This Week at the Global Math Department

Edited By Nate Goza  @thegozaway
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Online Professional Development Sessions

GMD Webinars take a Spring Break!

This is a great opportunity to catch up on past webinars: Click here for the archives or get the webinars in podcast form!

We will be back next week when Gerald Aungst will present on activating curiosity and creativity in our Math classrooms.  Register now!

From the World of Math Ed…

Pi Day

Mathematics does not get many holidays. One of the few and perhaps most popular holidays, which happened last Thursday, is “Pi Day”. Far from being entirely innocuous, it is often met with controversy. At issue is not the name of the holiday but rather when it should occur, how it should be celebrated, and if it should be celebrated at all. Some examples:

To be fair, debates about Pi Day are mostly just humorous banter. But as the old saying goes: every joke contains a grain of truth. In this case, the tweets highlight an issue about mathematics that go beyond Pi. They demonstrate how mathematicians and mathematics educators are often called to serve as advocates. Consider the following exchange, which anyone teaching mathematics will be familiar with:

Stranger: So what do you do?
You: I teach/do/work in proximity to math.
Stranger: Oh, I hated math.

In these scenarios, we’re being positioned into the role of advocates and, sometimes, the role of apologists. What kind of response is being expected, after all?

The same happens with Pi Day. We are asked, usually implicitly, to align ourselves with the holiday, actively rally against it, or ignore it entirely. In each case, we act as advocates for some position.

But using the term advocate in relation to mathematics is tricky. An advocate is usually someone who promotes or defends a group of people or a cause that has been marginalized or excluded. In this sense, “advocate for mathematics” becomes an oxymoron. Mathematics is not marginalized; it marginalizes. In conjunction with STEM, mathematics is a prism through which dominant ideologies express themselves – and not as themselves, but rather as the refracted images of seemingly more neutral concepts such as objectivity, rationality, and truth.

So rather than seeing math teachers as “advocates for mathematics”, it makes more sense to see them as “advocates for people doing mathematics”. Preoccupations with the digits of Pi is not just a disservice to mathematics but more importantly a disservice to the people who do mathematics. The mysticism often associated with Pi should be combated because math is not mystical and because elitism should be removed from the culture of mathematics.

So happy belated Pi Day everyone, in whatever way works best for you 😉

Written by Melvin Peralta (@melvinmperalta)

A Pi Day Take, Part II
Melvin has pictured above what we may call the “Orlin Interpertation” of Pi Day. Call it a “W” for mathematics, and embrace it!

Patrick Honner, in replying, has this to say, and a blog post he wrote on this topic:

All mathematics teachers need not hew to the Orlin Interpretation, as Melvin nicely points out above. Many of the activities are superficial, and we should take care to not make them too non-mathematical (or all about edible pies).

But taking the “W” here could mean letting Pi Day be a part of the culture, because how many mathematical things are truly embedded or woven into the culture? Awareness is good, but building on this math win hopefully means pushing other mathematical ideas and concepts further into the public sphere. i Day? Sure, “imagine” that? Tau Day? Have at it. Getting beyond just cutesy interpretations of date notation (e.g., 3/14) would be good as well.

K-12 teachers of mathematics are in a good position to push mathematics further into the culture than ever before!

Written by Matthew Oldridge (@MatthewOldridge)

Humanizing Math
(inspired by Darryl Yong and Becky)
Mattie B bravely acknowledges the tragedy in New Zealand with his students.  He clearly states that students should avoid watching the video or reading the manifesto as it should be starved of attention; only to quickly learn that some students had already seen it.

Teaching is political – I give credit to Mattie for attempting to talk about “the heavy stuff” even if imperfect (and without the structures), these are the moments that students will remember, this leadership, this willingness to engage with students as humans grappling with the world around.

Julie Jee shares a reading journey assignment  that asks students to reflect on who they are as readers.  With questions like:

  • Why did you choose this book/these books?
  • How does it/do they push you outside your comfort zone? What is so different about it/them? The perspective? The setting? The plot?
  • Mirror: To what extent do you see yourself reflected in the book(s)?
  • Window: What are you learning about this different perspective?
  • Wonder: What did you wonder or think about as you were reading your book(s)?
Tricia Ebarvia submitted this comic from incidental comics to help visualize the power books can have for our students; perhaps providing our students with powerful questions and diverse books will help facilitate “the heavy stuff” that Mattie B is willing to discuss.
Sharing with students what we are reading like Christie Nold does on her classroom door can inspire our students to see their math teachers are whole people, with interests outside of our math curriculum – with the hope that our students may also be inspired to pick up a book and expand their own world view.  I am wondering if Ms. Nold’s door sign could be expanded to somehow imitate the bookstores we grew up with (the kind with handwritten notes of recommendation under the book titles).  I imagine a book wall (or a wiki) where students can recommend books they are reading to each other.
Postscript aka One Cool Thing:

 

Written by Diana McClean (@teachMcClean)

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Meeting Students’ Mathematical and Learning Needs
Presented by Andrew Rodriguez
All students deserve a classroom where their learning needs do not hinder their access to the mathematics. Come learn about strategies that you can use to support your students while not sacrificing rigor. I will also discuss issues related to special education — accommodations vs. modifications in IEPs, co-teaching vs. self-contained classes, etc. — and how they intersect with the mathematics classroom.
To join this meeting tonight when it starts at 9pm Eastern (or RSVP if it’s before 9pm), click here.
Did you miss last week’s webinar? Click here to watch “Changing the Whole: Exploring Number Relationships Through Shapes.”

