CMC-S Day 1 (or why have I never hung out with Robert Kaplinsky?)

Today’s actually my second day at the CMC South conference in Palm Springs. I came a day early for the math coaches workshops on the pre-conference day–awesome chance to connect with other teacher leaders from all around. However, the highlight of my extra day had to be a walk through the Palm Springs street fair with Robert Kaplinsky. Though I’ve known Robert online and as a (powerful) presence at conferences, I’ve never had the time to hang out with him one on one before…so glad I did! Thanks, Robert, for the chat and for convincing me to attend your session! More on that further on in this post…

I wanted to give a quick thank you to all the people who attended my debate session! A copy of my slides are here: CMC Conference Slides! It was the first time I did the talk in a large room, a less intimate setting, and (though it all went well!), I’m starting to think about how I would re-work it in the future for a large space. I’m learning that I’m a teacher/presenter/adult that enjoys small group settings.

After a wonderful lunch with some of my favorite (and new!) math teacher friends, I made my way to Robert’s talk. If you haven’t seen his Open Middle problems or heard him talk, definitely check them out! I had a great time working alongside Eric Martin as we created our own open middle problems. A (messy) vision of what I did is below:

There’s something interesting that really stood out to me about these problems (and the presentation on a macro level)–I felt a similarity between the session I attended and the one I led. Creating these open middle problems and creating debate-able questions are two different styles/methods with similar goals. For one, we both want to help teachers see ways to improve their questioning. My style is to foster more discussion and debate through creating debate-able questions, and Open Middle is re-working questions in its way to challenge students and increase discussion/engagement around problems. We’re both deepening students’ understanding of the math and awareness of misconceptions. We’re both trying to increase student engagement and to allow for various methods. It’s just the details in how we do it that is different.

Of course there are plenty of ways to contrast the two, but sitting in Robert’s talk, I noticed how similar even the structure and style of the presentation was. We both take teachers through this journey of doing the kind of problems we want them to do, creating problems by sharing a method of developing problems similar to what we just did and sharing resources to extend their exploration and learning in what we are each doing. (Granted, Robert is waaaaaaay ahead of me on collecting and collating resources, but I’m just saying we have a similar flow.)

It’s really a feeling, and I still struggling to put the connection into words.

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More Barbies–in Calc

I start my (non AP) Calculus class every year with two days reviewing lines, slopes, functions, etc…and we spice it up by (quickly) doing the Barbie Bungee Jump activity! There’s lot of places to read more about that. So I won’t go into that any further.

However, I really wanted to add both more fun activities to the rest of my units AND have more of a continuous through-line. So, I tried to include a Barbie-centered activity in my introduction to derivatives, including average velocity vs. instantaneous velocity, etc. I came up with Barbie walking the runway!

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Page 2:

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It worked really well! They had fun, and we talked a lot about slope=velocity. The last page had some questions more textbook-y, asking them to apply the ideas in new problems:

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Email me if you want the full doc!

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Rearranging Limits

I struggled a bit with teaching limits the past few years. Not only are they difficult for students to grasp, but the texts I have used as guides have been a little bit jumpy. Add that to the fact that I teach a non-AP Calculus class. So, this year I really wanted to make a clear exploration of limits, building a strong intuitive understanding of what a limit was asking for. The result: instead of making daily objectives about limit concepts (what is a limit, one-sided limits and infinite limits), I changed my objectives to limit strategies. In other words, our objectives/topics for each day were:

  • Day 1 & 2: Finding limits by tables
  • Day 3: Finding limits on a graph
  • Day 4: Finding limits using algebra

The first two days, we just spent finding limits using tables (on Desmos and in the graphing calculator). I started with the “buffering” idea I mentioned here. Then, we just made lots of tables, explicitly talking about what numbers you would plug in to get “really close” to a certain x-value. Below is a screen shot of the worksheets I used. Notice that we got into infinite limits without talking about them as anything different.

