Wednesday, December 28, 2016

2016 Recap

I stumbled upon my biggest revelation in 2016. It's a question that always challenged me as a classroom teacher, but I often suppressed because too many other teaching responsibilities took priority. I've come to realize that was a foolish excuse. This question will be forever present throughout the rest of my career in education:
How do we balance the things we're supposed to teach and the things students need to learn?

I'm okay knowing there will never be an exhaustive and absolute answer to this question. I think it's more valuable we continue to work toward what we think might be an answer. Working toward the answer keeps us hungry, honest, and humble. If we pretend to know the answer to this question, then we have given ourselves the false illusion that our work as educators is complete. Having worked with hundreds of educators this year in workshops and presenting to thousands of teachers at conferences, I know I'm not the only one with this burning question. I see (and feel) their heads nod when I raise this question/concern.

I don't pretend to have an answer. I encourage us all to work toward that balance. For example, as a middle school teacher, I was supposed to teach proportional relationships, but my students needed to learn number sense strategies like skip counting, multiplication, decomposing numbers, and more. I don't blame the students, their former teachers, and parents for poor number sense. It's what it is!

I could whine about it to you, my colleagues, my principal, or my family, but that doesn't change anything. If I want my students to have better number sense AND be more successful with proportional relationships, that's on me to create, nurture, and refine systems that get them further along on their learning journey. Instead of whining or assigning blame, I can do my best to include my colleagues, parents of students, and administration to play active roles in that system, ergo one goal for 2017 is to learn more about successful systems and their design principles.

What are your thoughts? Does that question plague you too?

Professionally, I'm proud and honored to have:
  • Worked with amazing math teachers in TUSD who do their best, work hard, take risks and reflect on their practice.
  • Given my Classroom Clock Ignite talk at NCTM Annual because I believe in using time constraints to maximize the effectiveness of what we do as teachers.
  • Co-presented with Kristen Bennett (OCMC), JR Ginex-Orinion (CUE), Lynda Chung (CMC South), and Chris Shore (GMD) and learned a great deal from all of them
  • Worked with teachers in these states.
  • Received appreciative emails and tweets from teachers
I continue to work on:
  • Family time > math conferences
  • Looking up at people and the world > looking down at a device
  • To-do list > email list
  • Listening to > listening for (thanks Max) 
  • Listening to > speaking
  • Learning what's important to others > what I might think is best
I loved seeing my children:
  • play together
  • laugh together
  • argue
  • problem-solve
  • tickle me
  • talk about numbers
  • describe the world around them
  • enjoy being kids

I'm grateful for:
  • vacation and family time
  • those who have challenged my thinking
  • those who inspired me to do the best work I can do that supported student learning and effective teaching
  • teachers willing to share their successes and challenges in hopes of supporting their colleagues
Whatever 2016 brought you and whatever 2017 will bring you, I challenge you and myself to:
Be hungry. Be more honest. Be more humble.


Friday, December 9, 2016


Chris Shore and I drove from Southern California to Asilomar and back last weekend so we could attend and present at CMC North. On the way back, Chris introduced me to the idea of systems and how valuable they are to the success and longevity of a program, team, organization, etc. I realized I have so much to learn about systems.

In my current role as a Digital Learning Coach, I could ask,
"What systems have I put in place with fellows (teachers I support) so they can continue the work and mindset we started together?"

If I was in the classroom, I would ask,
"If I had to be away from the classroom for a day or more, what systems have I put in place so my students can successfully function without me?"

This last question can be truly sobering. I realize my systems as a classroom teacher could have been far better. Here are a couple reasons:
1) The systems that I did have in place, relied heavily on me being present. For example, when greeting students at the door, there was no guarantee the sub would greet them. Student thinking was valued, but this didn't always happen in my absence.
2) Did I establish and regularly execute systems so my students knew how to be successful each day they walked into class? Even when I was present, did I establish a system so my students knew how to share the most positive part of themselves with their classmates?

I could sit here and kick myself on many things. I could find at least 100 things I could have done better as a classroom teacher. Moving forward:
How do I build systems with my fellows so they are successful after our time working together?
How do I build systems with teachers in professional development workshops so they leave the workshop prepared to strengthen their own systems and instruction?
I'm thinking about reading Systems Thinking for Social Change over Winter Break. Has anyone read this book? If so, what do you think? Or do you have other suggestions?


Monday, November 14, 2016

Ten Letters for the President [99pi and GMD]

This is what I'm sharing in this week's Global Math Department newsletter:

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.

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.

Tuesday, September 13, 2016

"How much?" vs. "How many?"

Can you believe it? I haven't blogged since April... and it's been amazing!
You heard me right. I've been busy enjoying life and summer. On the scale of life, family time has definitely outweighed work time. This doesn't mean I haven't been thinking math. I have enjoyed lurking on Twitter and reading blog posts here and there. Keep up the great work everyone.

