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

This Week at the Global Math Department

Edited By Casey McCormick  @cmmteach
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Online Professional Development Sessions

Tonight!

A Computational Approach to Functions
Presented by Patrick Honner

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.

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

Next Week

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.

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

Fractions: Inside & Out of the #MTBoS

First things first, S/O to Liz Caffrey (@AsymptoticLiz) and her awesome shoes, who’re redefining fashion in sequence.

Lately, I’ve been fascinated by fractions and the conversations that we, (the #MTBoS community-at-large) have about them. When I did a Twitter search for the latest/top tweets (#MTBoS and Fractions), I saw the following words used to describe fractions or the relationship that students have with them: demystifying, challenging, struggle, gatekeeper, break down, and misconceptions. As math educators, we are aware that students’ learning of fractions feels like a make or break point for whether or not students will develop a productive disposition & positive identity in mathematics.So I thought it’d be interesting to look for cases in the #MTBoS and outside the #MTBoS where fractional understanding was of imminent importance.

This week, we got to listen in on a conversation in Marian Dingle’s (@DingleTeach) classroom as her students used the transitive property to make sense of fractions being division. Fractions are Sharing; Sharing is Division; SO FRACTIONS ARE DIVISION!

Berkely Everett (@BerkelyEverett) shared a #samedifferent post to help us think about the way we count denominators.

One of my favorite resources for understanding the conceptual fluency, strategic competence, and adaptive reasoning in fractions is Graham Fletcher’s (@gfletchy) video series on the Progression of Fractions. This was a really helpful video for me, as a high school teacher who sometimes forgets how students develop their thinking in fractions.

Here are a couple of examples I found outside the #MTBoS, where the understanding of fractions played a critical role:

This week, Amber Guyger, a former Dallas police officer who shot and killed her unarmed neighbor was sentenced to ten years in prison after a criminal trial. Several weeks ago, the defense attorney in this high-profile case requested that the case be moved to a different district, to “assure a fair trial”.

In this tweet, S. Lee Merritt, Esq. (@MeritLaw) discusses the importance of having the Botham Jean murder trial heard in Dallas County, where the crime took place, instead of relocating to a different site.

How are fractions being used in this case?  How closely does the jury’s racial makeup “reflect the diversity of Dallas County?” To what level of precision (SMP.6) is the prosecutor attending to when defining the diversity of Dallas County? Does the fractional relationship in diversity change depending on this definition?

In another critical example, an impeachment inquiry against the President of the United States of America was filed this week. The President (@realdonaldtrump) tweeted the following in response:

In the thread under this original tweet, the following maps were given as counterexamples to the map provided by the President. Several Twitter users cited the number of popular votes or electoral votes for the different candidates in the 2016 election (“That’s 65,844,954 blue dots for Hillary Clinton and 62,979,636 red dots for Donald Trump.”). Find the Official Election Results here.

Source: (Mark Newman/University of Michigan, 2016 election.)

What is the fractional relationship between blue and red in each map? Why are these fractional relationships so different, even though they span the same area (the United States)? What viable argument might each of the Twitter users be trying to construct (SMP. 3) with the map they chose to post? (Tangent Time: Why aren’t Hawaii & Alaska on all 5 maps?! Talk about erasure!)

It seems that fractions are not only of critical importance for developing a positive mathematical identity for our students, but also in making sense of the world in which our students live.

Written by Lauren Baucom, @LBmathemagician

Something Old, Something New, Something Borrowed, Something Blue.

It goes without saying that there is a lot that passes through the daily stream of tweets. What I’ve picked out below come from some significant MTBoS contributors and the four highlights are merely a taste of the gold they consistently sprinkle my Twitter feed with on a daily basis. I hope you enjoy it as much as I did.

Four Stages of Using Models

Brian Bushart (@bstockus) got us all thinking about what type of thinking we might be biased towards when facilitating a number talk by sharing his thinking on the Four Stages of Using Models. As Kathy Richardson (@letkidslearn) describes, these four levels unpack how students use models to solve problems, highlighting that although we’d love all students to be demonstrating thinking at Stage 4 (solving the problem mentally), there are some important distinctions between what students are doing prior to that, and that just because students are at Stage 4, operating in Stages 1, 2 and 3 can still support their learning. If your thinking resonated with what you read on that post, perhaps you want to also check out the one Brian pushed out four days later on Multiplication Number Talks Using Models.

Esti-Mysteries!

He’s at it again, folks. Steve Wyborney (@SteveWyborney) has started releasing the first of his 51 brand new Esti-Mysteries challenges. If you haven’t seen these before, Steve’s original post is a great starting point. One particular thing that I love about them is the range that appears and adapts based on the clue. Here’s an example, which would be great for introducing inequalities:

Can you visualise this? 

