Category Archives: Good Teaching
I’ve been off. For a long time. But I’m coming back with lots to tell. Firstly let’s do a then & now to summarize a fews items.
I wanted to get back to working with people, in classrooms, so I applied for and was chosen to work at Heritage High School as an instructional technology teacher. It feels good to be a regular on a campus. I get to hear, “hi Mr. Butler” again. I missed that. I’m working in depth with a handful of teachers, running some side projects with digital citizenship and social media, and showing teachers ninja moves with ed tech. A couple of those teachers I work closely with have been starting to use Desmos, particularly the activity builder content.
My wife and I are expecting a child on valentine’s day. We don’t know if it’s a boy or a girl, and honestly I’m not sure if I’m biased one way or the other. People keep asking us if we’ve at least got a name. Some have encouraged to follow the J-trend from our families. My name is Jed, and I have an older sister (Julia) and a younger brother (Jake). Both of my brothers-in-law are J’s (Justin and James), and my nephews are Jace and Jayden. I think we’ve about exhausted it, so we’re aiming for something from the other 25 letters from the english alphabet.
For those that don’t recognize it, the image is from Son of Flubber, the follow-up of Disney’s Absent Minded Professor. Friends and family sometimes listen to what I say and they imagine this guy in the picture, conjuring up crazy experiments for the classroom. In my position as a coach, I’ve lost the opportunity to use my own classroom as a lab, but the alternative is actually turning out to be awesome. After some convincing, the teachers that I work with volunteer to host my experiments. I’ve been able to see students use Google drawings and slideshows to improve vocabulary in a Spanish classroom by personalizing the content, 3 ELA teachers are piloting a new internal blogging system that utilizes the open platform from wordpress.org, help support the video production course in establishing a daily news show, desmos activities in math classrooms, and building a digital citizenship program for the freshmen foundations courses. The assistant director in my district now shares a workflow spreadsheet with me entitled “Jed’s Hair-Brained Schemes”.
With all this excitement, I still want to do some old favorites – so I have plans for two big math + tech series, both housed over at transformulas.org.
- I love transformations, and I see how it builds a backbone for secondary math in today’s classroom. I need to share this conversation with others. So I’m writing about it over the next while (let “while” be somewhere between 6 months and a year; I really have no idea of the time line)
- Desmos Activity builder is awesome. I need to push myself to use it more. (Others should too). I want to dive into lesson (re)design playing in the desmos platform. No set goal here, but more a desire to build.
If I had to pick a favorite teacher, I’d have to say it was my dad.
My dad encouraged everyone to
- serve a need if you see it (even if it’s not your responsibility)
- get your hands dirty, (he used to call me and my brother ‘elbow grease’)
- realize that you have strengths and intelligence, no matter your background
- maintain a clean and organized space
- ask questions, but don’t try his patience
I’d say that I’ve grown to be quite similar in my own teaching and learning style with one major exception. My dad often commented to me, “I don’t know how you can have patience for all those rugrats in the classroom. I’d go to jail for knockin’ one of them up the head.”
I don’t think he would actually hit a student, but his point of having patience for so many teenagers is valid. They’re trying to balance hormones with academics, not that easy. This patience that I gained for working with teenagers came from my second (equally) favorite teacher, my mom.
I also tended to have more divergent approaches to problem solving, especially with people. My dad showed elements of this, through MacGyver like rigs to fix something around the house, but when it came to working through people problems his approach tended to be more direct (and not always diplomatic).
So how am I different. I have patience to deal with crazy people in the classroom.
“I need you to quiet down class.”
“I mean it, we’re going to lose a chance to get to our fun activity at the end if I can’t get your attention.”
“Class can we get the volume down a bit here, I don’t think this is working type conversation.”
We know this doesn’t work. Sometimes we get a routine that gets the attention needed for direction, but it shouldn’t be like an on/off switch. I’ve resorted to the number system, “Alright we’re at like a 6, and we need to be more like a 4.” It kinda worked. Once.
We want students to talk. We want them to be active in their learning. Sometimes it’s just hard to give the students a structure for managing their own talk. One simple classroom management tool I worked on with a teacher was to use a wordless chart, and reference it for what the expected conversations would be like in the classroom. Here it is:
The grey markers are used for what’s our target volume (star) and where are we currently (arrow). The chart includes silent, partner talk / seated, table talk / standing, and all out loud.
