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.
I might be a groupie, or is it campie? I like to attend edcamps: (IE, LA, Murrieta, OC, 605, San Diego, and UCLAcenterX). I’m okay with it. I go for a lot of reasons.
1) Vote with your feet
The culture of EdCamp says, if you don’t like it, move on. This idea makes my heart sing because differentiation is determined by the participant. If a session is not meeting your needs, the only one responsible for that is you.
I’ve walked out on my own set of sessions, sometimes because the title didn’t live up to what I was hoping. Other times, it felt like a rerun that I didn’t want to experience a second time.
This concept is central to EdCamps, and without it I would not participate. This works out well because…
2) …only cost is time
Those capable and willing of giving their time show up for EdCamps. Someone displeased with their experience only sacrificed time. Attendance is optional, so only those wanting to attend actually show up.
Not to mention Freebies often supported by sponsors. I have yet to attend an EdCamp that didn’t have some type of welcome coffee and/or breakfast. Raffles and prizes are often waiting for those who stay through the end as well.
3) Connecting with People
I get to connect with a load of great people daily through the magic of technology, particularly twitter. I’m a big fan of #MTBoS, twittermathcamp, #caedchat, and reading blogs with feedly. These connections run deep for me, yet a face to face for five minutes can still be more. It’s not like EdCamp is the only place I talk with other humans, but it helps me keep a fresh perspective on everything. Others challenge me with ideas and questions I’d have never considered. I get to pose the same challenges to others in a safe environment. I also get a change to burst my Math bubble. At an EdCamp I get to interact with teachers, coaches, admins, parents, and even students to talk about pressing issues. These connections are what make me return the most.
Exploring big questions, Maker Spaces (and Breaker Spaces) with Scott Bedley and others
Wishes for the future
Attend more EdCamps (IE, LA, Long Beach, Murrieta, OC, RivCo, SD, SFBay, Yosemite, 605)
Establish new EdCamp with others at my employer (Perris Union)
Bring more people to EdCamp (carpool = awesome)
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
Upon returning from Twitter Math Camp 2014 I felt like this:
I didn’t really know how to process it. I couldn’t compare my experience to another TMC because this was my first. As the weeks approached, I felt a little like a the slow crescendo.
I arrived late with John Stevens, Mrs. Stevens, and Sadie Estrella late the night before the big event. We had great conversation and got to sleep a few hours after midnight, just a few hours before needing to be up for the big show at Jenks High School. Around 7am, we start seeing faces. For some this is a long awaited reunion, and for others this is a first encounter. No matter the previous experience, everyone seemed to be feeling like this as twitter handles turned into real life:
In some ways I didn’t truly understand what was happening around me. I’ve felt like the outlier in my incessant passion for math and learning. Our backgrounds were varied, the common ground of interests kept us bouncing from one conversation to the next.
Then we get to the facility.
It just kept escalating. Then start our morning sessions. This was a pleasant twist on conference workshops. Being able to meet for a few hours each morning over multiple days allowed us to truly develop a deeper insight into some specific math content, and package that understanding into something we could take home with us. It’s not really possible to do this at another conference. TMC keeps a good balance of meeting the masses, while supporting conversations in smaller communities. This is what makes it so special. I have heard some worries about TMC losing value as it grows, but as long as we have groups like the morning sessions in which we can have the intimacy and depth of relationship TMC will still maintain its appeal for me.
Then I get to be in a session with Pershan on complex numbers and geometric rotations. His craft as a teacher is what impressed me most. He let us work through some material in small groups, and guided us in the classic, “I’m going to pretend like I don’t know where this will end up.” Then another whoa.
Every night I would fall asleep exhausted from the constant mind blowing experiences. My awesome roommate, Chris Shore, was able to help me remember this experience.
— Chris Shore (@MathProjects) July 27, 2014
Occasionally I may have had a moment where the rise and fall seemed less impacting relative to other extreme moments at the conference,
but the bumps kept coming.
Then I return home, work for a couple of days and then off to more conferences. Only now is TMC truly starting to settle for me. This conference has transformed me, and only now am I able to process the experience. As this rollercoaster feeling diminishes, I’m seeing how the conference is having direct effect in my professional and personal life. Only 350ish days until we do this again.
to be continued…..
(I plan to follow up this post with another soon on how I plan to incorporate TMC into my work and that of my colleagues as well.)
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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All circles are similar, right?
Okay, maybe it’s not given. In fact, it needs to be proven. This proof is yet another that is so easily demonstrated with dynamic math tools (like desmos and geogebra
So long as you can move one center onto the other (translate) and dilate one radius to equal the other, similarity is achieved. This works for every circle. The perfect proportional balance achieved with circles lays the foundation for most of not all relationships found in them.
Similarity gives us a simple system for comparing measures in multiple figures.
You can even explore this with repetition of congruent triangles:
Below are a couple of applications that push further with exploring the measures of circles, proportionality, and relationships in the measures.