There aren’t many things I love more than seeing something and immediately thinking “hmmm is that right?” then going to check it out and end up thinking, “well, would you look at that? It is right!” I went through that exact process when I saw Mark Chubb’s (@MarkChubb3latest post:

The best thing, I thought, was that I was left with the “I wonder if…” types of questions. This is part of a nice little post he put out through the week, which is definitely worth checking out. Better still, let Mark know some of your answers!

The Domino Effect

Sarah Carter (@mathequalslove) showed her generosity by contributing her files she used to create a whiteboard display of the Domino Effect puzzle. Originally from Brainteasers : 195 Puzzles to Keep You Sharp, Sarah posted this on Twitter through the week and, if you were like me and read it as any eight dominos, you would have had the extra fun of finding eight dominos that could be possible.

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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Tonight!

Activities in the AP Math Classroom
Presented by Sharon Sterken and Randi Metz

Once we jumped on board the Student Centered Learning bandwagon, we found it very difficult to find quality, engaging, and fun activities in the AP math classroom. So, we decided to team up and share our ideas for other educators who are interested in adding pizzazz to their lessons.

This webinar was developed to have resources available to enhance instruction for fellow AP Calculus AB and AP Statistics educators.

Contact Info:
Twitter @girlmathX2
Blog: http://girlmathx2.blogspot.com/

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

Next Week

A Computational Approach to Functions
Presented by Patrick Honner

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.

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

Notice & Wonder 
Amber Thienel (@amberthienel)\

I love a good notice and wonder. It does magical things to get students thinking and saying things I couldn’t possibly think of on my own. Seeing the connections and ideas that students come up with is impressive.

I was diving into the hashtag for notice and wonder (#noticeandwonder) and found some ideas that I would like to share with you. One of the most popular tweets right now is from Robert Kaplinksky (@robertkaplinsky) way back in June.

Another one that peaked my interest is a recent conversation from Paige Sheehan (@MrsSheehanMath) asking about how you get your students to capture their noticings and wonderings. Join in on the conversation if you have an idea to share.

 

Start a Math Club
Christelle Rocha (@Maestra_Rocha)

If you haven’t started a math club at your school, I highly recommend it. Jennifer Dao (@JDaoMath) posted about their math club and asked others to share activities for the year.

While I encourage you to look through the thread yourself, some resources were shared to help teachers get started on the right foot:

I’m grateful that Jennifer has been sharing their math club experiences, because I’ve gotten ideas on how to revamp the club at my school for the new academic year. If you are getting started or already have a club at your school, I’d love to hear how it’s going; I am shamelessly starting a hashtag, #OurMathClub with the hope that we can continue to share and learn from each other.
 

Sourcer Sorcery
Benjamin Dickman (@benjamindickman)

In this week’s GMD newsletter, I want to focus on the ways in which ideas are sourced (or not sourced). This does mean, in particular, that I have omitted material around new mathematical progress, a conference/conversation on professional norms in mathematics, and more.

Two inspirational tweets to kick it off: the first from @LBMathematician [in her quote-retweet of @mathedmatters] and the second from @ChristieNold:

Notice in the first image the concerns by generators of original ideas, especially in a case for which one’s livelihood (e.g., earning tenure as a professor) can be a function of proper attribution, and the valid concern expressed in the second tweet around conveying one’s newfound understanding along with those who supported it along the way.

I recently came across an @edutopia article (via Jerry Becker’s listserv) about the “Talk Moves” used at a particular school in Portland, ME. But, the article attributes various Talk Moves to this school – even though they appear in the math education literature! In fact, the first four Talk Moves named in the @edutopia document are precisely the first four from the Chapin et al work below:

 

Not cool, @edutopia (1.12 million followers!).

I noticed another attribution issue from @fermatslibrary (281 thousand followers!) for whom this is not the first time that work has been tweeted without attribution. In fact, that same link shows another instance in which a reddit user’s original work was tweeted without credit being given.

While these large-follower-accounts are not doing their due diligence in sourcing the content that they are tweeting out to a hundred thousand+ or a million+ people, there are a lot of great examples of proper attribution that came across my timeline recently.

So: To pivot positively, I’d like to highlight some of the quality instances of good sourcing practices in action. First, though, even when attribution and quoting go generally well, there can be another problem with journalistic practices: Picking the title of an article. For example, check out Kevin Buzzard’s response to a Vice article in which he was quoted.

Contrast the bad sourcing from @edutopia and @fermatslibrary with the @ReadPRIMUS account [managed by BK] in which attribution is provided even when the source has no recollection of their helpful remark!

Continuing with the proper sourcing theme: In linking to a NYT piece on mathematicians’ chalkboards, @nattyover credits the photographer and the writer and the person who brought the piece to her attention [the “h/t” abbreviation stands for “hat tip”].

I added links to a few more pieces about chalk, which includes three items by @MBarany.

