“How much is the human race missing out on because the people with the genius ideas aren’t being heard, because of oppression?”

As a math educator, I’m so eager for people to see and discuss this movie. I want to hear what we are learning about what it means to do mathematics, about who can be good at mathematics, about what it means when we embrace new technologies and how that changes workers’ lives, about how racism and sexism manifest themselves in big and small ways, about what it takes to transform cultures, and more.

I’m especially eager for students in our math classrooms to get to think their way through *Hidden Figures*. There are a million lesson plans that could be written, and I know people like John Burke are encouraging teachers to collect them and share them in his post, “Let’s Start a Movement for Hidden Figures”

Here’s my first contribution, written for Philadelphia’s week of Black Lives Matter lessons. In this lesson, students play a game that my colleague Suzanne invented called Mission Control, in which they have to describe, using one-way communication, some mathematical object that their partners out in space have to recreate. It focuses on communication of math ideas (something Katherine Johnson worked on a much harder version of later at NASA, when she wrote papers about helping astronauts quickly calculate new trajectories on the fly, in time to change course and not get lost in space, when things go wrong), and also on seeing familiar objects in new ways when you’re forced to describe them under new rules (a very simple version of the problems Katherine Johnson was trying to solve when they knew what a basic orbital trajectory should look like but didn’t know of any calculations to plot it exactly).

My lesson also encourages students to reflect on their own lives and how their lives prepared them to be mathematical problem solvers, able to see things in new ways, cope with frustrations, share their ideas, etc. And then asks, “How might the women in Hidden Figures have drawn on their life experiences as Black women to help them succeed in this moment of crisis?”

Finding strength in the ways adversity has shaped us, and knowing those strengths serve each of us in our mathematical lives, is one of my takeaways from this movie. What’s yours?

And please, if you read the lesson or use it with your students, let me know how it goes and how it can be improved! Here’s the link to the lesson: https://docs.google.com/document/d/1DSZGK-qL40ldZft5Lb-OTTNPOBIlGSR4G-Dek0ta91k/edit?usp=sharing

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At a recent math conference, lunch was provided for the participants. To be sure that there was enough food for everyone, the kitchen staff made more lunches than there were people attending. In fact, the ratio of prepared lunches to people was 7:5.

Because they anticipated a large number of vegetarians at the conference, the staff made 2 vegetarian lunches for every 3 non-vegetarian lunches.

It turned out that the ratio of non-vegetarians to vegetarians at the conference was 3:4.

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This is off the top of my head… to me it feels like taking what I know from the Mathematical Practices, the Process Standards, others’ work on Habits of Mind, and trying to put it into a short, kid- and teacher-friendly list.

What do you think?

The next step is to connect these with some activities to get the kids doing and reflecting on these reasoning moves…

**Students who are ready to learn from problem solving, make and critique mathematical arguments, and apply their understanding to new problems do the following things:**

*Working on problems and applying their learning:*

- They read problem statements/scenarios multiple times and ask themselves: do I understand the story?
- They represent math scenarios in multiple ways, and understand other representations they don’t choose to use
- When faced with a problem that seems hard, they have ideas to try, like making a guess and seeing what happens, drawing a picture, using manipulatives, or estimating.
- If they aren’t sure, their go-to is NOT an algorithm or a process
- When they use an algorithm or a process, they ask themselves:
- Why did I do that?
- Does this answer make sense in the story?

- They check their work in different ways:
- Checking the story
- Solving the problem another way
- Using another representation
- Making sure their work is accurate
- Asking a friend to compare

*Reflecting, getting better, and learning from others:*

- After they have an answer, they are interested in other ways to solve the same problem
- When someone else shares a different approach, they pay attention to:
- Things that are similar
- Things that are different
- Things that don’t make sense, yet

- They ask questions to understand similarities, differences, and work through confusion
- They take notes on other people’s thinking, and mark up their notes to help them make sense and remember
- When they learn new ways to solve problems, they quickly try the new ideas out
- They ask themselves, “does this make sense?” and if it doesn’t, they ask a question
- They pay attention to processes and repetition in processes, in order to look for generalizations and shortcuts, and can explain why those generalizations or shortcuts make sense

*Being a good math community member:*

- They seek out collaboration and offer collaboration when asked
- They listen to ideas, and when they don’t understand or disagree, they ask a question
- They try to find common ground (I think we agree up to…)
- When there is a disagreement, they use definitions and assumptions to find the source of the disagreement (when you say this isn’t a rectangle, are you thinking that’s because it doesn’t have 2 long sides and 2 short sides?)

Our son Specialist Lee Alejandre wished us a “Happy New Year!” from his Army post overseas using his iSight camera and iChat AV connection. It was 12:01 am, January 1, for us in Philadelphia, PA, but it was 2:01 pm for him in Seoul, South Korea!

My husband and I were talking about the time zones. I looked on the web and found that Philadelphia is about 203 degrees of longitude west of Seoul. Once we realized that there are 360 degrees of longitude and there are 24 hours in a day, we understood why there is a 14 hour difference in time.

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**Ask the NCTM Community**. We set up a bulletin board in the NCTM Central Networking Lounge at the Regional conferences in Phoenix (October 26-28) and Philadelphia (October 31-November 2). We also asked visitors to our booth in the CMC-South Exhibit Hall in Palm Springs (November 4-5) to offer questions.

