet,” Ivy answered. “How can you check to see if you agree?” “Well, I could look in my math book, but I remember what yard sticks last year look like, and I know there are three rulers.” (I knew we’d need to convert from yards to feet to inches so they’d be able to convert the lengths they measured on their papers into the actual lengths)
“Well, then you need to multiply by three to get the length – 120 times three.” “Woah. How’re we going to do that?” “Use a known fact, 12 x 3.” “36?” “Yeah, 36.” “So it’s 360 feet.”
They did the same for the other side. Then a group of students wanted to determine the linear distance the ball traveled for each player. I asked how many inches long their picture was, and Marcos stopped us all.
Marcos: WAIT. You blew up the picture from your newspaper article. So our picture isn’t the same size as yours and the distances will be all different. (I photocopied the graphic at 121% so it’d be easier to read than my original copy of the newspaper.)
Me: Nice. That would be a problem if the image were STRETCHED like a rubber band and warped, but since it was enlarged to scale, we’ll be okay AS LONG AS you don’t let me use my original copy, okay?”
Marcos: Okay. So the field is 11 inches long.
“You know, if they would have just included a map scale on this picture, we wouldn’t have to do ANY of this measurement.” “I guess that’s why Miz Houghton wants us to be able to use map scales in social studies.”
Then a few of us worked to create this poster.
We knew the field was 11 inches in our image, but we wanted to know how far just ONE inch would be because then we could find out how far Jone Samuelson’s 6-inch kick actually went. We also knew how long an actual field was, so we tried to find the relationship between the two.
Using a fact family (the triangle drawn above) helped us figure out the ratio. Or. What I initially THOUGHT was the ratio. DO YOU SEE MY GLARING ERROR??? I didn’t notice until lunch. I neglected to convert the 240 feet into inches so the units matched. Drat. I frantically called AP Calculus teacher James Brown to make sure I didn’t make any further errors.
So after lunch we converted 240 feet into inches, THEN used the ratio and found out that one inch in our picture equalled approximately 33 feet.
Some students switched to using calculators for these larger computations, which gave us a chance to talk about how calculators represent 1/2, equivalent fractions (5/10), etc. Above, Alejandra calculated how many feet David Villa kicked the ball (5 inches, according to her measurements, making the kick 165 feet). I asked her about the “33 in. in a inch” she wrote, and she said, “Oh no no no, it’s not 33 INCHES or that would be like a mini soccer field.” So she was also looking at reasonableness of answers.
Another group wanted to know how far the balls would have gone if they were kicked on the moon. Again, I told them to ignore the parabolic motion and just look at linear distance. I know the physics of this aren’t entirely correct, but I didn’t think it hurt the integrity of the original problem situation.
Oh, actually! Selam originally asked how far the ball would go in SPACE, but Maya pointed out that if the they were in space, the player and ball would both push off each other and the ball would never land (AMAZING INSIGHT, RIGHT???). So we clarified that the ball would be kicked on the moon, where there was still a force acting on the ball, but a lesser force than what we’d find on Earth.
Adam went to the classroom library to find out what the gravity was on the moon. Here’s the passage he found, from the DK Eyewitness Book UNIVERSE.
Eayn: It says the gravity is one-sixths of Earth!
Me: So the gravity is 1/6 of the gravity on the Earth. So if we are converting from the moon, what would we have to do to the distance we calculated for the ball kicked on Earth?
Adam: Multiply it by three?
Me: Where did you get three from?
Adam: I dunno.
Milena: Multiply it times five.
Me: Five? Where did you get that from?
Milena: If the moon’s gravity is 1/6, then the rest of the fraction that’s left is 5/6.
Me: Ohhh, I think I see what you’re picturing in your head. But think of the gravity on the Earth as being one whole, and the gravity on the moon being 1/6 of that whole. You’re not looking at the other 5/6ths.
Vy: You’d multiply it times six.
Me: Where did you get six from?
Vy: If it’s dividing by six to get the pull on the moon, then you’d multiply by six to show how much further the ball would go when it has a sixth of the gravity slowing it dowwn.
Me: So you’re saying that fractions can be a way of dividing.
Vy: Yep. And then the opposite, er, inverse, is multiplying, so you times by 6.