Plus, an interesting comment about chalkboard handwriting from @katemath:

Among the many items tagged #NCTMBoston19 is the following from @beRealcoach. As to sourcing: Note that the tweet includes an attribution to the presenter, @NicoleBridge1, and that the slide includes an attribution to the writer, Zaretta Hammond.

@alittlestats links to a fascinating article about graphing calculators and their business model and cc’s @Desmos [see the article!] and includes another “h/t” [hat tip] to shout out @MathDoris.

Sam Shah writes a wonderfully reflective blog post in which he cc’s three people [spoiler: one of them is me due to my tweet here] and generously mentions the three of us at the start of the post, too.

Relatedly, @AlexPHoover posted about an Out List + Ally List from Spectra and credits @mikeahill.

Besides Ally Week, we have also been in Hispanic Heritage Month. Check out the #Lathisms hashtag, and the link provided by @zdearaujo here:

Finally, I was excited to read about David Eppstein’s efforts around wikipages for women in mathematics. I saw it in a tweet from @thegautamkamath; check out the link for more!

I hope those who have read this far enjoy the sourcing and sources in this week’s newsletter; as always, I will be grateful to anyone who wishes to notify me about other work that should be highlighted and/or amplified in and beyond math education communities. Hit my DMs, tag me, send me an email; whatever works!

Speaking of mathematical errors, I need to get one off of my chest: In the one REU math paper I contributed to there is a mistake in Remark 2.4. The constants should both be 1 [not both zero, which is what our paper says] if phi has good reduction [whatever that means]. This doesn’t affect correctness and is more of a “typo” than a “deep theoretical error.” But, it is not hard to imagine how small errors can ramify.

To see that this must be an error, one can note that cv and Cv are defined [see below] as being the maximum among various quantities that always include 1; of course, there is no way that 0 will be the max in a set that also contains 1. Logarithms are then applied to each, so it will be better not to be taking log(0)!

(Phew; I feel better already.)

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ELL Strategies for a Regular High School Math Classroom

ELL Strategies for a Regular High School Math Classroom

Presented by: Jennifer Thomas and Kari Ferguson

Presented on September 24, 2019

Students need more literacy support in a math classroom due to different language levels, math abilities, and global perspectives. Through examining practice, teachers can focus on their formatting to ensure they are best supporting students.

Hosted by: Amanda Riske

Watch the full presentation at: https://www.bigmarker.com/GlobalMathDept/ELL-Strategies-for-a-Regular-High-School-Math-Classroom

This Week at the Global Math Department

Edited By Nate Goza  @thegozaway
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Tonight!

ELL Strategies for a Regular High School Math Classroom

Presented by Jennifer Thomas & Kari Ferguson

Students need more literacy support in a math classroom due to different language levels, math abilities, and global perspectives. Through examining practice, teachers can focus on their formatting to ensure they are best supporting students.

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

Next Week

Activities in the AP Math Classroom

Presented by Sharon Sterken & Randi Metz

Once we jumped on board the Student Centered Learning bandwagon, we found it very difficult to find quality, engaging, and fun activities in the AP math classroom. So, we decided to team up and share our ideas for other educators who are interested in adding pizzazz to their lessons.

This webinar was developed to have resources available to enhance instruction for fellow AP Calculus AB and AP Statistics educators.

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

Renewing Our Commitment

It’s the third week of the academic year and the first round of runny noses and germy hands has begun. Along that vein, the Federal Election is about 30 days away and our Prime Minister has been revealed in “brown face” prompting yet another round of fragility from Canadians unwilling to accept the reality of every racialized person living in this country.

This tweet by @RitikaGoelTO highlights the misuse of statistics defending indefensible social practices and how ‘facts’ seek to move the conversation away from the reality of systems of oppression by using large numbers to emphasize the ‘good’.

So, as these conversations intensify and we start to flounder in our commitment to social justice and re-humanizing mathematics, I invite you to read (often and consistently) this collaborative piece by 36 educators on the Teaching Tolerance Advisory Board.

What we do is about the kids in our classroom, who are minute by minute soaking in every detail of our actions, words, facial expressions, and sighs.

I invite you to renew your commitment to;

  • continue to raise awareness of your own socio-cultural consciousness,
  • deepen your content knowledge for mathematics teaching,
  • and build and sustain a community that keeps you firmly planted in authenticity and love.

Yours,
@HKhodai

Classroom as Community, Students as Inviters

As the school year gets underway, we’re thinking about what it means for a classroom or a relationship to be “inviting,” and who gets to do the inviting. So often when we talk or hear or read about “inviting” spaces, we’re thinking about teachers signaling support and encouragement, creating physical spaces that are a comforting respite from the impersonal institution of school, designing lessons that are engaging and thoughtful.

But what if we were to think about students as the inviters instead?