So, I'm dusting off the blog and wiping away the cobwebs so I can share just one gift of parenting a six year-old, learning the English language. Well, at least one part of the English language: when to use "how many?" and when to use "how much?"

I provide my son with a healthy amount of questions that involve estimation. I know, big shocker. So it shouldn't surprise you (or me for that matter) when he fires them back at me. However, it's extremely interesting that most of the time he begins his questions with "how much".

Here are some examples. Hey Dad, I wonder
  • How much air is in the tire?
  • How much pumps of air the tire will need?
  • How much miles it is to the beach?
  • How much pancakes will we make?
Can you spot which questions need help?
What advice would you offer a six-year old (and his dad) so he is better equipped to know when to either use "much" or "many"?

Here's what I offered him:
If it something you can count, use "how many"
  • How many pancakes will we make? 10
  • How many eggs are in a dozen? 12
  • How many pumps did it take to fill the tire? 6
  • How many minutes until we leave for soccer practice? 5
If it is something that is difficult to count, use "how much"
  • How much air is in the tire? not much
  • How much sunblock did you put on? only on my face
  • How much ketchup would you like? a lot
I'm more fond of my criteria for using "how many", but I'm not entirely convinced my criteria for "how much" will win me English/Math teacher of the year. I know there is a way to quantify the air inside a tire. There is a way to quantify the amount of sunblock applied. Help me make the criteria better and easily comprehensible for a six-year old.

Hope the school year is going well!


Tuesday, April 26, 2016

Principles to Actions Book Club [phases]

Inspired by Kaneka Turner's #ShadowCon16 talk, I decided to form a Principles to Actions book club during the summer of 2016. Sorry, the club will be comprised of teachers in my district. I'm excited at how it is shaping up in the past week. I broke it into three planning phases before we actually start reading NCTM's Principles to Actions. I recommend you start your own. Here's why:

Phase 1:
I created a goal for the book club (inspired straight from Principles to Actions):
Collaborate with other TUSD teachers to strengthen our math teaching practice and improve the learning of mathematics by engaging students in mathematical thinking, reasoning, and sense making.
I reached out to a small group of (K-12) math teachers and coaches in my district to generate interest.
10 teachers replied with interest. We're ready for Phase 2.

Phase 2:
I will tap into the wisdom of these 10 teachers to help structure:
  • HOW we will accomplish our goal.
  • WHAT tools we will use to accomplish our goal.
I'm confident these 10 teachers will help structure how we discuss the book, how much time we spend as a book club, how we will collaborate (virtually or in person), etc. I also know these teachers will help suggest what tools we might use to help assist in the virtual collaboration. For example, Google Docs, Google Classroom, Padlet, etc. 

I asked them for input via Google Forms. Here are the questions I asked.

Once I hear back from this small group, I will move forward in structuring the PtA book club along with setting up the digital tools and spaces that make the most sense. Phase 3 is next...

Phase 3:
I plan to do a district-wide invite to the Principles to Actions book club so anyone who teaches math is invited. More importantly, I am counting on the small group of 10 teachers to reach out to other colleagues at their site and throughout the district to personally invite teachers to the Principles to Actions book club. I'm confident their reach and influence will make the collaboration more meaningful and fun for all invloved.

I've never done something like this before, but I'm excited because I am confident in the 10 teachers who have already expressed interest. I encourage you to find something mathy you can invite others to be a part in. Maybe it's a Principles to Actions book club. 

Please let me know if you have any questions or tips!


Friday, April 22, 2016

Open Middle and Google Docs

A few weeks ago Kassie, a teacher I support, came up with a great idea. The idea was inspired by one of our other Digital Learning Coaches, Michelle, who introduced Kassie to hyperdocs.

Idea: Incorporate Open Middle problems with Google Docs.

Here's how it went...
Kassie had her students work in eight groups. This happens often in her class. She pushed out one Google Doc to the entire class so every student has editing rights. However, you just need one group member to make edits for their group.

Each group was working on the following open middle tasks:
Use the integers from 0 through 9 only once to create an equation with:
Day 1: One solution
Day 2: No solution
Day 3: Infinite solutions

First, students work on their desks with whiteboard markers, discussing with their group members. Isn't that lovely!
Second, students enter their equation into their respective cell inside the Google Doc table.

Third, each group needs to test the equations that other groups submitted. Keep in mind, that each group could not submit an equation identical to another group. Once they worked on other equations, they entered if they agreed or disagreed with other groups.