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I just spoke with my brother, @jakebutler, just catching up on the latest. We eventually go into a conversation about concept development, and how it accelerates as history progresses. The gist was something like Moore’s law applied to the topic of impactful ideas.
A standard long term example he posed was the idea of language and documentation, tracing from spoken, to written, automated, then digital, and now multimedia. The next big thing comes faster than the last, and sometimes it feels like we’re always playing catch up. My brother works for an awesome company based out of Boston that focuses on a lot of the social aspects of healthy living, especially in the realm of technology integration.
He told me that they have long term goals, but when it comes to comprehensive and detailed planning, each of their sub teams never looks further out than 2 weeks. We started applying this format to technology in general and I in turn added the context of education and #edtech. For the most part, I would argue (as would my brother) that successful technology enhancements have gone away from the secret projects behind closed doors that take at times years to reach a level worth any public reveal, and instead have more of a micro step process. Upgrade a few things, and often. The short term plan to update and implement smaller, more frequent changes has been a necessary adaptation to the accelerating progress of technology in general.
As teachers are upgrading their curriculum and technology for near future integrations I think we need to consider the value of this short term cycle. Instead of having an entire year planned out to the day, we can maintain long term bench marks with the intention on updating our planning through small frequent upgrades. I doubt that teachers trying to implement formative and interactive technologies in the classroom would have predicted the introduction of @peardeck (read more here).
This hard for an educator to manage. We already have plenty on our plate between and the hard requirements and soft skills necessary to achieve them. If a teacher truly wants to match the current culture of technology and conceptual progression we need to have an appropriate design for our planning. We need to anticipate the change and build in the flexibility so that we can adapt on the fly.
I don’t know if I’d take it as far as this guy…
…but refusing an adaptive attitude is assuming we can predict the future of every step in growth of our students. And that sounds silly.
I’d love to hear how others have integrated this adaptive planning, with small frequent updates, into their classroom planning (tech and non-tech contexts)
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.
Just read about a blogging challenge for the month of July. I tried this with #MTBoS30 and only got up to 12. This time around I’m going to divide and conquer across four blogs I have various levels interactions with: transformulas.org, DailyDesmos, and #ggbchat.
For post 1 of 31, the theme is a derivative from others and it focuses on the past, present and future goals with 3 items for each of the Start, Stop, and Continue theme.
- Desmos API: I am so excited about this one. I’m a huge fan of @geogebra and @desmos (and pretty much any other dynamic math visualization tool). After an open invitation from Chris Lusto, I’m excited to learn from others.
- Books: I read one book this summer so far. Looking forward to the next. There’s something about the raw nature of a book that balances out my passion for and interaction with technology (my wife would probably say it leans more toward addiction).
- Cross Curricular: Late in the year this last season of school, I spoke with a science teacher about integrating geogebra applets into a physics setting. There’s too many overlaps with math and science NOT to exploit the potential collaboration opportunities. With the CCSS Standards for Mathematical Practice we are also seeing an increased focused in constructing arguments, organizing evidence, and making sense of problems. These type of frameworks lend to collaboration with Humanities. This conversation of cross curricular collaboration is too far overdue.
- Driving (as much as possible): My car, a lovely Buick that has passed from my grandparents, to my great aunt, and now onto me, is nearing it’s end. I only live 6.5 miles from work. There is also a Super Target less than a mile away. I like to ride my bike, and I feel like I don’t show it the love that it deserves. Time to stop driving (when possible) and start riding more.
- Frustrations with Growing Pains in CCSS: There is plenty of argument and frustration with the changes in education. Progress and growth doesn’t jive well with those who have established systems in place. Education is a continual evolution that I’ve learned to embrace. Those that resist this change often take plenty of shots at new ideas. I will concede that new ideas without proven track records can be a gamble. However, I feel that the mantra, “If it ain’t broke, don’t fix it” has little place in education. I feel it’s better to apply a growth mindest and look at education as “Don’t knock it till to try it.” Learning that something doesn’t work is still learning, and that should be our focus, learning.
- Playing Candy Crush: Level 140 has been stuck on my phone for a month. Seriously, why do I continue. I’m done.
- CCSS: it’s not that I have to re-learn math, or teaching, or learning. This label is probably overused if nothing else. I look at recent transitions in education, especially in math, and am glad for the increased coherence and creativity. My most recent ambition is learning more about the progressions.
- Geogebra: Recently a group of colleagues and I started a #ggbchat on twitter. I’ve only been using this software for about a year, but the potential has only grown the more interactions I have with it. I plan to get more organized with my work, especially in ways that makes the applets more user friendly for students.
- #MTBoS: OHHHH, EMMMM, GEEEEE. If you’re reading this post, hopefully you’re already aware of the gold mine that exists out there on the net. Get plugged in, buckle up, and try not to blink. You will be overwhelmed, and it will be awesome.
So now, your turn: What do you plan to Start, Stop, and Continue?