This Week at Global Math – 11/12/19







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Edited By Chase Orton  @mathgeek76

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Online Professional Development Sessions

This Week!

Assessing for Understanding

Presented by Daniel Kauffman

During this webinar, we will explore the value of assessing for understanding. We will discuss methods to shift our assessments so that students have an opportunity to showcase their understanding of concepts, not just an ability to produce answers. Additional discussion will be focused on tools and strategies to utilize in the classroom to promote understanding.

Register by clicking here!

Next Week 

GMD Rewind!

GMD Rewind: Watch a session that you wanted to see, but did not or rewatch one of the sessions you attended! Then blog or tweet about what you learned and will apply to your own classroom!

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

Information Gap

A ‘math language routine’ refers to a structured but adaptable structure for amplifying, assessing, and developing students’ language according to this document from Stanford University Graduate School of Education.

One of my favorite math language routines (MLR) is the Information Gap. The purpose of an Information Gap is to create a need for students to communicate. Achieve the Core (@achievethecore) has a recent webinar about the math language routines and has some wonderful explanations. In it, Chrissy Newell (@MrsNewell22) talks about how she takes a problem from a 4th grade standard and creates an Information Gap to use with students. There is also a video of students participating in the Information Gap.   

Another resource for Information Gap is from Cathy Dickson (@mathreflective). In this tweet she shared a video from her YouTube channel describing what an Information Gap is and providing an example.

Written by Amber Thienel (@amberthienel)

#DesmosDemo & Data Literacy

Although @Desmos & Data Literacy overlap [e.g. What’s Going On In This Graph? partnership with the New York Times] this post is not about their intersection.     

Desmos Demo: I would like to see the hashtag #DesmosDemo become more popular, and my succinct[ish] rationale follows.   

I have noticed some very impressive Desmos graphs. One recent example arose when I was perusing the Desmos subreddit, which led to this origami graph of a piece of paper folding into a crane [click through for the GIF]:

 

Another pair of examples arose when I asked [on behalf of another math teacher] about having students recreate the following in Desmos:
Three people [Desmos links via creators: @mrchowmath, @pattystephens, @melvinmperalta] made or already had something to this effect:
 

These are all great, but they leave me [and I’m sure others] wondering about the creative process behind these graphs. This can manifest as inspiring – I’m curious about these great graphs and want to get better! – or as discouraging – these people are doing incredible work that is simply beyond me and anything I could make.

Idea: What if math educators [and graph enthusiasts, more generally] did screen captures as they made these creations in Desmos? Viewers could observe the process directly and (1) learn techniques to build on their own curiosity while (2) noting the confusion that inevitably arises, which might reduce discouragement.
I have proposed #DesmosDemo as a hashtag to accompany such descriptions; so far, we already have a couple of great examples from @aknauft:
Ae you willing to make one? No graph is too simple, and I’d be happy to see ones that didn’t work out, too! If you @ me, then I will amplify as best as I can.
 

Data Literacy: I have noticed a recent uptick in calls for shifting mathematics classes towards “data literacy” [or something similarly named] which coincide with a Jo Boaler [@joboaler] appearance on @Freakonomics as well as an op-ed that she coauthored for the LA Times:

You can find some responses to the Freakonomics podcast located in various tweets, but here I’d like to recommend a paper from Laurie Rubel [@LaurieRubel] and Thomas Philip:
 

Below are two excerpts, which come from a paper that I think deserves the attention of most anyone thinking about shifting towards data literacy:
Excerpt 1, Power-With versus Power-Over

Excerpt 2, Conclusions [Emphasis Added]
The full paper is available [for free!] here. I know that reading a research paper is a Big Ask if one’s preferred consumption of information is in tweet-sized chunks. So, please know that I do not make this recommendation whimsically.
Closing ICYMI [aka Saving the Best for Last]: There is a Must-Listen podcast discussion “about the culture of mathematics” between Marian Dingle [@DingleTeach] and Cathery Yeh [@YehCathery]. Less than 30 minutes, and worth listening to more than once! The link above contains a transcript, too.
As always: Feel free to get in touch with me – by email, by @’ing me, by DM, snail mail, carrier pigeon, etc – if there is work in/around the world of mathematics education that you believe should be highlighted.
Written by Benjamin Dickman [@benjamindickman]

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This Week at Global Math – 11/5/19







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Edited By Nate Goza  @thegozaway

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Online Professional Development Sessions

GMD Rewind

There’s no new session this week which provides an opportunity to watch a session that you wanted to see, but did not or re-watch one of the sessions you attended!

Next Week 

Assessing for Understanding

Presented by Daniel Kauffman

During this webinar, we will explore the value of assessing for understanding. We will discuss methods to shift our assessments so that students have an opportunity to showcase their understanding of concepts, not just an ability to produce answers. Additional discussion will be focused on tools and strategies to utilize in the classroom to promote understanding.

Register ahead of time by clicking here!

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

Why It’s Okay to Cry At Work
 

Teaching is HARD. This should come as a surprise to no one reading this, but it is important to name, to accept, and to take a deep breath and remember every once in a while. Not only is teaching hard, it can also be a deeply personal, vulnerable, and emotional profession. On top of that, it’s November – you have almost three months of school under your belt, you are about to enter into the exciting but grueling holiday months, and you are tired.
 
