Online Professional Development Sessions

The #MTBoS Never Sleeps

The SMPs in Geometry

I agree with Mike! Graham Fletcher has taken his SMP lens to the realm of elementary geometry! Recently, Graham shared a post about Geometric Subitzing Cards. In the past he has also created great geometric and measurement 3-act tasks like The Big Pad, Packing Sugar, and Piles of Tiles. Now he’s done it again!

Graham developed a geometry task he’s calling Geo-Dotting. The TL:DR is it is an open-ended task that allows students to discover and explore the properties of shapes. Students get an image like the one below. They use it to create shapes by connecting the dots, and then they discuss the properties with classmates. Each image has different pathways and highlights Graham’s personal commitment to the integration of mathematical practices in his, and most importantly, children’s work.

Written by Andrew Gael (@bkdidact)

My Mind is on Special Education

This week I had the privilege of speaking with two special education teachers about their feelings of hopelessness and sadness with a system they feel is failing students with disabilities.  In their words, they are expected to hold their students to the same standards as their regular education counterparts and are discouraged from doing what they deem necessary to meet their students where they are.  For some time now it has been my belief that special education teachers should be allowed autonomy for meeting students’ needs and helping them progress towards the grade level standards.  Unfortunately, at least at my school, teachers feel pigeon-holed by grade level standards and revert to teaching from the textbook and teaching by telling.  Without the proper resources and mindset, it’s easy to give into assumptions about the learning capabilities of students with disabilities.

That’s what makes this presentation by Andrew Gael and friends so amazing.  It challenges you to consider both your assumptions and mindset about student learning.  Within this presentation various strategies are shared from real classrooms with real students. (I stress this because these aren’t hypothetical ideas.)  I can only imagine how engaged teachers were as they watched this presentation, as reading through the slides made me want to scream, “Students with disabilities can do math!”  

This post and this post by @Mathtechy explain how she has applied her learning from the book From Patterns to Algebra in her special education classroom.  These posts provide even more evidence about the effects of resources and mindset on student success.  From these posts it is safe to say her classroom does not reflect the “one inch deep, one inch wide” dilemma discussed in this post by @bkdidact.  It is also backed up by this article from TERC.

Those two special education teachers and I ended our conversation with this statement, “Be sad, but not hopeless.  Use the sadness to be the change you want to see.”  To engage in the discuss about supporting students with disabilities, noin #SwDMathChat every 2nd and 4th Thursday at 9pm.

Written by Jenise Sexton (@MrsJeniseSexton)

On Twitter, It’s Gift-Giving Season All Year

I’d say “Christmas came early for math teachers this week” but let’s face it, Twitter is a non-stop sharing palooza for teachers.

This isn’t about a blog post, but a GeoGebra book created by the stunningly prolific Tim Brzezinski (@dynamic_math). This book contains discovery-based learning activities, both his own creations and that of the ultimate GeoGebrainiacs: Jennifer Silverman (@jensilvermath) , Steve Phelps (@giohio), and Dr. Ted Coe (@drtedcoe).  It’s organized by CCSS. Just go. It’s amazing, and Tim promises there’s one on the way for functions.

I’d also like to share this post by Manan Shah (@shahlock), which is a continuation from my last post 3 weeks ago, about students developing and using their own formulas.  I love the idea of “breaking” formulas to scrutinize them. And I’d never heard of the butterfly method!

Written by Audrey McLaren (@a_mcsquared)

Online Professional Development Sessions

Highlights from last week: 

As everyone knows, students learn math at different rates. What should we do about it? I propose a two-prong strategy based on alliance with the strongest students, and support for the weakest. On the one hand, relatively easy-to-implement ways to insure constant forward motion and eternal review. On the other hand, a tool-based pedagogy that supports multiple representations, and increases both access and challenge.To listen to the recording, click here.

Great Blogging Action

The Magic Octagon

Have you seen the Magic Octagon?

No, I mean it. Have you seen the Magic Octagon?

