Category Archives: productive struggle

Second semester

I’ve been enjoying second semester so far.

In geometry, we just finished up the unit on triangle congruence. I felt like it was kind of rushed, but progress was definitely made. We revisited proofs after a brief introduction back in October, and I enjoyed seeing kids reasoning again.

One practice that I used several times was having small groups write out proofs on the whiteboards and then sharing them with the rest of the class. I asked each person to contribute one thing to the board (the diagram, marking the diagram, writing the congruence statements, using cpctc, etc) which was a good way to make sure no one was dead weight. One thing I’d want to improve is what the kids in the. audience are doing while the other groups share. Too many were tuned out and I felt like I was the only one listening and asking questions. However I think everyone was listening when one student ended up saying FU is congruent to FU.

I’m now teaching stats in FST. The curriculum is… lacking to say the least. I feel like stats could be so cool, but these crappy worksheets with blurry images are pretty uninspiring. My mentor said she’d help me come up with some cool stats projects, so I have to remember to follow through on that.

Speaking of curriculum, during the last inservice, the math department met and had a pretty kickass discussion on equity in our curriculum. Nothing concrete came out of it, but it was refreshing to hear everyone’s ideas, and I was glad to learn that I’m not the only one who thinks much of our curriculum is really out-dated, non-rigorous, and inequitable. I really do feel like I’m teaching something that was written in the late 80s or early 90s. I can’t relate to it all, and I sympathsize with my students when they can’t either.

So there’s much work to be done, but so far second semester has been shaping up nicely. It’s frickin cold out and we won’t have any vacation until spring break, but I’ve been enjoying every day so what more could I ask for? I’ve been feeling pretty lucky lately.

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Filed under collaboration, Geometry, group work, productive struggle

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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Filed under classroom management, productive struggle

Keep Yo Head Up

I came home from school on Tuesday and told my boyfriend that I wasn’t going back. Of course, I was overreacting to one bad day, and after a good night’s rest, I went to school as normal the next morning. The rest of the week went great, so there you go. It’s so easy to focus on the negative and forget the positive that I have to continually remind myself of what’s going well in my classroom, or I’d never make it.

Last week, my administration granted me the privilege to watch an experienced colleague teach a class. I watched a Biology class that was so well taught that I left feeling inspired. I used to think classroom management was my biggest issue, but after watching that lesson, I realized that time management might actually be my biggest problem. I wasn’t managing time at all. (That sounds crazy, but it really shouldn’t surprise me. I won “Most Likely to be Late to their Own Funeral” in high school. The clock in my car is always set to a random time. I never rush anywhere or feel a sense of urgency.) For example, I used to set the kids off on a task with absolutely no time-frame. I guess I thought that every kid had to finish before moving on.

To avoid wasting so much time, I need to keep things moving fairly quickly. I need to set time limits on activities. I can’t have kids messing around because they think they have the rest of the class period to accomplish something that really only needs 10 minutes of concentrated effort. I need to have tasks for kids who finish early, and I need to recognize that there’s not enough time to wait for 25 kids to each discover something on their own. One thing that has been effective for me is to have a list of two things that students need to accomplish within a given time-frame, with the second item being one that doesn’t require all students to get to before moving on.

Lessons learned there for sure, and that’s a good thing. Other good things: Had a good 1-1 conversation with a student who acts out in my class and likes to challenge me. Two students I’ve been trying to get a hold of for awhile finally came in after school to take missing tests and even waited 10 minutes extra for me because I was in a meeting that went long. Did a a fun investigation in FST (blog post coming soon, hopefully). Taught some algebra-heavy topics in Geometry and no one threw a fit, including me.

Did a long problem in Geometry, and at the end a student pointed out “that answer doesn’t make sense”. She was right, it didn’t, but I couldn’t see a mistake in my work. I stepped back and told everyone to try and find the mistake. Finally, one of my favorite delinquents (he’s not really) piped up, and said “The point is labelled wrong in the diagram. It should be (1,0) not (0,1).” Dang it, a typo on the handout. But all was well because I got to model mistake-making in front of my students. Then I had to go through and basically re-do the entire problem which was also good because the students got to see it again and hopefully understand better.

