Polygraph Vocab Jar

If someone is trying to curtail their use of profanity, they might set up a Swear Jar. Every time they use a swear word, they deposit an amount of money inside the jar. Since there are a variety of swear words, the incentive is to consciously be aware of your profanity with the intention to minimize your profanity and find other (less colorful) ways to communicate.

I'd like to introduce the idea of a Polygraph Vocab Jar when playing Desmos Polygraph activities. Whereas the Swear Jar might have a negative connotation to it, I see the Vocab Jar as having a positive connotation. The purpose of the Vocab Jar would be to invite and encourage students to increase the frequency of use and variation of math terms when playing Polygraph activities. Check out what I mean in this video:


You might remember I blogged about the power of Command-F (Mac) and Control-F (PC) when finding a specific term within Desmos activities. I'm utilizing the same tool here when looking for specific math terms in student conversations when playing Polygraph. I also like the idea of keeping track of the frequency of terms used from the word bank. If you want a math swear jar, I added two columns to keep track of taboo words. On a related note, I recently blogged about word banks and taboo words in Polygraph. Check it out.

In the video, I mentioned the idea of having some incentives in your math classes. For example, if you're a single-subject teacher and have multiple sections of Algebra, you could turn it into a friendly competition between class periods. The class with the most variation and use of terms from the word bank with successful polygraph games gets [fill in the blank].

Click here if you want copy of the spreadsheet featured in the video above.

As much as I love the Command-F feature to find terms on a webpage and keeping track of them in a Google sheet, I would love to see a Vocab Jar integration into the Desmos Polygraph. I think it would be a valuable tool for teachers to continue their formative assessment of student conversations and use of mathematical language.

What do you think?
If this is something you would find useful, would you send a +1 to Desmos for me?
If you have a way to improve this idea, leave a comment below and Cc desmos.

Swear,
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Polygraph Word Bank

Have you ever wanted your math students to get better at using math language?
Have you ever wanted your math students to be able to compare attributes of visual mathematics?
Desmos Polygraph activities supported through word banks is your jam!

Over the past three years as a Digital Learning Coach in my district, I've been able to see Polygraph used in a variety of ways. This post will share a few of the many things I've learned.

My first year, I supported a high school Algebra teacher. We debriefed after she ran the Parabolas Polygraph activity with students. She was a little bummed that students weren't using more of the academic language they had been learning. For example, minimum, maximum, x-intercepts, roots, vertex, etc. I offered the suggestion of providing students with a word bank, possibly carved out on a section of the whiteboard, with the words she wanted her students to use. She one-upped me and put them on a half sheet of paper and printed them out to give to her students next time she played polygraph. I'll revisit this technique in a few paragraphs.

My second year, I supported a Math 8 teacher. She was running the Lines Polygraph activity with her students. I looked at the dashboard while students were playing and many of the students were asking questions about the slope using either "uphill" or "downhill" as their descriptor. I asked the teacher about this. She said this is the way she taught it. I asked her about the mathematical association with uphill and downhill and she replied, positive and negative, respectively. I paused the class (before the pause feature existed, ha!) and drew two lines to represent the "uphill" and "downhill" slopes on the whiteboard. I told the class I noticed they have been using the terms uphill and downhill to describe these slopes. I went on to tell them, this is a great place to start, and now we're going to make your language even stronger by referring to uphill slopes as positive and downhill slopes as negative. For the remaining time, we're inviting you to use positive and negative.

I love this experience, because it validated the work the teacher did while raising the bar for the students to strengthen their mathematical vocabulary. I believe if you set the bar low for students, they'll often meet it with a high success rate. If you set the bar high for students, they'll work toward that high bar, often with a comparatively high success rate.

Back to the word bank.
My third year, I supported an Algebra teacher at our continuation high school. She ran the Parabolas Polygraph with her students and had a word bank up on the whiteboard. We debriefed and talked about making a half sheet of the words she would like students to use. Furthermore, let's make a Taboo list of words we want students to avoid using. She tried the Polygraph again, using the word bank handouts and noticed students were using the academic language a lot more than when the words were up on the whiteboard.