For some teachers, it is in this time of extra-tiredness that our emotions are heightened. Most teachers reflect – or judge themselves – after each class they teach on whether they’ve hit the high bar they set for themselves, considering questions like Did my kids learn as much as I had planned for them to? Did I check in with all my students? Do I know what they’re understanding (or not)? Teachers are constantly comparing their pedagogical actions – what they do in the classroom – with their pedagogical responsibility – the expectations they set for themselves. When teachers identify that their actions and sense of responsibility aren’t aligned, we refer to this as the introduction of a conflict. It is this conflict that has the potential to contribute to an array of negative emotions like discomfort or frustration.
 
Our research team has found that identifying this conflict – and all the emotions that come with it – may actually make you a better teacher.  First, these emotions can act as a signal to you that what is actually happening in your classroom isn’t exactly what you had wanted to happen. By addressing your feelings head on, you can make sense of what the nature of this conflict is, including potential causes or solutions. In this sense, emotions can be a powerful motivator to help you make sense of your current teaching practice and make necessary adjustments so you can continue to grow as a teacher.
 
So the next time you are at school and your class didn’t go perfectly and you feel upset or discouraged or maybe even that you want to cry, lean into those emotions instead of suppressing it. It means you are doing something right. Use that feeling or those tears to clue you into the conflict and motivate you to think about ways you could address it. Try something different tomorrow, seek out a colleague for support, or leave school a little earlier than planned to take time to process your day. Most importantly, give yourself a little grace and find comfort in knowing that it’s okay to cry at work.
 
Written by Katherine Schneeberger McGugan (@kath_schnee)
with support from Brette Garner (@brettegarner) & Ilana Horn (@ilana_horn).

Math Ethnic Studies Framework

 
In early October, the Seattle Public Schools (SPS) released a draft ethnic studies framework for K-12 mathematics. The framework seeks to situate mathematics in its historical and cultural contexts and highlight mathematics as a site of power, oppression, identification, and resistance. The framework is built off work to extend ethnic studies to other subjects within the K-12 curriculum. According to Tracy Castro-Gill, the ethnic studies program manager at SPS, the framework is not a legal mandate on schools but rather suggestions for teachers to have new types of conversations in their classrooms.


 
I was curious about the story behind the framework. This is what I’ve pieced together so far. In 2017, the Seattle King County chapter of the NAACP passed a resolution calling on SPS to adopt an ethnic studies requirement for elementary and secondary schools. This led to the development of an ethnic studies task force and, eventually, a working group to support and implement the development of an ethnic studies curriculum. Information on the resolution and task force can be found here: Ethnic Studies – Seattle Public Schools. In 2019, Senators Hasegawa, Conway, Frockt, Wellman, Wilson, and Saldaña sponsored a bill to:
 

  1. “adopt essential academic learning requirements and grade-level expectations that identify the knowledge and skills that all public school students need to be global citizens in a global society with an appreciation for the contributions of diverse cultures” (SB 5023(2)), and 
  2. “identify and make available ethnic studies materials and resources for use in grades seven through twelve” (SB 5023(3)).

 
The bill also created an Ethnic Studies Advisory Committee. The draft mathematics framework grew out of these efforts.
 
The framework has been met with much controversy. One criticism comes from those that ridicule the idea that 2 + 2 = 4 and the quadratic formula can be racist. This, I believe, is a misunderstanding of the framework. In my reading, the framework would suggest that reciting the quadratic formula without knowing some kind of derivation of it represents just as much an incomplete understanding of the concept as not understanding its roots (no pun intended) in the Middle East and Northern Africa. Just as a culture of rote memorization has prevented many people from entering the mathematics community, a culture of decontextualized mathematics can prevent many students from seeing themselves as potential contributors to the subject. The question, of course, becomes whether cultural and historical knowledge belongs in a mathematics classroom. It raises the questions: what, exactly, counts as mathematics? And what are the purposes and uses of mathematics education? At the very least, this is a deeper conversation worth having than simply shouting that the authors of the framework are themselves racist.
 
@melvinmperalta

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This Week at Global Math – 10/29/19







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Edited By Casey McCormick  @cmmteach

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Online Professional Development Sessions

Tonight!

The Era of Resource Abundance

Presented by Hilary Kreisberg

Tired of spending hours searching for fun activities and tasks to elevate your lesson? Tired of being distracted by “imposter resources” which look pretty but don’t truly support conceptual understanding? Come learn how to stop being tired and start being productive by understanding how to analyze resources to transform your teaching.

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

Next Week 


GMD Rewind: Watch a session that you wanted to see, but did not, or re-watch one of the sessions you attended! Then blog or tweet about what you learned and how you will apply it to your own classroom!

Find the archives of previous sessions here!

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

The delicate balance between solidarity & erasure

For the past 10 days, our fellow educators in Chicago have been teaching. But, they haven’t been teaching their normal lesson plans, filled with rich tasks, investigations, and developing mathematical inquiry. Rather, they’ve spent their last 10 days educating their students, community members, local political officials, and the rest of the world what it looks like to organize a strike that is about more than money. 



The Chicago Teachers Union (@CTULocal1) has not only been striking for fair pay, but for smaller class sizes, affordable housing for students, sanctuary policies for immigrant families, and the assurance that every student would have access to a nurse and a school psychologist. Since October 18th, 32,000+ Chicago Public School teachers and staff have been standing their ground as their local unions (Service Employees International Union Local ‘73 & Chicago Teachers Union) have negotiated terms with Mayor Lori Lightfoot (@LightfootforChi). 