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The next day, we talked only about finding limits on graphs. I gave lots of graphs, and we found the limit by reading what the graph is approaching on each side.

The last day we spent some time using “algebra tricks” to also find limits.

My goal was that by the test, students could find limits using whatever method(s) they prefer, having a deep intuitive understanding of what a limit is. And the scores were so much better this year!

As an additional test of how it worked, the day before the test, I gave the following as a warm up problem. I’ve done it every year, and this is the first year students could do it on their own, without any help! They did a great job!

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RSBCMTA Conference

Yesterday, I crashed the Riverside San Bernadino Counties Math Teachers’ Association first annual conference, and I am so glad I did! Just the day of inspiration and insight I needed.

The day started with a great call to action from Chris Shore, focusing us on the Common Core Standards for Math Practice.

He also demonstrated the difference between traditional quizzing and some variation, but more on that later…

Chris’s key note focused our sessions around the SMPs in a good way. I gave a session on debate in the math class. Then, inspired by Tracy Zager’s TMC16 talk, I went to an elementary school teacher’s session on classroom discourse. It was a great session led by Mary Vongsavanh, and it got me thinking more about classroom discussion structures. Something she said that really struck me was “if want want them to do x, give them that experience”…as well as “The more you talk about something, the deeper your understanding.”

One take away is an extension of a Falsification activity I already do. Her example is below. Based on the picture, what is the rule for what fractions go inside the circle? You can “test out” the rule when you think you know it by naming a fraction that you believe goes in (or out of) the circle, and the teacher will confirm.

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I have lots more to say about discussion and assessments and all that, but I’ll get more into that later. Thanks RSBCMTA for a great conference!

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Start of Year: Introducing Vocab

In the past two years, I’ve been convinced to introduce definitions always using the Frayer Model. If you don’t know of it, there’s a video I just found online here. This is what a blank one looks like:

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Now, let me say that I avoided it for many years because it felt to me to be a bit too contrived or too geared towards younger students. However, I’ve come around on my thinking, and I use it in all my classes, 7th grade through Calculus, and I LOVE it.

Part of the reason I love it is that it forces me to thoroughly flesh out the new vocab word, for the benefit of my students.

Another reason I like it is that I’ve found two ways of structuring how we fill in the boxes (see below).

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Let me just add that I hand out to students a page where this box covers half a page (pictured to the right). I usually have two boxes on the front and one or two on the back, depending on how many important definitions I plan to go over in the span of a class or two.

I then also display one box on the board when we are filling it out in class.

Now, on to the two ways I work through the boxes:

 

Style 1:

A nice, straightforward way to use the model is to follow it in a U-shape. It flows like this:

  • Start in the top left corner: I give a formal definition.
  • Move to the bottom left corner: as a class, let’s come up with some examples.
  • Move to the bottom right corner: with a partner, come up with some non-examples (which I may have some students put on the board).
  • End in the top right corner: As a class, we add any notes that came up during our examples of things we want to remember. I may also come back to this box in the following day or two to add more notes if necessary.

Here’s an example we did in my Integrated Math 3 (Algebra 2) class.

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We filled in the examples with tables and sequences that had a quadratic pattern. The “Essential Characteristics” popped up as an animation after we filled in the bottom boxes. We later went back to fill in “Essential Characteristics” with notes like forms a parabola when graphed.

 

Style 2:

My newer use of the box (inspired by one of my awesome colleagues at TMC17) forces students to create good definitions based on examples. I fill out the bottom boxes and they come up with a definition that is “unbreakable.” It flows like this:

  • Start in the bottom left and bottom right: Prepared examples or on the spot examples. Have students look at those, consider.
  • Move to the top left box: have students pair share a good definition (that is unbreakable) and then discuss as a class. The teacher tries to “break” the definitions students come up with using examples and non-examples (possibly the ones already there), until the class comes to a solid definition.
  • End in the top right box: fill in notes about anything important that came up in the “trying to make a definition” process. I may also come back to this box in the following day or two to add more notes if necessary.