I experienced Day 1 and it was awesome to see the collaboration and community of learning throughout the room. When debriefing with Kassie about Day 3, she told me students realized an equation with infinite solutions couldn't be done if they use the numbers 0 through 9 only once. That's awesome! Good work kiddos! She ended up allowing them to use a number more than once. I'm wondering how it might change if we allowed them to use the numbers 1-10 (only once).

Since our middle school students work on iPads, a large Google Doc table like the one above might not let the math breathe on a smaller screen. I adapted her Google Doc to look more like this as a template:
  • I split the eight groups into two tables on two separate pages.
  • Each group still enters their answer into their respective highlighter-yellow cell.
  • Each group has a vertical column so they work downward when entering agree/disagree

I inserted this Open Middle question as a placeholder above the table inside the template.

Make your own copy of the template by clicking here

This is definitely a way for students to create their own answers which turn into questions their classmates can use to practice procedures and challenge their understanding of specific math concepts. It is student focused. It's a great way for students to generate questions that both the teacher and students can use. It makes math a social experience through the use of technology. All of the student answers are housed in one location.

Open Middle,

We have Google Classroom in our district which makes it 200 (student) times easier to push things like this out to students. If you don't have Google Classroom, there are other ways to get this out to your students' devices. If you need ideas, hit me up in the comments or on Twitter.

Monday, April 18, 2016

2016 #NCTMannual reflection: Purpose

There is a lot to process from NCTM 2016. Being a contributor for the Global Math Department this week, I decided to feature snippets on the blog here in order to kill two birds with one stone.

I found it useful to connect all the NCTM goodness with a theme: PURPOSE.

• Marilyn Burns (@mburnsmath)
Be purposeful about what we want our students to do. I loved this slide, connecting reading and math:

• Christopher Danielson (@Trianglemancsd):
Be purposeful with knowing the ability of students. Christopher said,
"Students can. We should let them."
This idea lends itself to students discovering properties in math. Often, when things get discovered in math, they are named after the discoverer. Why don't we do this more with students?"
Goods here.

• Elham Kazemi (@ekazemi):
Be purposeful with a school/department/grade having a shared vision of quality math instruction. Create a structure at your school to learn together. We went on to explore numberless word problems where the purpose is to help students make better sense of the context before applying the numbers. She shared this post by Brian Bushart.

• Carl Oliver (@carloliwitter):
Be purposeful with the space you provide students to explore mathematical ideas. Be purposeful with selecting the task.
Goods here.

• IGNITE talks:
Max Ray (@maxmathforum):
Be purposeful with the resources, tasks, activities, and ideas you pull from the internet. Be purposeful with the coherency in your teaching. Do the resources, tasks, activities, and ideas you pull from the internet add to the coherency of the mathematics you teach?

Jennifer Wilson (@jwilson828):
Be purposeful with the time you allow students to solve math. It's not like fast food, it's like slow food. Enjoy the math students can do when we make it a purpose to do #slowmath.

• ShadowCon16
Kaneka Turner (@KanekaTurner)
Be purposeful in making math a social experience by inviting others into this awesome experience. Kaneka shared the importance of being invited. Call to action: invite at least one person to be part of the math experience.

Robert Kaplinsky (@robertkaplinsky):
The purpose of empowering others through influence can have huge positive results. Robert shared a couple of personal parts on his life and how influential people throughout his life have helped shape who he is today. Call to action: your your power to influence and empower others.

Graham Fletcher (@gfletchy):
Be purposeful in knowing what/how you teach by understanding the standards. Be a better story-teller in your classroom by accurately knowing the standards. Call to action: find out more about a standard you teach.

• Brian Shay (@MrBrianShay):
Be purposeful with polynomials and probability. Brian had us working on using spinners and coins to add meaning to multiplying polynomials.
Goods here.

• Peg Smith:
Be purposeful in framing the task so it "invites everyone in." Furthermore, ask purposeful questions when working with students during problem-solving tasks. Lastly, it's critical for the teacher to explain the goals because it's hard to have a conversation if it's unclear what you're trying to accomplish.
***Let's invite Peg to the #MTBoS and Twitter.

• Andrew Stadel (@mr_stadel):
Be purposeful in the feedback we give students after they make mistakes. Thanks to Robert Berry and Dylan Wiliam, I shared with teachers the importance of providing feedback that benefits students and at the same time challenging them to take traditional feedback and rework it so it's better at moving the learning forward.

• Christina Tondevold (@BuildMathMinds):
Be purposeful in working toward the terminology in the standards, specifically "fluently" and "using strategies" in the K-5 standards. We looked at examples of subitizing, cardinality, and strategies like making ten, double-plus-one, finding fives. We need to be purposeful in students making sense of math for themselves.