(It is perhaps worth noting that Vy has not voluntarily spoken in front of the class in the past year and two months)
Wow. So now that we knew how to find distances on Earth and on the moon, we plugged away, with at least three people needing to agree on their measurements to the nearest half-inch before we would post the results. (reviewing our estimation and rounding unit from earlier in the year)
As we approached second recess, we posted what we’d come up with so far.
We also reflected on what we’d learned over the course of the day, and on the math we used.
As you can see, we didn’t finish everything, so some students asked if they could finish the calculations during Math Daily Five. UM, YES OF COURSE.
What suggestions or modifications do you have to offer me and my students? Where can we take things from here? Other thoughts?
I’ll start with a quote that resonated with me so I can begin on a positive note. Despite my best efforts at having positive intent, this conference unfortunately didn’t meet many of my needs.
“We need to stand up to the politics of learning that do nothing to benefit kids.” ~Roger Fisher
I started off my day with the stereotypical edtech presentation that Dan Meyer talked about at #nctm12. You know the presentation I mean.
It’s the one that starts out with the picture of the baby with the iPad next to the picture of students back in the dizzay looking tortured by their lives in the dark ages. Then there’s a video with sinister, throbbing music or heartbreaking overly calm music that incites panic that we’re JUST NOT DOING ENOUGH.You know, like this one:
Then the edtech presentation goes on to hit all the overworked, oversimplified tropes that education presenters like to trot out when they want a quick burst of laughter or nodding heads. You know, things like:
“Not all of us can have the technology that Bellevue has.”
The presentation goes on to grumble about charters and questionable instruction methods.
The presentation then continues to say that Common Core doesn’t address thinking strategies, and he then went over Marzano’s strategies and said all sorts of “isn’t this a shame teachers can’t do this.” Well, MAD PROPS, FEDERAL WAY, because this is crazy-old news to me because you’ve been focusing on these strategies for the past three years. So this last bit was good information, I just happened to already have training in it.
And then, the end of the presentation.
I don’t need more negativity at conferences. I don’t need sarcasm and snark and negativity from PRESENTERS at conferences. I get enough of that during my everyday interactions with disgruntled educators. I came here to channel our collective energy into something effective. Diane Ravitch told me that public education is a negative place, and I kind of need to suck it up and just accept that, but I don’t believe that avoiding destructive negativity means I’m keeping my heads in the clouds or avoiding big issues. Anyway.
Then there were speed sessions, where we had a chance to talk with folks from other schools. I didn’t move around because I wasn’t ready yet. So I stayed at my table with my district folks. It wound up making me want to barf because of comments such as “none of my kids are actually gifted,” “I don’t even have kids who are able to do any work.” Thankfully, MY PEOPLE get me and they helped me not scratch any eyes out.
“A gifted child is JUST AS DIFFERENT from “the norm” as a severely handicapped child.” ~Roger Fisher.
Next session. “10 Things Students Should Know about Math and Science.” Actually, I only got through two of the ten things before I had to evacuate. Our presenter was excellent at reading his slides out loud. I had an opportunity to read many Dilbert comics and plenty of cartoons of Albert Einstein. Then I saw this!
I was fortunate to see Briana was enjoying her session a few floors down, so I hustled to join her. Surprise! Presenting was Lisa Van Gemert, Gifted Youth Specialist for Mensa. She covered lots of information about how gifted kids’ minds work. It bolstered what Dani and I had been saying earlier in the day when we were freaking out about the perception that “you can just put gifted kids in a gen ed class and all they need is harder work.” WAT.
The lunch keynote was another fascinating PowerPoint-let’s-read-the-text endeavor. I don’t remember what it was about.
I entered a session about “real-world high-level independent projects,” but then saw expensive binders bursting with color photocopies of a student’s pretend application to U of M, and an educational trip to Washington, D.C. Not really my bag. Not really my students. So I left.
I’m glad I did because I saw a pretty solid presentation by Adam Brock called The Beauty of Independent Technology Projects! The presenter was nervous and admitted to as much, but he had GREAT information! Rock on! Present again! “This is authentic, this is authentic, this is authentic!” Dani says. “I needed this session really bad.”