If students are the ones doing the inviting— into their space, into their lives, into their experience in the mathematics classroom— and we as teachers don’t have permission to barge into that space unless invited, how does that change the way we thinking about teaching and relationships?

Do students own any of the space in math classrooms, or does the space belong to us, giving us the authority to decide who gets invited in based on the rules we set and the conditions we place on their welcome (…only if they “behave;” only if they “dress appropriately;” only if they “contribute”….)? Or are classrooms shared spaces where students and teacher negotiate the rights that each has in entering the other’s physical, intellectual, and emotional space?

And what if students invite us into some of their spaces but not others? In the same class we saw one student who would consistently invite their teacher into conversations as long as they weren’t about math, or invite them to help with problem #3 but then shut the door before #4 and another who was out on the front porch with lemonade all the time, constantly inviting the teacher into both mathematical and non-mathematical conversations. How many times do we knock on a door before accepting that it’s not open to us? Do we try to finagle an invitation, maybe by promising to bring cookies? Are there ever times we might barge in to their space anyway, out of concern or frustration?

To extend the analogy, we thought about classrooms as a large plot of land:

Students set up residence on some plot of land, and in exchange for enjoying the amenities provided by the community, take on some shared responsibility for making the community an enjoyable place to live. This might mean abiding by particular norms in shared spaces, regardless of what they do in their private spaces. If this were the case, how do we ensure that students occupy equitable amounts of space, and that different resources are valued? That the high status kids aren’t setting up huge homes with sprawling lawns and racing their Mercedes through the street? And how could we encourage students to develop the kind of community where everyone’s got a chair out on the front stoop, ready to collaborate with whichever neighbor drops by?

In your classroom “neighborhood,” what kind of zoning requirements and bylaws are enforced? Are the rules there for resident safety (like requiring fire escapes on every floor), for collective well-being (like limiting how often lawns can be watered during a drought), or for aesthetics (like outlining acceptable exterior paint colors)? And are these rules set in advance, or does everyone move in and just figure it out when someone wants to install an “unsightly” sculpture or have drum practice on the sidewalk at midnight?

We’d love to hear what you think.

Grace Chen (@graceachen) & Nate Goza (@thegozaway)

Mathematically Meaningful Choices

@TracyZager has begun assembling a list of mathematically meaningful choices that students can make on a daily basis. The responses include some great mathematical choices that weren’t in the original Tweet. Reflecting on the list makes me think about the moments when students ask us to “tell me what to do” or get stuck, thinking they “don’t know what to do”. Seeing all these choices helps me see that as a learner and doer of mathematics, I am probably freer than I think I am. I wonder if students would agree or if, like the paradox of choice, this list would cause the opposite reaction. Tracy, as usual, has given us a lot to think about!

Mathematically Meaningful Possibilities

@RichardElwes wrote a blog post reflecting on the responses he received to the following question:

Before reading Richard’s thoughts, it might be interesting to think about what you think and why. The post goes through several alternate justifications for each response. Each justification highlights the importance of defining terms and concepts but also all the rich mathematical possibilities that come from different starting points.

I’m reminded of the NCTM article, Is 1 a Prime Number?, which talks about one form of teacher development where participants share differing views of multiplication and how that impacts whether 1 could be a prime number. In a way, these kinds of activities of diving deep into definitions and working together to figure out their implications helps me see that not only can mathematics be beautiful but also mathematics pedagogy.

And Much More

There’s so much more happening in the online math ed world, I know I will have missed stuff (lot’s of stuff) with the list below. I apologize in advance!

@DavidKButlerUoA introduces us to Digit Disguises, a two-player game of algebraic deduction.

@math_mrestrada shares a strategy for collaborate proof writing and justification making.

@amynoelleparks recently published a paper in the American Educational Research Journal titled Centering Children in Mathematics Education Classroom Research. From her Tweet: “It’s what I’ve been trying to say since I was a grad student: Children have their own stories. They are not data points for evaluating teachers’ pedagogy”.

@mathwithmsyi pushes for descriptive mathematical language such as reading 2.3 as “two and three tenths” instead of “two point three” to help students make mathematical connections.

@carloliwitter points out that NASA has interactive graphs that track CO2, global temperature, sea level, and ice sheets. He’s thinking about turning it into a Desmos activity. It’s also worth checking out #makemathjust.

@geoffkrall shares a WODB (Which One Doesn’t Belong) that has elicited quite a few varied responses. Let’s add to the thread!

@melvinmperalta

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Moving to SBG (Part 2)

Moving to SBG (Part 2)

Presented by: Farica Erwin

In my journey to make my grading policies match my teaching philosophy, I found Standards Based Grading. Six years of some trial and error, I now have a policy that works for my classroom. Join to learn about how to incorporate SBG, what worked, what didn’t work, how it affects homework policy, and how to still use a traditional online grade book.