Jennifer Wilson took an idea from Andrew Shauver who took an idea from Dan Meyer. I love how Jennifer uses quick poll with her students to tap into student intuition and keep track of their thinking. She gives students chances to make conjectures. She reflects on the questions she asked students and the questions she wished she had asked students. Lastly, her reflection is spot on with me:

“I used to say that my most important work happened before the lesson, collaborating with other teachers and deciding what questions to ask. I’ve decided otherwise, though. My most important work happens in the moment, not just asking, but also listening. And then, if needed, adjusting what I planned to ask next based on the responses of the students in my care. And so the journey will always continue…“

I agree with Jennifer and will add that the value of the “in the moment” is stronger as a result of her anticipation, collaboration, and listening. See Jennifer’s post.

~by Andrew Stadel (@mr_stadel)

Online Professional Development Sessions

Thanks to the #MTBoS

Thankful Teachers

It’s been a helluva November – wouldn’t you agree?

So it was lovely to read some good reminders of how much we have to be thankful for.  Here are a couple of my faves:

Under the category ‘Multiple Representations’, we can always count on Indexed to accurately depict the human condition:

Elizabeth Statmore, or our beloved Cheesemonkey reminded me of the very best thing about the #MTBoS, besides giving me the best professional development every day in so many different ways.

And Fawn Nguyen, the Queen of many things in the math education world (including teacher snark), delivered a brief but humbling note of thanks, reminding me to always check my privilege at the door.  Note in her post that she is writing a book!  While you are on Fawn’s blog, make sure you read her post Irrelevant from earlier this month as well.

Teaching Stuff

If you are looking for any ideas for cooperative learning in your classroom, Glenn Waddell has compiled a hyperlinked list of resources for you.  Thanks for letting us share in your graduate education, tuition free – no less, Glenn!  

A great idea from Pam Wilson – the Reverse Quiz!  Having students find errors in work promotes critical thinking skills and deepens understanding.  Pam suggests we let the students make mistakes and explain why they are wrong.  Brilliant!

Jonathan Claydon, writing at Infinite Sums, makes a strong case for slowing down your curriculum pacing to ensure your students have enough procedural fluency to actually solve problems with the Big Ideas you want to teach them.  As teachers, all of us are answerable to some end-of-year goal, whether it’s a Regents exam, a departmental final, or just making sure our students are adequately prepared for next year.  Jonathan (who has also shared some interesting assessment ideas in a previous post in answer to a tweet for help), challenges us to let that go just a bit in order to close some of our students’ the proficiency gaps.

Cheers – Wendy Menard  (@wmukluk)

Vlogging Action

If you’re reading this newsletter I’ll assume you’re aware of the MTBoS community. The blessing and curse of our amazing community is that as more people contribute and share, the harder it is to keep up with it all.

So when Christina Tondevold shared that she was changing her blog to a vlog I couldn’t help but think how much easier it would be for me to consume her goodness, as the “reader.”

Christina recently posted a vlog describing the ins and out of Subitizing and shared some games to support her work.

I’m excited to see what else the Recovering Traditionalist will share and wondering if there’s any other vloggers out there amongst us.

Written by Graham Fletcher (@gfletchy)

The Problems of Teachers

At this point in the year some teachers may be grappling with many kinds of problems. The blog world has examples of some teachers, thinking through some thought provoking problems.
      

Manan Shah (@shahlock) writes about a problem that was tweeted by Audrey McLaren (@a_mcsquared): “I get why we discourage kids using formulas, but what if they’re the ones who came up with the formula? #mtbos” In his response, What’s the Formula for Formulas?, Shah describes why we want students to understand the meaning of the formulas they use, and goes on to talk about how to push the thinking of students who create their own formulas.

Blogging is a good place to break down thoughts about problems teachers face with their students, as well as with their own lessons. Jon Orr (@MrOrr_geek) has an interesting series of Fav and Fix posts that describe “my favourite” from that week’s lessons, and “Something I hope to fix”. This week’s post describes how Would You Rather Math, along with a warm up from Mary Bourassa, sparked a great class discussion. His fix for this week is a work in progress as Jon highlights his thinking about a fledgling 3-act task.

