Proving his knowledge

I just received the following email. It made me smile, so I thought I’d share.

— Hi Ms. Cummins, this is ______ from your 2B Geometry class. I was wondering, would it be worth my time to go back and complete the Classifying Triangles assignment, even if I have proven my knowledge on the subject with a perfect unit test grade? I want to know because my mother is unsatisfied with the current state of the assignment, and has taken drastic actions until the “problem”is resolved. Thank you for being an awesome geometry teacher, and before you ask, this is a serious question. —

I’m glad he felt comfortable asking me this, and I agree- it wouldn’t be worth his time. He demonstrated mastery on the unit test, so why bother with an old incomplete assignment?

Kids are the best.

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A quick anecdote on feedback

I passed back some Geometry tests the other day, and there was a problem on similar triangles in which students had to agree or disagree with a statement and explain why. While grading, I wrote “well said” or “nicely stated” next to any convincing explanations.

A student saw this comment, and asked me, “Is this supposed to be sarcastic or what?”

I was surprised. “No… I meant that. I thought it was a good explanation.”

The kid responded, “Oh, well it was in red so I thought it was bad.”

So that was interesting, and it has me thinking about different types of feedback. What does effective feedback look like? How do kids perceive feedback?

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A cold day, followed by a beautiful display of student initiative

Yesterday we had a cold day! It’s like a snow day, except it’s really cold out. With wind chill, temperatures around here were -35 F. The timing was good because somehow I ended up being really sick yesterday. So I didn’t particularly enjoy myself on my day off (in fact, I felt terrible), but thankfully I could nap by the fire, drink tea, and spend the day recuperating.

Anyway, I wanted to post about a proud moment from my FST class today. These kids are used to a lot of hand-holding and spoon-feeding, and many of them rarely do independent work (unless I really hound them). Most days, I’ll hear this from at least one FST student: “I’ll be honest, Ms. C, I’m not gonna do this.”

These kids are mostly seniors who’ve been placed in “lower track” math classes their whole life, so changing their mindset isn’t easy. But they did elect to take 4 years of math in high school, plus they’re all good kids, so I know it’s worth it to keep trying.

Today, I told them I would walk them through one example of each type of problem (unit circle stuff), but that was it. No more.

A few kids said, “Aw, can’t you keep going.”

“Nope. I said that was all I was going to do as a class.”

Here is where one kid said, “We can keep doing them as a class, I’ll just go up there.” And he did.

The awesome thing was this kid didn’t know how to solve the problems. But he was willing to go up there and try to figure it out. It probably helped that he’s in the drama club and is an anchor on the school announcements.

So he starts to play the role of the teacher. “Ok, so let’s do problem 2: 495 degrees. We need to find an equivalent rotation between 0 and 360 degrees. How do we do that?”

Miraculously, the rest of the kids played along.

“It’s 45 degrees.” “No, it’s 135 degrees.” “How’d you get that?”

The 135 degree kid explains his thinking, the kid at the board follows along, agrees, and writes down 135.

I quickly snap out of my state of shock and try to remember good techniques for facilitating student discussions.

So I ask, “S, could you please repeat how you got 135?”

So he does.

“Thank you. Can someone summarize or rephrase what S just said?”

Someone does.

And, oh man, it was beautiful. Students were participating without any prodding from me. I managed to remember to ask good questions (Who can rephrase that? Who did it differently?) and to occasionally ask for a collective pause to let something sink in for everyone before moving on. Most importantly, I remembered not to interrupt too much.

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Filed under classroom management, collaboration, culture, FST / Algebra 2

Plans for the New Year

Happy new year! What a wonderful winter holiday this has been. I think I really lucked out as a first year teacher getting a two-week break from school this year. It was been a period of relaxation and rejuvenation, as well as a celebration of family, friends, and good times. And it’s not even over yet!

As a result, I’ve had plenty of time to reflect upon my teaching experience so far, and as a result, I’ve developed some ideas and plans for the new year and next semester’s classes. I still have two weeks left to wrap up before finals week, so while I may implement some fresh ideas now, I might not get around to all of them until the new semester starts.

Here are some thoughts I’ve had, in no particularly order.

1) Change up the seating arrangement. This one I’m going to save until second semester because I don’t want to throw off the kids right before finals week because I swear I’ve read somewhere that a person tests best in an environment that he or she is familiar and comfortable with. Anyway, my plan is to arrange my students in pairs. Right now the kids are seated in small groups of four to facilitate collaborative learning, but the tables are simply too big for the kids to work across. I encourage them to stand up and move to the other side, but sometimes they’re reluctant to do that. Additionally, partner work has been more effective than group work in my classroom so far. I’d love to do more group work, but it’s a dream in progress, and I think the days would just run more smoothly with students in pairs.

2) Figure out a good system for warm-ups. I have to decide what I want my expectations to be for warm-ups, and I think they’re going to be different for my Geometry classes and my FST classes. For Geometry, I think I might have the students do a weekly warm-up sheet (a la Fawn Nguyen, etc.), but for FST I think I’m going to have them do a daily half-sheet that is either prepared by me with review of some Algebra skills that will be needed for the day’s Functions, Stats, or Trig concept OR that is some sort of writing task. Which¬† leads me to idea number 3.

3) Incorporate more writing into math class. Still have to think about this one, but I love, love, love it. The ability to communicate is so important in mathematics (and in life, as my mother would say).