Hosted by: Rana Hafiz

Special Note:  Due to the size of this file, this is part 2 of 2.

Note: Watch the full presentation at: https://www.bigmarker.com/GlobalMathDept/Moving-to-SBG

Presented on September 10, 2019

 

Moving to SBG (Part 1)

Moving to SBG

Presented by: Farica Erwin

In my journey to make my grading policies match my teaching philosophy, I found Standards Based Grading. Six years of some trial and error, I now have a policy that works for my classroom. Join to learn about how to incorporate SBG, what worked, what didn’t work, how it affects homework policy, and how to still use a traditional online grade book.

Hosted by: Rana Hafiz

Special Note:  Due to the size of this file, this is part 1 of 2.

Note: Watch the full presentation at: https://www.bigmarker.com/GlobalMathDept/Moving-to-SBG

Presented on September 10, 2019

This Week at The Global Math Department

Edited By Casey McCormick  @cmmteach
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Online Professional Development Sessions

Tonight!

Moving to SBG

Presented by  Farica Erwin

In my journey to make my grading policies match my teaching philosophy, I found Standards Based Grading. Six years of some trial and error, I now have a policy that works for my classroom. Join to learn about how to incorporate SBG, what worked, what didn’t work, how it affects homework policy, and how to still use a traditional online grade book.

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

Next Week

ELL Strategies for a Regular High School Math Classroom

Presented by  Jennifer Thomas and Kari Ferguson

Students need more literacy support in a math classroom due to different language levels, math abilities, and global perspectives. Through examining practice, teachers can focus on their formatting to ensure they are best supporting students.

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

Welcome to Palindrome Week

This past week, the number in the calendar if written in American numerical format, can be read the same both forwards and backwards. While we all love to celebrate pi day (either 3/14 or 22/7, depending on your calendar format), Palindrome Week offered math teachers everywhere the opportunity to look for patterns in numbers.  In American numerical format, we have been able to celebrate Palindrome Week every year since 2011, but we won’t have another one until 2021. Can you figure out which week will be the next #PalindromeWeek?

If #PalindromeWeek didn’t set your little pattern recognizing heart a puttering, then quite possibly the probability of a Friday the 13th also being a night with a full moon could. It’s been 19 years since the last full moon on a Friday the 13th (although the moon will not be fully illuminated until 12:30am, on September 14th). This month’s full moon has been called a Harvest Moon, an agricultural term used to describe the moon closest to the autumnal equinox used to indicate a time when farmers and enslaved persons used the moon to harvest crops of the season. The last time a Harvest Moon fell on a Friday the 13th was in 1935, and the next intersection of these two conditions will not occur until 2171.

____________

There’s a new chat in the #MTBoS world on Tuesday nights at 8PM EST. The #GhostsInTheSchoolyard chat is helping members of our community come together as they read the book Ghosts In The Schoolyard, by Eve Ewing. The chat is being moderated by Tyrone Martinez-Black (@teachnext_tmb), Marian Dingle (@DingleTeach), & Kelly Wickham Hurst (@mochamomma), as they lead us through a conversation on the intersection of racism, segregation, and education in Chicago’s South Side. With @NCTM preparing for its centennial celebration of its annual meeting in Chicago in April of 2020, this book chat allows educators to learn and unlearn some of the history of Chicago, and develop place consciousness before attending this event. When you go to a math conference, do you take time to learn the history of the land that you stand on and who stood there before you?

This week, Robert Kaplinsky (@robertkaplinsky) wrote a blog about how he is beginning to recognize systemic racism and white privilege in his life and work through his participation in the #CleartheAir chat moderated by Val Brown (@ValeriaBrownEdu). In his blog he writes, “If you’re a long time reader of my blog, you might be wondering why I’m talking about systemic racism and not just sticking to math. The reality is that the more I learn about how common injustices are, the more I realize that I cannot sit back and do nothing.” It is also important to realize that as mathematics educators, our course content is not apolitical or unbiased. Take a look at the ORC data of Calculus enrollment of schools and districts in your area for just one example of how systemic racism and mathematics overlap.

Written by Lauren Baucom, @LBmathemagician

Not everyone is equally gifted in mathematics.
But there are reasons to teach like everyone could be.

Dan Finkel (@MathforLove), posted what would seem from the outset to be an against-the-grain commentary on the role of growth mindset in mathematics classrooms. His own comment on the tweet in which he posted the link displayed a great intention on being perceived in the right way.

 

 There’s a lot I love about the post and some things that challenge my current thinking, which is another thing I love about the post. Dan’s comment that “For it to be more than an empty platitude, or a blatant falsehood, we have to be precise” spoke to my condition in a profound way. I think in a similar way to how we support our students to make sense of complex ideas, we need to help the teachers we work alongside with to know what is meant by the messages we send about growth mindset.

