Learning Slow

My spouse and I have been learning Tai Chi with a seniors' class, and it is awesome.

We've been going for maybe 15 months, and we haven't finished the first form yet. (Yang 24)

Marna is the teacher, and she is great. She knows her students, what they need, and how to help them reach it. She does lots of formative assessment, watching us, trying just hands and just feet, sometimes having us watch her. If a student forgets, it's okay. If a student is new, "just fudge it until you understand." She lets us know the benefits of what we are doing. She shares with us stories from when she learned from Paul Lam. She knows that doing what we're doing is the point. Even if some students really want to know and keep the form.

We had a short break while she had two knees replaced, and then she was back teaching exercise classes over two counties.

I'm learning patience as a learner. I hope I'm learning patience as a teacher.

As well as to focus on what doing math is doing for my students.

Let's breathe, shall we?

p.s. I know the title sounds like bad grammar, but it's what I mean.

Teacher Preappreciation

Yesterday's post was feedback from a group of students that I want to do better for. That applies to this group of preservice teachers as well, but today's post is just going to be some bon mots from these guys about teaching.

I am such a teacher fan boy; I consider myself so fortunate to spend so much of my time working with people who are dedicating themselves to others. Hopefully this post shows that this extends even to before they're in the classroom. I encourage you to click on the link to their blogs and poke around a bit. I hope you have the time to read these - it's like getting a dozen semesters of elementary math ed. And you'll be able to see why I am going to miss these guys.

Kalyn gets us started: "Getting together a small group of soon-to-be teachers with the goal of having students understand and even like math more than what typical stereotypes say, creates a strong classroom. During the semester we had the opportunity to work with different people and learn from each other. We didn’t always agree on what we thought the answer was or on a particular way to solve a problem, but that was kind of the point of the class. We learned to express our ideas, and hear others ideas, and LEARN from each other. The ideas that many of my colleagues had were great and it is said that two works better than one, and I am pretty sure that 13 works even better than 2." 
     One exemplar: "Half of It: The last writing I want to submit is based on a problem that I explored. The problem was simple in nature, but contained a lot of strategy and mathematical thinking. Breaking down a problem and writing about it was something that I never did before this class, and I felt that I learned a lot from it. http://kalynjoy.weebly.com/blog/half-of-it"

Dayna: "One of the main ideas i learned from this class is to let the kids make discoveries about the content. I am now a firm believer in that students learn a lot when working with new things on their own. this also goes with being able to work with others. We demonstrated this idea in class everyday and i found myself learning so many new ideas and methods from everyone in our class. I also learned about time and how it is going to take every student a different amount of time to do their math problems."
     One exemplar: CGI story types. http://daynaball.weebly.com/mth223/through-the-eyes-of-a-teacher, "I choose this blog because i think it is a great take away from a class that confused me. I think it is important to know these strategies and making sense of them so i can help my students make sense of them in the future."

Dana: "The big idea I will take away from this class is that we need to delve into the student's thinking.  It is not enough for students to get the right answer on math problems, they need to be able to think mathematically and explain their answer.  I never thought about asking a student for their thinking before this class, and now I cannot imagine teaching math without do so"
    One exemplar on Sorting Geometery. http://danamspielberger.weebly.com/blog/the-unasked-question "For this one, I liked the challenge of writing a math blog post.  On all of my other posts, I think I tried to stay way from talking about anything that had something to do with math, but for this one I was specifically challenged to do the opposite.  This allowed me to explore math problems and pick one that I thought was interesting.  This post is one of my best because I was able to talk about something interesting to me while still being challenged."

Sarah: "This course has made me re-evaluate teaching and see the impact of looking deeper into mathematical concepts. Even the concepts that we consider simple and elementary level contains patterns and characteristics that we never evaluated as a child. An example would be double-digit subtraction. If a student asked me exactly why do we borrow, would I be able to give them a complete answer? When I think about it, I was never taught why and I honestly never questioned it. Math is so full of “just do it” and any questions are often answered with “because you just do.” How can you teach children to do it without fully understanding it yourself? This class has made me explore concepts deeper so that I can answer those difficult questions."
     One exemplar, Teaching with a Purpose: https://sarahacoutts.wordpress.com/2016/03/19/teaching-for-a-purpose/, "because I was the most passionate about this writing. I wrote it shortly after my mission trip over spring break and I reflected on my time in Dallas while also connecting it to the kind of teacher I want to be."