• Jason Zimba
Be purposeful in decluttering what we teach, what we ask of students, and what we give to students. Something he got me thinking about: do we Math 8 teachers need to teach the "elimination" process when solving linear systems. Does the procedure support the conceptual understanding? and can we allow high school teachers to teach it while Math 8 teachers focus on graphing and substitution?

I hope to see you at NCTM 2017 in San Antonio.
Send in a speaker proposal here by May 1, 2016.

San Fransisco,

Sunday, March 20, 2016

CUE 2016 Takeaways

This past weekend was CUE 2016 and I only attended one day of the three conference days. Even though it was just one day, I was able to leave with some great takeaways.

Session 1:
Making the Hard Parts Easy: Teaching in 2016 and Beyond
by Matt Vaudrey
Great session. Matt is always a treat to watch in a presentation, and he continues to deliver solid, engaging, practical, and useful sessions. He had us up talking with each other, moving around the room, learning from others in the session. He modeled music cues by giving us a 60 seconds to discuss focused questions with a partner (different every time). The music stopped and we knew to stop our conversation so that Matt could allow two teachers the opportunity to share out their conversation.

The session was focused. I love when a presenter tells the attendees in the beginning what we will be doing and sticks to it. We focused on:
  • Focus on what matters
  • Mess with Curriculum
  • Give students authority 
My biggest takeaways:
  • Look into Kaizena to offer students voice feedback inside Google docs. 
  • Assign less work to students... just one way to make grading easier.
  • Quicken transitions in class with music cues by Matt Vaudrey (found here).
  • Matt's slides can be found here.
Session 2:
Another great session. Both JR and Gerardo encouraged the attendees to focus on the "why" when preparing professional development for your site (teachers and admin). Essentially, define the purpose of your session because time is valuable for everyone. I also loved how they had us take a PD title we recently used and rewrite it so it includes the "why" (purpose). Great idea!

My biggest takeaways:
  • Use empathy with teachers and administrators
  • Value everyone's time!
  • Start with the "why".
  • Their goods can be found here.
Session 3:
It was an extreme pleasure to prepare and present with JR. I love his enthusiasm and excitement for science, good PD, and Desmos. The focus of our session was simple: play, tips, and build. We allowed attendees to play two Desmos activities (one from JR and one from Cathy Yenca). We showcased the teacher dashboard for each activity and then we shared our activities so the attendees could see how the activities were built in order to explore the building part of desmos activities. We reassured the attendees that they don't need to necessarily build their own activities, because they could find one in the Desmos library or the Desmos Bank and adapt it for their needs. Thanks to all the teachers who came to our session. We hope it was helpful and you will let us know how is transforming your classroom.
Thanks JR. It was a blast to collaborate. I learned a lot.

Session 4:
I came in late to this session, but it didn't matter. It was easy to know where they were in their presentation.  Within minutes, we were working on the floor categorizing these cards with different colored shapes as a segue to the importance of the Periodic Table. It was a splendid activity. Both Dan and JR shared their experiences in their science classes. A big part of their class was using media to create mystery so students are asking questions. Similar to a 3 Act task. It was a wonderful way to end the conference.

My biggest takeaways:
  • Create mystery with students. Use stories to explain the mystery
  • Our brains, chemically, enjoy stories. Use them more often in class.
  • Their goods can be found here.
Thank you to all the presenters who worked so hard to prepare great sessions. By reflecting on the highlights, it will allow me to incorporate many of the techniques, resources, and ideas with the teachers I support and the professional development I offer.


I loved this on display at the Hard Rock Hotel. Sorry, I didn't grab the artist behind this gem. Look close, those are vinyl records. So cool!

Monday, March 14, 2016

Classroom Clock Questions

I'm curious about the precious classroom time we [math] teachers have with students.
Enlighten me.

Please take 1 minute to fill out this form as I prepare for an upcoming Ignite talk at NCTM.


Monday, February 29, 2016

Square Dance

I recently debriefed with a fellow (teacher I support) about two activities focusing on Squares, Square Roots, and Irrational numbers. Let's build number sense. Here are the goods:
She ran both activities with students, starting with the Clothesline activity. She used the cards linked above for students to first place the visual representations on the number line. It looked something like this:
Followed by:

Students then completed the first 7 screens in the Desmos Square Dance activity. Screen 6 includes a validator when done correctly, compliments of Nathan Kraft.

*Please note that part 1 of the activity uses only whole numbers as rational numbers. I highly recommend using the activity as a launching point for students to know that perfect squares include other rational numbers like fractions and decimals. 

Back to Clothesline:
This week she will use the next set of cards for irrational numbers. It might look something like this on the number line:
Followed by:

Back to Square Dance 
Students can build better conceptual understanding of irrational numbers in the desmos activity. Also look for teachable moments throughout the activity. 
*Please note screens 11 & 15 include non-repeating and non-terminating decimal notations. 
Screen 11

Screen 15
Just like Screen 6, Kraft-y validators are included on screens 12 & 16.