It's not enabling the students by providing them with a half-sheet of math terms you want them to practice and use. It's enabling if you're the one telling them what questions to ask their partner, or worse; you're typing in the questions for them. Providing students with the half-sheet, a physical token, places an emphasis on your invitation to students to practice and use specific math language associated with the concepts at hand.

I've learned a lot over the past 3 years, implementing both Desmos Activities and Polygraphs. I would say the use of a word bank handout is one of the most effective ways to get students practicing and using the math language you want them to use. Here are my current word banks (and Taboo lists) for Parabolas and Lines. You'll notice I intentionally left some blank spaces in the tables so students (and teachers) can add their own. I can't think of everything.

Consider the Low-Tech versions of Desmos Polygraph so students can practice using academic language more frequently without devices.

What words would you add to my word bank (and taboo) lists?

Bank,
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BONUS feature:
You've heard of a swear jar, right?
When someone is trying to curtail their swearing and/or use of bad words, they'll set out a swear jar, placing an amount of money in the jar every time they use a bad word.
*Consider the idea of a VOCAB jar in your math class. (future blog post coming soon)

Low Tech Polygraph

Imagine classrooms full of math students without devices missing out on opportunities to play wonderful Desmos Polygraph activities. It's a miserable thought, right?

Unfortunately, classrooms like this exist. I've been extremely fortunate the past three years to work in a district where every secondary student is provided with a device and can enjoy playing (and learning from) Desmos Polygraph activities. What can we do for students and teachers who aren't 1:1 yet?

I've also been honored to provide professional development for math teachers in various districts across the country. They LOOOOOOVE playing (and learning about instructional uses of) Polygraph during the workshop. However, I often hear comments from teachers like:

• We're not 1-to-1 yet
• We're BYOD and many students just bring cell phones
• I have to book the computer lab because we're not 1:1

I also get questions like:

• When do you recommend we do Polygraph? We have limited time.
• This [Polygraph] is a great tool, what if students are absent?
• I love the idea of students playing Polygraph on more than one day, but how do I do that?

Here's my idea:

Provide students and teachers with a low-tech version of Polygraph. 

Here's the setup I've tried with teachers and the response has been fantastic.

1. Print out four different versions (A-B-C-D) of the sixteen Polygraph graphs
1. I've already made Lines and Parabolas
2. Make double-sided copies of {A-B} and {C-D}
1. Make enough {A-B} copies for half your class and {C-D} copies for the other half
3. Insert one copy into a plastic sleeve
4. Store in a highly accessible place in your classroom
5. Have some dry-erase markers nearby
6. Provide students with a word bank & taboo bank (follow-up post)

You can have students play Polygraph at anytime!. Imagine the possibilities. Imagine even MORE students being able to play Polygraph. Just remind students they can play any other letter besides their own letter. For example, Page C can play A, B, or D. 

Have a go and let me know!

Low-tech FTW,

1104

Estimation 180 Bins

I'd love some feedback on this tool I'm tinkering around with right now.

I was inspired by Graham Fletcher, seeing him place student estimates inside ranges, or bins if you will. My goal was to make a tool that replicated this experience, is efficient for teachers to use, and added some visual enhancements. The tool could be used with Estimation 180 challenges and was made in Desmos.


What successes might you see happening in your classroom when using this tool?
What challenges might you see happening in your classroom when using this tool?
What advice do you have for improving it?

Thanks in advance for your responses.

Bins,
303

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:

• Clothesline activity using these cards
• Square Dance desmos activity

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.

Dance,

945

My Tech Tools [Kahoot!]

Here is a tool that does not meet my criteria:
Kahoot!
• 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 Criteria
• Pear Deck
• Desmos
• Google Forms

Kahoot,

519

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:

• My Criteria
• Pear Deck
• Desmos
• Kahoot!

Google Forms,
519

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.

Wishlist:
- 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.

Wishlist:
- 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.
Wishlist:
- 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 Criteria
• Pear Deck
• Google Forms
• Kahoot!

Desmos,

519

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.

Wishlist:

- 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.

Wishlist:
- 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:

• My Criteria
• Desmos
• Google Forms
• Kahoot!