Sometimes the problems teachers face aren’t tangible in a student interaction, or in a lesson as a whole. Sometimes the entire idea of teaching needs to be called into question. In What even IS good teaching?, Lisa Bejarano (@lisabej_manitou) takes a very broad approach at how to measure classroom success. A highly decorated teacher and PAEMST awardee, Lisa should feel sold on her effectiveness. Yet she writes “Most of my class periods end with me thinking about what a mess it was…” as this post goes on to raise questions about traditional measures of teacher distinction. “There is too much focus on what is observable in a class period…and not enough on the culture and connections that teachers develop with and among their students.” She goes on to describe some of the strategies that build the connections and culture that she needs in her class.

Problems facing teachers can arise because they are focused on larger goals that may not be noticed or awarded in their schools. Luckily deep thinking about the problems of teachers can be noticed and celebrated across the blogosphere.

Written by Carl Oliver (@carloliwitter)

Online Professional Development Sessions

The #MTBoS Never Sleeps

Don’t Wait for Problem Solving

Tracy Zager has a nice summary of a talk given by Megan Franke and the way that Tracy changed her classroom in response to Megan’s ideas. Megan is one of the authors of Young Children’s Mathematics, the newest book by the authors behind Cognitively Guided Instruction.

In the book, the CGI authors make the case that young children can develop their skills as counters and problem solvers simultaneously. Many teachers only give students opportunities to solve problems once they have become fluent with the underlying skills, but Megan and her co-authors argue that children become more fluent and agile with counting facts (and later math facts) when they are practiced in the context of problems, not solely in isolation.

Tracy realized that she had been doing lots of work with counting collections, but she hadn’t used these counting activities as a springboard for problem-solving. So she recounts how she and her colleague Debbie Nichols turned a traditional counting activity into a multi-part lesson where students were counting, solving problems, and even posing and sharing problems that they invented. Tracy’s report includes a couple of examples of students stumbling upon new mathematical ideas through their problem-solving experiences. I won’t give them away – you’ll have to click through!

Although this post has a focus in early elementary, I think the lesson is one that can be extended into all levels of math teaching. It’s important to remember to give kids problem-solving opportunities as they build fluency with counting, addition, multiplication, factoring, and so on. We shouldn’t wait or expect total mastery before giving kids a chance to think through an interesting problem with their new tools.

Written by Kent Haines (@KentHaines)

One Good Thing…And Another…And Another

As Thanksgiving approaches I cannot help but to put thoughts of math on the back burner and bring thoughts of thankfulness to the front. This school year I was introduced to the hashtag and blog #onegoodthing by @crstn85. I can think of no better time to highlight tons of good things happening within math classrooms around the world than now.

These tweets are the type to lift your spirit when you’re feeling low. It’s a reminder than even when things appear bleak, you can find one good thing. Like this tweet celebrating student work and their admiration of one another’s work.  Or the celebration of student strategies in an era where many are still struggling to get used to Common Core. I’m sure every math teacher would love to have these stories – story 1, story 2, story 3, and story 4.

Moments like these are elaborated within the blog.  Posts like Basic Trust and Allowing about a student finally finding the potential already within him. Or Handout Passer Outer, which reminded Rebecka and the readers to listen to the stories of perseverance our students possess. Or even Listening, which shares the pain of a student and the teacher’s love for him. Read them and see if they don’t prompt you to share one good thing from your classroom.  

After this Thanksgiving break, come back in search of the one good thing from each day and continue the thankfulness agenda.

Written by Jenise Sexton (@MrsJeniseSexton)

Math and Memory

On a recent test, one of my students used a formula to answer a question. Normally I would have insisted he show his work, but I happened to know that he had derived and verified the formula himself. Since he had done the important work prior to the test, I decided to give full marks, even though during the test he was technically just remembering the formula. This made me tweet to the #mtbos: “I get why we discourage kids using formulas, but what if they’re the ones who came up with the formula?” As usual, the Twitter conversation was fascinating and enlightening. Manon Shah (@shahlock) proposed the conversation continue on blogs, and for a starter, he offered up his comic. I have to admit I haven’t even started my own blog post about this, but I found this one by John Mason about how memorizing formulas can be used to forge deeper understanding. It also includes a fabulous idea about posters.