With the announcement of the strike, Mayor Lightfoot announced the canceling of classes for approximately 360,000 students until a settlement can be reached. Parents, impacted by the sudden lack of consistent and free childcare offered through the services of public school, may fear that their students will fall behind in their studies, having missed six days (and counting!) of formal schooling. Yet, as educators, we must consider that students may learn far more during this six-day reprieve of formal education with the informal learning they are currently garnering. It is in this same vein that I read Glenn Waddell’s (@gwaddellnvhs) tweet, posted earlier this week: “Every act of teaching is a political act. Every. Single. One”. While this post was directed at the topic of lesson planning with a monolingual and monocultural lens based on the work of Dr. Josè Medina (@josemedinajr89), the concept transfers to acknowledge that the learning of these 360,000 students is also political in nature.



In the event of the Chicago Teachers Union Strike, students may be learning about the politics involved in what can often appear to be an apolitical public education. Students may begin to gain understanding as they watch their teachers model what it means to stand for justice. Students may begin to feel the local inconvenience of having a public right (e.g. the right to education) paused in the name of a larger, global civic right and duty. Students may even recognize the agency and power that they hold within themselves to create change. 



There is a great deal of education that we fail to name and/or honor because it does not fit in the nice, neat confines of the public schooling of which we have become accustomed. And so, out of necessity, oppression, or ease, it is erased. 



Below, I share three examples of erasure in education that I found this week on the wide open world of Twitter. 

 

  1. The amount of land loss of Native Americans in the last 150 years.  Shared by Ranjani Chackraborty (@ranjchak)


This is an example of physical erasure. Many still refuse to recognize the effects of colonization on Native American people, and the acculturation enforced on their children as they attend schools that are centered on the Eurocentric values of their oppressor. Yet, this graphic makes that erasure evident. 



What do you notice and wonder about the differences between these two graphs? (Click for the dynamic video; also scroll for others, & follow Rajani). 

       

 

  1. #BlackWallStreet & the #TulsaMassacre: With the hit show “Watchmen’s” premiere featuring the Tulsa Massacre, many observers were left wondering why they had never heard of 1) one of the largest massacres in US history, 2) the existence of Black Wall Street, and/or 3) how our public education could erase such a pivotal event. Regina King (@ReginaKing), the star superhero of the show, shared the following tweet to assist viewers in (re)learning the history behind this event. 

 

  1. Doug Robertson (@TheWeirdTeacher) discussed his desire to erase the phrase, “Does that make sense?” from his teaching vocabulary. The replies in this thread give great examples of how to replace this question with others that may distribute power to students that issues them agency to participate in question forming and answering. 

 

 I share these three examples to demonstrate how easily events can be erased from history, from our presence of mind, and from our vocabulary. I also share these examples as an act of solidarity with the teachers of Chicago, as they continue to place their mark on history, and refuse to be erased, while also refusing the erasure of their students’ needs. I celebrate the movement of bringing those on the margins towards the center, and the (re)learning and (re)centering of what we want our students to learn as citizens of our society-at-large. It is most certainly more than just the mathematics we are tasked with teaching in school. 

There have been many acts of kindness shown towards the teachers on strike in Chicago. Some have sent pizza, others doughnuts and coffee, and others have shared their time. Chance the Rapper (@ChancetheRapper), a Chicagoan by birth, shared his platform on “Saturday Night Live” to demonstrate solidarity with the teachers, staff, and students, and to remind them that the fight is worth it. 

You may wonder how you, individually, can show solidarity with our fellow educators in Chicago. On Twitter, they are using the tags #CTUSEIUstrike, #PutItInWriting, #FairContractNow. The more traffic to these tags, the larger presence that the strike receives from local and national media, and the more pressure applied for both sides to come to an agreement over the terms at stake. The Chicago Teachers Union has asked for educators across the country to use social media to show support by wearing #RedForEd, a similar demonstration of unity in the unprecedented number teacher strikes in 2018, including my home state of North Carolina. We also know from last year that this teacher strike is not specifically about Chicago, and that this movement for justice for this group may usher in justice and opportunity for others. 

 

Whatever your choice in showing solidarity for this group and this moment, may it simply not be to erase it from consciousness and history. 



Written by Lauren Baucom, @LBmathemagician

Hidden Gems of the MTBoS

Sitting on the couch, scrolling through the seemingly endless number of TV series at my fingertips, I found myself searching for something to watch that was as close as possible to the previous series I had just binged my way through. My wife and I are obsessed with British crime shows, especially those featuring David Tennant. After little success, I habitually picked up my phone to keep up-to-date on the 100 Twitter users I closely follow. In that moment I realised that, just like my Netflix choices, my Twitter choices represented an extremely narrow and unvaried sample of what is available. I had previously convinced myself that I was supportive of the growth of the #MTBoS and #iTeachMath communities, but the mere presence of my Top Drawer list shows my bias towards users with an already large number of followers. My rule of “I’ll follow any teacher that follows me” was clearly not enough. So, this week on the Global Math Department Newsletter, I’ve picked five fabulous teachers with 100 followers or less. If you’re wondering how you can do the same, head here for inspiration and here for the roadmap to get there.

@KP_CUi 

It’s no secret that Maths Twitter folk love a good Open Middle problem. I myself have gotten my fair share of the MTBoS limelight for a few problems I’ve shared with the community. What I love about this post is the simplicity of the prompt this teacher gave to their students, the mode in which they set the challenge to them, and their thoughts on the experience overall. A lot in one tweet!