Pear Deck,

519

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):

• Pear Deck
• Desmos Activities 
• Google Forms

*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,
516

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,
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Productive Struggle [part 2]

Recently, I started thinking more about productive struggle:

• Blogged part 1 here
• Desmos activity here
• Comments and questions contributed here

Thanks to all (approximately 100) who participated. Here's an overlay of the Desmos activity:

I noticed (of those who participated):

• there isn't necessarily a one-to-one relationship of struggle to frustration.
• most participants will struggle for a bit before getting frustrated.
• some participants thought their frustration was logarithmic or exponential

Here are a few of the graphs.

I love that there's a story behind each graph. I love that the graphs are practically all different. Looking at the responses of math educators, it convinces me that we are just like a classroom of math students. Not surprisingly, we're all different and the relationship between struggle and frustration is different for everyone, much like the students in our classes. So what's next?

As teachers, we need actionable steps when working with math students who might be at various levels of struggle and frustration during an activity or task. From my experience, I believe the best actionable step is communication. Communication is what's next.

This idea of communication was shared by many math educators in the Desmos activity. At the conclusion of the activity, I asked for some final thoughts. If students are allowed to reasonably struggle with a math task, what would be a teacher prescription of actionable steps to:

• move the learning forward and 
• avoid a meltdown level of frustration?

Here are a few responses:

• using well-timed and small hints as needed
• humor helps
• constructive feedback that promotes reflection on the students thought processes
• have a set of scaffolded supports easily available and in multiple mediums
• hints and scaffolds are appropriate, preferably after significant struggle has already been felt
• reminders that everything worthwhile takes work 
• look at mistakes together and see what we can learn collectively
• let students explain their thinking, then discuss as a class
• turn and talk to your neighbor about this problem.
• develop a series of hints/question schemes to use with students
• determine the "breaking point" where the teacher should use whole group/small group instruction to address misconceptions to alleviate frustration
• remind yourself to ask questions before dispensing information
• remind your students that taking a break and coming back to the problem is sometimes a great idea
• pair them with someone else, ask them to break the problem down
• chunk the task or you can take a break and come back to it later
• learn to judge frustration level, have some strategies ready for each level
• I like using VNPSs so that they can look at other groups for ideas.

In my teacher mind, these all include some form of communication. Communication is happening either visually, orally, conversationally, or with questions and hints. THANK YOU for sharing these ideas so we all can make our classrooms a better environment for communicating. Many of these resonate with me, especially the scaffolded hints and questions. I'd like to share a few from my experience with students (and adults in workshops):

• be sincere in your communication and questioning
• anticipate student mistakes/misconceptions before students do the task
• compliment a strategy/idea/mistake students make that might nudge them forward
• ask another student to explain the task or sticking point to a struggling student
• explore a list of 26 questions to ask students (from Max Ray-Riek)
• listen to student thinking, not for the right explanation (see Max's Ignite)
• reassure students that you're confident they can solve it (or progress before the end of class)
• give hints that might refocus their energy on a small part of the task that's solvable or might gain them some momentum
• don't game students
• don't ask, "what do you think you did wrong?"
• don't ask, "do you think that's correct?"
• don't ask, "does that make sense to you?" (about the student's work)
• don't let students work too long on an incorrect strategy

These are two LOOONG lists and I could add even more to them. These lists are not for every student or teacher in every situation. The length of the lists and their variety convince me that it's best we know our students best when communicating with them during a math task in which they most likely will struggle. Some of these steps might appear as though I'm bailing a kid out or robbing them from some learning experience. Maybe. However, I believe we all have students that need strong encouraging hints that will give them momentum instead of me letting them struggle for too long and take the chance of losing them for good. Likewise, I don't see any point in letting students work too long on an incorrect strategy if I spot it while they're working. I'd rather use that valuable time to ask them questions and redirect them. 

I thought about writing a few conversations I've had with students, but every conversation is different because every student is different and their mathematical thinking can be different. The result is that conversations with students during a math task are many times like fingerprints; they're identifiable and we can learn a lot from them, but no two are the same.  Therefore, our communication with students should be customized to that moment. Does it help to have some "go-to" responses? Absolutely! Here are mine.

When walking up to a student for the first time, you can find me initiating the conversation with:

• Show me what you've tried so far.
• Tell me about what you've done.
• Do you know where you're stuck? If so, show and tell me about it.
• Where are you confused?
• I noticed you did this [something in their work]. I'm curious why you did that.
• I noticed you have something circled here. Explain that to me or tell me why that makes sense to you.