Not really formula related, but another idea that I loved was Pam Wilson’s (@pamjwilson) reverse quiz, in which students choose the wrong answer and back up why it’s wrong – kind of a combo of Math Mistakes and Plickers!

Since I’ve been doing a lot of presenting on Desmos Activities lately, I’m ever on the lookout for posts about best practices. This one by David Cox (@dcox21) speaks directly to what I struggle with in my own practice – how to really get the most math out of a fantastic activity like marbleslides.

Written by Audrey McLaren (@a_mcsquared)

Online Professional Development Sessions

Highlights from last week: Children Living in Poverty Can Solve CCSS OA Word Problems

Kindergarten, grade 1, and grade 2 children from backgrounds of poverty and non-native speakers of English can solve the ambitious types of addition and subtraction word problems in the Operations & Algebraic Thinking domain of the Common Core standards. How children represent and solve with math drawings was discussed and examples were shown. The learning path for teaching and helpful relationships among the OA CCSS were described. If you missed it, check out the recording here.

Great Blogging Action: Election 2016

Election Reflections

Unless you’ve been living under rock, which is completely possible and no judgments here, then you know that the United States has a new President-“elect”. This event has had a ripple effect among citizens of the United States the like of which has not been felt in recent memory. It has also equally affected American children as much as it has the adults who actually voted in the election. Many teachers woke up on Wednesday, November 9th wondering what to say to a room full of young, impressionable minds. Luckily, the Huffington Post gave this message as a jumping off point that morning, “We will protect you.”

In the days since the election, math and non-math teacher/bloggers have taken to the internet to tell how they handled November 9th and the days that followed. Chris Lehmann, a principal in Philadelphia, wrote a letter to educators who voted for Donald Trump. Lehmann asks these teachers to live up to the words in the Huffington Post piece and to protect their students. Michael Pershan gives this plea to listen to our students. Bree Pickford-Murray tells the tale of her week after the election, for which she has no words. And finally, Megan Schmidt gives us her take, which ends in one vote for kindness, but it’s the only vote that counts, her’s. Please if possible, share how you handled the days after the election in your class and how you will protect your students for the next four years and provide them with a venue and the skills to voice their fears and concerns!

~by Andrew Gael (@bkdidact)

Ten Letters for the President

I’ve mentioned my favorite podcast before. Recently 99% Invisible released Episode 235, Ten Letters for the President. It’s definitely worth listening to in light of recent events in U.S. politics.

Photo: Pete Souza

The podcast does a thorough job explaining the process of President Obama receiving tens of thousands of letters a day from people across the country. In reality, he only reads 10 letters each day which turns out to be less than 0.1% of the letters received. Those 10 letters are a small sample of the pulse, emotions, heartaches, and thoughts of thousands across the country. The president says, “These letters, I think, do more to keep me in touch with what’s going on around the country than just about anything else.”

I share this podcast episode for three reasons:

1. It’s a reminder of the impact our current events can have on all of us; teachers, students, family, strangers, friends, enemies, cities, states, countries, and all humans. No matter how large the impact, I believe we as individuals can have a far greater impact with how we treat those we have contact with each day. Our students need to see us be good humans. We are in their daily world. Be good humans.

2. These letters to the president are super important. If less than 0.1% of the daily letters received can positively inform and impact the president, then these letters could very well be more valuable than any tweet, blog post, or Facebook comment one might dispense into their social media bubble.

3. I hope these letters continue to pour into the president, especially after January 20, 2017. I hope 10 letters continue to be read by the president each day. I hope those letters keep the president in touch with what’s going on. I hope that if something is on your heart, you write the president. I hope that if something is on your students’ hearts, they write the president. Be good humans when doing so. That 0.1% might be the most important percentage we ever teach in math.