Two closing thoughts:
1) My fellow was so happy to use these conceptual representations with clothesline and desmos. 
2) She hasn't seen students making mistakes like she has in the past. Here's an example (crossed out) of a common mistake she has seen regularly in the past.

If you have time, head over to this post and have your students play War with the Rational-Irrational cards provided.


Tuesday, February 16, 2016

Clothesline Cards Hit the Floor

A colleague and I stumbled upon an opportunity to strengthen number sense with students using a double clothesline. The video says it all:

 *For more fun with clothesline math, go to Chris Shore's designated site:


Monday, February 15, 2016

My Tech Tools [Kahoot!]

Here is a tool that does not meet my criteria:
• Capture
Anyone can log in. There's no Google login like Pear Deck, Desmos, or Google Forms. The teacher must rely on students honorably entering their name. There are four design features that could possibly hinder the accuracy at which a teacher is able to capture student thinking:
  • multiple choice
  • timed questions
  • points driven
  • selecting answers in the form of different colored shapes
Multiple choice
Multiple choice will never 100% accurately capture what a student is thinking because the student could get it correct by guessing or for the wrong reason. This can be referred to as false-positives.
Timed questions
By default, questions are timed in order to fall in line with the gaming feel of Kahoot! Therefore, students with the best recall will typically score higher. This option can be turned off. You have 15 seconds. HURRY!!!!!!
Points driven
Kahoot! could be considered a gamified tool that checks for understanding. One component of games could be points. Kahoot! rewards students who answer accurately and more quickly than their peers with more points. There's a leaderboard.
• Different colored backgrounds and shapes as answers
This feature requires additional decoding by a student who might also struggle with the math being questioned. Not being a quick processor, I have struggled with this feature a handful of times. I think the use of different colors is a great design feature. I would suggest Kahoot! ditch the white polygons or give the teacher the option to turn them off.

• Sort
There is no real-time sorting of student thinking. If a teacher would like to see how specific students answered questions, they have to wait until the session is finished and look at the data on a spreadsheet. Granted, this data is better than nothing. After having teacher dashboards available in other tech tools like Pear Deck and Desmos, I need the data NOW! Again, after the students go home is better than nothing. Because answers are multiple choice, the results from a question are displayed as bar graphs. Unfortunately, the teacher cannot click on a bar graph to see which students picked that answer.

• Assess
Multiple choice questions can always present a teacher with false positives as I mentioned above. The bar graph could be generally informative to me as a teacher. I do appreciate the option that a teacher could export the results of the game after the session has ended. This could help inform their instruction for the next day if they decide to use Kahoot! as an exit slip.

• Discuss
After students have answered a question and the bar graphs are displayed, the teacher does have the option to click on the image and discuss the mathematics. However, I wouldn't feel that well informed as to what students were thinking or the reasoning behind their choices, especially if they were being timed and the timer caused them to quickly guess.

Kahoot! conclusion:
I can't help but feel like a game-show host when I've run Kahoot sessions. No thanks. I'm a teacher, not a game-show host. You might be wondering why I don't have a wish list for Kahoot! I have found other tools that can do the same exact thing without students being timed, earning points, or having to additionally process colors and shapes when answering. If you're a fan of Kahoot!, then I welcome arguments that might convince me to reconsider the tool. However, if you'd like to present arguments, I request you consider the tech tool Quizalize. It has a gaming feel to it, but just might be more informative to you, the teacher.
Learn more about Kahoot! here.
Learn more about Quizalize here.

More from the My Tech Tools Series:

My Tech Tools [Google Forms]

Google Forms
• Capture
I like using Google Forms to quickly capture student estimates and their thinking behind it. Since my district is a Google district and each student has a Google account, I can set up the form to capture their student ID. More importantly, I can capture quick estimates at the intro of an Estimation 180 challenge or a 3-Act task with the goal to quickly sort and assess the student thinking after seeing the first act. Here's an example of a form I would typically send students. Click here to have your own copy.

• Sort
The input from students feeds into a Google Sheet and I can quickly sort the student thinking. For example, I can sort the numerical columns (specifically "Estimate") from least to greatest and vice versa. I can have students enter their name when filling out the form, but I can hide the "name" column when displaying the results to the class.
Bonus sorting: Install the add-on called "rowCall" and give the form to multiple class periods. The add-on rowCall will create a separate sheet for each class period at the bottom of your file. Learn more here.

• Assess
I've learned to use Google Forms to ask students the information they think might be useful to know in Act 2. I can use "Conditional Formatting" to fill a cell with a specific color when students enter trigger words. For example, when students do the File Cabinet task, I set the conditional formatting for words such as length, width, dimension, height, sticky, face, etc. I can see the informal (or formal) language) students provide and help connect the math to their terminology before we work at formalizing it together.

