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“Hey dad, am I going to be a genius when I grow up?”
I remember asking this way too many times as a kid, always wondering about what things will turn into. My dad had the perfect comeback.
“Of course, you’ll be whatever kind of genius you want to be.”
The youth in me didn’t understand my dad’s wisdom. He answered me, but that felt like a general answer. Kind of.
Educators and professionals everywhere talk about pursuing interests, passions, developing your interests. Some talk about #20time, #geniushour, or whatever structure encourages the pursuit of understanding and problem solving. My dad was doing this before it was popular. And it drove me nuts.
Somehow my father was able to get his children (older sister, myself, and younger brother) to fall into a self directed question and answer session. He started by posing notices and wonderings in objects around us, then as soon as we offered our own questions he knew we were baited. “That’s a great question.” The moment of triumph over coming up with something of value was followed by a challenge. As soon as we asked for the answer to our curiosities, my dad simply said, “Go look it up, see what you can find out.”
I used to hate this, but now I plan to submit my own children to the same process.
— Inland Empire EdChat (@ieedchat) June 27, 2016
What do I do for DIY learning? First I ask questions. Lots of them. If you ask my wife, I ask too many. Questions are important. They are the driving force to learning. When we talk about access to information for the current generation I think we need to also look at access to questions, and the art of questioning. One of my favorite sites that encourages the generation of questions is 101qs.com.
Maybe I’m not exactly answering the #ieedchat prompt, how do I DIY, but somehow there seems to be wisdom in if you’re not asking enough questions, you’re not really growing anyway. Think back and ask yourself, what queries have you had today?
PS: my dad has done volunteer gigs as Santa Claus, and he gets a kick out of waving to kids and reminding them to be on the nice list.
— Inland Empire EdChat (@ieedchat) June 13, 2016
This has been a really tough prompt for me. I feel uncomfortable. There hasn’t been a lot of hate in my life, and tragedy doesn’t stick with me for as long as it seems to with others.
First, let me address the last statement. Tragedy exists, and our awareness of it is higher than it ever was, I think. But I feel uncomfortable because for me sometimes it almost feels like the media has done to tragedy what Facebook has done to friends. It saddens me to hear about unnecessary death and destruction in the world, but I also don’t often have a contextual relationship with the victims in these situations. That lack of relationship is actually what I think the problem is with hate in the first place.
When I think of the classroom, and unnecessary pain or victimization, I remember a very specific day, my third year of teaching. I’m walking by a girl and notice her whisper to another student. I’m still learning what to filter and what to take note of as a teacher. Some actions require guidance, and many do not. I don’t remember what was said in the whisper, but I remember writing it off as innocent and non-disruptive. Somehow another girl didn’t filter it the same way.
Amy: “What’d you call me b*tch?! You don’t have to whisper. Say it to my face. Let’s go.”
Brianna: “Who do you think you are, b*tch. I’m not afraid of you.”
Amy: “I ain’t afraid of you. Right now, let’s go”
That all happened in a maybe 2 seconds. Somehow I hit the right button in my response.
Me, sternly: “Amy, why are you yelling? I bet you don’t even know what Brianna said. You assumed something but you attacked without even knowing. And you, Brianna, I don’t get why you’re yelling either. Amy, ask Brianna what she said. No yelling.
Amy: “What’d you say about me?”
Brianna: “Nothing. Not about you. It’s other stuff.”
Brianna became a little embarrassed at this point as her whispers were now almost public knowledge.
Amy: “Then why’d you yell?!”
Me: “Amy, not like that.”
They softened their stature a little, shoulders dropped, and faces relaxed.
Brianna: “You yelled at me. I guessed you were coming at me.”
They both paused here. Didn’t say anything for what felt like a full minute but was probably more like 5 seconds.
Amy: “Mr. B, why don’t other teachers do that.”
Me: “Do what Amy?”
Amy: “Talk to us like people. Not like trash to throw out of class.”
This is the moment where my understanding of students as humans, and how often teachers, students, and many other groups forget that people are human and should be treated as such. The challenge I noticed in reaching an understanding of how to treat your peers, with kindness and with sympathy, is that it takes time, honesty, and human interaction to get there.
So what do I do in a classroom when tragedy takes place on the other side of the country/world? Sadly there’s not much conversation regarding that incident so far away. My discomfort with the topic is that I don’t know the people, and I struggle with talking about them with context, information, or getting to know the situation. But, it is always a good reminder that if we take a minute to get know each other, hate will often dissipate quickly as if it were never there. This isn’t to say that everyone will naturally get along, but it is to say that learning more about people and their background often makes it hard to hold them in contempt. Another imbalance I feel with this perspective is the presence of justice, and what does it mean to truly balance social justices. That’s also uncomfortable for me to write about, and probably the real reason it took me so long to write this.
Amy and Brianna got along for the rest of year, probably better than the average relationships of most of my students.
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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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.
So it’s that Wednesday in the month, which means for the 3 o’clock hour we have a school site staff meeting.
The first thought that comes to mind is a comparison between this and the classroom. We come in, sit down, and digest information (for about an hour). The most traditional delivery is verbal, with an occasional slide for visual aid. There is no formal test but we are still expected to be responsible for the content.
I know the information has value, but is it possible that a staff meeting can have a little more interest? Educators are willing to use creative planning of activities in the class to break the monotony of classic lecture. Sometimes it’s even expected. Is it fair to ask for something similar of those organizing the staff meeting?
1) #edchat style
2) compose the information in a shared web document/slideshow and have questions/comments fielded early
3) make it interactive with polls or something like @peardeck, even if it’s just for fun
4) incorporate media, please
6) things that suck
The meeting is over and so is this post.
Like any recurring event, there’s always a first. I’m considering this to be my first official blog post. Though I’ve written a post prior to this one, I feel that it was more of a dipping my toe in the water. I’m diving in. I was trying to think of what to write for this, and it took me back to high school writing strategies simplified by my humanities teachers in 11th grade. The wisdom of communication they passed on could be summed up as follows:
- Tell them what you’re going to tell them
- Tell them
- Tell them what you told them
- Formative versus Summative and why we need both
- Goldilocks’ Comparison
- Interaction, Distraction, and other kinds of action
- The immersive experience
- Lo-tech done right
- Speak the language, say what you mean
- Area for All
- Why teachers of all levels (and specialties) need to communicate more
Cheers to change. It’s a year where I’ve changed jobs, become engaged, improved improved my health, and embraced the latest overhaul of the American education system. I was recently inspired to participate in the reflective side of teaching and learning. I’ve always been excited about my job, teaching kids how cool math can be. With all this change happening one might assume some type of exhaustion. I’ll admit this year has been tiring, but awesome in its excitement. Speaking of excitement…
…just around the corner my fiance and I will be tying the knot (November 27th). We’ll be enjoying sandy beaches, tropical paradise, and of course hanging out with family. So cheers to this, cheers to change.