The #MTBoS Never Sleeps

Making Sense of Groupwork Monitoring

Do you use groupwork in your classroom? Do you ever wonder if it looks anything like groupwork in other teachers’ classrooms? In our research we get to see a lot of different teachers do groupwork, and we’ve noticed that teachers circulate and interact with groups in a rich variety of ways. From what we’ve seen we don’t believe there are “best monitoring practices” that always work for all teachers, but we’re curious how understanding the variety can help teachers better understand their own context and goals around groupwork.

For example, do you approach a group only when they ask for help? Or do you systematically check on each group? The two graphs below describe two classrooms during groupwork activity. The horizontal axis represents time and the vertical axis represents the group the teachers visit (group number -1 indicates the teacher was monitoring the whole classroom instead of visiting a certain group). Each colored rectangle represents an interaction of the teacher with a group. Green rectangles signal teacher-initiated interactions, while blue rectangles signal student-initiated ones.

 

  • What do you notice about the graphs?
  • What do you wonder?
  • What situations might the left graph be more appropriate for, and what situations might call for something more like the right graph?
  • What would a graph from your last groupwork lesson look like?

In our research, we consider five key decision points (intentional or not):

Initiation – Entry – Focus – Exit – Participation

In other words:

  • How do teachers approach groups and initiate conversations?
  • What do they first say to the group as they enter the conversation?
  • What is the focus of the teacher’s interaction with the group? Participation norms? Math? Which type of math?
  • How do they exit the conversation? Are the conversations open-ended or close-ended?
  • Do all students in the group participate in the conversation, or just some of them?
If you’re interested in more, read a summary on our project website or see more classroom graphs here. 

As this is a work in progress we would love to know what you think. Critique is also welcome, so feel free to let us know what you think is missing. Tweet us with your ideas!

Written by Nadav Ehrenfeld (@EhrenfeldNadav), Grace Chen (@graceachen) and Ilana Horn (@ilana_horn).

Pi Day is Coming

Several school systems are gearing up for Spring Break 2019, but if you are still in school this week you might be gearing up for #PiDay2019. I was reminded of Pi Day 2019 coming on March 14 when I saw a tweet from @MathIsVisual with this great visual of a “Would You Rather?” and a blog post called “Understanding Area of a Circle Conceptually” with visual prompts that will help students generate the formula for finding area of a circle.

If you want more ideas or videos, @CarneigeLearn also tweeted this link with a few more resources and a fun video. I would also suggest checking out the hashtags #PiDay and #PiDay2019 for even more great ideas. Help build a great search by adding those hashtags to your Pi Day tweets for other #MTBoS-ers to find!

By Amber Thienel @amberthienel

GMD is Looking for Presenters!

Do you know someone who you think should lead a GMD Webinar?

Did you see something amazing at a recent conference that needs to be shared?

At Global Math we are proud of our Webinars!  We appreciate all of our presenters and look forward to bringing you the best “PD Iin Your Pajamas” on the internet.  We’re always on the lookout for fresh faces and new ideas.

Please use this recommendation form to let us know who/what should be shared next!  We will take your recommendations and reach out to try to make it happen!

Stay nerdy my friends! Got something you think should go into the GMD Newsletter, hit me up on Twitter at @mathgeek76

Chase Orton

This Week at The Global Math Department

Edited By Casey McCormick @cmmteach
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Changing the Whole: Exploring Number Relationships Through Shapes

Presented by Molly Rawding

Students benefit from hands-on tasks exploring number, area, and fractional relationships when the value of the whole changes. We’ll explore different ways to provide opportunities for students to make connections and develop number sense.

To join this meeting when it starts at 9pm Eastern (or RSVP if it’s before 9pm), click here.

Last week   Amanda McGarry presented the webinar, ” Foster Student Engagement and Exploration with Interactive Simulations.” If you missed it, make sure to catch the recording!Don’t forget – recordings for all previously held webinars can be found here.

The #MTBoS Never Sleeps

Hook – Line – Sinker

John Rowe has recently release a free eBook titled, Hook Line Sinker.

This book is a collection of problems, lessons and activities for mathematics teachers organized by topic. Many of these are links to activities described or created by #MTBoS teachers. John sequenced these activities into three categories:

  • Hook – Introductory activities that might generate interest in the topic, don’t rely on prerequisite knowledge and help to “create the headache” or a need for the skills introduced

  • Line – Activities to build on students existing knowledge.

  • Sinker – Activities to help consolidate learning and make connections to other topics.