• Discuss
I love the wisdom of crowds during a 3-Act task and gathering as much information as possible. We can take the "Estimate" column and find the average number of stickies the class thinks it will take for me to cover the file cabinet. There have been numerous times when our class average is astoundingly close. Using conditional formatting and trigger words allows me to locate informal words such as "sides" and strengthen student vocabulary by referring to the cabinet's sides as a faces of a rectangular prism.

Google Forms Conclusion:
A Google Form is a quick way to capture, sort, and assess student thinking, estimates, and information we might need in a problem-solving task so we can discuss the mathematics ahead of us. Furthermore,  since we captured student estimates during Act 1, it makes it extremely easy to go back and do two things:
1) Check our answers for reasonableness
2) See who had the best estimate after watching Act 3.
Learn more about Google Forms here.

More from the My Tech Tools Series:
Google Forms,

My Tech Tools [Desmos]

Desmos Activities (Activity Builder)
• Capture
Not completely necessary, but students can log in with a Google account. One benefit to logging in with a Google account is that a student can access previous sessions (their work) at any time because Desmos activities save in real time. Desmos also has a teacher dashboard to know which students have shared their thinking on a specific question in REAL TIME. The teacher dashboard does a wonderful job capturing student graphs and text responses. Note the progress bars below. Unlike Pear Deck, the Desmos activities allow students to move at their own pace. I love this feature, but it might make the sorting and assessing a tad more challenging at times.
- I wish logging in with Google did not allow students to edit their name.
- I wish the teacher could choose the activity to be "student-paced" or "teacher-paced"
- I wish there was a way for students to enter mathematical notation in the text boxes.

• Sort
The teacher dashboard allows the teacher to sort ALL student responses:
- as an individual student
- as thumbnails (of graphs)
- as a list (of text responses)
- as an overlay
With so many ways to sort student work, the teacher dashboard can allow the teacher to focus either on specific questions, a single student's graph/work/note, or the overall climate of the classroom. There are many great sorting features that can make the session extremely informative when assessing. One feature Desmos Activities lacks is sorting student work alphabetically. As a teacher, I'm still able to assess student thinking, but I know sorting alphabetically would make the process more efficient.
- I wish student names could be sorted alphabetically on the left and with thumbnails.

• Assess
Since students can work at their own pace during a Desmos Activity, it makes it a tad more challenging to assess student thinking at times. The more screens your students have to see or interact with during the activity, the more a teacher needs to assess. This can be both informative and daunting to a teacher. I prefer using or creating activities with a specific focus, making it clear to the teacher if students are working toward learning objectives. The Match My Parabola activity (seen here) allows the teachers to visually assess the progress (and understanding) of students matching parabolas. A picture is a thousand words of student understanding, and Desmos graphs do that.
Two tech tips:
1) Use the power of Command+F on your computer for assessing academic language.
2) Log into your dashboard on a tablet and circulate the room.
• Discuss
A well-designed Desmos activity will allow both students and teachers to discuss their thinking and the mathematics. This presents the teacher with many teachable moments. Since you currently can't hide student names, a teacher can log into the session and use their screen (session) to discuss the mathematics. Personally, I love using student work to discuss the math. Until the dashboard can hide student names, you might need to be creative and use the Snipping tool (Windows or Mac) to quickly grab student work and display it in another presentation-style program for students to see. I have had so many rich discussion with students because of the thinking I am able to assess. Here's a nifty little trick to make your workflow more efficient.
- I wish there was a button to toggle between hiding names and viewing names on the dashboard
[update] You can now toggle between student names and pseudonyms.
- I wish there was a button to lock student screens when discussing specific parts of the activity.

Desmos Activities Conclusion:
In conclusion, pick activities that are focused and have a clear learning objective that can be assessed best with minimal screens. The awesome Desmos team continues to release updates to their Activity Builder and I'm hopeful that many things on my wishlist (and yours too) will soon become realities. For example, sorting student names alphabetically is important to me because it would make my workflow much more efficient, essentially allowing me to assess student thinking quicker. I'm confident Desmos Activities will see all green from me soon!
Learn more about Desmos Activities here.

More from the My Tech Tools Series:


My Tech Tools [Pear Deck]

Pear Deck
• Capture
Because each student must log in with a Google account, the teacher can use the teacher dashboard to know which students have shared their thinking on a specific question in REAL TIME. There are numerous ways to capture the mathematical thinking of students: draggables, text response, number response, multiple choice, agree/disagree, free-hand drawing tool, and more. Below is an example of draggables.

- I wish there was a way for students to type in mathematical notation at times.

