Tag Archives: math

End of 3rd Quarter

Hi everyone.

It’s the end of 3rd quarter, and we’ve got a grading day. Actually half-day. So I thought I should blog since I got the time! No kids! It’s some sort of miracle. I’m fortunate at my school to have a prep period and a department planning period… but during my prep, I can expect to supervise 8 to 10 up-to-no-good-but-so-lovable seniors. Up-to-no-good is definitely putting a positive spin on it. During my plan period, I can expect to supervise two or three accelerated freshmen for whom school comes easy and are mostly bored with it, and two or three sophomores who care, but need me to give them 1-1 tutoring in Geometry.

In short, having some time to myself in my classroom is some sort of miracle. It never happens. Now if only I had something interesting and substantial to blog about.

The kids are the best part of the job though. Forget grading, planning, and prepping. I do what I do because I believe in those little punks. They’re beautiful, lovely, funny, and smart. They deserve the best.

OK, here’s something worth blogging about. I just taught right triangle trigonometry to my Geometry kiddos. I love introducing trig. This year it conveniently followed a similarity unit, so I introduced it with a quick lab measuring sides of triangles and computing SOHCAHTOA ratios. Huh, weird, for any 30 degree angle in a right triangle, the ratio of the opposite side and the hypotenuse is the same. Huh, weird. (Similar triangles, anyone?)

Then we do some boring, but straightforward practice. Then the next class we go on a field trip. I love to advertise this next bit as a field trip, even though we only go down two floors to the Commons.

I start by having them estimate the height of the ceiling in the Commons (we regularly do Estimation180 in Geometry). Then I have them take out their telly-phones and download a free clinometer app. The only issue is the kids who say, “but I don’t have any room on my phone”. Maybe if you deleted some of those dang selfies, kid.

I crappily, but enthusiastically, model what they’re supposed to do. (My teaching career is a work in progress, OK? Year two is better than year one, at least.) I pass out the awesome, giant tape measures that the math department owns. We disperse down to the Commons. Chaos ensues, naturally, but we’re on a field trip in math class, so it’s a good thing. Tape measures are being stretched out, kids are pointing their phones at the ceiling, and most kids are sketching a triangle and writing down some sort of trigonometric equation. It’s my favorite day of the year.

Eventually we return to the classroom. My least-focused kid (one of those with an ADHD star next to his name in Infinite Campus) happily sits down and gets to work solving trig equations. How could he not? I just let him run around the Commons for 10 minutes.

They’re beautiful creatures, ya feel?

IMG_1956

8.4 trig lab

8.5 trig invest how high is ceiling (I think this was adapted from something from Tina Cardone @ drawingonmath ??? Not sure. But I definitely stand on the shoulders of giants. Thank you all.)

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Filed under fun, Geometry, grading, trig

Why Do We Memorize the Unit Circle?

Let me preface this blog post by saying I teach a “lower-track” Alg 2/Trig class. (The school tries to spin it as “we have many options for math classes, blah, blah, blah, so that students can be successful”, which is great, but it’s also silly not to call it what it is.) Almost all of my students are seniors, and the average student is going to a 2-year college. Some will go to a 4-year college. They’ve got a lot of potential, but they’re not particularly motivated by academics.

So keep in mind I’m thinking of my students, not a group of juniors in Pre-Calculus who will take Calculus AB next year; however I think the following question applies to those students as well.

Why do we make students memorize the unit circle?

Isn’t it more important to understand what the unit circle is? Memorizing a few selected values didn’t help with conceptual knowledge of the unit circle, and I ultimately felt like I was making them memorize it simply because I could. And then I could give them a quiz. I almost feel dirty about it because instead of making sure they actually know what the unit circle is and why it works, I had them memorize a bunch of numbers.

I love trig and love teaching trig, but I’m not sure memorizing the unit circle is helping any of my students actually learn trig.

Any feedback is appreciated! Thanks!

 

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Filed under FST / Algebra 2, trig

Take Aways from Green Lake

Yesterday I had the good fortune of attending the Wisconsin Math Council Conference for the first time, and it was a lovely experience.

I went with my colleague who is also a first year teacher, and we ended up in some really great sessions.

My favorite session was definitely Get Up and Move, which was exactly how it sounds. I learned some great new strategies for getting kids out of their seats and moving, including Bucket Sort, Musical Math, Relay Race, and Clue. I think my kids sit too much, and I want to get better at doing fewer, chunked activities rather than long work times, so doing a practice activity where they’re out of their seats and moving sounds like a win-win.

I also went to Jo Boaler’s keynote. I’ve been following Boaler’s work for awhile now, so I didn’t really learn anything new, but her presentation was so lovely and her message so true. I can’t agree with her more, and I hope to see a major shift in mathematics education soon that encompasses her ideas on mindset, mistakes, and success in the math classroom.

One session that I wish would have existed is lesson planning or unit planning. I feel like maybe I should have learned that in teacher school, but whatever. I want to get better at planning.

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Filed under collaboration, conversations, Uncategorized

Fun with Expected Value

I just taught expected value in FST and really enjoyed it. The two main tasks I used were: The Carnival Candy Game and Dan Meyer’s Money Duck.

The Carnival Candy Game

You’re at a carnival and you get to pick one piece of candy from a bag. The color candy you draw determines how much money you win. I used starbursts, and I set it up like so:

starburst data as jpg

The students didn’t win money; rather they won that many starbursts. (I had a different bag of starbursts for prize winnings because I made sure that the candy drawn was replaced each time to keep the probabilities the same for everyone.)

This was enjoyable because naturally all the kids wanted to pick the purple one. Not surprisingly, most picked pink, yellow, or red, but I have 45 FST students (two classes), and the 44th student did pick the purple one.

Then I asked them to calculate the expected value for their prize winnings when playing this game.

Then I said, suppose it costs $5 to play this game. What does that mean for the player? What does it mean for the carnival game host?

Money Duck

Love the Money Duck. The students were very engaged by the idea of the money duck. I basically followed Dan Anderson’s lesson plan for this one. Like Dan’s students, and as I commented on his post, my students also wanted to determine the possible/impossible distributions based on what they saw in the video instead of in theory. I slightly fixed that in my second class by stopping the video after the first $1 money duck, explaining that the video was made up, and stressing that we were interested in what is possible, not necessarily what the company actually does.

Like Dan, I had my students come up with company names, probabilities, and price. They then had to compute expected value and their profit. I also compiled the data in a spreadsheet, but didn’t really do anything with it, unfortunately. If I did it again I would like to have the students do some more sharing and comparing between groups.

money duck groups jpg

I definitely recommend both tasks.

And then things got even better. Today was the grand opening of a new Cabela’s nearby my school, so several of my male seniors told me how they all skipped class this morning (well, some of them probably had open campus 1st period… I hope) to get in line at the new store because the first 500 customers received a gift card up to $500. One of them said, “But Ms. Cummins, they didn’t tell us how many were for $500″. It turned out that they all got $10 gift cards except for one who got a $25. It was perfect. I told them I was going to write a test question about that.

 

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Filed under FST / Algebra 2, fun, probability

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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Filed under culture, grading

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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Filed under planning