Amie Albrecht suggested on Twitter that the Hook-Line-Sinker categories map nicely onto the first three levels of Depth of Knowledge with Recall and Reproduction (DOK1), Skills and Concepts (DOK2) and Strategic Thinking (DOK3).

The book also contains some links to some great online resources and problem banks.

You can get John’s free eBook at http://mrrowe.com/book or download it from Books at  https://itunes.apple.com/au/book/hook-line-sinker/id1452938209

Written by Erick Lee (@TheErickLee)

A Rabbit Hole Worth Falling Into… TWICE

Do you want students to have meaningful math talk more often. If so, follow this rabbit hole:

Cathy Yenca’s recent blog post Using Apple Classroom for “Stand & Talks” is Cathy’s personal testimony for using Sara VanDerWerf’s “Stand & Talks.”

A few soundbites (I mean textbites) from Cathy’s post:

  • The vocabulary I heard was impressive!

  • I have found that using a “Stand & Talk” before a Desmos Activity can be highly effective!

  • During the share-out phase, students not only CORRECTLY matched the graphs, but ALSO entertained the idea of what the graphs might mean if the descriptions beside each graph DID represent the graph.

  • So silly and fun!

Follow the rabbit hole, people. Go!

Written by Andrew Stadel (@mr_stadel)

Learning About Teaching

February has been difficult, for a number of reasons, in a number of ways. The stress of our profession is a real one, and mathematics is no exception. Tweets about leaving teaching, searching for meaning, and avoiding burnout are not uncommon. Some are brave enough to blog about it as Lybrya Kebreab has done.  She was courageous enough to pursue her passion, share her learning with us through her blog,  and also share her uncertainty as she navigates her current transition.

However, what is admirable to me is that while in her transition, she is still pushing herself to learn how to teach mathematics well. It is her passion. It is her life.

In her latest piece, Lybrya discusses teaching a lesson on functions as delineated in Making Sense of Mathematics Teaching: High School, from #DNAMath. Students are to decide which population has the greatest growth from four functions, which she brilliantly turned into a WODB activity that allowed students to display their wealth of knowledge.

After the first class period of the two-period lesson, she challenged them to reflect on their learning, and charted the results.

Lybrya closes her blog humbly, asking readers for feedback on her lesson. She is someone who truly humanizes her lessons, attending to students’ identities and agency. Her blog is highly recommended.

Written by Marian Dingle (@DingleTeach)

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Edited By Nate Goza  @thegozaway
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Online Professional Development Sessions

Foster Student Engagement and Exploration with Interactive Simulations

Presented by Amanda McGarry

PhET simulations are free interactive simulations that provide students an open-ended space to play with and explore mathematical concepts from place value to calculus. Teachers can guide students toward specific learning goals by combining simulation exploration with a guided activity and facilitating student discussions. Learn how to design and facilitate sim-based lessons that engage your students and encourage conceptual understanding. This session will focus primarily on pre-algebra and algebra topics, but will be useful for any teachers new to PhET.

To join us at 9:00 PM EST for this webinar click here!

GMD is Looking for Presenters!

Do you know someone who you think should lead a GMD Webinar?

Did you see something amazing at a recent conference that needs to be shared?

At Global Math we are proud of our Webinars!  We appreciate all of our presenters and look forward to bringing you the best “PD Iin Your Pajamas” on the internet.  We’re always on the lookout for fresh faces and new ideas.

Please use this recommendation form to let us know who/what should be shared next!  We will take your recommendations and reach out to try to make it happen!

You can always check out past and upcoming Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

From the World of Math Ed…

What It’s Like to Be the ‘Only One’

Mathematics is often touted as the ‘human universal’, a subject that does not discriminate on the basis of race, gender, nationality, or sexuality. If only that were true. The harsh reality is that mathematics is done by people, people create institutions, and institutions reproduce structural inequities. Universities are not immune to the reproduction of structural racism and sexism, despite their pride as institutions of intellectual freedom and liberalism.

Hence Amy Harmon’s recent piece in the NYTimes, For a Black Mathematician, What It’s Like to Be the ‘Only One’, is a timely reminder that it can be difficult to be a black mathematician in a community of predominantly white and Asian peers. The piece centers Edray Goins, currently a professor at Pomona College, who wrote an AMS blog post in 2017 explaining why he left a research position at Purdue University. In his piece, he talks about the lack of priority given to teaching at research-oriented universities, the social isolation of research, and the isolation of being only one of two black faculty in the entire College of Science.