Less talk from the teacher makes it harder for students to talk back to a teacher, argue, or escalate in some other way. Using simple cues like this can help structure your students into a productive classroom. If you’d like to get the poster for yourself click the picture and it’ll take you to the Google Draw file. I enlarged the poster using a poster making machine at our student services center. Your district may have something similar.
If you have other ways of managing productive volume in the classroom, please share them in the comments.
This word has been on my mind a lot lately. One of the most awesome things in education in celebrations of success. A successful teacher, student, school, program, anything. With all the variables in teaching and learning, it’s often challenging to make significant gains.
When a little bit of the awesome does happen, people notice. Here are some reactions that seem common:
Admin and leadership:
How do we replicate that experience for a bigger group?
Let’s grow that.
(and within budget)
Would it work for me?
(my classes are unique)
I wish school could be more like this.
Why can’t school be more like this?
(school is always the same)
I’ve had some great times in the classroom, often working with other teachers to get some of this awesome to happen. Now I’m in a position to support teachers as a district Math Coach/TOSA. I get to help them incorporate or expand the awesome. No matter what I’ll be doing, this concept of scale is sticking with me. How do we take something and make it fit for the teacher on his/her scale?
Let’s make the awesome work, for each person and everyone.
How do you not worry about time? Or how can I better plan or pace my class time?
I promise to eventually get to my favorite formative assessment. First I want to describe how it became to be my favorite.
One of the things that really bugs me about pacing out a class period is doing an activity without a purpose. I don’t have the perfect answer as to which activities are the most valuable for class time. In fact I don’t think it’s universal. The activities must flow with the culture of the teacher and the class. Two activities that used to bug me were:
- Exit Tickets
Why not Exit-Tickets?
I’m starting with the end here. And that’s the part that I struggle with the most. I remember the first time I heard of an exit ticket, it sounded like a hidden treasure. Then I quickly saw a need to adapt it. If I could have a class complete a quick write assessment, I needed to be able to look through it (quickly), and address issues of misunderstanding so that feedback would be fresh and current with context. The exit ticket turned into a quick write assessment I went through as students started some type of independent practice. I approached students that seemed to struggle with the quick write, or helped redirect misconceptions.
This took too long. It felt like trying to finish a pile of grading that would grow faster than I had time for. If I couldn’t assess quickly and address the issues immediately, how purposeful would it be to bring it up the following day, 24 hours after the experience. David Wees gives some comments on the value of feedback in the moment if you’d like read more. So I stopped using quick writes as a form of assessment. It wasn’t a bad activity, just didn’t make sense to me in terms of formative assessment.
What’s wrong with warm-ups?
When we think warm-ups, there’s an inherent purpose. I think educators understand that purpose of activating prior knowledge or sparking conversation. Those that stick to the purpose of warm-ups can make this work, and sadly there are instances when a “warm-up” turns into the diluted time filler so that teachers can take attendance.
(imagine finger quoting here, or just look at Dr. Evil)
Sometimes I fear that a warm-up may serve as just a reminder for what a student has forgotten, or even worse never even learned in the first place. Then we as teachers feel better about our classrooms because we reviewed it. (More finger quotes, but you can just imagine them this time).
If we really want to warm-up a student, it needs to be something consistent in content over multiple days, and consistent in structure. Sadie’s counting circles does this in a pretty awesome way. A warm-up should help build the student’s confidence, structured in such a way that growth is built in, and it leads into further learning through a strong foundation.
Warm-ups should not be a reminder of failure.
Don’t get me wrong, formative assessment and growth activities require failure in their nature. However, the activity is then combined with feedback and opportunity for growth. Failure is encouraged, so long as it is a step in learning, not a finish line.
So what makes a good formative assessment? (and replaces warm-ups and exit tickets)
- Warm-up at start of class
- Skill/standard based grading assessment.
- Topic is always from week prior.
- Success erases failures (formative, not summative).
- Difficulty progresses throughout week.Student must pass highest level, or pass multiple times for full score. Otherwise intermediate score for passing moderate skill level and/or only passing one time.
- Developing a question bank takes time, but it’s worth it.
I’m going to address each point on it’s purpose.