• Sort
The screens inside a Pear Deck session are controlled by the teacher. The teacher-paced sessions make it easier to sort through the student responses. The teacher dashboard allows the teacher to sort ALL student responses:
- as a Grid (thumbnails)
- as a Table (list)
- by a proximity sensor (draggables)

• Assess
Because Pear Deck captures every student response and allows the teacher to sort student thinking efficiently, the teacher can assess it many ways. For example, the teacher can use the Table view to quickly see text responses, number responses, or multiple choice answers. The Grid view (thumbnails) can be used to assess draggables or student writing. The teacher can also click on any student's name and immediately get their thinking.
- I wish less lag would occur when a teacher runs the dashboard on their iPad.

• Discuss
In addition to seeing answers from every student, the teacher can get the climate of the class when looking at the teacher dashboard. When I say climate, the teacher can get the general (majority, average, etc.) thinking of the class. The teacher can also anonymously project student answers on their classroom wall so everyone can see how the class is thinking. This allows the class and teacher to discuss both their thinking and the mathematics. Furthermore, the teacher can choose to project specific student responses (that are still anonymous).
Additionally, Pear Deck has a lock feature that allows the teacher to lock student screens. The strength of this feature (in my opinion) is for students to come up for air from their devices and pay attention to the projector view and discuss the mathematics.

Pear Deck Conclusion:
Yes, certain features of Pear Deck cost money. However, I'd gladly pay this money (out of pocket if I had to) in order to be more informed as a teacher. I think students take more risks because their answers are anonymous to the class. Pear Deck can be used to launch a lesson, check for understanding throughout a lesson, or as an exit slip. It's extremely versatile, anonymous to students, informative to the teacher, interactive, and integrates smoothly with Google.

Learn more about Pear Deck here.

More from the My Tech Tools Series:
Pear Deck,

My Tech Tools

In a recent post, I defined what's important to me, my tech tool criteria, and a video version too. I want to be clear, this is a very specific focus. I will say it again:
I need tech tools that allow me to focus on student thinking because student thinking will better drive my math instruction.
Here is a series breaking down the tools that meet my criteria (comments welcome):
*And one tool that does not meet my criteria.

A video intro with more detailed thoughts.

P. S. 
Here are a couple math tech tools that meet a different set of criteria.
• Motion Math (extreme fun talking math with my son)
• CueThink (a great problem-solving framework)
Formative (a tool I hope to learn more about)

Tech Tools,

Tuesday, February 9, 2016

Desmos & Command F

Today a fellow used Cathy Yenca's Reflections activity with her students. It's a wonderful activity for Math 8. The most recent "copy previous" feature from Desmos kicked it up a notch too.

Have you ever found it challenging to quickly read through all the student responses in a Desmos activity? Here's an idea:
Use your browser's "Find..." function.
Google Chrome is my browser of choice. See how the simple combination of Desmos and Command+F (Ctrl+F on a PC) made Yenca's activity informative to both students and teacher.

When class time is precious, Desmos activities are awesome, dashboards are informative, and student input is rich, it creates great potential for teachable moments in math class. I hope this tip is helpful and further enhances your formative assessment of student thinking inside Desmos activities.

Command F,

Thursday, January 28, 2016

5th Grade Fun

Yesterday was AWESOME!

I had the great fortune of visiting Jen Sandland's classroom in the morning.
Jen is a 5th grade teacher in my district. Her students and I spent an hour having a blast:
Jen's students have done a few Estimation 180 challenges this year. Therefore, I assumed they already knew my height. WRONG! So, we started with estimating my height. The best part of the conversation was helping students deliver their answers like 6.2 as 6 foot 2 inches. It was sooooo cool to hear students catch themselves, and work at eliminating the decimal point when referring to feet and inches. Once they found out my height, I took three student volunteers for the class to estimate their heights?

The tallest student, (we'll call her Jane), came in at a towering 5'2".  I was holding a part of  the clothesline in my hand as the remainder of it was outstretched on the floor. I asked the class:
"How many Janes would make the length of the clothesline?"

Oh, man. You should have seen these kids talking about this? Some made guesses like four or five Janes. Naturally, I asked, "So how long are four Janes? How long are five Janes?"

I wish I took a picture of our model, but it looked something like this:

One student explained his method of adding the feet first and then the inches. It was amazing! So we came up with the length of the clothesline as a range of 20'8" to 25'10". I then had two students help me measure the clothesline against Jane's height and we almost got five Janes. That makes sense because the rope is actually 25 feet long.

We used the clothesline to talk about Day 150 on Estimation 180.
What will be the value of the finished cent sign?