Amber: "Students have fixed mindsets when they shut down with math. They might be convinced that they are not ‘math people,’ be afraid of failure, or have outside sources telling them that math is unattainable. Students often shut down, and many associate math with torturous fact-memorizing and stressful timed tests. It is my role as the teacher to discourage this type of mindset in students. This means being flexible, accepting and encouraging mistakes, and modeling how fun math can be. This is especially important with people of color of women-all marginalized groups in math. I am all about equity and equal opportunities for all my students, and I can indirectly influence their future success by promoting math as a non-threatening, creative endeavor worth doing. There are no ‘math-people.’ There are just people and math, and everyone should find value in math."
     One exemplar, Whole Number Sense. http://ambergerrits.weebly.com/blog/february-07th-2016, "this one is so different from my other posts. It is an in-depth analysis that I honestly put a lot of work and time into (probably at least 4 hours of work). Like you mentioned in your comment, after writing about the whole number concepts, I have internalized them even more. There is more to write about with respect to instruction, but that is a whole other post. I edited it slightly-I proof read it and added spaces between paragraphs for clarity."

Ally: "Children are crazy creatures. They're just tiny little adults, but you know really small. Then, something I've learned from this class is that although they're small, they're mighty. They are SO smart. When we went to teach them I had this preconceived idea that they wouldn't understand some of the math that we were trying to teach them. For example, the last time we went to teach them, so on Friday. We had a set ratio, but the children needed to get the amount of sticky notes that used that ratio. At first, I had a hard time trying to figure out how that was going to work, let alone a child that is half my age trying to figure it out. I walked into that class room Friday morning having very little faith in them. This I understand is awful and I shouldn't think this way, but if I couldn't figure it out, how could they? Then, one group by one group they were understanding... WHAT?! I was amazed. This was fantastic."
     One exemplar, Flip for Math. http://allyboomsma.weebly.com/blog/i-flip-for-math-or-do-i "My last post I believe is one of my best because I was creative, and full of detail about my person gymnast life. This was the first blog post we did and I was happy that you enjoyed it too." 

Chris: "When we began our first counting circle on the first day of class, I was immediately nervous because I was afraid of being put on the spot. However, I learned quickly that this class, like the counting circle was open for mistakes, and was accepting of all kinds of input. This is encouraging for someone who is naturally introverted. Being able to come to class and worry about the important topics and not about the atmosphere of the classroom seems like a small aspect, but it makes a huge difference in my learning. It has also opened my eyes to the way I want my future classrooms to feel. This class has truly helped me foster an open mind about making mistakes, and using them to grow."
     One exemplar: Letter to a Concerned Parent. http://stromelemntarymathblog.weebly.com/blog/making-sense-of-new-methods "I worked hard to write a piece that combined daily life for me into my passion to teach and what we have learned in class thus far. I think this writing accomplishes taking the class to the next level. I did my best to take a scenario that I think teachers today are facing and came up with a solution that applied both the mathematical strategies and other teaching strategies I adopted from the class. I think this paper is decently written, and shows my understanding of what we have learned in class in a unique way."

Danielle: "Throughout this semester we have discussed several content areas that intimidate me, mostly because of my experiences learning them in elementary school. When we covered an area of concern for me I always learned new methods for approaching and solving the problems. Coming away from this class I feel much more comfortable and confident in my teaching abilities because I feel more comfortable and confident in my understanding and ability to solve the problems."
     One exemplar, Relearning How To Multiply. https://minsterd.wordpress.com/2016/01/27/relearning-how-to-multiply/ "I believe that this is an exemplar because I was able to reflect upon my previous knowledge, what I learned in our class discussions, and how I want to teach in the future to write on a subject that I struggled the most on and showed several ways someone can use to solve a problem."

Kathleen: "What I've learned about teaching is how to take a student's thought and write it down. Being able to record what someone is thinking is very hard. I want to know what they're thinking. I don't want to assume anything. As a teacher I need to be able to express what they're thinking. I never want them to feel cheated, or like I'm not understanding them."
     One exemplar, Math and Gym, http://mathleen.weebly.com/blog/lesson-idea-math-and-gym "an actual lesson I've done and put together for another class here at GV and I like the way it incorporates gym and math."

Oriana: "I chose a math major because I want to teach in elementary schools and show young learners what fun and amazing things we can do in math. Math consists of creativity, exploring, and not just one right answer every single time. I want to create an environment where math is fun and intriguing. Here at Grand Valley, as I go through different math classes, I feel as if am equipped with tools to share and create an environment that portrays the fun, and exciting side of mathematics."
     One exemplar, Learn the Facts. http://obenin.weebly.com/blog/learn-the-facts "I chose this one because I've tutored in elementary classrooms and helped children who struggle in math. One of the ideas that kids keep coming to me for is no knowing their facts. It's been hard for me before this class because I tried to explain repeated addition, but they still struggled because students didn't have them memorized. This topic really hit home and is applicable. I know methods to help students out."