 

 

@pokybloom

Here’s a post that, when I started using Twitter a few years ago, would have seen veteran MTBoS users come to the rescue. A lot of Maths teachers who have persevered through the early stages of using Twitter often recall having their cries for help answered. Sadly, too many tweets go unheard. Whether it’s through a slightly incorrect hashtag (as appears to be the case here, although using #nctm is arguably better than the official ones for NCTM events), a quiet time of day or year, or just a lack of active followers, getting help is not easy when you’re starting out.

 

 

@MsAYoungren

I picked this next one out because Annette’s experience on Twitter seems quite common amongst many of the maths folk who jump online for some inspiration. From her feed, it appears that Annette likes to share good stuff that comes her way through retweets and jumps online every so often. This tweet typifies the love that is so often shared through the platform, while also including such a courageous reflection and a commitment to contribute to the community. Quite early, I took on the approach “Dance like nobody’s watching and sing like nobody’s listening”, which enabled me to use Twitter first for myself as a mode of reflection, leaving any attention or insight from others as a welcome, but not expected, bonus.

 

@talking_math

Many frequent users of the MTBoS started engaging in the online sphere through their blogs. Well, I certainly did. Typing up a post was often the result of my mind overloading with thoughts about something that caused my eyebrows to scrunch – whether it was for good or bad. Mrs. Portnoy (AKA @talking_math) occasionally shares her blog posts through her Twitter account. She’s been teaching for more than twenty years, so there’s clearly no lack of substance in what she writes. Here’s my favourite bit from her latest post in which she’s reflecting about her own children’s views toward mathematics:



“I just wish, somewhere along the line, someone, or something had sparked a love of math… Math can be more than just learning concepts and completing assignments.”

 



 

@mramarupareja



Amaru is a frequent user of Twitter and regularly retweets great highlights from the iTeachMath and MTBoS communities, often with a nice little insight. He also tends to post great little snippets of his students doing and talking about maths, which is guaranteed to enrich anyone’s feed. I decided to include Amaru in this post mainly because I wasn’t already following him before! Somehow, his account slipped past my “follow back other teachers” rule and I’m so glad that I was able to discover his account and bring more maths joy to my screen. This tweet is just a sample of the great things he shares regularly.

 

I’m going to leave this here as a call to action to regular users of the Twitter maths community to continue to support those who are still determining whether they are getting as much out of the Twitter community as they themselves put in. These are only a handful of many amazing educators whose number of followers does not represent the quality of the tweets they put out.

 

Written by John Rowe, @MrJohnRowe

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This Week at the Global Math Department

Edited By Casey McCormick  @cmmteach
View this email in your browser
Tweet
Forward

Online Professional Development Sessions

Tonight!

The Era of Resource Abundance
Presented by Hilary Kreisberg

Tired of spending hours searching for fun activities and tasks to elevate your lesson? Tired of being distracted by “imposter resources” which look pretty but don’t truly support conceptual understanding? Come learn how to stop being tired and start being productive by understanding how to analyze resources to transform your teaching.

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

Next Week

GMD Rewind: Watch a session that you wanted to see, but did not, or re-watch one of the sessions you attended! Then blog or tweet about what you learned and how you will apply it to your own classroom!

Find the archives of previous sessions here!

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

The delicate balance between solidarity & erasure

For the past 10 days, our fellow educators in Chicago have been teaching. But, they haven’t been teaching their normal lesson plans, filled with rich tasks, investigations, and developing mathematical inquiry. Rather, they’ve spent their last 10 days educating their students, community members, local political officials, and the rest of the world what it looks like to organize a strike that is about more than money.

The Chicago Teachers Union (@CTULocal1) has not only been striking for fair pay, but for smaller class sizes, affordable housing for students, sanctuary policies for immigrant families, and the assurance that every student would have access to a nurse and a school psychologist. Since October 18th, 32,000+ Chicago Public School teachers and staff have been standing their ground as their local unions (Service Employees International Union Local ‘73 & Chicago Teachers Union) have negotiated terms with Mayor Lori Lightfoot (@LightfootforChi). 

With the announcement of the strike, Mayor Lightfoot announced the canceling of classes for approximately 360,000 students until a settlement can be reached. Parents, impacted by the sudden lack of consistent and free childcare offered through the services of public school, may fear that their students will fall behind in their studies, having missed six days (and counting!) of formal schooling. Yet, as educators, we must consider that students may learn far more during this six-day reprieve of formal education with the informal learning they are currently garnering. It is in this same vein that I read Glenn Waddell’s (@gwaddellnvhs) tweet, posted earlier this week: “Every act of teaching is a political act. Every. Single. One”. While this post was directed at the topic of lesson planning with a monolingual and monocultural lens based on the work of Dr. Josè Medina (@josemedinajr89), the concept transfers to acknowledge that the learning of these 360,000 students is also political in nature.

In the event of the Chicago Teachers Union Strike, students may be learning about the politics involved in what can often appear to be an apolitical public education. Students may begin to gain understanding as they watch their teachers model what it means to stand for justice. Students may begin to feel the local inconvenience of having a public right (e.g. the right to education) paused in the name of a larger, global civic right and duty. Students may even recognize the agency and power that they hold within themselves to create change. 

There is a great deal of education that we fail to name and/or honor because it does not fit in the nice, neat confines of the public schooling of which we have become accustomed. And so, out of necessity, oppression, or ease, it is erased.

Below, I share three examples of erasure in education that I found this week on the wide open world of Twitter.