- I still did a “warm-up”. I was able to take attendance and other administrative duties as needed. I let the kids talk every day, (except for the summative experience on Fridays).
- Students were completing quick assessments on discrete skills. Dan gives his opinion on Standards Based Grading, which this is a derivative of. It differs in that the quiz is the same for every student on that given week. However, a student can return to any skill/standard (outside of class time) up until the day of summative grades at semester end.
- Letting the students wrestle with a topic for a week meant that they were now ready for an assessment experience with it. This delay and the numerous attempts also gave flexibility so that students could work through absences and keep current with content.
- Growth, it’s a mindset. We need to encourage it by rewarding effort and encouraging multiple attempts. Students would trade and grade papers Monday through Thursday with guided feedback from the instructor. I would model correct and incorrect responses based on what I had observed from walking around the room after taking attendance. Students would write in feedback for each other in colored pencil/ink.
- I wanted to have some incentive for students to continue practicing and growing in each standard/skill. Friday would be the most challenging presentation of the exercise. In order to receive full scores, the student had to perform on that level. Passing on Monday or Tuesday still received partial credit.
- These formative skill assessments often were drawn out of sample questions from high stakes standardized tests, standards list like these (1,2,3). Writing the questions took significant time. Knowing that my students were retaining foundational skills, and learning that growth gets rewarded were invaluable to me.
I have lapsed from time to time in implementing my Skill of the Week Assessment. This last year I was much more experimental, trying multiple activities and formats. Given that CA had no state test for Spring 2014, I felt a desire, and even need, to try new things without any pressure from standards on a standardized test. I learned, however, how significant the Skill of the Week was. My students missed it, because they thought it helped prepare them for material and gave them good feedback on how to identify and self correct errors in calculations. I don’t regret experimenting. It was a necessary part of my growth. But I do plan to find every opportunity to get meaningful, formative assessment back into the classroom.
Remember that epic yoga ball fail. With opportunity for growth, and appropriate feedback, you may eventually get something that looks like this:
I plan to update this post later with resources and samples of slide decks for the Skills of the week I used. Those should replace this text here at the bottom. I’d also invite others to share resources and/or methods they’ve used in successful formative assessment.
Here is a link to a folder with a sample of slides I would use: https://goo.gl/C67gTv
Once similarity intuition has been built with circles, we can start getting into more specific relationships with angles and segments. This post will look at using visual information from central angles and inscribed angles.
Students sometimes lack intuition for the measure of something. Andrew Stadel has developed this idea into a thorough curriculum on estimation. In my classes we started reasoning through similar exercises. Once we had a decent understanding of circle parts and whole, we moved on to other types of angles.
At this point most students have the common sense that a circle has 360 degrees, and a triangle is half that at 180 degrees. Built with this intuition in mind, we look at a triangle created by inscribed angles.
The next day we get to see the formula that collapses 3 ideas down to 1.
Dynamic Angles in…
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I have some ideas for the next few days of posts, mostly dealing with metaphors for teaching. So far on that list is Farming, Cooking, and I’ve heard that there’s also some thoughts on fishing. Let’s take a quick commercial break brought to you by the folks at Waco, Swordsoft, Peardeck, Google, and I’m sure some others might creep in.
I used to loved interactive whiteboards. Yes, that is a past tense reference. Most of my experience with these is with the Promethean Company.
I learned to be proficient with the standard slide software ActivInspire in which I made plenty of flipcharts. It was awesome. I could make interactive presentations, I could screencast the material or export it to multiple other standard formats. Then I realized the down sides. Cost. The handcuffs that anyone in the education industry is all to familiar with. These boards are expensive. The accessories are expensive. And one major downside to the standard entry level interactive whiteboard was it’s own built in shackles. The board required that you be within arms reach to interact with it. Of course, one could buy a mobile tablet that goes with the board/software, and that brings us back issue #1: cost. Companies justify this cost by showing the awesome capabilities of the hardware and software that comes with the package.
I tried some alternatives, like Johnny Lee’s low cost interactive whiteboard that was even featured on TED. This worked every once in a while, but it still required close proximity to some board as well as constant recharging and calibration. It started me thinking on how to find low cost alternatives, something more practical for the average teacher.
