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Doing Math, Sharing about Teaching, and Personally Meaningful Mapping: A Math/Teaching Mini-Conference!

Join us for a day of math and sharing about teaching in NYC! Connect with other passionate math educators in this small gathering. You’ll have the chance to do and think deeply about math and learning through meaningful sessions and thoughtful discussions. Plus, we still have space for presenters. Read below if you’re interested!

The gathering will be in the spirit of our summer gathering, which has been meeting every summer since 2016. This will be our first time also coming together to meet in the spring.

 

When: Saturday, May 11, 2019, from 9 to 4. (You can join us in the AM, PM, or all day.)

Where: City-As-Schoolcas-logo2.png, 16 Clarkson St New York, NY 10014. Contact us if you are interested in babysitting (only for kids 5 and up).

Registration: To register — or to express interest without registering — just complete this form.

What will it look like?: In the AM, there will be sessions about teaching, and we will be studying personally meaningful map-making with Professor Jasmine Y. Ma (see below).

In the PM we will be doing math, hosting sessions about teaching, and drawing math outside on the sidewalk (weather permitting).

Here the is draft schedule for the one-day event:

9 – 9:30: Welcome

9:30 – 10:45: Personally Meaningful Mapping with Jasmine Y. Ma

11 – 12: Sessions

12 – 1: Lunch

1 – 2:15: Doing math

2:30 – 3:30: Sessions

3:30 – 4: Sidewalk math

Register now to join us for the morning, afternoon, or the entire day of mathematics and sharing about teaching in May!

What is “Personally Meaningful Mapping”?: Great question! Here is a description of the morning session.


Personally Meaningful Mapping: Place-making as representational practice

In popular imagination, values play no role in math or math education. From this point of view, the only questions in mathematics are ones that can be answered with certainty; likewise, values have no role to play in questions about mathematics teaching or curriculum.

Making and interpreting maps is an activity that puts pressure on this popular view. While the most familiar maps have the aura of timeless objectivity to them, every map is a representation of what the map-maker values. This can be seen, for example, in maps of the United States which attempt to scale a state’s area in accordance with its ability to influence an election:

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But electoral influence is just one way we might scale maps. What would it look like to make a map that represents what is meaningful to you? A neighborhood map that shows places you love? Places you fear? What rules would you use to design your map? How will you make it comprehensible to others?

In this session, Professor Jasmine Y. Ma will lead us in thinking about the ways maps can represent the meaning made by their makers. In this way, she will raise questions about the relationship of personal meaning and mathematics, challenging the popular view that mathematics is divorced from human emotions and values.


We’re excited to share more information as we nail down details over the next few weeks. Register to keep getting info!

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Doing Math at TMCNYC, Part 1

After this year’s TMCNYC, we sent out a survey to everyone who attended. We asked, “What was your favorite part of TMCNYC18?”

Here are most of the responses:

  • Doing Math and hanging out with people.
  • Probably Doing Math with Ben, Cici and Melvin. Really interesting series
  • Being able to do interesting math with other participants, math that I could see how it directly related to high school math, without being high school math.
  • Doing Math sessions & just chatting with people
  • Doing math. I always think the most beneficial PD for math teachers is being engaged in math. I wish that session after lunch was longer.
  • Probably the “doing math” sessions! All three were fun, engaging, thought-provoking, and well-run.
  • Doing Math
  • The Doing Math sessions were fantastic!
  • Doing math – I loved each of the math sessions.
  • The expanding math strand!!!!! I also enjoyed the doing math sessions.

It seems that pretty much everyone’s favorite part of our conference was the hour we spent in the middle of each day, doing math together.

In light of this feedback, we’re going to engage in some public reflection. What made the three Doing Math sessions so popular? What makes a successful Doing Math session? How can we (and others) replicate the fun that we had at TMCNYC18?