Harmon builds upon her own and Goins’ ideas in a follow-up piece What I Learned While Reporting on the Dearth of Black Mathematicians. Some striking insights and takeaways:

  • Black Americans receive about 7% of doctoral degrees across all disciplines but only 1% of doctoral degrees in math.
  • There are 1,769 tenured mathematicians in the 50 U.S. universities producing the most math PhDs. Probably, 13 of them are black.
  • In addition to the social costs of the dearth in black mathematicians (which I feel is the most important factor to consider), there is a significant economic impact from the mathematical community’s lack of diversity. It is important to consider that math research receives large funds from our own tax dollars through federal grants.
  • The idea that there are few black mathematicians because they are not as intelligent is simply circular. The lack of black representation leads to bias and assumptions about the abilities of black mathematicians, which in turn create obstacles to enter the field.
  • In 1969, the leadership of the nearly all-white American Mathematical Society told members to reject a resolution to address the shortage of black and Hispanic mathematicians in the community. My take on this is that the AMS has a responsibility to take decisive action in redressing the historical discrimination placed upon black and Hispanic mathematicians, whether it is through a more active role in advocacy, an increase in publications that feature black and Hispanic mathematicians, or increased coordination with the K-12 community in ensuring that black and Hispanic students do not give up on the field in elementary, middle, or high school.

Written by Melvin Peralta (@melvinmperalta)

Peter Liljedahl’s Thinking Classrooms Research
On February 23rd, Peter Liljedahl gave the Margaret Sinclair Memorial Lecture, on his receipt of the award in her honour, at the Fields Institute at the University of Toronto.

Peter’s thinking classrooms research has been developed and refined over the last 15 years, and this lecture was a short review of things he has learned. Chances are, if you are reading this newsletter, you are aware of this research. For many teachers, particularly secondary, this research has changed practices, and changed lives.

Dave Lanovaz also presented on group testing: The simple, effective tweak he came to use was adding in a review day before the group test.

Thinking classrooms have now been presented 276 times, in 8 countries, and are used in subjects as disparate as Home Economics. Liljedahl described the “exponential growth” of thinking classrooms. Basically, they suddenly were talked about everywhere, after a lengthy quiet period, from 2012 to 2014. This quiet period coincided with research into the conditions that make thinking classrooms in hundreds of individual classrooms.
Vertical non-permanent surfaces are surely the most famous aspect of this research. Visibly random groupings is another.

Liljedahl has described his research as “mucking about”. The original paper he put out is here.

This research continues to evolve, and is, in my opinion, a model for good educational research-large scale, exploratory and open-minded, and thorough.

Written by Matthew Oldridge (@MatthewOldridge)

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Edited By Chase Orton @mathgeek76
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How I Humanize the Math Classroom
Presented by Howie Hua
The math classroom can easily be turned into a class where students wish they were robots: just memorize formulas, theorems, and definitions, and “plug and chug.” How do we bring back the human aspect of math? How do we show that we value our students’ voices? In this session, I will share many pedagogical strategies that you can start using in your classroom next week that humanize your math classroom, making your students feel that they are more than their ID number.
To join this meeting tonight when it starts at 9pm Eastern (or RSVP if it’s before 9pm), click here.
Did you miss last week’s webinar? Click here to watch “Rethinking Math Homework.”

The #MTBoS Never Sleeps

Hidden Mathematicians

Math belongs to all of us. Anyone can be a mathematician. Unfortunately, many faces in history go unacknowledged and what we are learning in the math classroom can be biased.

For example, a quick Google search can tell us that even though we call it “Pascal’s Triangle,” the Chinese created this triangle centuries earlier, calling it “Yang Hui’s Triangle” but we do not acknowledge that in American classrooms.

As math teachers, It is our job to do some research and see whose voice we are leaving out in our math classroom. What I love about @DrKChilds is that he is educating us about a black mathematician for Black History Month.

We can only grow and get better by learning and acknowledging contributions that we might not have known about. @MrKitMath printed the posts out to share with his students.

If we want a diversity of our students to imagine themselves as mathematicians, we must  show our students that math is filled with a diverse field of mathematicians.

Howie Hua
@howie_hua

Ask Me Two Questions

It’s hard to get students to realize when they don’t understand something or when they are confused about new material. Finding a way to get inside a student’s head can be challenging for any teacher. The strategy of asking students “what questions do you have?” has led to some success, at least more success than “any questions?” that we used to all ask.

Enter Christina’s tweet:


You can read the entire thread here. Inside the thread you can see where Mr C (@TeachingisSTEM) said a colleague asks, “What’s tricky about this?” and Lori Owen (@mrsowenmaths) asks students, “Where may someone go wrong?.” Molly Fast (@sofastm) said she also likes to ask, “What would a confused student ask right now?.” As Mr C put it, asking questions like these “normalizes the challenge of learning.”

Amber Thienel
@amberthienel

Inspired Notes From the Editor

Hello Math Nerds! If you dig Howie’s post, you might enjoy Chrissy Newell’s (@MrsNewell22) project of inspiring girls (and all of us) by focusing on the valuable, and largely unrecognized, roles that women have played in the field of mathematics. Click on this link to find out more information. As a man, I’m proud to wear my shirt and have learned more about my own biases and blindspots by researching the phenomenal accomplishments and courageous lives these women gave to humanity.

Also, did you know that our own Howie Hua is giving the webinar this week? Check it out! I’ve heard Howie talk about some of these ideas in person. He’s an inspiring speaker, and I think your time is well spent listening to what he has to say as an presenter.