I doubt that I’ll attend WAETAG next year, or if I consider it, I’ll definitely take a much closer look at the presenters. Bring Brock and Van Gemert back and I’ll be back.
Anyway. More reflection to come. Did I leave with some new learning? Yes, but I had to dig really hard to get there…
Yesterday marked the first (half) day of the NCTM conference. I am SO very glad I took the extra day to fly in.
I can’t say enough good things about the Belmont Hotel folks. The shuttle service was low-drama and speedy, and everything I’ve inquired about has been answered kindly and efficiently. My greatest discovery was locating the blow dryer. Yessss.
Most of Wednesday was spent sleeping and doing final tweaks on my presentation. I ate delicious food at SMOKE, the restaurant connected to the Belmont (hangar steak salad, BBQ beans). I slept some more, then I headed down to the convention center.
The opening keynote was Scott Flansburg, the Human Calculator, a dropout savant who spent most of his hour-and-a-half presentation name-dropping all the TV shows he’d been featured on and all the famous people he met. The presentation was pretty mediocre, and I was forced to depart early due to excessive cologne application by my neighbor (who was three seats away). I found myself longing for a return visit from the brilliant and charming Jane McGonigal, who was our opening speaker at the Title I conference.
Trundled back home, ate dinner at SMOKE (mac and cheese), read books, watched Sherlock, slept poorly. The only thing that kept me from freaking out about my lack of sleep was marathon guru Hal Higdon’s advice. He says that you probably will get an awful night’s sleep before the race (or presentation), so it’s actually more important that the two nights leading up to the night before the race are solid. Seeing as how I slept through most of Tuesday and Wednesday, each time I woke up, instead of panicking, I was able to tell myself, “Aren’t you glad you slept so much before?”
Have I publicly mentioned how much I adore Skype? Because I adore Skype. In addition to the tremendous potential it has in my classroom, it’s also really freaking amazing to be able to see my sweet husband’s face before going to sleep when I’m away feeling insecure. Also, I got to see my kitty cat. Who is admittedly cuter than my husband. And equally furry, given the current unshorn state of Toby’s beard.
I arrived in Dallas yesterday evening.
This is an enormous city. I flew into the airport featured in Gila Monsters Meet You At The Airport. It is an enormous airport. I was met, not by a gila monster, but by the lovely educator-history-buff-museum-gal Elaina (Hauk) Carlisle, who I’ve known through MSU-genius-friend-and-roommate Franny Howes for close to ten years, but have never met in person. She has a fantastic house with epically tall ceilings and a friendly, happy mutt who looks like a Muppet. And a husband, who is accustomed to lengthy teacher-talk conversations.
We drove through Dallas. I saw the place where John F. Kennedy was shot, which is frankly still giving me extreme feelings related to creepiness and the power and gravity of history and all sorts of other random emotions. Yes, I saw the grassy knoll (it’s small). Yes, I saw the book depository (it’s ordinary). I am still processing how such a short glimpse — we literally just drove through the intersection, not stopping — of an historical site can have such a big impact.
I’m trying to be reflective and thoughtful about tomorrow’s presentation without freaking myself out. I’ve been only marginally successful.
My most significant crisis of confidence came this morning, when I sat up in bed (or rather, flopped over in bed, pushing the aforementioned Sherlock Holmes volume off me) and said, “I can’t possibly read a book as a part of my freaking session; no one’s going to sit around and hear a whole book!”
I fretted. But I reread the speakers’ notes and focused on this bit, “Your presentation method should be consistent with and model strategies that NCTM advocates for classroom teaching (Example: Principles and Standards for School Mathematics).” Hm.
We’re always complaining about math standards going a mile wide and an inch deep, right? So I got myself in check. What better way to demonstrate the importance of deeper understanding by anchoring this brief (hour-long) session around one common text? After all, I told myself, THE TITLE OF MY FREAKING PRESENTATION IS DEEPENING LITERATURE CONNECTIONS. I mean, this way, even if they hate my presentation and the strategies presented, they’ll be able to bring news of a fantastic new picture book back to their schools.
So I’m sticking with sharing Extra Yarn and using it to illustrate how the language of teaching comprehension strategies used in literacy can be math. I’m sharing student-derived examples of how math can be taken from the book. People will be able to try out their own problems and I’ll post them on this site.