Oh yeah, and I’m the advisor of the newly formed snowboard and ski club. Held a brief meeting in my classroom after school just to see how many people were interested, and within a few minutes, my room was packed. It was awesome. One of my Geom kids has stepped up as the student leader of the club, which is exactly what I needed.

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Filed under classroom management, productive struggle

Factor Craze

I didn’t have the greatest teaching day today, so I thought I’d try to remind myself that I CAN do this teaching thing by describing an activity from a few days ago that was successful.

Factor Craze, which I think I found via Fawn Nguyen, is one of NCTM’s monthly “Problems to Ponder”, and it asks:
Which numbers have exactly three factors?
Which numbers have exactly four factors?
Which numbers have exactly five factors?

This problem was a great introduction to factoring with my FST (2nd half of an extended Algebra 2) kids. They saw factoring last year, but this year I wanted them to really understand how they were coming up with the equivalent expression instead of following a list of steps from the teacher. So I used Factor Craze to spark some conversations about factors.

I have my students seated in groups, but I had them think on their own for a minute before working with their group. I actually started with the question Which numbers have exactly two factors?, which may seem rather elementary for high school juniors and seniors, but as I suspected, many had very little knowledge or experience with the concept of prime numbers.

Most groups started by writing down examples of numbers that had the required number of factors, but I prompted them with, “What’s a way to describe ALL numbers that have exactly ___ factors?”. All groups eventually came up with prime for exactly two.

When they got to exactly three, most groups found out that 4 and 9 worked. I asked them if there was anything special about numbers 4 and 9. “Oh, oh! They’re perfect squares! Perfect squares have exactly three factors!”

So I respond with, “Do all perfect squares? What about 16 and 25?”

“16 doesn’t work. Oh. But 25 does!”

So I say, “Nice. So some perfect squares but not all perfect squares. What type of perfect squares work?”

And so on. Most groups figured out that squares of prime numbers have exactly three factors. Only one group in each class was able to delve into exactly four factors before we ran out of time.

I really liked how this problem posed a challenge for every student. For some, just remembering what prime numbers are like was a challenge. For others, it was recognizing a theme for exactly four factors. Either way, all students were developing an understanding of factors.

We later moved on to greatest common factors and factoring expressions, and I think laying the ground work with Factor Craze made a difference.

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Filed under FST / Algebra 2, group work, productive struggle

High and Lows (Mostly Highs!) of the First Two Weeks

I survived my first two weeks as a high school math teacher! So many things have been running through my mind, but right now I’m going to make a list of things that are going well and things that need improvement. I just want to get it all out. I hope to blog more regularly from now on!

Things that are going well

  • I love my school. It’s so, so, so good. My colleagues are incredibly supportive and amazingly talented. Our students care about their school and each other. I am very fortunate to be part of such a strong community.
  • There are some very effective school-wide policies in place that administrators, teachers, and students are all on the same page about. I feel like this really promotes school pride and diminishes behavior problems.
  • My Geometry and FST students are awesome kids. I am so impressed by them.
  • Creating a classroom that values mistake making. This is a work in progress, but I’ve got a decent start.
  • Establishing a classroom community where the kids feel comfortable talking to each other. Seniors are good with this (too good, actually), and I’m still working on Geometry kids.
  • I have established some classroom routines! Phew. Thank you Andrew Stadel for Estimation180. It’s been a great way to start class every day. Similarly, ending class with an exit ticket lets students know that we work until the bell, as well as provides me with some great feedback.
  • Using whiteboards (both big and small) has been an effective way to get students to share their thinking and to just get some students to write something down.
  • I’ve done some deep activities, problems, tasks, or whatever you wanna call ’em that have produced good results.
  • I am learning every day.
  • I am finding time to exercise and cook dinner. (Sleep is another matter. Looks like I might pick up drinking coffee again…)

Thank you to all the inspiring teachers who share their wonderful ideas and activities so that I can use them. I stand on the shoulders of giants.