4) Continue to build relationships with my students, my school, and the MG community. I just read this article, which was a good reminder to finally attend a basketball game, as well as organize another MG SNOWBOARD AND SKI CLUB!!!!!!! trip. I agreed to be the advisor of the new snowboard and ski team, and it has been mildly hectic, but fun, so far. The other day I realized I have a more experienced background in sports and recreation teaching than I do classroom teaching because I started teaching sailing lessons when I was 14.

Ok, that looks like a pretty good list. Now I just have to work on the enormous pile of grading that I have to do.

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‘Twas the day before break…

My goal for my Geometry classes today was to be as mathematically productive as possible, given that it was the last day of classes before break. The plan was to review the last assignment, take the quizlet (what my department calls formative assessment), do an extension problem, then make a Koch Snowflake if there was still time.

The extension problem was the “Shortest Path Problem” which I highly recommend.

Shortest path problem

It turned out to fit perfectly with what we’re learning right now. It also sparked some rich conversations and good reasoning, and everyone could at least venture a guess, even if they didn’t really know what to do to figure out the exact shortest path.

This plan was carried out differently in each of my three Geometry classes. In the first class, I reviewed several problems and concepts, kids followed along, asked questions, the usual. They took the quizlet. I passed out a half-sheet with the scenario typed out on it. I didn’t include a diagram, thinking that the kids should make the diagram. That was a mistake because the wording isn’t exactly clear, so some kids drew the tent and camper on opposite sides of the river and all sorts of random things. So I had to draw the diagram up on the board for everyone, which slightly killed the magic, but at least we were all on the same page.

A few kids calculated the distance of a path, but not the shortest, and then wanted to be done. I needed a way to motivate them to keep working. In a rare moment of brilliance, I decided to keep score. I announced “Jesse found a path that’s 1,518 feet, can anyone beat that?”. Then I’d write the student’s name and their shortest path on the board. It became a competition to see who could find the shortest path. I let things linger too long in my first class because a few students were really getting into it and asking wonderful questions like, “how do you know that’s 450 feet” and “can you show me how you got that”. So unfortunately several kids had checked out, but at least everyone did something with the problem.

In my other two classes, I skipped the homework review and went straight to the quizlet because there was no way they were going to sit and listen to me blah blah blah about their homework problems on dilations and scale factors. In my first afternoon class, student behavior dictated that decision. In my second afternoon class, I asked them what they wanted to do, and almost everyone said, “let’s just take the quizlet”. So in those classes, there was plenty of time to do both the shortest path problem and the Koch Snowflake.

This time I just asked them to read the problem on their own, and then I read it aloud and drew the diagram as I read so everyone started out with the correct diagram. In one class several kids said they didn’t know what to do to get started, so I said “guess and check” or “if you were the camper, where would you go if you wanted the shortest distance”. This was an excellent starting point for those kids.

The snowflakes were fun too. We saw the Sierpinski Triangle this year, so I brought that up again as a reminder of what a fractal is, but then said that the fractal they were about to make was going to be more holiday-themed. I gave everyone some triangle graph paper to help them with their triangles. At first I thought maybe I’d have them construct the equilateral triangle, but using the graph paper was a good call.

photo (3)

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The teacher learns

I’m getting better at making my expectations clear. Giving quick, short directions right away and repeating them until all students are with me sounds obvious, but it’s easy to move on without some kids and then you never really get them back.

Always be one step ahead of the kids. Pass out and explain the next task to the kids before they start their quizlet so that kids who finish early have something to do.

I freaking love warm ups. Haven’t figured out a system for them yet though. Should I preprint the questions on a half sheet? Should I grade it? I think the answer is probably yes to both of those questions, but I don’t love the idea of using more paper or having more things to grade.

Graphic organizers are great. A few phrases in a few boxes is more writing than we usually do in math class. They work on it individually, then in groups, then I solicit answers and go over it as a class.

That reminds me: cold-calling = awesome. I have cards with student names on them that I use. Open ended questions or questions with more than one right answer (give me one of the transformations we’ve talked about) are best.

I’m almost half-way done with my first year! The lows have been low, but the highs have been high, and I keep reminding myself just to be better than I was yesterday. Always learning.

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Functions. Also, snowboarding.

Two things are occupying my mind right now: functions and snowboarding.

First, functions. Just finished up the unit on functions and transformations in FST (2nd half of an extended Alg2 course) , and I’ve been reflecting on what was good and what was bad.

The good? Using Desmos and sliders to see the effects on the graph. Doing a simple but effective investigation on f(x)=1/x. Color-coding graphs of transformations when there are multiple happening at once.

Could be better? I didn’t start color-coding until we were transforming sine and cosine. Kids like colored pencils and picking out what color to use. Next time I’m going to start doing this right away. I also did a function wall project where the students had to transform a function and add it to the wall (see picture). This was OK but I waited until the day before the test and had them do all at once. I should have had them add to the wall gradually, as we did each function.

photo (4)

The bad? My review day. I feel like I didn’t do much of a summarizing activity. I threw the function wall project at them and then gave them a practice test. Not the most helpful. Next time I’d like to culminate the unit with a final summary. Maybe some sort of writing activity or graphic organizer.

What else? Curriculum. The curriculum I was given just confines the idea of functions and their transformations to one unit, which is ok, but I’m intrigued by the idea of examining the functions and their transformations one by one, a la Greg Waddell.

On to snowboarding. I had the crazy idea to start the snowboard and ski club at my school. It turns out the idea was popular enough that I’m taking 30 kids to a ski hill on Friday. Organizing everything and collecting money has been annoying (I don’t have the patience for record keeping, unfortunately), but it should be a really fun trip. I’m glad so many students are interested, and I’ve had two students step up as leaders. It’s been a good experience so far, and we haven’t even hit the slopes yet!

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