Brittany: "For me that really hit home because as a student I HATED math. I was the quite student in the classroom that teachers liked to call on to hear me say something in class. I was terrified by that at all times but especially so during math class, because I didn't think I was any good at it and didn't want everyone in my class to know that. I would spend hours at home sitting trying to do my homework, and trying to get help from my parent, who didn't either understand what I was doing or didn't know how to explain it to me so I would understand. Now I'm not going to go into that right now because that is a whole other bag of worms that I won't open up today, but those are real issues that I had and my future students will have."
     One exemplar, Math as a Foreign Language. brittanykloe.weebly.com/blog/math-foreign-language "I picked this one because it really speaks to who I am and what I think."

Stephanie: "My favorite aspect of the class was the openness, and the acceptance of everyone. No one judged anyone for being wrong, or for not understand something no matter how easy the topic might have seemed. We were able to learn from our mistakes instead of being yelled at or put down for not being perfect all of the time."
     One exemplar, Why so negative? http://stephanieepetersen.weebly.com/blog/thoughts-can-be-deceiving was one of my best works because it was something that hit home with me, and I was able to relate with the topic really well. I am very passionate about rooting for the underdog, so actually read text proving my point on how we always give up on the underdog so easily was a fun read, and it made writing the blog very easy.

Heather's one exemplar is her course reflection, and she has a fitting conclusion: "Often I found myself questioning everything I had previously known about math and education. I know that the main purpose of this course was to give us future educators the chance to learn techniques and practice teaching math to young children, however I found that many of the things that we were taught I can use in my life. ... Above all else it was respect that made this class stand out in my mind. A true respect for my peers and knowing that I had their respect in return, as well as our respect for the professor and most importantly his respect for us as students and future educators. He truly took in our ideas, helped us develop them into something even better. It was this same respect that helped us blossom throughout the year, questioning more and becoming more confident in ourselves rather than seeking approval."

I am officially verklempt.

Student Takeout

OK, maybe more like student takeaway. 

The last writing assignment in College Algebra (of 6) is a bit different. The first 5 are them writing up a problem in depth, explaining thinking. I give them feedback, and they can revise or not based on their wishes. At the end of the semester the writing grade is half % out of 6 writings written, and half evaluation of three exemplars the student chooses on the 5 Cs. 

Five Cs: developed with David Coffey, based on NCTM's Communication Process standard.

1. Clear (occasionally will find things not clear because of penmanship, accumulation of grammar/spelling or lack of paragraphs.)
2. Coherent - there is a point and the writing addresses it.
3. Complete - shows 2 hours-ish of work. Contains important relevant support towards the point of the writing.
4. Content - the most relevant math is included, reasoning is shared and correctness of idea use and computation.
5. Consolidated - the writing has a conclusion, synthesizing or summarizing or extending. (This is the hardest aspect for students to adopt.)

When working with Dave things should alliterate or rhyme.

The last writing was to be on these questions: What do you see as the big ideas of algebra? What did you learn about them? 

I'm under no illusion that these are objective since they are not anonymous, but they align more or less with my impressions.

Some responses moving towards my goals:

• "I liked this class because it was the first class I have had where the students were running the math class, and the professor was there to guide us, not tell us that we were wrong. Our ability to voice our opinions was very nice..."
• "Now, I feel like these concepts are things that I will actually be able to apply because I understand WHY they are done." 
• "Logs have always been tricky to me, really tricky. What we did in class allowed me to break them down and really understand the rules and properties. " (Introduced them without the name. I call them  pixies because - pxe - reverses exp.)
• "However, I really appreciate how easy going the class was, there are not grades to define us and SBARS did not have to be straight forward answers (in fact, they were not supposed to be at all), they helped us explain why we got the answers we did and that was a big factor for me. " 
• "This course was more focused on learning how math works, not just memorizing and regurgitating. I really appreciated this because it made math much more interesting to me. I learned how mathematical properties worked, why and how. The way that the course was graded I believed was great. Some people, including myself are just not good test takers. The SBARs were great, you could work on your own time to show understanding as well as ask questions if you could not figure something out, For me this is a much more effective way of learning."
• "It was nice to actually figure out where answers to problems came from, and how equations made graphs." 