We (the organizers of TMCNYC) asked each of the Doing Math presenters to reflect a bit on their session this past August. The first post comes from Benjamin Dickman, whose Doing Math session was about problem posing and the multiplication table, a context that we had a ton of fun with at TMCNYC and that some have already brought into their own classrooms:

 


 

Facilitating a Doing Math session on Problem Posing [Benjamin Dickman]

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I see a lot of mathematics education through the lens of problem posing. I see problem solving as asking oneself a lot of questions – posing problems, in some sense – like, “Does this remind me of a related, or simpler, problem?” or “Can I represent this problem using a picture or a diagram?” or “Who is awake right now and might have an idea about how to solve this problem?” But, what is the actual source of the problems with which we are engaged?

I worry that too few of us have had the opportunity to create a problem that was our own. In my anecdotal experience, people get excited when they make something novel that engages others, and I want to see more of this – the excitement from being creative, and the engagement around new problems – in the vast, ever-expanding world of math and math education.

Two ideas that are central to my decision to present on problem posing:

(A) Problem posing is a skill that can be introduced and practiced during a short session; and

(B) Problem posing is a skill that can be developed over a lifetime, and brought back to the classroom – or other learning sites – in many different ways.

I think these are themes. Specifically, can you answer the following?

(A*) What is a topic that you can broach meaningfully during a short session?

(B*) What is a topic that participants can continue to explore after your session ends?

I presented at TMCNYC18 on problem posing with the multiplication table. I picked the topic of the multiplication table because:

(1) Problem posing is so wide-open that I felt it needed some constraints to keep us on the same page, or at least in the same book;

(2) I expected most participants would be familiar with the times table, and might even harbor negative conceptions about it based on perceived proximity to rote memorization or drilling; and

(3) I have thought a lot about the multiplication table in the past: enough to feel that I had something original to contribute, enough to feel that I could respond effectively to ideas or questions that arose as relates to this topic, and enough to feel that new ideas could provide opportunities for more careful thought later on.

I think these are themes, too. Specifically, can you answer the following?

(1*) What is a big topic that you can home in on, whether through focused questions, a sequence of problems, or some other approach to structuring?

(2*) What is a subtopic, or object, or idea that will be accessible to a wide range of participants – and how might you think about differentiating instruction so that rich mathematics can be surfaced?

(3*) Related to the previous two questions, and perhaps worth asking yourself beforehand: What do you know a lot about – meaning that you have given it thought in the past, and are excited to give it further thought in the future?

I hope that what I have written above can be helpful to someone who might facilitate a future Doing Math session, or something like it. The only prerequisite that I can think of for facilitating such a session is that you genuinely want to; even then, you might wish to run a session, but be concerned that it will not go well. I have certainly experienced this type of worry or anxiety or dread, and my experience has been that it subsides only with experience. But, I know that you have something worth sharing – even if you have not yet identified what it is – and it would be a shame to let your self-doubt deprive others! If you want to contact me about planning for a potential Doing Math session – whether initial brainstorming or finishing touches – then email will be a great choice: firstnamelastname[at]gmail[dot]com

Notes on Numbered Themes for my TMCNYC18 Doing Math Session:

I begin with (1) and (3) and then return to (2) to investigate just one specific problem posed by a participant, Brian Palacios, during this Doing Math session at TMCNYC18.

(1): Perhaps the best I can do is link to a write-up of the actual talk! Problem Posing with the Multiplication Table. (Many thanks to Andrea Kung for typing out the problems, and her solutions, for that which was presented!)

(3): A couple of participants (Sam Shah and Dan Anderson) used the numbers adjacent to the main diagonal of perfect squares to connect the times table – a square display of multiplicative, number theoretical information – to Pascal’s Triangle – a triangular display of additive, combinatorial information. This provided me with new fodder for thought: What other connections exist between these two representations? I have not [yet] given this much thought, and I invite the reader to marvel at will!

Also (3): I was pleasantly surprised that Grace Chen, in her closing session on the last day of TMCNYC18 (Structured Reflection on “Expanding Mathematics”) re-mentioned an aspect of the definition that I gave for a problem. This definition can be found in the link above, but here it is:

Problem: A question for which the method of solution is unknown at the outset.