Speaking of presenters…

GMD is Looking for Presenters!

Do you know someone who you think should lead a GMD Webinar?

Did you see something amazing at a recent conference that needs to be shared?

At Global Math we are proud of our Webinars!  We appreciate all of our presenters and look forward to bringing you the best “PD Iin Your Pajamas” on the internet.  We’re always on the lookout for fresh faces and new ideas.

Please use this recommendation form to let us know who/what should be shared next!  We will take your recommendations and reach out to try to make it happen!

Stay nerdy my friends! Got something you think should go into the GMD Newsletter, hit my up on Twitter at @mathgeek76.

Chase Orton

This Week at the Global Math Department

Edited By Casey McCormick @cmmteach
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Online Professional Development Sessions

Rethinking Math Homework
Presented by Frank Wapole and Evan Borkowski
Do you have 100% of your students completing your homework? Are students in your classes routinely using your homework assignments as learning tools? Yes? Then this session is not for you!!! This session is designed to challenge your views on HW, and help you utilize research based HW strategies.

To join this meeting when it starts at 9pm Eastern (or RSVP if it’s before 9pm), click here.

Last week  Cal Armstrong presented the webinar, Learning Math in a Digital Environment. If you missed it, make sure to catch the recording! Don’t forget – recordings for all previously held webinars can be found here.

The #MTBoS Never Sleeps

Desmos Statistics

Desmos just added statistics features to its already amazing free online graphing calculator. Dot plots, box plots, histograms, distributions and t-tests are all now available. This is great news for teachers who teach one variable statistics and data displays.

Bob Lochel created a short video to explain how to use these new features:

And while we’re talking about Desmos, don’t forget that the application for the fourth year of the Desmos fellowship are now open. This amazing professional development opportunity is open to teachers across the US and Canada. If you want to hear more about the fellowship weekend, check out the recent Des-blog featuring past participants experiences.

Written by Erick Lee (@TheErickLee)

Homework: a Problem or a Solution?

Do many of your students struggle to complete math homework?

Recently, Julie Reulbach blogged about Meaningful Homework and CPM. She doesn’t grade homework anymore, but she does check for completion. The CPM curriculum she uses has homework that includes spiral review. Julie has made some purposeful decisions about the quantity and timing of homework where her “students absolutely love the new system.” Read her blog post to learn what steps she took to increase the completion rate and connection to student learning.

Written by Andrew Stadel (@mr_stadel)

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Edited By Nate Goza  @thegozaway
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Learning Math in a Digital Environment

Presented by Cal Armstrong

Learning mathematics for students requires a lot of diverse materials : notes, pictures, graphs, interactives, worksheets, equations, feedback, review materials. How do they have a workflow that works for all these different media; how do they collect, manage and cope while at the same time meeting with accessibility & language needs? And how do teachers manage to deal with all of that along with the need to do assessments, give feedback, observe, reflect and just “teach”? We’ll go through how #digitalink & OneNote have made all of this manageable and has in fact increased learning time in the classroom while adapting to the desire to engage in discussions, #vnps, student voice/choice, visualization and other common practices of the modern classroom.

To join us at 9:00 PM EST for this webinar click here!

GMD is Looking for Presenters!

Do you know someone who you think should lead a GMD Webinar?

Did you see something amazing at a recent conference that needs to be shared?

At Global Math we are proud of our Webinars!  We appreciate all of our presenters and look forward to bringing you the best “PD Iin Your Pajamas” on the internet.  We’re always on the lookout for fresh faces and new ideas.

Please use this recommendation form to let us know who/what should be shared next!  We will take your recommendations and reach out to try to make it happen!

In next week’s webinar Frank Wapole and Evan Borkowski will be here to challenge us to rethink Math homework.  You can get more info on the session and register here.

You can always check out past Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

From the World of Math Ed…

Much Ado About Taxes

In recent weeks, the media has been abuzz with talk of tax rates. Most visible has been the headlines surrounding Rep. Alexandria Ocasio-Cortez’s talk of increasing the top marginal tax rate to 70%. This news has sparked much debate from all sides of the political spectrum. But regardless of your political beliefs, it’s been illuminating to witness the conversations and, in some cases, misunderstandings surrounding the system of income taxation in the United States.

So what’s this got to do with the math ed community? Well, if there was ever a moment for us to shine, this is it!

First up, Dan Meyer has written a blog post with some ideas and resources for helping our students understand marginal taxation. Dan also mentions an amazing collaboration between the New York Times Learning Network and the American Statistical Association called What’s Going on in This Graph? and, even better, Desmos teacher activities that enable teachers to have these conversations through the Desmos platform.