This time, the thing I start with looks like this:

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Here, students started to say things like “it goes through the vertex.” However, my horizontal and diagonal lines go through the vertex, too. So I was able to “break” that definition. Students love playing this “game” of making a solid definition, and in this class they eventually honed in on the point that it had to vertical and cut the parabola “in half.” The fact that it went through the vertex was a “cool side effect” as one student said, and that went in our Essential Characteristics box.

 

 

 

 

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Start of Year: Day 2 (Introducing Debate)

After my first day activities, which (I hope) build some community and positive culture in my classroom, I like to begin Day 2 by introducing my debate format. I have a whole blog post sharing more of the details of how I go about it here. I just wanted to show the two start of debate activities I used in my classes. The earlier blog post describes all the steps I follow.

Note: The debate activity only lasts 5-10mins. If I have a small enough class, I try to get everyone to stand and say one claim/warrant…but I also feel out the room and stop if we’re getting repetitive or I’m losing engagement.

In Calculus class, I started with this slide:

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In my Integrated Math 3 (Alg2-ish) class, I started with a Which One Doesn’t Belong. The first slide was:

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I then dive right into our first Unit. During this time, I have students go to the board to do problems, introducing another routine of my class. Using Vertical Non-Permanent Surfaces (VNPSs) is something I blogged about here. I have 6 different dry erase boards around my room for students to work on in pairs or groups of three.

 

 

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Start of Year: Day 1

I read this article a few days before school started, and it really got me thinking. The gist is that I want to start with my actually curriculum, rather than “cool/fun math” activities because I don’t want to send any subtle messages that the curriculum is too boring to start on day one…or the curriculum can’t build community. The quote that stuck with me is:

if you’re teaching content well, the class culture stuff will fall into place.”

So here is a run down of how my classes tackled Day 1:

  • When students enter, they fill out a notecard with name, best person to contact at home, favorite number, and if you were a creature, what would you be and why. I found this summer that changing the word animal to creature allowed for a wider umbrella, including fictional creatures, plants, and Cinderella.
  • When students enter, they also fold a large notecard in half and make a nameplate. I have them use markers (I provide) and write their name (just first name, what they want to be called) on both sides of the nameplate, in case it gets turned around.
  • While students are filling out the notecard and nameplate, I quickly go around the room taking a picture of each one with my phone. I make sure to get the nameplate in the picture. I now have a photo directory to learn students names at home.

Here’s what the first slide of the day looks like for all my classes:

Day1 Screen

  • After quick introductions (tell me one thing about you I can’t tell just by looking), I pass out the syllabus. On Day 1, I only have students look at the supply list. I don’t go over anything else. I will go over other parts (homework policy, grading, etc) when those things actually arise the first time (i.e. when I give the first homework, when the first quiz grade is put in the grade book, etc).
  • Next, I do want to get students talking more about classroom rules and culture, but I do it in the form of Talking Points (a la Elizabeth Statmore). Here is my list of statements. I leave some blank space at the end for students to come up with their own controversial statements. They have a lot of fun with those!

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  • Now that we are about half-way through the class period, in the spirit of that article I mentioned above, I have students work on content. In Calculus, it was the first part of Barfing Monsters (a la Sam Shah). In my Integrated 3 (think Algebra II) class, it was this great problem that I got from Bill Thill and Peg Cagle about patterns (see the picture below). It’s a great open ended problem, that eventually lets students pull sooooo much math from a simple pattern. Students create linear and quadratic equations based on what they use to fill in the blank.

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  • Lastly, inspired by Sara Van Der Werf, I have students write about their thoughts on the first day of class inside their nameplate they created. Just a sentence or two. That evening, I write back to each student, and we continue to have a brief written, private conversation in this nameplate throughout the first week. It does wonders for making connections and building relationships!
  • The homework for the first week is to email me two paragraph about themselves in general and as a math student. It’s called a Mathography, and in the first weeks of school, I respond to each email.

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