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Why I’m #MfAProud

#MfAProud

Two years ago I drafted a post entitled “MfA and its Impact on My Career.” I knew at the time that I had a lot to say, but I could only compose one sentence, a thesis of sorts: MfA has spurred my professional growth and connection with like-minded educators. I revisited the draft many times since then with the hopes of publishing it, but never did. In fact, I wasn’t even able to add a second sentence, let alone complete a paragraph. Every time I wanted to, it seemed far too challenging to articulate what MfA meant to my career.

Fast forward to the present. With the start of a new school year, Math for America has outlined a campaign for its corps of teachers to share why they are proud to be a MfA teacher. Given this, the time is ripe for me to finish that initial draft and showcase my relationship with MfA. Besides, I’m long overdue.

I’ve hinted at this proclamation before; other than deciding to become a teacher, MfA is hands-down the best professional decision I’ve ever made.

For many teachers, including myself, MfA is a dream come true. Seriously, I’m still waiting to wake up. When you realize the woefully complex system in which we operate and contrast it with the die-hard passion for teaching that all MfA teachers possess, MfA is a breath of fresh air. I have met MfA teachers that have cried when discussing their relationship with Math for America. I can relate. Math for America changes careers in unforgettable ways.

When I think about it, MfA’s success doesn’t hinge on anything that’s all that extraordinary. They do something simple, really well: honor teachers. Period. Positively impacting teaching and learning in today’s cutthroat educational climate isn’t like brain surgery. MfA figured this out long ago…and it’s the root of my pride in being a Math for America teacher.

On the most fundamental level, they do this by providing community, structure, and a space where teachers can exchange ideas and resources, all the while feeling valued and trusted. MfA’s teacher-organized, teacher-designed, teacher-led workshops have transformed my classroom to a risk-taking laboratory. I’m constantly working with the best STEM educators in New York City and, I would argue, the country. In addition, I’ve been called on to lead colleagues like never before, which has helped me extend the arm, and mission, of MfA to empower my colleagues. I have also been fully funded to attend a conference. I have a paid membership to NCTM. And though nowhere near an expert, I have even been asked to speak at a research-based institute.

I’m also distinctly proud of the little ways I’ve been able to give back to MfA. To contribute to such an outstanding community (the gold standard in teacher development, if you ask me), means so much to me. Over the years, a certain responsibility has surfaced within me to help maintain the integrity of what MfA stands for and help it evolve over time. Best of all, I know that I still have so much more to give.

But, most of all, my pride shines every time I walk out of a MfA workshop at 7:30pm on a school night. During these moments, I am reminded that my job is a top priority, that I make all other professions possible. I am reminded that I am not an island unto myself. I am reminded why I never want to be an administrator. I am reminded that my students’ futures depend on my continuous development. I am reminded that I am a learner first, a teacher second.

I am reminded of why I am a teacher.

Write me a letter

I need to improve how I get to know my students at the beginning of the school year.

I already knew that I was weak on this front, but when Sara VanDerWerf detailed launching tasks by creating context that honors students, it really inspired me to get the ball rolling.

I already have a couple of routines that allow me to connect with my students. Namely, personal notes, Friday letters, and end of year letters that I open at the start of the next school year. But what I’m missing is something substantial at the start of the year that will help me design the class around my students (that’s not content-based).

So this year, during the first week of school, I’m going to have students write me a letter. It can be handwritten or an email and serves as an opportunity for students to personally communicate whatever it is about themselves that they think I should know. I may provide prompts for those that need guidance, but I want the letter to be somewhat open-ended. I want them to tell me what they feel is important. Some prompts I’m thinking of are:

What’s something about yourself that I wouldn’t know by looking at you?
What’s your family’s background? Do you speak any languages other than English?
Who do you live with? Do you have any siblings?
In all of your years of school, who is/was your favorite teacher? Why?
Who is/was your least favorite? Why?
Was mathematics invented or discovered? Why do you think that? (Thanks Elizabeth.)
If you had to be any number, which one would you be? Why? (Thanks Matt.)

What’s more, over the course of the first few weeks of school, I’ll write every student a detailed letter in reply. This way they can get to know me on a more personal level as well. It’s a significant time committment, but one that I feel will be worth it in the long run.

Speaking of Sara, she also wrote about how she uses name tents during the first week of school, which I hope to adopt this year. This is a crafty, yet simple, way of not only learning student names, but also learning all that is behind those names.

End behavior of functions via Connecting Representations

As the second and final assignment for the Structured Inquiry course I’m taking with New Visions, I was asked to create a task using the Connection Representations instructional routine (#ConnectingReps). More on Instrutional Routines here.