~by Andrew Stadel (@mr_stadel)

Online Professional Development Sessions

It Came From the #MTBoS

Thinking Deeply about Depth of Knowledge

Robert Kaplinsky has been doing great work on depth of knowledge for years now. In short, depth of knowledge is a way of classifying math problems based on the level of thought required to solve them. This post from 2014, in which he shares some wonderful videos of students solving problems at various depths of knowledge, is an excellent summary of the big idea.

Robert isn’t resting on his laurels, though. Instead, he is still thinking deeply about DoK and refining his own understanding of how to evaluate math problems using this framework. In his most recent post, Robert talks about shallowness of knowledge. In other words, what is the least amount of thinking that a student can do to get the right answer? Students tend to initially engage with math problems on a superficial level no matter their depth of knowledge, so it’s important to find problems that can’t be solved on a first pass.

If you’ve ever sat through a PD session on depth of knowledge and had trouble wrapping your head around what it looks like in a classroom, give Robert’s blog a read.

Written by Kent Haines (@KentHaines)

More on Problem Solving

@KentHaines and I are thinking along the same wavelength, problem solving. My focus is the lack thereof. In recent conversations, I have begun to notice more and more, the problem with Common Core is teachers’ lack of understanding of the standards’ rationale and of the standards themselves. My point is proven in @JSchwartz10a most recent post. If teachers understood just because a worksheet is stamped with a standard, it does not mean it actually matches the standard.  

Joe referenced another post which speaks to another gross misconception of many teachers. The Common Core works to create multiple entry ways of understanding concepts. Teachers who lack understanding of the rationale turn concept strategies into cumbersome procedures or tricks which undermine the original intent.

Written by Jenise Sexton (@MrsJeniseSexton)

Desmos Does It Again!

I had just come home from giving my second ever teacher-training session on Desmos activity builder when I saw on Twitter that my session was already outdated. We can now add videos to our activities AND multiple choice questions! I loved this article explaining the rationale.  

Doing that teacher-training made me realize it’s been a while since I read any blog posts about the Desmos activity builder, so I went searching for recent ones and found Cathy Yenca’s post about combining Desmos with Nearpod (@mathycathy) and Jennifer Vadnais’s post about ordering fractions (@RilesBlue). Both of these posts talk about using the new teacher tools – another new feature, but I did manage to put that into my presentation – just in the nick of time!

Written by Audrey McLaren (@a_mcsquared)

Online Professional Development Sessions

Highlights from last week: 6 Hand Signals that Bring Learning to Life! The research-based practice of making thinking visible with non-verbal signals elevates the level of student participation in elementary classrooms. How can signals be used to even greater purpose in the math classroom to build problem-solving stamina, develop students’ ability to describe patterns and make conjectures, and aid teachers in assessing student learning? We considered the impact of several powerful signals in the present-day elementary math classroom. Missed it? Get the recording here.

Great Blogging Action

Visualizing Standard Deviation

Imagine getting into the driver’s seat of any modern day vehicle. Chances are really good, you can adjust the seat’s height, backrest, and its distance from the pedals. Now imagine getting into a vehicle manufactured back in the 1960s or before. Chances are slim those same adjustable features don’t exist. I ask you to picture this scenario because we live in two worlds: a world designed for adjustability (modern day car) and a world designed on averages (vehicles before 1960s).

Sam Shah’s wonderful post about Visualizing Standard Deviation took me to a few familiar places:

• Sam is focused on using visuals to give students a solid conceptual understanding of Standard Deviation and students often deserve visual representations to build conceptual understanding

• Sam’s post reminded me how many things in our world are still (unfortunately) designed around averages (one of them being education)

• Sam’s post reminded me of Todd Rose’s great TED talk “The Myth of Average” where Todd explains the reasoning behind adjustable seats and how this might translate to education.

Check out Sam’s post and Todd’s TED talk. Both are winners!