Before reading through the questions that we gathered, imagine what you might ask if given the chance to **Ask the NCTM Community**. Would it be a question about

- a particular math topic that you find difficult to present to students? Might you want an activity suggestion?
- your room environment?
- how to best assess student learning?
- where to find a particular journal article that you saw but can’t remember where it was?
- using technology as a tool to help students understand a particular concept?

*click image to view larger version*

*Regional Conferences Networking Lounge – bulletin board*

Below are the **specific questions** and even **some community responses** we gathered at the three conferences. Do you have a different question to post as a reply? On a related note, view T2T’s Facelift. Consider posting your question to the existing T2T service which is one of our starting points as we think about what will make a useful **Ask the NCTM Community** service.

**Regionals – Phoenix and Philadelphia
Bulletin Board Community Questions and Responses**

[Q] How do we convince our school not to use timed tests in math?

[R] Show them research about timed tests causing stress and negative attitudes/mindsets.

[Q] Coaches & Instructional Leaders: What baby steps do you take to encourage traditional teachers to move in the direction of more effective teaching practices?

[Q] How can teachers help move the needle in their district when traditionalism is so ingrained.

[R] I find that using HATTIE’S Visible Learning Research helps. It gives a resource-based starting point.

[R] We use the MQI rubric and a “describe then elevate” process. Come to booth #507 – I’d love to chat! Or: @MQ1claire on Twitter

[Q] What is an effective yet easily implementable way to unlock BYOD potential?

[Q] Does NCTM have a position on whether this is a trapezoid?

[Q] How do you make teaching logarithmic functions fun???

[Q] Any ideas on teaching proofs in Geometry??? Thanks.

[R] Teaching Geometry Proofs: When first starting proofs, I use “Puzzle Proofs”. I cut out the statement and reasons and mix them all up and then the students have to put them in the correct order. I’ve found this help them to see how things fit together and it’s more hands on than doing just fill-in-the-blank types.

[Q] Teachers/Curriculum People: If you’re using good tasks + listening to students, where do you get resources for what to do next

- For students who are struggling?
- When the whole class is struggling?
- When you uncover gaps?

[Q] I know I’ve seen a journal article on using algebra tiles – can you point me to it?

[Q] Admins: What resources help you “sell” Common Core to parents?

[R] See Common Core Math for Dummies by Christopher Danielson for some ideas?

[Q] Is there a crosswalk between CCSS and NCTM Standards?

[Q] I am trying to incorporate modern teaching techniques and activities but am somewhat afraid that these will take so much more time. Is this true? What about the pressure to cover so much material in the course of a year?

[R] Engaging students in sense-making using rich tasks does take more time than telling—but that time is an investment…an investment in building understanding & retention of conceptual knowledge vs. the unlikely recall of factoids.

[R] I agree. The initial time investment pays off w/ deeper understanding. Also once students get in the routine, they become more independent, questioning one another rather than waiting for you.

[Q] Argh! Proportions in 6^{th} grade. Activities please??

[R] Try prodigygame! You can assign topics in a “pokeman” style game that encourages learning.

[Q] How are you using Standards-based grading authentically?

[Q] Admins: What suggestions do you have to promote “Assessing as you go” instead of a bombarding of Diagnostics 5x per school year?

[Q] How do I encourage more coherence in our curriculum?

[Q] I’d love to use more problem solving with my 7^{th} graders but there just isn’t enough time. Do you have ideas to help me?

[Q] Who can suggest an engaging activity for a kick-off lesson about quadratic equations for my Algebra I students?

**CMC-South: Bulletin Board Community Questions and Responses**

[Q] How can I make factoring trinomials more applicable/interesting to students?

[Q] Will and when will NCTM create an “Open” research journal?

[Q] What are some good, interactive apps that would help students make sense of linear functions?

[Q] What does it mean for students to feel ownership of the classroom? How do I create that?

[Q] Which is better for creating student understanding? Individual work or group work?

[Q] What can I do to better integrate cell phones in the math classroom as a tool?

[Q] What can we do to create an “easy” way for teachers connect in forming a learning network?

[Q] How do we encourage more coherence in our curriculum?

[Q] Does NCTM have a position whether this is a trapezoid?

[Q] How can I register for the San Antonio Annual in person while I’m here at CMC-South? How can I volunteer at NCTM San Antonio? And do volunteers get discounted registration?

[Q] Student: How do I solve 2/5 + 9/10?

[R] Teacher: (give breakdown w/ more examples)

[Q] Comparing numbers (2, 3, 4 – digit) is tedious. It’s always about just place value understanding. Which is important…but BORING. What are some good contextual compelling problems that create the headache that comparing #s is the aspirin?

]]>Harriet was wondering what might be the least number of area codes necessary to guarantee that for each phone in Pennsylvania there will be a distinct phone number. She determined that there are approximately 30 million phones in the state (this includes cell phones).

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The students in Mrs. Garcia’s class get a star each time they give a book talk to their class.

In September, Juanita earned 4 stars. Matt earned 2 more stars than Juanita.

Maria received 4 more stars than Matt. Brian got half as many stars as Maria.

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