Second, Ben Orlin includes talk of taxes in his critically acclaimed book Math with Bad Drawings. As Ben mentioned on Twitter, the chapter stemmed from a “make your own income tax system” project that he used to give to his precalculus students. He also points out that, interestingly, marginal tax rates are a piecewise-constant function of income while tax paid is a continuous, piecewise linear function.
Third, @voxdotcom came out with a fairly well-made video explaining how tax brackets work. It may be interesting to connect the visual representation of tax brackets as “pockets” with the algebraic concept and notation of piecewise functions. I was particularly impressed by the fact that the video also mentions deductions, a concept often overlooked when people talk about income taxes in the United States.
Ultimately, what’s at stake is not just our students’ mechanical understanding of marginal tax rates. Rather, this is about the aspect of our work as teachers that involves helping our students develop mathematical literacy. In Paulo Freire’s words, before we teach our children to read and write, we must teach them to “read and write the world.” Beyond focusing on high test scores and college acceptances, we must help our students approach the complexities of the world with an array of intellectual tools. We must also help them develop the social and political sensitivities to use those tools with wisdom, agency, and compassion.
Written by Melvin Peralta (@melvinmperalta)
Black History Month, is a time to celebrate and amplify Black voices, stories, shed light on injustices, and teach.  Look at this article Teaching Black History Month from Tolerance.Org for inspiration and lessons.

Click on the image below for some people to follow on Twitter:

Here are some books to read by Black authors;

  1. White Rage by Carol Anderson (Thanks again to Val Brown for leading rich discussions on #ClearTheAir.)
  2. PUSHOUT by Monique W Morris EdD

See Morris’ Retweet with 100 books by Black women authors (image is link):

Finally, if you are teaching about Math History check out Mathematically Gifted and Black.

Contributions compiled by Diana McClean (@teachMcClean)

Number and Space are Inextricably Connected

Try this: close your eyes, and think of an open number line. You just need to picture a line, no intervals marked, just a certain amount of space. That line will have a length, although it is difficult to tell how long your mental image of this line is.

We know this line could stretch from some starting point, to infinity, or rather to some infinite length, which we cannot measure. We could mark an infinite number of points on this line, and actually, we could mark two different types of infinity on this line: counting numbers, and real numbers, which are demonstrably at a higher level on the “tower of infinity”.

But we are getting ahead of ourselves.

Close your eyes, and picture a line of length 10 units. Hold up your hands however long you think that line should be.

Now open them. Where are your hands?

Try the same exercise for 20. Where are your hands?

Here is an interesting tweet thread about some experiences I had working on number lines with grade ones. My colleague asked them to visualize 20.

Consider trying this with your students. Whether “shoulder width” is a preferred human length for number lines is an open question. Perhaps “body scale” is most relatble to us humans.

If you want to blow their minds, ask them to draw an open line of some length, mark 0 and one million as the ends. Where is 1000? Now do the same for one billion. Where is one million?

Space and number are mysteriously connected. As I understand the research, we know they are connected, there is no doubt, we just don’t really know how.

Work is being done in this area. See the pre-print in this tweet below, and consider reading it. Zach Hawes and Daniel Ansari are working on what happens in the brain to connect space and number. Basically, there is an emerging body of evidence that spatial reasoning and thinking about numbers are connected, as shown by fMRI mapping of the regions of the brain responsible for each.

Research continues, seeking to find this “missing link”. In the meantime, an open number line is a tool “with legs” in grade 1-12 education. (Typically, Kindergarten students aren’t quite ready to go past concrete counting objects, ten frames, and on to the number line).

Written by Matthew Oldridge (@MatthewOldridge)

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This Week at the Global Math Department

Edited By Chase Orton @mathgeek76
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Online Professional Development Sessions

Fractions Forever — A Rational Aproach
Presented by Margie Pligge and Nancy Mueller
Don’t wait until your fraction unit to introduce fraction problems. We will use a framework to explore problems and number choices that help students make sense of fraction operations. Attendees will experience math talks, look at student work, and leave with specific grade level guidelines to teach fractions forever.
To join this meeting tonight when it starts at 9pm Eastern (or RSVP if it’s before 9pm), click here.
Did you miss last week’s webinar? Click here to watch “Building a Badging System: Let Your Students See Math In Action.”

The #MTBoS Never Sleeps

Drop Everything and Math

I saw this tweet from my friend Alecia Ford (@AleciaHiggFord) talking about how Madison Knowe (@knowemath) had a list of questions in her classroom and the last question was “What would the math equivalent of drop everything and read time look like?”

This has been a question on my mind a lot this year as we implemented “silent sustained reading” (SSR) time in my school. I was a little jealous and have been considering ways that we could potentially help students have this same relationship with math. So I posed the question back to Alecia. This was her response:

Then Madison weighed in with the ways she has been trying to incorporate it more in her own classroom with this tweet:

I love the idea of a “math play toolbox” and having games and puzzles as well as math books. And then Joel (@joelbezaire) offered up a newsletter from Kent Haines (@KentHaines) and a few games (Cat Stack and Manifolds) to pick up as a starting point.

How about y’all? What strategies have you tried to be able to have “drop everything and math” time as part of your school day? How do your students respond to this idea?

Amber Thienel
@amberthienel

[Editor’s Note: If you want to read more on the phrase “drop everything and math,” check out this Tracy Zager’s (@TracyZagerpost.]