I try to ask questions or give commands that allow the student to communicate to me what they've tried, what they're frustrated with, or what sense they've made of the task. More often than not, I will try and ask the most-efficient and revealing question. In other words, the question that tells me the most information about their thinking in the shortest amount of time. The goal is to use this ice-breaker question/command as a quick formative assessment while I look at their work (or lack thereof). Okay, so what's next?

Depending on their response, this is where it gets tricky. Once a student has shared their work, thinking, mistake, or blank paper, we need to be in tune to what the student gives us or doesn't give us. We need to allow the communication thrive. I love the post AND comments in this blog post by Annie Fetter, titled One Example of a "Bad Hint." Bookmark this post and revisit it when you need it. There's some great insight from Annie and everyone in the comments. Since many math educators mentioned hints, it reminded me of her post and how it has helped me get better at questioning/assisting students during math tasks. What if hints don't always work? What's next?

Offer some assistance. There's nothing wrong with this. Yes, I agree with Being Less Helpful. However, we're working with students. Their brains are still developing. They (and some parents) see us as adults in positions to offer assistance in the learning process. I'm not advocating we bail students out. Yes, it's a fine line we have to walk between productive struggle and meltdown frustration with students (and parents) at times. Trust me, I've learned the hard way. I've walked away from students after making some naive comments like, "You'll figure it out." or "Keep working on it." or "Does that make sense to you?" when I knew all too well that they wouldn't figure it out, or working on it more will cause them frustration, or that of course it makes sense to them because they're the one who came up with the answer. DUH! I'm good with offering some assistance to students who really need it because it will save both of us some frustration and I'm not about gaming students. I've tried the following inexpensive response and it's gotten me some mileage so far:

How about we work on this together for about a minute? We'll get started together and then I need to go check in with other students. 

We're knocking at the door of perseverance with everything mentioned above. I should address it a bit. Again, communication is our ally here. I've found I get a lot more from my students when I communicate to them something like, 

I know today's task might be challenging. I'm confident you will work hard individually and together. Most of you will make mistakes, but I've seen how well you learn from mistakes in the past. You know I'll check in with you throughout the task, and might offer some hints if you're stuck. However, remember that I want you to first explain your strategy to me first.

Whatever you tell your students, be sincere and honest. Admit when you know a task will be challenging. Admit when you've given them a task too challenging. Likewise, admit when you've given them a task too easy. We're getting better at this teaching stuff, just like they're getting better at that "student" stuff. Honor the fact that one of your roles as a teacher is to both model and encourage perseverance. A lot easier said than done, right. But that's why we're here (#MTBoS) for each other. We share ideas with each other to make our math classrooms a better place for learning and teaching.

I'm not sitting down to write this post because I'm claiming I know all the answers. I had a few goals when initiating these two posts on productive struggle:

• learn how others perceive the relationship of struggle to frustration
• share actionable steps from other math educators
• share actionable steps that have and have not worked for me
• stress the importance of communication
• encourage others to offer timely assistance without bailing students out or being too helpful
• learn from other math educators how to best communicate with students so that they persevere through struggle

SO there it is. Your turn, please. What is your experience?

What are your go-to responses or actionable steps in moving the learning forward while encouraging students to persevere?

Steps,

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*Here's the link to the Desmos Activity if you want to adapt it and use with your students.

Productive Struggle [part 1]

I want to know more about "Productive Struggle".

Let me be more specific:
If students are allowed to reasonably struggle with a math task, I want to know more about a teacher prescription of actionable steps to:

• move the learning forward and 
• avoid a meltdown level of frustration

I built a Productive Struggle Desmos Activity if you would like to share your thoughts and learn from others interested in this topic.

Robert Kaplinksy recently gave a wonderful Ignite Talk on Productive Struggle. Communication was a big part Robert's message. I want to think more (in part 2) about communication as one of the actionable steps in that prescription.

Struggle,
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Part 2 is here.

Barbie Zip Line (2015) Part 1

Last summer I tried Barbie Zip Line and reported the experience here. I also supported a handful of Math 8 teachers interested in Barbie Zip Line during the school when they explored the Pythagorean Theorem. I have to admit, with every experience, it always felt like it could be different, possibly better.  This year, I went a different route and Part 1 just documents what I've done so far. Part 2 will be the conclusion.