Additionally, I found this part of my speakers’ email useful:
New this year! Attendees will have the opportunity to rate presentations using the survey on the Dallas Conference App.
Using a 1-5 scale attendees will rate the following:
• Overall rating of session
• Presenter’s knowledge and understanding of the topic.
• Presenter’s use of appropriate and effective teaching and learning strategies
• Likelihood of attending another session by this presenter. (Yes/no/maybe)
I know I won’t be able to please everybody with my presentation, but JUST LIKE WITH OUR KIDS, it’s so helpful to know what I need to do with the end goal in mind, so seeing what I’m going to be rated on helps me narrow my mind from the bloom of concerns that are crowding each other out in my brain.
One last worry that remains is that I’m breaking copyright laws by projecting Extra Yarn. But… a picture book read-aloud isn’t a freaking copyright violation, is it? Lawd help us if it is.
Oh, also, I’ve been working to make sure I won’t be doing emphatic karate-chop gestures all presentation long.
Anyway. Enough. Time for lunch and reading.
In preparation for my talk in Dallas this October, I’m trying to read all the available literature on integrating math and literature, and my first book is Exploring Mathematics Through Literature, compiled by the NCTM.
There are plenty of resources for basic connections between math and literature (such as graphing from information in books), but I’m interested in developing longer-term project-based learning around a book. In the introduction to the NCTM book, the editors list several basic ways to integrate math and literature.
So when I first read that list, I completely freaked out. Like almost barfed the calamari and lemonade I consumed while waiting for my husband to finish his MAGIC draft. That pretty much covers everything, I thought. I have nothing to add to the conversation of math and literature, I thought. SHOOT ME IN THE FACE, I thought. I AM GOING TO MAKE A TOTAL FOOL OF MYSELF IN FRONT OF HUNDREDS OF PEOPLE.
So then one of Toby’s geeky friends dumped a bunch of marble counters all over the lounge, and I realized that in the grand scheme of things, I was just fine.
In addition, I realized how to clarify my topic of “Deepening Math and Literature Connections.” All the books I see as examples in math lessons have some nugget of explicit math mentioned somewhere in them. And kids love that. When we read an excerpt from Little House in the Big Woods talking about unfair division of cookies, my students used that as an anchor example for weeks to come. So what do I have to offer that’s different?
I can show teachers how to see the math in books where concepts aren’t obvious. One of my favorite examples is the geometry-based assessment I made for Barbara Kerley’s What to Do About Alice? Whenever I do stuff like that, that’s when my colleagues throw up their hands and say “I don’t understand how you come up with stuff like that, Shannon.”
So now I have to figure out how I come up with stuff like that, and come up with it quickly. Because that’s at the core of what I want this conversation to be: it’s all well and good for the NCTM to publish AMAZING literature-based math units, but we really need to get math and literature to live together EVERY DAY in a sustainable way so teachers don’t feel overwhelmed….. As a newly-elected union rep, I believe I need to say, “It’s a workload issue.”
That gives me a little more focus…. Please come to Dallas. Please listen to me talk REALLY REALLY EARLY. It will be fun, I promise.
Tomorrow we’ll have a chance to see Rick Hartman and learn more about his School of Toy program. Feel free to nose around the website before our 9:30 AM assembly tomorrow!
After the positive reception from my students about our Uno’s Garden review activity for estimation and multiplication, I decided to create a similar activity to practice the skills from our geometry unit.
You can see our district power standards here. I’ve modeled the activity directly from the state standards, though, because there are a few holes. Also, looking to the future, here are the geometry Common Core standards. I linked each of the problems to Barbara Kerley’s great biography, What to do About Alice?
We’d been reading So You Want to be President, and I remembered this image from Kerley’s book:
The couch! We could find the perimeter of the couch! So I developed a set of six questions related to the book, posted them around the room, and had students move from question to question at their own pace. Because we’re a 2nd/3rd grade class, there are questions at a variety of difficulty and depth of knowledge to permit everyone some successes.
You can see the questions and my answer booklet below (I always print it on special paper because students have told me it makes the activity feel more like a quest or a scavenger hunt rather than just skills practice).
Please let me know if you found this lesson useful! I’ve found it to be a much better alternative to a straight-up assessment.