 Something that challenged my thinking was that Dan’s post left me with a feeling that some students will just not fall in love with mathematics. Like a Netflix show I recommend to a friend who doesn’t get past the second episode, I can’t help feeling that, if students would just persist with mathematics, they’d see the beauty I see. I wonder if there’s anything wrong with thinking that.

Some handy tips from the Desmos team

Christopher Danielson (@Trianglemancsd), with the help of Sean Sweeney (@SweenWSweens), put together a great post on the Des-blog about a few moves for teachers using the Graphing Calculator and Activity Builder.

The Estimation 180 Podcast is back!

Creator of estimation180.com, Andrew Stadel (@mr_stadel), is back with a brand new episode for the start of the school year kicking off the second season of the Estimation 180 Podcast. In this episode, Andrew talks about his favourite question to gauge student number sense. What I love about the podcast is that the episodes are only twenty minutes long, in which he’s able to succinctly give some extremely valuable insight into asking better questions. His latest episode also features the stars of the show, Annie and Patrick – the Math Minions.

Written by John Rowe, @MrJohnRowe

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Online Professional Development Sessions

Tonight!

Catalysing a Culture of Curiosity in Mathematics

Presented by John Rowe

Doing mathematics is an amazing way to truly harness the curiosity we naturally bring to things that capture our attention. We play with ideas to explore our intuition and attempt to reason the way the world works. We create models that tell stories of patterns and relationships between what we can see and what we cannot, between what we understand and what we do not.

Teachers can be a catalyst for creating a culture of curiosity in mathematics, serving as a model for working mathematically conducive to learning experiences where students are captivated by the beauty of mathematics.

This webinar will provide participants with examples of how we might foster a classroom culture where students ask more questions than their teacher and where learning is a process of reflection, sharing the insights made and resolutions reached.

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

Next Week

Building Visual Patterns Into Your Warmup Routine

Presented by Fawn Nguyen

Calling all teachers (grades 1 through 12+) who are new to visual patterns! I’d love to share with you how I use visual patterns as one of my warmup routines. I’ll share key questions to ask students, helpful structures to build algebraic reasoning, and ways to kick it up a few notches once your students are familiar with working with patterns. With faithful implementation, using visual patterns provides a powerful tool to build confidence and flexibility in writing equations.

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

Readings for Pleasure

One of the symptoms of beginning the school year is that I sometimes find myself with less time or energy to read or study mathematics purely for pleasure. It’s a shame, really, because one of the sources from which I draw strength and joy in teaching mathematics is the joy I feel when I do mathematics for its own sake either at home or in community with others.

Instead of sharing resources dealing directly with the classroom this week, I’ll shout out a few longer-form resources and recent articles about STEM, which can be read with students or read simply for fun. Maybe you will find some of these articles enticing or, at least, a respite from the demands and excitement of the new school year.

Quanta Magazine

If you haven’t already, spend some time seeing if you enjoy the articles in Quanta Magazine. The publication dives into current science and math research in an accessible way through what they describe as “public service journalism.” Just as many math educators strive to spread the message that everyone is a math person, Quanta approaches math and science journalism with a similar lens: that all readers are STEM people capable of accessing the forefronts of the field in meaningful ways.

Dr. Chanda Prescod-Weinstein (@IBJIYONGI) teaches us about Ann Nelson, a theoretical particle physicist who passed away last month and who fought against misogyny and racism in the scientific profession.

Kevin Hartnett (@KSHartnett), in A Mathematical Model Unlocks the Secrets of Vision, helps us understand how mathematics can be used to explain how our brains create images of the world despite receiving very little actual information from our visual system.

Erica Klarreich (@EricaKlarreich), in Decades-Old Computer Science Conjecture Solved in Two Pages, breaks down a proof about the structure of computer circuits using analogies and beautifully crafted diagrams.

Symmetry Magazine

Symmetry Magazine is about particle physics with links to outside resources but also many articles of its own. I only learned about the magazine recently through the article Channeling Shuri as a physicist at Wakandacon, which talks about Wakandacon, a 3-day Afro-Futuristic celebration that took place in Chicago last July.

AMS Blogs

The American Mathematical Society website hosts a diverse body of blogs about mathematics and the mathematics profession. I have recently enjoyed reading entries from inclusion/exclusion, a blog about underrepresented groups in mathematics. In particular, read Decolonize Academia #KūKiaʻiMauna, which takes up the Thirty Meter Telescope (TMT) project planned on Mauna Kea and which challenges readers to think about ones research as also impacting the world outside the explicit inquiry of the researcher.

The passion we feel for the math and science we teach is one way in which we continue to push ourselves as educators, but that passion must be nourished and sustained. Whatever you do to sustain your passion—whether it’s doing math on your own, with adults, or with your students—just make sure that passion drives you to love your students for who they are, regardless of whether they share your same love for the field.