A New Form of Flashcards

Tired of traditional flashcards? Me too! That’s why I was excited to see Berkeley Everett’s (@BerkeleyEverettMath Flips resource. Rather than having a question on one side and the solution on the other like a traditional flashcard, Math Flips have an exercise on one side and a related exercise example on the other. For example:

Berkeley’s purpose for this is to promote relational understanding rather than answer-getting. I love this progression of questions:

He credits other math educators including Chrissy Newell, who created a number talk with two related problems and the question sequence “How many? How do you know?” and “How many NOW? How do you know?”, Annie Fetter and Joe Schwartz, who say “Ask about ideas, not answers,” and the amazing number sense routines shared by Steve Wyborney (www.stevewyborney.com). He invites YOU to send ideas/feedback to Berkeley (email or Twitter) or make your own.

Berkeley has many downloadable flashcards. Try them out and let us know what you think.

Howie Hua
@howie_hua

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This Week at the Global Math Department

Edited By Casey McCormick @cmmteach
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Online Professional Development Sessions

Building a Badging System: Let Your Students See Math In Action
Presented by Joel Bezaire
Seventh Grade teacher Joel Bezaire uses a collection of over 125 resources he’s gathered from around the web to let students see how math is used in a variety of contexts outside of a math classroom. In this Global Math session come hear how his system works, see some of the resources, see student work samples, and discuss together the ins-and-outs of making a system like this a success in your own classroom (As seen in 2018’s NCTM MTMS Blog on MyNCTM).

To join this meeting when it starts at 9pm Eastern (or RSVP if it’s before 9pm), click here.

Last week Shannon Kiebler presented the webinar,  Fostering the Equitable Math Talk Community. If you missed it, make sure to catch the recording! Don’t forget – recordings for all previously held webinars can be found here.

The #MTBoS Never Sleeps

Numberphile and “The Klein Bottle Guy”

I’m positive that many of you are familiar with the videos that Numberphile have produced about mathematics. If you’re not, you should stop their website https://www.numberphile.com/or YouTube channel https://www.youtube.com/user/numberphile to check them out. Here are three of my favourites:

Numberphile is produced by video journalist Brady Haran and features mathematicians describing some really interesting mathematics in an entertaining and easy to understand way. They recently started a podcast, and their newest episode features an interview with the “Klein Bottle Guy” Cliff Stoll, an astronomer, author and educator.

Michael Jacobs tweeted that “This @numberphile podcast with Cliff Stoll is a must listen for any teacher. What struck me is the massive impact (positive or negative) we can have on our students by the way in which we respond to their curious questions.” I couldn’t agree more with Michael. Cliff describes the powerful and profound impact that teachers and mentors in his early years had in shaping his career and educational trajectory. He described tracking down his eighth grade math teacher, fifty some years after being her student, to let her know how thankful he was that she took his questions seriously and fostered his curiosity. Cliff’s stories highlighted for me the important role that teachers have in the lives of their students and how teachers’ words and attitudes have consequences far beyond the walls of their classrooms.

This message is especially poignant this weekend as my Twitter feed is filled with descriptions of students on a school trip to Washington, DC behaving in racist, ignorant and disrespectful ways, seemingly within sight of their teachers. Teachers have an important role in naming, addressing and countering these racist attitudes.

Written by Erick Lee (@TheErickLee)

Once a Teacher, Always a Teacher

When I first entered the world of Twitter, Jenise Sexton was one of my first follows.  I knew of her math contributions as a state curriculum writer, and as a follower of her blog, learned of her impressive career. With only fourteen years in the profession, she has taught at the elementary and middle school levels, been a team leader, and has been in a coaching capacity at the site and district levels. It was evident to me that Jenise is a natural teacher who believes that teaching is at the center of getting better at mathematics, because twice, she chose to leave her coaching position to reenter the classroom to give her more insight.

When I finally met her in person at TMC17 in Atlanta, I was not surprised that she not once spoke of her many accomplishments, contributions, or speaking engagements, but only of the teaching and learning of mathematics, and the elevation of the profession.

Now coaching at the district level, her latest blog is unsurprisingly entitled A Case For Teacher Envy. In it, she speaks of her teachers who are just hitting the ball out of the park for their students. She specifically highlights eighth grade educator @tenaciousXpert, whose photos below give a hint of her practice.

Her room is divided into four quadrants, reinforcing vocabulary, and she methodically creates natural opportunities for students to build their math intuition.

I suspect this educator, like Jenise, sets high expectations of students, often motivating students to continue to work out the math long after class has ceased. I encourage you to read this blog and follow both educators if you haven’t already. Surely, there is much more to come from both.

Written by Marian Dingle (@DingleTeach)

I Don’t Give Two S**** if They are Real-World

Fawn took a Would You Rather math challenge (with context) and created a similar math challenge stripping the context. She then conducted a survey and blogged about it in Jelly Beans or No Jelly Beans.