The thinking, strategies, and conversations were so cool. We placed our too lows, too highs, and just rights on the clothesline. We talked about order, magnitude, and spacing. If you do Day 150 with students and you're watching the answer as a class,
Cent Sign of Pennies from Mr.Stadel on Vimeo.

Give students a chance to revise their initial estimates. It's such a powerful experience. Pause those video answers and let students change their answers once they have more information.

Before my farewell, the students asked me a few questions:
How'd you make the video to the pennies answer?
Take a picture of the complete layout. Subtract a penny. Take another picture. Repeat.

What program do you use to make the counters on Estimation 180 videos?
Apple's Motion

What are your favorite Estimation 180's?
The music challenges. HANDS DOWN!

Did you always like math?
No. I loved music and art in school. I was just good at remembering math rules. Now, I love getting better and understanding numbers.

My question to them:
What is your favorite thing about numbers?

They are expected to answer this when I return to their class. When I return, I'd love to just blend in, if that's possible, while they are doing math centers or other activities and learn from them. Man, these kids were so fun to hang out with for an hour.

Thanks Jen! Keep up the fantastic work you're doing with them!


Monday, January 25, 2016

Tech Tool Criteria

Why get out of bed tomorrow and teach math?
I love student thinking because it helps drive my math instruction.
*this is just one reason for me

So when it comes to tech tools in the math class, I need tech tools that allow me to focus on student thinking because student thinking will better drive my math instruction. This video shares a few more detailed thoughts:

Here's my criteria:
In order to focus on student thinking, my tech tools need to :
  • SORT
Let me explain:
  • I need tech tools that capture student thinking as best possible. And I mean ALL students.
  • I need tech tools that sort the student thinking efficiently and effectively. 
  • I need tech tools that allow me to quickly assess what students are thinking. In REAL-TIME.
  • I need tech tools that allow the students and me (the teacher) to discuss the thinking and mathematics that has been captured, sorted, and assessed.
My next post will include:
  • my rubric
  • examples of tools that currently DO and DON'T meet my criteria 
What's your criteria?

Student thinking,

Wednesday, January 13, 2016

Integers [temperatures]

Yesterday, I co-taught an integers activity with a colleague. It was a blast! Before I share the lesson, I'll back up and give the backstory on the context. During winter break, I ventured over to Brian Head, Utah to do some snowboarding. I knew it was going to be cold so I went into the trip with the intention to frequently check my phone's weather app and take screenshots of temperatures. I figured I might be able to make an activity out of it and/or use it with 6th graders at some point when discussing integers. (official lesson page with resources)

My fellow displayed this slide and asked, "What do you notice? What do you wonder?"
(the 3 in the lower right is the slide number)

Students noticed and wondered great things. Here are just a few:
  • What's the temperature at 9am?
  • Why is it warmer on the days it is supposed to snow?
  • Thursday is the only day with a negative temperature.
  • It's 4:13 am.
  • It's zero degrees at 5am.
  • It's cold!
  • How cold does it get?
We established that -4 degrees Fahrenheit is cold, below zero, and the temperature at 4:13 am. Let's plot this on a vertical number line today, just like a thermometer. Does -4 degrees go above or below -5 on the vertical number line?

I told students that we're going to show them five more times and their temperatures throughout the day. Most importantly, I asked students to first predict the temperatures at those given times (tap into student intuition). Here are the times:
  • 6:00 am
  • 7:00 am
  • 9:30 am
  • 2:30 pm
  • 8:00 pm
Essentially, we're tapping into student intuition, a free resource in our classrooms. I want them to predict the story of temperatures and degree change for the remainder of the day. If anyone has experienced winter weather, they know it gets cold at night and warmer during the day, possibly peaking midday. It's a small part of the activity to keep it moving along and gain student investment.

Here come the temperatures. For each time and temperature revealed, here's what were going to do:
  • Plot the temperature on your vertical number line.
  • Find the degree change between the last temperature given.
  • At the end, we'll find the largest difference in temperature during the day.

Here's a few of our whiteboard representations:

This was a simple and fun context to work with integers and the vertical number line. I also took screenshots of the temperatures in Celsius and might be able to make a Math 8 activity out of it. Here's the desmos rough draft.

The best part for me (as a teacher) was listening to students make sense of the temperature changes and explaining their thinking. There were so many opportunities to help students with their vocabulary. For example, when asked, "what's the difference between 12 degrees and -8 degrees?" it was interesting to hear how students wanted to change -8 to a positive in order to add it to 12. There was our intro to absolute value and a number's distance from zero. Love it!

One student came up to me on his way out and showed me his paper,
"Hey Mr. Stadel, I predicted the temperature correctly for each time!"
I asked, "Do you want to pick my Powerball lottery numbers for this week?"
He declined. Drat.

Again, official lesson page with resources here.

Brrrrrrr! it's cold,