I tried some Wacom tablets, starting with my first, a bluetooth model refurbished from eBay.
This again was alright, but still inconsistent and cumbersome.
A little more than a year ago my student teacher and I tried a newer model of the Wacom Tablet with an added RF wireless adapter.
I LOVE IT. Here’s why:
- connects over RF, no wifi required (you can go wireless anywhere, up to about 30′)
- low weight, I can easily hold it in my hand without feeling a strain as a roam the classroom
- reasonable cost: $80 tablet + $40 Wireless adapter kit
- battery: single charge easily lasts more than a full day of HEAVY use, often I get at least a week off one charge
But wait, what about that fancy software? Aren’t all the built in math tools wonderful? Yes they are, but Google Drawings, Google Slides, Geogebra, Desmos, and EduCreations have pretty much matched anything I’d done before. Also, that screen annotation available in those fancy software packages have been replaced by ScreenInk by Swordsoft for a whopping $2.
For those of you that are partial to iPads and apps like AirPlay mirroring, Reflector, Splashtop or SlideShark, I respect that. A tablet stylus tends to not be as precise as the Wacom technology, and this tablet with RF adapter doesn’t have a time delay like the others.
With many classrooms incorporating technology into the classroom, teachers need to be mobile now more than ever. I would also qualify that with maintaining a balance of tech use in the classroom. Electronic does not imply engaged, and a mobile teacher is needed to manage the 21st century classroom. By the way, if you didn’t catch the primary advantage, the total cost of this Wacom package (~$120) is about %10 of most other solutions. Go bug your principals and edutech purchasers to look into this. I’d be more than happy to field any questions or comments on the issue.
If you have another alternative, I’d also love to hear about that.
People joke with me and say, “You must do calculations in your head for fun.” My instinct is to deny this accusation, but it probably is true. Math educators run through numbers all the time. We play numbers games in our head like would you rather, without prompt or encouragement to do so. I see a fraction that could be written in different way, so I try. I see a complex shape that can be broken into parts, so I do. These instincts were fueled by years or even decades of me talking numbers in my head.
I should never assume that this is normal, even though it is one of my life’s missions to make it so for the general population. The CCSS Standards for Mathematical Practice says to make sense of problems and persevere in solving them (among other things). This idea of having a sense for numbers has been discussed by some awesome educators like Fawn Nguyen, and Sadie Estrella, and it’s been the hot topic of journalists and bloggers alike. I’m in the camp that says, “Feeling comfortable with manipulation of numbers directly supports comfort with manipulating the abstract.”
So today we were talking circles, and proportions of circles. Instead of just giving a formula…
…we developed our own.
It started with a spreadsheet.
then a geogebra applet
then into paper practice.
Students shouldn’t be given a formula, and then be expected to make sense of the abstract values without having developed a sense for the concrete values.
Math educators need to talk numbers with students daily. It just makes sense.
The are only a few givens in geometry, building on those we derive many other patterns theorems. One theorem I often prefer to focus on visually is the sum of the interior angles of a convex polygon. There’s different ways to approach the process, and most of them refer to creating a fan of triangles inside the polygon:
Early on in most geometry studies, we learn that the sum of the interior angles of a triangle is equal to 180, building off of this we can use the above animation to calculate the sum of the convex hexagon: (180)(4)=720.
There’s often the student who wants to divide the hexagon up differently. The student wants to draw lines criss crossing all over the shape.
Too often I would have totally passed up this opportunity and said, “That’s not how we do it, so it can’t work.”
Taking The Long Way isn’t an Error:
Thankfully, this year we saw something different. There were still triangles inside, and with a few more lines added, the picture had only triangles inside.
Once we have all triangles, we can just count those and multiply by 180.
(16)(180)=2880. That can’t be right, can it?
From here we get a better definition for what is an interior angle of a hexagon. It’s an angle inside the hexagon, but still attached to the edge of the shape. Somehow we need to get rid of the angles that are inside the hexagon but not touching the edge of the shape, like these red circles:
There are 6 of these circle sets of angles, each of them having a value of 360 degrees. We just need to discount those (aka subtract).
This kind of process also builds a more flexible understanding of how to decompose a geometric shape in multiple ways. I encourage all math teachers out there to try this next time a student chooses to slice it up however he/she wants.