~by Andrew Stadel (@mr_stadel)

Teachers as Content Creators

In an ignite talk at the 2016 NCTM annual Meeting and Exposition, Max Ray-Riek warned of the risks of getting all your lessons from blogs (coherence, alignment, and consistency). But he also highlights why reading about and getting lessons from blogs feels like a successful endeavor for teachers across the country. You get a first hand account of the teacher who not only created the lesson, but how they used it in their classroom.

So, in order to heed Max’s sage advice, I will not encourage everyone to throw away their current expensive curriculum mandated by their district. Instead I will just list some teacher creators who are sharing lessons they’ve created and some first hand accounts of how they used them in their classrooms.
 

Carl Oliver and Kristin Gray recently made Desmos activities through teacher.desmos.com. Carl teaches high school and Kristin’s lesson is for kindergarteners. That’s pretty cool, in my opinion! The best part is, both of them asked and received feedback on their lessons from other teachers through twitter.

Graham Fletcher just posted how 3-act tasks are used in the elementary grades. If you’re interested in trying one out here are some from Graham, Kendra Lomax, and me.

Simon Gregg recently wrote about how he uses Cuisenaire Rods. These fantastic manipulatives can be used for a variety of mathematical content as well as a sense-making tool.

Also if you haven’t heard about Open Up Resources, then you don’t follow me on twitter! Many teachers from the #MTBoS have been recruited by Illustrative Mathematics to develop an open education resource curriculum for the middle grades!

Finally, let us know how you are creating or using teacher-created content! See you on the interwebs!
~by Andrew Gael (@bkdidact)

Online Professional Development Sessions

Highlights from last week: Teaching Ideas to Prepare Your Students for the AP Stats Exam
Presented by Amy Hogan (@alittlestats), Doug Tyson (@tyson_doug), and Bob Lochel (@bobloch)

 AP Readers Amy Hogan, Bob Lochel and Doug Tyson reviewed three of the questions from the free response portion of the AP Statistics exam from 2016. Ideas related to avoiding common errors and practical teaching tips were shared. Listen to the recording here.

Great Blogging Action

Showing Math some Love

There was an interesting blog post from the other side of the Atlantic from me that caught my attention. Last week there was an article by an anonymous teacher about a number of issues facing the UK’s math curriculum. This was a Secret Teacher article from the UK newspaper The Guardian that invites teachers to “[lift] the lid on teaching… [and write] about the trials, tribulations and frustrations”. Blogger Miss Blilly wanted to respond to the negative tone of this article by highlighting the positive and encouraging other teachers to do the same using the hashtags #loveteaching & #NotSoSecretTeacher. Scottish blogger Julie Moran followed that with a #loveteaching post of her own and mentions other #MTBoS initiatives that spread positivity including the One Good Thing blogand the hashtag #mathsrockedtoday. If you’re interested in spreading positivity and connecting with with teachers in the UK you should check out either of those articles.

If you’re interested in branching out to other bloggers, you may want to check out the blog post from this newsletter’s own Wendy Menard! In this post Wendy discusses her own blogging history, as well as the blogs of a number of her friends, colleagues, and people who have inspired her. If you want to learn more about how one teacher fills up her feed reader, head over to Wendy’s blog and check out the post Enrich and Enhance Your Professionalism through Blogging.

Written by Carl Oliver (@carloliwitter)

Great Blogging Action Spotlight: Simon Gregg

It’s always great to watch fellow teachers explore and work with the primary grades. In particular, it’s interesting to see how teachers of the intermediate grades interact and learn with younger students whenever they get the chance.  
 
This year our friend Simon Gregg has taken the leap from teaching 10 year olds to teaching 5 year olds.  What’s awesome in watching his journey is that Simon’s brought his Cuisenaire Rods with him and the exploration that’s taking place shouldn’t go unrecognized. I’m just thankful he’s continued to share his experience.
 
Sure it’s early in the year but Simon will keep on sharing and we’ll all be better because of it.  
 
Written by @gfletchy (Graham Fletcher)