Melvin Peralta
@melvinmperalta

Problems of Practice

As researchers, we spend a lot of time with experienced secondary math teachers thinking about, well, math teaching. In the context of a larger study, we’ve been looking at conversations with small groups of teachers where they reflect on their practice with the help of video and audio from one of their recent lessons. We’ve discovered that these conversations are full of rich problems of practice –– questions and concerns that these experienced teachers grapple with in their everyday work. Across the groups, it became clear that many teachers faced similar problems, despite teaching in different schools and having varied backgrounds. Here are some of the challenges they are facing in their classrooms (out of 33 conversations with 15 different experienced math  teachers):

This chart shows the top six most commonly surfaced problems of practice in the context of these conversations. Across these discussions, there were 1,331 instances where teachers or facilitators problematized the practice of teaching. Of these instances, teachers wondered about setting up effective group work 193 times, making this particular problem of practice the most frequently named. Clearly, facilitating group work is incredibly complex, dynamic, and challenging. The second most frequent issue involved preserving instruction to the intended lesson goals. The prevalence of this challenge indicates how hard it is to make decisions that preserve the intent of instruction in the realities of the classroom. Although it did not make the top five, we found it noteworthy that the question  ‘How do I manage the constraints and demands of being a teacher’, came in sixth place. This suggests that what teachers are able to do does not entirely depend on them: teaching goes far beyond the classroom and into navigating a complicated world.

The entire process of cataloging problems of practice, as well as the sheer number that we found, indicates that even the most experienced of teachers face a multitude of challenges over the course of their days in planning, implementation, and in-the-moment decision making.

As the new school year begins, what problems of practice are you facing? What are you discussing with colleagues as you head back to school?

Ilana Horn (@ilana_horn)
Jessica Moses
Patricia Buenrostro
Samantha Marshall (@sammieamarshall)
Vanderbilt University

* All teachers had at least 5 years experience and were a part of a professional development program.

Back to Work

It’s back to school time for educators in Ontario, Canada and this long weekend I am looking ahead and accepting what promises to be an adventurous school year. Teacher contracts expired yesterday, and provincial leaders continue to undermine public education; yet I know many educators who are preparing to return to classrooms and supporting roles not with trepidation but a renewed commitment to better serve students and their communities.

In her closing keynote for the Virtual Conference on Humanizing Mathematics (#VConHM) hosted by Sameer Shah (@SamJShah2) and myself, Dr. Rochelle Gutiérrez offers her insightful thoughts on rehumanizing mathematics and invites us to take stock of our praxis with the following reflexive questions:

  1. In mathematics, what feels dehumanizing to my students?
  2. In mathematics, what feels dehumanizing to me, other teachers, or families/communities?
  3. What might feel more rehumanizing?
  4. Who can help me rehumanize this space?

Let it be known this is not entry-level Equity 101 Work. This Work requires continual reading, processing, collaborating and most importantly dialogue with critical thought partners to push through cognitive dissonance.

Upcoming this week is a new chat #GhostsInTheSchoolyard led by @DingleTeach@MochaMomma, and @TeachNext_TMB to prepare #MTBoS for the Centennial Annual Exposition and Meeting of NCTM in Chicago in April of 2020. Please check out Marian’s latest blog post, Mathematical Ghosts.

By the time you read these words, Ontario educators will be almost halfway through the first day of the 2019-2020 scholastic year and in Dr. Gutiérrez’s words,

“I am hopeful about where we are as a field in being willing to acknowledge the violence that is regularly perpetuated (knowingly and unknowingly) against students, teachers, faculty, and members of society through mathematical practices, policies, and structures.” 

Wishing you a scholastic year of discomfort, unlearning, and relearning.

Hema
@HKhodai

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This Week at the Global Math Department

Note: This newsletter is a few weeks old and was sent to subscribers on August 13, 2019.

Edited By Nate Goza  @thegozaway
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PART 2: How Might Our Beliefs Impact Our Identity as Mathematics Educators?

Presented by Megan Holmstrom and Ryan Grady

As we engage in professional development with teachers mathematics teaching & learning, we have found that asking three questions is a crucial place to begin the work with any group. As you think about the teaching and learning teams you are a part of, consider these three questions:

  1. Who are we?
  2. Why are we doing this?
  3. Why are we doing this, this way?

Further, NCTM’s Guiding Principles for School Mathematics states that, “Professionalism [exists] in an excellent mathematics program, [when] educators hold themselves and their colleagues accountable for the mathematical success of every student and for their personal and collective professional growth toward effective teaching and learning of mathematics” (Principles to Actions p.5 – NCTM 2014). How are we holding our collective accountability in shared professional growth?

Please note: this is Part 2, consider reviewing our conversation from June 18 as front-loading for this chat.