This was followed immediately in my talk, and write-up, by a remark that begins:

There is an implicit human in the definition above: the word “unknown” entails the

existence of a living entity…

I think that the [implicit] human in mathematical problems is a topic to which more attention should be directed, and look forward to thinking it through to greater depths.

(2) By applying the approach to problem posing that was discussed during the beginning of this Doing Math session, Brian formulated the following problem:

Consider a table in which the entry of row a column b is ab-(a+b). What is the sum of all

entries in that table?

I do not recall dimensions being given, so I will solve it below for a 10×10 table; the generalization to an nxn table or nxk table is left to the reader!

My solution to Brian’s problem: Add 1 to each of the 100 entries in the 10×10 table; this adds a total of 100, so when we find the modified table sum, we will go back and subtract that 100 off. Each entry is now ab-(a+b)+1, which factors as (a-1)(b-1). In a standard times table, we would have row a column b containing ab; here, we have simply reduced each of those factors by 1, which results in a topmost row and leftmost column of zeros, and the rest of the table looking just like the 9×9 table. To compute the sum of that 9×9 table, we use the same method described at the start of the talk (and in the link to its write-up) to find a total of 45^2. But, we still need to subtract off the extra 100; so, our answer is: 45^2 – 10^2 = (45-10)(45+10) = 35(55) = 1925.

I feel fairly certain that the reader has known about the multiplication table for many years, but has never seen Brian’s problem before. (I had never seen this particular question, but my experience thinking about the topic of multiplication tables, factoring, and summing table entries definitely prepared me to broach it effectively!) This question, for me, provided a wonderful opportunity to explore a familiar mathematical context in a novel way.

Read over the presentation if/when you get a chance, and let me know: What multiplication table problems can you create?

What are people interested in learning at TMCNYC?

We are still taking proposals for sessions for this summer’s TMCNYC (August 22-24). Because our conference is local and small (by design) we can say with some specificity what some people are looking to learn when we gather.

Of course, we can’t comprehensively say what everyone attending our conference is interested in learning. But based on conversations, notes from registrants and the session proposals we’ve already gotten, certain themes are emerging.

In hopes of inspiring more people to register or to submit proposals, here are some of those emerging themes:

Making connections between educators involved in elementary, middle/high school and adult education. We already have a group working on angle routines for elementary students, and that group involves educators that work in elementary, high school and university education. We also have a session proposed about connecting calculus ideas to the material in earlier — even elementary — grades. Finally, there is a great crew of educators who teach math to adult students who will be attending the conference, and they often are working with material from across the k-12 spectrum.

There is energy behind ideas for connecting mathematics across grade levels at this conference. Have an idea for how to take this further? If so, please propose a session on your idea.

What is mathematics? Who is someone who does mathematics? There is a session that has already been proposed about how one’s identity impacts their ability to teach or learn mathematics. Through conversations, we’ve learned that some participants would be interested in thinking more about what mathematics is and what students think mathematics to be. These two questions (who does math? what is math?) are potentially deeply connected. It would be wonderful to receive more session proposals connecting to these themes, so if you have one in mind — share it please!

Routines that help kids do deep mathematics. This has been a major theme of past TMCNYC conferences, and it seems that people are still eager to learn more. We have several sessions submitted about instructional routines for supporting inquiry, and the aforementioned elementary angle group is developing new routines to share at the conference. But what other ways of mathematical engagement can be supported with a routine? We could use more submissions along these lines too!

Art, Games, and Algebra. These aren’t one thing — unless you have a game that combines art and algebra! — but these were other areas that people told us they were interested in when they registered. We could definitely use more proposals along these lines.

If your interest or your session isn’t part of these topics — all the better! We all benefit when people share things they are passionate about.

But if you’re looking for a sense of what our conference will be about or thinking about what others might be interested in, consider this list a partial snapshot of where some of the interest lies.

Looking forward to hearing your idea!

Propose your idea for a session at TMCNYC 2018

The session proposal form for TMCNYC is here!