The instructor, Kaitlin Ruggiero, mentioned that multiple choice questions are good starting points for developing these tasks. Adopting her suggestion, I used #4 from the June 2016 Algebra 2 Regents Exam. The question focuses on roots and end behavior of a function. (F.IF.8). I chose to narrow my focus to strictly end behavior.

Here are the first set of representations, graphs of several polynomial functions:

Here are the second set of representations, statements about the end behavior of each graph:

During rehearsal, I showed graphs A, B, and D and their corresponding end behavior statements. We followed the routine to match the representations. I then revealed graph C and had them come up with the statement, which is 4. Lastly, the class reflected on what they learned using meta-reflection prompts.

I don’t have a formal write-up of the activity, but here are the above images.

Reflections:

I designed this for my algebra 2 class. My gut is telling me that it may fit in well at the beginning of my rational and polynomial functions unit. I may also consider using it if/when we review domain and range.
Initial noticings about the graphs had more to do with the “inner behavior” rather than the end behavior. In other words, the class was drawn to the minima, maxima, and roots.
There was some blank stares when I revealed the statements. This will most likely happen with students, too. The mapping symbol (i.e. function arrow) can be confusing if you’ve never seen it before. But that was the point.
Most of the class chunked all of the “x approaches…” statements and realized that they were the same in each representation. Since two of the given graphs (A and B) had both ends going to either positive or negative infinity and the other graph (D) didn’t, this led them to conclude that graph D had to match with statement 2. From there they reasoned that since graph A is going up on both ends, it should match with statement 1. Similar reasoning was used to match graph C with statement 4.
By giving the class three graphs and three statements, the third match (C and 4) was kind of boring. I still made them justify why C and 4 matched, but it didn’t feel as meaningful.
In retrospect, I wouldn’t change any of the representations, but I would revise what I give the class and what I have them construct on their own in order to help them move between representations more fluidly:
- Give only A and B and their matching statements (1 and 3). Students reason through the matches.
- Then give graph C and have them construct the corresponding statement (which is statement 4).
- As an extension, I would give statement 2 and have them sketch a graph that goes with it. All student graphs will be similar to graph D, but the “inner behavior” will be all over the place. Because of the infinite number of possible correct responses, we could show several graphs under the Elmo to guide this part of the routine. I could save these student-generated graphs for later analysis on other properties, including even/odd, roots, maxima/minima, etc.
I didn’t use the words chunk, change, or connect at any point during the rehearsal. This is somewhat disappointing since I want my students to use these terms to describe their reasoning during this routine. Mental note taken.
Instead of me selecting the next presenter, sometimes I should allow the student that just presented to choose. This is student-centric and I like it (when appropriate).
Compared to Contemplate then Calculate, I feel that Connecting Representations is a slightly more complex in nature. With that said, Connecting Representations uses matching, which is really user-friendly. Both routines emphasize mathematical structure, but it seems to me like Connecting Representations emphasizes structure between different representations while Contemplate then Calculate focuses on structure within a representation. Dylan Kane and Nicole Hansen hinted at this during TMC16.
Though I didn’t use Connecting Representations, this past spring I foreshadowed this work with my Sigma notation lesson. Given two representations (sigma notation and its expanded sum), students used reasoning to connect the two.
This in-depth experience with both of these routines will allow my students to surface and leverage mathematical structure through inquiry like never before. So exciting!

Mental Math

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Continuing the process of letting some ideas breath on the blog this summer. Here’s another.

It’s a simple activity for those few unexpected extra minutes near the end of the period…or if I just want to hit them with some quick mental stimulation. I picked it up from my fourth grade teacher: mental math.

I simply call out a sequence of operations with a pause between each operation. For example, I might say “2 plus 5 (pause)…times 8 (pause)…minus 10 (pause)…divided 13…what’s the answer?”

Students can’t allowed to say anything out loud and, obviously, any electronic device is prohibited. I don’t require that everyone plays (most do). The students must wait until I say ‘What’s the answer?’ before raising their hands. I call on a different student each time and if that person’s answer is wrong, someone else gets a chance. Because it’s a terribly simple idea, it’s always engaging. The trick is to make it challenging to the point where they get hooked and want more.

Some tidbits: I’ll usually start with one that’s pretty straightforward with long pauses – especially at the beginning of the year. Things get interesting when I start to call out the operations lightning fast or the sequence contains something like 15 operations. Make things fun by using numbers in the millions – or even billions. Also, depending on the class, the level of the math can vary from basic arithmetic to roots and exponents to evaluating trig functions. It’s endless. And fun.