 Some responses point out where to grow:

• "I am never somebody whose been good at math and this new way of learning was definitely a bit of a difficult transition for me. Learning why we do problems the way we do was something I struggled to wrap my head around, considering I often didn't know how to do some of the problems in the first place."
• "Generally as a student, explaining things are not how I learn, so to have to explain things was a new type of learning for me."
•  For a College Algebra class, it was challenging and interesting!
• "I still struggle with explaining why just because sometimes i don't really know what to say, other than it just is what it is. As a student i learn with direction and this type of class was less of  direction and more free flowing which is okay. Just hard to get used to."
• "This class was actually really difficult for me, personally. I have never been good at math, so I was kind of doomed from the start."
• "it has been a little challenging for me to understand what my grade in the class has been throughout the semester. I prefer to know my overall grade in a course so that I can prioritize my workload and be as efficient with my time as possible. "

And a warning to you K-12 colleagues: "I took up to Calculus in high school but I never once was asked to explain how i found the answer." I'm sure this is not true, but it was the student's perception.

To sum up, I think I will also use a student's words. This seems to capture both sides. "This class was quite difficult for me because it was a new style of education. I am a person who likes things black and white, which has allowed me to succeeded in math classes in the past. In most math classes once you find the answer, the problem is considered done, and you move on. However, this course has challenged me to think deeper into what I am actually doing in order to reach an answer. I think this type of thinking is more realistic as to what math really is."

What I am asking the students to do is real to them, but I need to find more ways to support them and build culture in 28 meetings.

Nova Now Notes

This is the school. Srsly.

One of the questions posed during Nova Now 15, a state conference focusing on discussions among teachers, was 'should conferences end with a reflection session instead of a keynote?' Any opportunity to encourage teacher writing.


So now I feel obligated.

As with Twitter Math Camp and EdCamp, this is a conference organized on the principle of creating teacher conversation and collaboration. It's hosted at Kent Innovation High, where, frankly, I wish I could send my kids. It's a tech friendly, open design, project based learning school. Kids attend in the morning for core classes (science, math, ELA, social studies) then return to their home schools all over the ISD for the rest of their schedule. The conference starts off with a tour and chance to see the learning happen, and then several students take the option to stay and be part of the conference, even coming back on Saturday. The single most frequently heard comment for me was about the eloquence, maturity and phenomenal perspective of these students. My favorite #KIHway quote from Peyton: "Students have to shift from doing this to make people happy to 'I'm learning how to be creative and productive'."

Even before the conference started, I had a great talk with Laura Chambless. She's the K-7 math/science support for St. Clair region schools. She's got her resources organized in a protopage. (Free start pages that can also do RSS feeds.) She's a big believer in fact fluency and has been trying to find ways for teachers to get at that constructively.

#michED is our statewide Twitter chat. Wednesday evenings, 8pm ET. The first big session was a meet between the east side and westside collaborative groups, Innovation Now and the Bluewater Group, moderated by Rushton Hurley. He did a good job of guiding a discussion, and using that to also make his points. Some big ideas raised:

• Isolation is the cancer of the teaching profession.
• Good ed leader question: how many times have you deviated from your plans? Because that's a measure of how many cool moments you've facilitated.
• We are not good at sharing successes. Why are you a good teacher? "I care about kids." Who doesn't? Share specific successes as individual teachers and as a school. Share them with voters!
• Gamestorming, co-creation tools.

Derek Braman led a session on student blogging. Mostly ELA teachers - I want to hear how content teachers are using it, too.  My big takeaway was an activity he uses to introduce blogging. Have students write a list of some of their passions. Pick one to write about on paper. Then circulate and leave comments for people on stickies. I'll try that next fall and share how it goes.

'Math: are we doing it wrong?' was led by Rick Jackson, who kept good notes on resources - http://bit.ly/1zWbae1. Dan Meyer came up, PBL in math with the KIH teachers, SBAR, flipped classroom ... all the good stuff. Infuse Learning was recommended for BYOD formative assessment. Teachers were surprisingly reluctant to discuss, surprisingly given the context, but there were two KIH students who killed it in the conversation. 

• "We have to still follow state standards, which have nothing to do with learning or critical thinking."
• "The pioneering spirit is a big part of KIH, shared between teachers and students."
•  "Students have to shift from doing this to make people happy to 'I'm learning how to be creative and productive'."