She surveyed her students, Twitter, and even her own children about which math challenge they’d rather tackle. There’s a 50% chance the results of the survey will surprise you and there’s a 50% chance it won’t surprise you. However, you can be 100% certain Fawn’s choice and reasoning are insightful, entertaining, and heartfelt because she doesn’t “give two shits if they are real-world”. Click here to enjoy Fawn describe the beauty she finds in mathematics.

Written by Andrew Stadel (@mr_stadel)

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This Week at the Global Math Department

Edited By Nate Goza  @thegozaway
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Online Professional Development Sessions

Fostering the Equitable Math Talk Community

Presented by Shannon Kiebler

Engaging students in math discourse is reliant upon a strong math community. How can we empower students and defeat helplessness in efforts to reach higher levels of math discourse? Come explore simple, yet transformative ideas to better your community and therefore better the discourse.

To join us at 9:00 PM EST for this webinar click here!

Next week’s webinar features Joel Bezaire who will share how he helps students see mathematics outside of the classroom.  You can get more info on the session and register here.

You can always check out past Global Math Department webinars. Click here for the archives or get the webinars in podcast form!

On the Topic of Twitter Chats…

Twitter chats have been an amazing resource for the online math ed community. They’ve allowed math educators worldwide to engage in a wide range of focused, public conversations, where anyone is welcome to join. Two recent chats come to mind as representing some of the best that the Twitter platform has to offer: #ClearTheAir and #SWDMathChat.

#ClearTheAir had its first chat around the book “White Rage” by Carol Anderson last Wednesday (1/9). The #ClearTheAir chat is focused on issues of race in education and in general, and Val Brown gives an excellent introduction to the chat and its origins in this blog entry. I have yet to catch up on reading the book, so I chose to lurk rather than actively participate this time. However the schedule for the next three sessions are here:

And I must say, the chat was . Some people have been contributing to #ClearTheAir even after the last question was asked Wednesday night, so I strongly encourage reading people’s thoughts and contributions if you haven’t already done so. There’s a lot to process, but here’s just a sample of what went down. Shout out to Christie Nold!

The other chat I have to mention is #swdmathchat, which as you can probably guess focuses on math education issues impacting students with disabilities. The most recent chat (1/10) was facilitated by Theodore Chao, who is an amazing math ed professor at OSU. Check out he spring schedule for #swdmathchat:

The theme for this most recent chat was “What is Possible?” Participants discussed what was possible for engaging students with disabilities in mathematical thinking and reasoning. The common denominator denounced, rightly so, the isolation that can occur when special education students are physically, intellectually, and/or socially isolated from their gen ed peers, especially in math class.

@ScottGeisler12@Julie12129030, and many others participated in last week’s chat.

I’ll close with a short list of books that I’ve read or are next up on my reading list in addition to “White Rage”. Such books highlight the multi-faceted, political nature of the work we do as educators.

Written by Melvin Peralta (@melvinmperalta)
Like Melvin, the book “White Rage” by Carol Anderson is on my mind.

The book details the extent and depths and insidiousness of white rage, from “Reconstruction”, all the way through to voter suppression. Some sections will make you want to throw up (either from intense violence described, or from a “how can this even be real?” feeling).

Some brief notes about 1957, “Sputnik”, and Brown vs. Board of Education. Many of us are often scolded for tweeting about things other than mathematics, as if we have no humanity, no interests, outside of our jobs as eduators. Many who come from more conservative perspectives, both about the world and about mathematics, suggest that it can and must be “neutral”.

Some things are about mathematics are neutral, like the square root of any number, or counting to 100. Sure, fine. But the systems that mathematics are embedded in have their own axioms and their own beliefs that become encoded in what mathematics is taught, and how.

The book goes briefly into Sputnik, and the moral panic it inspired about mathematics. A clarion call for “back to basics” was issued, and the fault laid by some at the foot of “progressive education” (plus ca change…)

But at the same time, many states were fighting to keep segregated schools, outright defying Brown vs, Board of Education, the 13th, 14th, and 15th amendments, ostensibly in the name of “state’s rights”. (What is it with America and “state’s rights”? Isn’t it possible that the conception of federalism your country uses just doesn’t work? Maybe the wrong compromises were struck, way back when?)

There was a school district in Virginia that closed all schools for 5 years, rather than let black students in. This is called “cutting off your nose to spite your face”, and yes, the powers that be were willing to close the schools even to the poor whites who might have needed them, rather than let blacks in (the rich, presumably, had their own schools).

So forget Sputnik, forget “back to basics”, and forget about mathematics as “neutral”: many students weren’t even allowed in to learn the basics.

That doesn’t even get us to gerrymandering, a whole other cruel and unjust use of mathematics. And that doesn’t even get us to human prejudices, encoded in algorithms (I am reading Hannah Fry’s “Hello World” now, and algorithmic prejudice is a new frontier of prejudice, don’t you think?)

Are we feeling “neutral”, yet? Not after reading this book, I am not.

I would add to Melvin’s list above of books for the #ClearTheAir shelf, Ijeome Oluo’s So You Want To Talk About Race.

Written by Matthew Oldridge (@MatthewOldridge)

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