  1. The amount of land loss of Native Americans in the last 150 years.  Shared by Ranjani Chackraborty (@ranjchak)

This is an example of physical erasure. Many still refuse to recognize the effects of colonization on Native American people, and the acculturation enforced on their children as they attend schools that are centered on the Eurocentric values of their oppressor. Yet, this graphic makes that erasure evident.

What do you notice and wonder about the differences between these two graphs? (Click for the dynamic video; also scroll for others, & follow Rajani).

       

  1. #BlackWallStreet & the #TulsaMassacre: With the hit show “Watchmen’s” premiere featuring the Tulsa Massacre, many observers were left wondering why they had never heard of 1) one of the largest massacres in US history, 2) the existence of Black Wall Street, and/or 3) how our public education could erase such a pivotal event. Regina King (@ReginaKing), the star superhero of the show, shared the following tweet to assist viewers in (re)learning the history behind this event.
  1. Doug Robertson (@TheWeirdTeacher) discussed his desire to erase the phrase, “Does that make sense?” from his teaching vocabulary. The replies in this thread give great examples of how to replace this question with others that may distribute power to students that issues them agency to participate in question forming and answering.

I share these three examples to demonstrate how easily events can be erased from history, from our presence of mind, and from our vocabulary. I also share these examples as an act of solidarity with the teachers of Chicago, as they continue to place their mark on history, and refuse to be erased, while also refusing the erasure of their students’ needs. I celebrate the movement of bringing those on the margins towards the center, and the (re)learning and (re)centering of what we want our students to learn as citizens of our society-at-large. It is most certainly more than just the mathematics we are tasked with teaching in school.

There have been many acts of kindness shown towards the teachers on strike in Chicago. Some have sent pizza, others doughnuts and coffee, and others have shared their time. Chance the Rapper (@ChancetheRapper), a Chicagoan by birth, shared his platform on “Saturday Night Live” to demonstrate solidarity with the teachers, staff, and students, and to remind them that the fight is worth it.

You may wonder how you, individually, can show solidarity with our fellow educators in Chicago. On Twitter, they are using the tags #CTUSEIUstrike, #PutItInWriting, #FairContractNow. The more traffic to these tags, the larger presence that the strike receives from local and national media, and the more pressure applied for both sides to come to an agreement over the terms at stake. The Chicago Teachers Union has asked for educators across the country to use social media to show support by wearing #RedForEd, a similar demonstration of unity in the unprecedented number teacher strikes in 2018, including my home state of North Carolina. We also know from last year that this teacher strike is not specifically about Chicago, and that this movement for justice for this group may usher in justice and opportunity for others.

Whatever your choice in showing solidarity for this group and this moment, may it simply not be to erase it from consciousness and history.

Written by Lauren Baucom, @LBmathemagician

Hidden Gems of the MTBoS

Sitting on the couch, scrolling through the seemingly endless number of TV series at my fingertips, I found myself searching for something to watch that was as close as possible to the previous series I had just binged my way through. My wife and I are obsessed with British crime shows, especially those featuring David Tennant. After little success, I habitually picked up my phone to keep up-to-date on the 100 Twitter users I closely follow. In that moment I realised that, just like my Netflix choices, my Twitter choices represented an extremely narrow and unvaried sample of what is available. I had previously convinced myself that I was supportive of the growth of the #MTBoS and #iTeachMath communities, but the mere presence of my Top Drawer list shows my bias towards users with an already large number of followers. My rule of “I’ll follow any teacher that follows me” was clearly not enough. So, this week on the Global Math Department Newsletter, I’ve picked five fabulous teachers with 100 followers or less. If you’re wondering how you can do the same, head here for inspiration and here for the roadmap to get there.

@KP_CUi 

It’s no secret that Maths Twitter folk love a good Open Middle problem. I myself have gotten my fair share of the MTBoS limelight for a few problems I’ve shared with the community. What I love about this post is the simplicity of the prompt this teacher gave to their students, the mode in which they set the challenge to them, and their thoughts on the experience overall. A lot in one tweet!

@pokybloom

Here’s a post that, when I started using Twitter a few years ago, would have seen veteran MTBoS users come to the rescue. A lot of Maths teachers who have persevered through the early stages of using Twitter often recall having their cries for help answered. Sadly, too many tweets go unheard. Whether it’s through a slightly incorrect hashtag (as appears to be the case here, although using #nctm is arguably better than the official ones for NCTM events), a quiet time of day or year, or just a lack of active followers, getting help is not easy when you’re starting out.

@MsAYoungren

I picked this next one out because Annette’s experience on Twitter seems quite common amongst many of the maths folk who jump online for some inspiration. From her feed, it appears that Annette likes to share good stuff that comes her way through retweets and jumps online every so often. This tweet typifies the love that is so often shared through the platform, while also including such a courageous reflection and a commitment to contribute to the community. Quite early, I took on the approach “Dance like nobody’s watching and sing like nobody’s listening”, which enabled me to use Twitter first for myself as a mode of reflection, leaving any attention or insight from others as a welcome, but not expected, bonus.

@talking_math

Many frequent users of the MTBoS started engaging in the online sphere through their blogs. Well, I certainly did. Typing up a post was often the result of my mind overloading with thoughts about something that caused my eyebrows to scrunch – whether it was for good or bad. Mrs. Portnoy (AKA @talking_math) occasionally shares her blog posts through her Twitter account. She’s been teaching for more than twenty years, so there’s clearly no lack of substance in what she writes. Here’s my favourite bit from her latest post in which she’s reflecting about her own children’s views toward mathematics:

“I just wish, somewhere along the line, someone, or something had sparked a love of math… Math can be more than just learning concepts and completing assignments.”