Ben Rimes led a session the next morning. (His notes, which include the cards.) Out of all the good stuff going on,  he won me with teases about the world premiere of his Keynotes for Humanity game. The game itself was a great discussion piece - I should think about how to use the Cards Against Humanity structure in math class. (Make your own.) The point about the keynote's role in ed meetings was that we need to think about it's purpose and utility.

Jeff Bush (@bushjms) and Rebecca Wildman (@RebeccaWildman) had a session on student centered classrooms. (Their ) One of the hallmarks of a meeting like this is that being discussion driven, the sessions may not go according to plan. Two of their tasks for us took over the discussion. Find a video that represents you as a teacher. The most fun:

• Rebecca thinks about digital natives.
• Jeff thinks teaching is like... this.
• Tara Maynard feels like this some days.

The second task was to make an infographic of a topic. I haven't tried this yet. Rebecca assured us that there are infographics on everything, and that seems to include math topics. Good synthesis assignment. Kate Kling recommends http://piktochart.com for a free tool.

The last session I attended was Jennifer Bond's creative play. (@teambond; her Google site.) What I learned is she has the best toys. The littleBits are very curious. Another good resource is the Imagination Foundation. Best quote: "if you give them open-ended time, you'll have their attention week after week. They don't have time to play." Sad to think about students not having time for real play. Jennifer ran a creative play club for which students applied. Every single form I saw, these elementary students considered themselves creative. By the time we get them in college, few people claim that. What are we doing so wrongly?

My session was on Talking Points.  I'll write about that separately! I had an awesome group of teachers to share them with and discuss them in other disciplines.

Some other neat bits from the conference:

• Ted Talk by @TrevorMuir who led "Do It Big".
• Todd Bloch's (@) storify of the conference.
• David Theune (@DavidTheune) on attending conferences with students
• Tara Maynard (@tmaynard5) What is Flipped Class?
• Ron Houtman's (@ronhoutman) photos from NovaNow

Flip Flop

Jennifer Silverman made this cool motions maze the other day. (More here.) We collaborated on it a little bit, after she did all the heavy lifting. I added buttons. (I may have a button problem.) It put me in mind of these motion puzzles I used to make in Geometer's Sketchpad, and I got to thinking how much better I could make them now. So I started, with the main new feature I wanted being the ability to generate new puzzles instead of being one static dynamic puzzle.

The user moves points A and B to try to find the line of reflection between the two flip flops. When you hit the Check button, it shows you the reflection over the line you're trying. 

What follows is my GeoGebra geek out over trying to make it look right. Here's the puzzle if you want to skip that: Flip Flop.

One thing I love about Jennifer's sketches are her excellent images. So I tried to step it up with some nice flip flops from openclipart.org.

It turns out the trickiest part was getting both sandals to always show up. That's why I'm writing this post. (A lot of my individual sketches I post at the tumblr.) The key to being able to do this is that in the graphics window you can put variables in for the window dimensions. Define those from the objects in the sketch, and,  voilà, you can see both the sandals. So I defined xmin, xmax, ymin and ymax from the two sandals. E.g.,

xmin=floor(Min[{0, x(F1'), x(F2'), x(F3'), x(F4')}]) - 1
But there's a problem then - the graphics won't be in 1:1 scale, which is always nice, but especially important for motions where the two objects should look congruent!

The Corner[ ] command is my new best friend. Corner[n] for 1, 2, 3 & 4 return the coordinates of those corners. Corner[5] returns a point with (width, height). Corner[image name, number] returns the corners of an image. This was handy for finding the corners of the reflection, F1' etc. in the command above. 

So using Corner[5] I could find out the aspect ratio of the graphics window. It took me a few minutes, but I hit on the idea of making the bottom left corner steady, and then altering the top right corner based on the aspect ratio. I defined r = y(Corner[5])/x(Corner[5]) (so, height:width) and:

• xm = If[(ymax - ymin) / (xmax - xmin) < r, xmax, xmin + (ymax - ymin) / r]
• ym = If[(ymax - ymin) / (xmax - xmin) < r, ymin + r (xmax - xmin), ymax]

If the sandals give a screen that's not wide enough, it uses the aspect ratio to find a suitable width. If the sandals give a screen that's not tall enough, it uses the aspect ratio to find a good height. (The If[ ] command works like If[condition, then, else], where the else is optional.

The puzzle, as it turns out, is pretty challenging. Give it a try, and let me know what you think. Or let me know an easier better way to do my GeoGebra graphics hacking.

Here's the teacher page for download or the mobile page.

EDIT: Bonus! Jennifer created an assignment to give it more structure as a lesson. (PDF in dropbox.)