Things to improve

  • Classroom management. Can you tell I’m a first year teacher?
  • Similar to the first point, I struggle with engaging every student when I’m talking to the whole class. Group work is my strength: students discussing with each other with me floating around from group to group asking questions and guiding them along. In contrast, I feel like I’m not strong enough at whole-class lecturing and encouraging note-taking. I think I just need to be more strict about it. No talking when I’m talking. Pick up a pencil and write something down.
  • Kids who are absent. And the kids who are just now switching into my class. How can I get them up to speed?
  • Checking homework and going over answers. What a big ol’ unproductive time sink.
  • Better hand-writing. I save my Smart Notebook documents and upload them to my class website for students to use as a reference. Neater hand-writing would be easier for kids to read and follow.

Have a lovely weekend, everyone! Here’s to a great year!

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Filed under culture, productive struggle

My Automathography

I’m taking Justin Lanier’s smOOC called Math is Personal, and one of our first assignments is to write our “automathography”. So here’s mine. Enjoy!

Mary’s Automathography

I love math, but I didn’t fall in love with it until college. I was good at math in high school, but I was good at all my classes, so nothing stood out about math in particular. I definitely had a fear of getting the wrong answer in math class, and I was happy to just follow the procedures given to me by my teachers. At this point in my life, I don’t think I understood what mathematics actually was. I won the conference quiz bowl in math my senior year, and it was great to get that recognition, but I graduated high school thinking I would study chemistry in college.

I soon discovered that I did not enjoy working in the lab, but that I did enjoy my math courses, so I ended up majoring in math. I went to a huge university (40,000+ undergraduates), so my first two years of math classes consisted of lectures with 300 students. Despite this, I found myself completely inspired by the professors. I was enamored with how passionate and genuine they seemed. In other subjects, I felt like the professors and TAs were egotistical or arrogant. In contrast, everyone in the math department seemed friendly and easy going. I’ll always remember when one of my calculus professors introduced Euler’s identity. His voice wavered, and I thought he might even cry when he described how this one equation related the most important numbers in mathematics.

Even those first few years of college, I was still focused on answer-getting. This quickly changed when I started taking courses like Real Analysis and Modern Algebra. In these classes, I was finally challenged to think for myself. There were no recipes to follow, and it was completely up to me to decide how to prove or demonstrate something. It was both terrifying and liberating. Math became a creative endeavor for me, and I loved it. I truly came to understand and appreciate Georg Cantor’s quote: “The essence of mathematics is its freedom.”

Besides the creative aspect of math, I also thrived on its collaborative aspect. Getting to know the other students in my classes was so much fun, and struggling with them on math problems late into the night will always be one of my favorite college memories. I also always appreciated how there wasn’t a competitive atmosphere in math, compared with most of the science classes I took. Simply put, I learned so much from doing and talking math with my peers. I became more confident and began to embody the mathematical habits of mind.

In particular, I will never forget the group I worked with in Real Analysis. The professor assigned problems every class which were due the following class (this course required more of my time than any other), so the five of us would get together almost every day, sometimes for several hours, to struggle through them. We would meet in the student union in the evenings, staying later than everyone else and having conversations about math or maybe not about math. Before class, we would meet in the math library to share any last minute insights, often getting looks from others for being too loud. Naturally, a strong bond formed between the five of us. On weekends (or Thursdays, or whenever we could no longer stand to stare at our papers) we would go out and get drinks together.

The experiences I had in classes like Real Analysis really transformed my idea of math. I learned the value of productive struggle and collaboration. I learned how to be creative in math and make it my own. I really felt mathematically strong at the end of it all.

Fast forward to the present- five years after that Real Analysis class. I am now about to start my first-year teaching high school math. I hope I don’t suck.

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Filed under culture, fun, productive struggle