 

@mramarupareja

Amaru is a frequent user of Twitter and regularly retweets great highlights from the iTeachMath and MTBoS communities, often with a nice little insight. He also tends to post great little snippets of his students doing and talking about maths, which is guaranteed to enrich anyone’s feed. I decided to include Amaru in this post mainly because I wasn’t already following him before! Somehow, his account slipped past my “follow back other teachers” rule and I’m so glad that I was able to discover his account and bring more maths joy to my screen. This tweet is just a sample of the great things he shares regularly.

I’m going to leave this here as a call to action to regular users of the Twitter maths community to continue to support those who are still determining whether they are getting as much out of the Twitter community as they themselves put in. These are only a handful of many amazing educators whose number of followers does not represent the quality of the tweets they put out.

 

Written by John Rowe, @MrJohnRowe

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This Week at the Global Math Department

Edited By Chase Orton  @mathgeek76
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Online Professional Development Sessions

Tonight!

SmartSlides for Engaging Students

Presented by Lynda Moore

In this session, you will see how Lynda Moore (teacher of 30 years) uses hyperslides to engage her students and build confidence and ownership in their learning. She uses live data, immediate feedback and self assessment to teach HS Geometry. The use of Teacher Time, Think Pair Share and looping of content are some of the tools that you will learn in this webinar. Math can be paperless, Math can be engaging, and Math is AMAZING, and Learn to KnowMooreMath with Lynda Moore.

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

Next Week

The Era of Resource Abundance

Presented by Hilary Kreisberg

Tired of spending hours searching for fun activities and tasks to elevate your lesson? Tired of being distracted by “imposter resources” which look pretty but don’t truly support conceptual understanding? Come learn how to stop being tired and start being productive by understanding how to analyze resources to transform your teaching.

Register ahead of time by clicking here!

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

Storytelling and Mathematics

Recently, Desmos posted a blog post titled, “How Might You Launch a Lesson?” where Christopher Danielson (@Trianglemancsd) and Michael Fenton (@mjfenton) share three ways to get students involved in a math lesson. Launch 1: One Question draws on Dan Meyer’s Three-Act Tasks, and Launch 2: Notice and Wonder draws on the work of Annie Fetter (@MFAnnie) and Max Ray-Riek (@maxrayriek), both of which have become popular strategies in #MTBoS as these strategies tend to invite and validate students’ natural curiosities and instincts regarding math exercises.

Launch 3: Storytelling, suggested by Lauren Baucom (@LBmathemagician) brings forth the practice of telling stories from African-American culture. While the other two launches elicit students’ mathematical thinking, and may allow students to share their personal experiences, storytelling has an additional benefit of explicitly making space for students to bring forth parts of themselves that are not normally honored in the math classroom. Students can inform and compose these stories through their lives outside of the math classroom, which can allow students to feel heard, understand that creativity and imagination have a role in mathematics, and create personal and mathematical connections through the lesson.

Shraddha Shirude (@ESMathTeacher) writes how storytelling, and the lack thereof, affects how students engage with mathematics in her blog post titled, “Math is Life. Life is a Story. So why aren’t we telling stories in math class?” Shirude notes that omitting stories and the human aspects of mathematics in math classrooms can create barriers for students to connect with each other and the mathematics, which, in turn, can push people away from math. She also shares her love of mathematics and stories, and how the two merge to inform her implementation of Ethnic Studies into practice. Shraddha’s writing as an Ethnic Studies Math Educator was invaluable for me so I encourage you to read the post in full and follow her on twitter.

By Christelle Rocha (@Maestra_Rocha)

Tell Me Everything You Know

My team (@musiccitymath) and I brought back a somewhat old idea of “tell me everything you know.” We were using it as a way to create a mastery experience for teachers to help build collective efficacy. The idea came from a blog post in 2016 by Joe Schwartz (@JSchwartz10a) titled “Unknown Unknowns.” He talks about changing the question of a problem to “tell me everything you know about…” and this brings forward not only what students know but also unfinished learning. My favorite quote from the post is, “The questions we ask and the tasks we post yield information about our students.”

Kristin Gray (@MathMinds) has a video from 2017 on Teaching Channel where she does this routine with kindergarteners. Here is the tweet where she posted about it.

Have you used this routine? Tell me everything about it! I’d love to continue the conversation on Twitter.

By Amber Thienel (@amberthienel)

Transdisciplinary Learning: Mathematics Blending & Intersecting
I’ve been thinking recently about transdisciplinary–different from interdisciplinary or multidisciplinary–learning, especially as it occurs in mathematics education. I realize this may be a new term, as neither the adjective nor the noun has appeared in any #MTBoS tweet at the time of writing:

Pulling a sample definition [source] for ‘transdisciplinarity’ yields the following:

“Transdisciplinarity occurs when two or more discipline perspectives transcend each other to form a new holistic approach. The outcome will be completely different from what one would expect from the addition of the parts. Transdisciplinarity … output is created as a result of disciplines integrating to become something completely new.”

One source of interest for me is around whether one can/should call ‘mathematics education’ itself a discipline, or whether it is fundamentally transdisciplinary. Another source of interest for me is around various combinations of disciplines, and whether the work happening is inter/multidisciplinary or truly transdisciplinary.