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

Next Week

Observational Feedback that Sticks: Google and Extensions that Create Actionable Feedback

Presenters:  Brandi Simpson & Brooke Lucio

Based on the work of Chip and Dan Heath, authors of Teaching That Sticks, this session will demonstrate how observational feedback can “find the core” to develop a productive coaching relationship. We will share our protocols and system for providing feedback that integrates AutoCrat and the Google Suite. Participants will walk away with the skills to design and customize feedback tools to meet their needs at any level.

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

Welcome Back!

The Virtual Conference on Humanizing Mathematics

Last summer, Sameer Shah (@SamJShah2) hosted a Virtual Conference on Mathematical Flavors featuring blog posts from educators who shared their everyday practices that shaped students’ understanding of mathematics. This summer, he invited me to collaborate with him and I accepted the incredible opportunity to create a space for critical engagement and reflection on a theme that has been central to my learning this year; belonging. Our initial conversation revealed a mutual interest in the doing of mathematics as a human endeavor, mathematical identity, belonging in mathematics education spaces, and the rehumanizing of mathematics.

We offer to you for the month of August, the Virtual Conference on Humanizing Mathematics featuring keynote bloggers who are addressing the prompt(s):

How do you highlight that the doing of mathematics is a human endeavor?

How do you express your identity as a doer of mathematics to, and share your “why” for doing mathematics with, kids?

#MTBoS contributors from K-16 are also participating by responding to weekly mini-questions and sharing their mathematical experiences, mathematical identities, and reflecting on what scholarly terms (like ‘mathematics for human flourishing’ and ‘re-humanizing mathematics’) have to come mean in their practice.

Click on the image below to introduce our topic for Week 4 of the conference:

Readers of the first edition of this school year’s GMD Newsletter are the first to know that we are honored to host Dr. Rochelle Guttiérez as our closing keynote blogger on Thursday, August 29, 2019.

We whole-heartedly invite you to visit the virtual convention center and learn with us.

Written by Hema Khodai (@HKhodai)

Getting Specific About Equity and Humanizing Mathematics

I’d like to highlight what I see as a burgeoning trend in many parts of the math edutwittersphere. Roughly, this trend involves ideas like equity, humanizing mathematics, critical theory, and power and identity. This trend seems to be distinct from other topics in math ed like cognitive science and mindset research but still closely connected, and I’ve noticed at least three general types of activities surrounding this idea of equity, humanizing mathematics, and applying a critical lens:

  1. Spread, Reflect, Critique: Calling out others and ourselves to attend more fully to the work of unlearning, self-reflection, and critique.
  2. Research: Collecting, analyzing, and reporting qualitative data on moves and practices that support this work.
  3. Specification: Being specific about the ways we operationalize ideas about equity and humanizing mathematics.

Item 3 might be the toughest to do well but it’s also vital for us if we want to move forward as a math ed community. Thankfully, the Virtual Conference on Humanizing Mathematics represents one of several ways we as math educators are helping each other put our ideas about equity and humanizing mathematics into practice. The specific blog posts and Twitter threads can be found at the convention center, and instructions for submitting a contribution can be found here.

One Twitter thread caught my eye. It was by Jimmy Pai (@PaiMath), who went through every single contribution from week one and gave thoughtful, reflective comments on each one.

His feedback highlights the kind of conversations and exchange that can occur when we talk at all levels of grain size, from the critical-analogical-macroscopic reflections of Marian (@DingleTeach) and Hema’s (@HKhodai) keynote address to Chris’s (@cluzniak) share of #DebateMath and journals.

Besides the virtual conference, @JessicaTilli1 asked folx: “If you could conduct interviews for a middle school math teaching position, what are some questions you would ask?”. This triggered a host of responses, many in the realm of equity, humanizing math, and critical theory. I’ll end by highlighting just a few:

Written by Melvin Peralta (@melvinmperalta)

Great Prompts from Summer

I love when a good prompt catches fire on Twitter. The result is a mile long thread full of ideas, strategies, advice, etc that’s just loaded with goodness. Do these things have a name?  (I feel like they need a name!)  Below I’ve shared a few of these loaded threads.  Click on the image of the tweet to take you to the thread and get scrolling!

As we start the new year it’s always good to have some norms:

Math is beautiful.  Check out this collection of “mathematical mindfulls”:

If you’re new to the profession there’s an embarrassment of riches here. Going into my 15th year next week there’s plenty I need to hear too!

For everyone who finished their reading lists this summer (I’m joking, right?), Ibram X. Kendi’s book “How to Be an Antiracist” comes out today and inspired this:

When you find amazing threads like this #pushsend and chime in, and/or retweet so the rest of us don’t miss all the goodness!  Happy Back to School Everybody!

Written by Nate Goza (@thegozaway)

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