As you think about proposing a session for our August meeting, it could be helpful to keep in mind the ways TMCNYC is different from other professional meetings you might have experienced:

  1. It’s smaller, by design.
  2. It’s local, by design.

These factors don’t limit what you can propose — rather, they can open up new possibilities.

So, for example, if you have something that you’d very much like to learn about, but you don’t want to lead the session, we can try to find someone to lead that session.

Another example: if you want to try something that wouldn’t be possible at a larger conference in a large room, you can do that too. Last year’s sessions included a facilitated discussion about race in the classroom, and a math fair with interactive stations.

We’re local, by design: feel free to host a session that focuses on things happening in NY.

But these are just ideas to spark your imagination. We’re eager to hear your ideas, so please be in touch if you have any idea for a session, but aren’t sure if it would make sense for our meeting in August. We’d love to chat about it with you!

All the best,

TMCNYC Planning Team

Geometry Routines for Elementary Students – This Year at TMCNYC

What we’re doing, in short.

We’re trying to develop an instructional routine that is custom-designed for exposing elementary-age kids to the ideas of geometry (especially angle measurement).

The goal of our group is to have something ready for testing and sharing at TMCNYC in August. Then, we’ll improve the routine further and have it ready to use in the coming school year.

(Register now to participate in August!)

The longer version.

Our group came together around a shared desire to help students better understand geometric ideas in the elementary grades, when geometry often is neglected by teachers. In addition, while we’ve had a lot of positive experiences surrounding instructional routines involving arithmetic, we’ve found that there are far fewer routines and resources for teaching geometry to younger children.

After sharing our favorite topics (and those whose teaching was most in need of improvement) we decided to give a special focus to angle measurement. As we prototype routines and develop materials to share in August, here are just some of the questions we’re asking ourselves:

  • for young students, what is an angle?
  • how do we help students understand that “size” doesn’t matter for angles?
  • how can students learn to use a protractor effectively?
  • can physical movement help students understand important angle concepts?

We’ll share much more at the conference in August, and hopefully have something we can share much more widely during the following school year.

Who we are!

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Charlotte Sharpe (@getting_sharper) is an assistant professor of mathematics education at Syracuse University, where she works with pre-service and in-service elementary teachers to plan and enact discourse-focused math instructional routines into daily instruction. Charlotte used to teach high school math (including geometry) in Texas, and is still buzzing from a week working with 4th graders around angle measurement, construction, and classification at an urban school in Syracuse.

 

 

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Tina Cardone (@crstn85) is currently writing high school geometry curriculum with Illustrative Mathematics. She spent over ten years as a high school teacher of courses from pre-algebra to AP calculus. She worked with diverse populations and specialized in classes for students with disabilities.

 

 

 

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Deidra Baker (@dbmpmath , @dlfbaker) is currently teaching geometry, algebra, and practical math at Mid-Prairie High School in Wellman, Iowa. This is her 25th year teaching in Iowa. She has also taught at Iowa City High School in Iowa City and was the high school math Teacher at Keota High School. She enjoys learning and working on extra projects. She has presented at a National Council of Teachers of English annual conference, as well as presenting at a National Council of Teachers of Mathematics annual meeting. She is the current Iowa Council of Teachers of Mathematics president.

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Marta Kobiela is an assistant professor of mathematics education at McGill University in Montreal, Canada where she teaches mathematics teaching methods courses to elementary pre-service teachers. She has taught math in different contexts (both in and out of school) and is especially passionate about learning how to support geometric thinking and reasoning.

 

image5Lynn Selking (@LynnSelking) is a math consultant serving K-12 schools in southeast Iowa for Great Prairie Area Education Agency.  Lynn has previously taught secondary math in Missouri, Michigan and Iowa. She is a life-long learner and her passion is for every student to be able to meet his or her full potential in life.

 

 

 

Also featuring…

  • Jenna Laib (@jennalaib)
  • Max Ray-Riek (@maxrayriek)
  • Michael Pershan (@mpershan)
  • Scosha Merovitz