Here are a few twitter-based examples of discipline-interactions that are on my mind. [I’d love to hear about more!]

Math & Math Education: Check out this brief thread from Dr. Wandering Point. It begins with the tweet below [the “preface” clues that there are some criticisms to follow!] and contains a link to Askey’s Good Intentions Are Not Enough.

Relatedly, Michael Pershan [@mpershan] has an observation and a question related to who criticizes whom in the context of Math and Math Education:

Dr. Diaz Eaton [@mathprofcarrie], a math professor, poses the following questions around Programming & Ethics:

[BTW: I strongly recommend @_KarenHao’s recent article on making AI fairer.]

Math & Ethnic Studies: A group out of Washington has put out their K-12 Math Ethnic Studies Framework [pdf]; check out co-creator @TCastroGill’s tweet mentioning collaborators @ESMathTeacher and @fearnonumber:

The aforementioned materials inspired Jenna Laib [@jennalaib] to tweet a blog post well worth reading over:

Math & History: Check out @MathHistFacts, which is definitely and certainly not drawn from the research of @mbarany, for tongue-in-cheek takes on these two disciplines. [See Michael Barany’s main account for more serious work on historical theories of mathematics.]

Math & Gender Studies: My work environment has continued to push my thinking around math and gender studies, or math education and feminism, as my colleague Georgina Emerson [@teachaboutwomen] alludes to here:

As in the above-tweet: Recommended readings are strongly desired! In the meantime, I’ve been threading a number of paragraph-pulls after Georgina, my history teacher colleague who founded Teach About Women, pointed me to work by Suzanne K Damarin. I hope I can interest you in taking a glance at some of these threads; below is a sample excerpt from yet another thread [about a math text inspired by work of Peggy McIntosh, Joan Countryman, and others] to whet your appetite:

What *is* that different mathematics that Shelley refers to in the excerpt above? Or what could it be?

A few bullet-pointed items, without commentary, at various intersections.

Math & Social Media: See Dave Richeson’s [@divbyzero] three part thread [click for more!]:

See also Ayesha Rascoe’s [@ayesharascoe] quantitative approach to (un)presidential tweets:

Math & Motherhood: This was the topic of a special issue in the Journal of Humanistic Mathematics in July 2018 [JHM link]. See also: Francis Su [@mathyawp] tweeted out a link to Allison Henrich’s [@KnottyAllison] AMS Math-Mamas-blog post:

Math & the Prison System: See Darryl Yong’s [@dyong] blog post on working with students inside of a men’s prison:

As a closing note: Last week I highlighted some positive examples of sourcing practices, but also pointed out two instances in which there was a clear lack of proper attribution: two from @fermatslibrary and one more from @edutopia. I am happy to report that folks behind the scenes from both accounts contacted me, and have both recommitted to avoiding these omissions in the future [and moved to correct the ones that were pointed out].

As always, please reach out to me [DMs, email, @ me, etc] with any happenings in or around the world of mathematics education that you believe should be amplified!

Benjamin Dickman @benjamindickman

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This Week at the Global Math Department

Edited By Nate Goza  @thegozaway
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Online Professional Development Sessions

Tonight!

Strengths-Based Mathematics Teaching and Learning: 5 Teaching Turnarounds to Build Student Success

Presented by Beth Kobett

Explore teaching turnaround strategies that can reframe and open up students’ mathematical learning opportunities. Learn to identify and leverage students’ strengths to develop powerful and strategic learning moments that recognize and bolster students’ strengths to build mathematical success.

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

Next Week

SmartSlides for Engaging Students

Presented by Lynda Moore

In this session, you will see how Lynda Moore (teacher of 30 years) uses hyperslides to engage her students and build confidence and ownership in their learning. She uses live data, immediate feedback and self assessment to teach HS Geometry. The use of Teacher Time, Think Pair Share and looping of content are some of the tools that you will learn in this webinar. Math can be paperless, Math can be engaging, and Math is AMAZING, and Learn to KnowMooreMath with Lynda Moore.

Register ahead of time by clicking here!

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

Self-reflection

As teachers who believe that equity is a central concern in math education, we are always looking beyond ourselves but also within ourselves, adopting a critical lens toward the systems, practices, and institutions that marginalize and harm certain mathematics students, but also turning that lens back onto ourselves to see how we are implicated in those same systems. I’d like to share the powerful stories and advice from two math teachers who have applied this duality of extra- and introspection in their practice.

Idil (@Idil_A_) has written an incredible post on self-study. It may be tempting to think that self-study is simple and straightforward, but as she points out, it raises deep questions about the nature of what counts as knowledge. Do we tacitly organize knowledge in a hierarchy? Do we place our own particular experiences below the “generalizable knowledge” developed in academia? These are some of the questions I found myself asking as I read her post. Beyond the what of self-study, Idil also engages in the how by giving five pieces of advice. I’ll outline them here, but please read her words to see how she elaborates on each one.

  1. Have a clear focus
  2. Be systematic
  3. Be honest
  4. Include feedback on others and external artifacts
  5. Result in professional and personal change

Finally, she concludes with perhaps her most important point: the question is not if we are part of the problem, but how.

The honesty with which Idil approaches her practice is equally evident in Esther Song’s (@eugoogleypart 1 and part 2 in the Nepantla Teachers Community (@NepantlaTC). First, a word on the community. Read what they’re about and then subscribe if you haven’t already done so. It’s a mind-blowing organization of teachers committed to social justice mathematics education. I’ve learned so much from them.

Esther’s two pieces are a demonstration of vulnerability, reflection, and growth. Her dilemma is one that likely resonates with many of us: perceived math apathy among students. Like the Nepantla Teachers Community state in their norms, I’d suggest sitting and reflecting on the first piece before moving on to the second. But do read the second piece. It’s so beautifully written. And I’ll just leave it at that.

@melvinmperalta

How do people think about “teacher learning” and why does it matter?

We know a lot about different ways teachers are supposed to learn: we have credentialing programs, where teachers typically take coursework and earn their certification. As a part of that, we have student teaching, where pre-service teachers interact with students in classrooms and do the challenging and exciting work of trying to help other people (some of whom are reluctant to engage) to learn. Once teachers are certified, they participate in professional development, that highly variable “system” of workshops and inservices that offer them new ideas, tools, techniques, or opportunities to reflect on instruction. Some teachers learn from colleagues, with whom they can share ideas and resources, or maybe even consult with about challenging situations.

But all of these primarily describe situations that purport to help teachers learn. None of them actually describe how teachers go from one understanding to another, one form of practice to another, changing what they do from day to day in their classrooms.

In research, a lot of accounts of teacher learning focus on changes in instructional practice. For instance, maybe a teacher starts out, say, giving a lecture and using their whiteboard ineffectively, with notes scattered around without a clear sequence. We then give them feedback about how to organize that information so students can follow the lecture’s logic. Then, if the next time we watch them lecture and we see improved whiteboard use, we can say that they have learned.

But eventually, the notion of change in practice as a way to describe teacher learning falls short. How we draw a boundary around where an instructional practice begins and ends, especially when its success is not entirely up to the teacher? In the whiteboard example, the teacher has a lot of control around their board use, organization, diagraming, color coding, and the relationship between their spoken words and scribblings. If we think of more interactive practices, however, that depend more on student inputs, the situation becomes more complex. Even in the whiteboard example, we can extend our consideration to how the teacher annotates the whiteboard to account for students’ ideas and questions. In this case, the expanded view of whiteboard practice no longer only comes down to the teacher’s actions; it also involves the students around them, how they engage with students’ ideas, making the practice variable from class to class.

Most of the instructional practices that we promote in mathematics education are more interactive than whiteboard use, and thus more contingent on teaching situations. As a consequence, the boundary of instructional practice becomes even more complicated. For instance, say that a teacher went to a professional development workshop on using a Notice and Wonder conversation structure in the classroom. They work through some examples with their colleagues, identify what kinds of tasks might lend themselves to a rich Notice and Wonder discussion, and even get some examples from teachers who have used them a lot. They have learned some useful things.

Maybe then our hypothetical teacher tries Notice and Wonder in their first period class and has a dynamic discussion. Students make good observations. They raise interesting (and even amusing) questions. So we ask: has the teacher learned the practice?

What if we extend the story to the teacher’s next class? They try the same activity second period. Students stare the teacher down. After an uncomfortable amount of silence, one student, out of pity, volunteers something that kind of misses the point. In short, the Notice and Wonder activity bombs. Do we change our assessment? Has the teacher learned the practice?

In my research project Supporting Instructional Growth in Mathematics (Project SIGMa), we are pursuing questions about teacher learning by looking not only at teachers’ changes in practice, but also their sensemaking about their work. All teachers know that not every practice works equally well all the time. So the ways teachers make sense of the problems of practice that arise as they take on these complex, interactive practices may matter almost as much as whether they can recite the steps of the routine or do it unproblematically some of the time. For their understanding to be robust, they have to understand the elements of their teaching situation that may impede the practice’s successful execution and, relatedly, how to troubleshoot the practice.. When things work well, how do they think about it? When things don’t work as well, what conclusions do they draw? What evidence do they marshal to warrant their interpretations? What does that tell them about how to adjust the practice in the future?

Since so much of what happens with interactive instructional practices depends on the particularities of classrooms, students, and content, in our view, it is not sensible to say that teachers learn an interactive practice through one (or even five or ten) successful executions. Instead, we view teachers as learning these interactive practices when they know the routines, can bring them to life with different groups of students, adjust sensibly in response to a range of  student inputs –– and have productive ways to interpret what happens when things do not go as expected. This means that instead of concluding simply, “That practice doesn’t work” or, even, “That practice doesn’t work with my students,” they consider the variables that make one lesson, one class, or one day different from another. Their adaptations consider the goal of the practice, and they adjust it to make sense of the teaching situation while keeping those goals in mind. They think ecologically about how these differences might affect students’ participation and sensemaking. This kind of robust understanding takes time to develop, and it requires high quality feedback to support the teacher’s interpretation of what is happening in the classroom.

Written by Ilana Horn (@ilana_horn)

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A Computational Approach to Functions

A Computational Approach to Functions

Presented by: Patrick Honner
Presented on October 8, 2019
Looking for a new approach to teaching domain and range? Or an opportunity for students to use their crossover computer science skills? Taking a computational approach to functions allows for the rigorous development of all the fundamental concepts in an active and creative way, while at the same time offering endless opportunities to extend deeper into both mathematics and computer science. If you teach about functions—and what math teacher doesn’t?—you will leave with something new to think about for your math classroom.

Recommended Grade Level: 7 – 12

Hosted by: Rana Hafiz

Watch the full presentation at: https://www.bigmarker.com/GlobalMathDept/A-Computational-Approach-to-Functions