First, I avoided the Pythagorean Theorem (for now). On Monday, my students already knew we would be starting Barbie Zip Line on Thursday. That was about as much information as I revealed. Everything else was structured to elicit as much student insight, information, and ideas as possible.

I started by projecting this slide:

Students discussed in their groups and a few shared whole group. I jotted down a few quick notes:

I love this informal language. Would this be an opportunity to work in slope? Maybe. I wouldn't force it as I'm confident we'll have plenty of other opportunities.

Me: Has anyone her gone zip lining before. 

A few hands go up.

Me: How would you describe it to someone in the class who has never been?

Katherine: Awesome!

Me: How would you describe what zip lining is to someone unfamiliar to it?

Katherine: You wear this harness. You ride down a line...

Mateo: You have two cables attached to you in case one of them breaks, there's a backup. Someone pushes you at the beginning and you ride along a cable...

Me: Great. Thanks. Would it help if we saw pictures or video of someone zip lining to give everyone a better perspective?

Everyone: YES!

Me: Here's what Google Images has for "zip line pictures". 

Me: A good business model will provide their customers with a safe and thrilling experience. Therefore, I'd like you all to fill out this Google Form with the following prompts and questions:

• Briefly describe the characteristics of a DEATH zip line.
• Briefly describe the characteristics of a BORING zip line.
• Briefly describe the characteristics of a JUST RIGHT zip line. 
• What information would be useful to know when building a zip line?
• If we had a small scale zip line in class, what data can we collect from the small scale? 

I'm fascinated by the results. I learned I need to truly value, trust, and use my students' intuition way more often and when launching a lesson/activity. Check out their results here. These results will help guide Desmos Part 2. However, first we need to do Desmos Part 1.

The actual zip line quad.

Desmos Part 1
Students go to this Desmos graph and quickly create three zip lines.

Once they are done, they head over to this Padlet page and post their Desmos graph for their classmates (and me) to see.

Created with Padlet

Desmos Part 2
*I will post what students do in Barbie Zip Line (2015) Part 2.
Before going outside, students begin doing a small scale version of the zip line inside the classroom. Here are the materials:

• 3 paper clips
• 2 measuring tapes
• 1 string (100 inches)
• iPad (for Desmos part 2)
• iPad or phone timer

Record their data inside of this pre-made Desmos template.

*If you go the route of the Pythagorean Theorem, adjust your table accordingly.

Here's a handout for each student. After collecting their data, students will be expected to draw a pretty descriptive scale picture of their zip line on this handout. They'll also need to predict how long it will take their doll to complete her zip line ride.

As you can see from the handout and expectations, I'm placing a big emphasis on the following:

• Scale
• Proportional reasoning
• Rate of change (or slope)
• Rate

No mention of Pythagorean Theorem. Find out if it stays that way in my Barbie Zip Line (2015) Part 2 post, next week.

Zip 1,
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P.S. Most importantly, my son was really excited to visit my class today and partake in the Barbie Zip Line adventure. I was really excited too. DUH!

Using Google Forms and Sheets

If you've ever used Estimation 180, you'll notice there's a Google Form on each day where anyone in the world can input their estimate. Although it's not what I envisioned when initially designing the site, it has served a purpose. And it's free. So until I have a million dollars or someone is willing to donate a bunch of money to Estimation 180 so there can be a classroom type interface like teacher.desmos.com or Pear Deck, the Google forms will have to do for now.

My suggestion: create your own form so that you can capture rich data from your students. I believe it's so important that we capture, sort, assess, and discuss student thinking. I put together three short screencasts on:

1. Suggestions for using your own Google Form with students.
2. How to make the Google Form in video 1.
3. How to sort and use the data in the Google Sheet. 

Part 1: The finished form

• Form fields and parameters
• Daily pic in the form

Part 2: Creating and setting up the form

• Text fields and advanced settings
• Insert the image URL into the form
• Creating sentence starters
• Using a shortened URL

Part 3: Sorting the data in a Google Sheet

• Using Add-ons, specifically rowCall to separate class periods into their own sheets
• Conditional Formatting
• Finding the average (and more) of a column

Please let me know if you have any questions or suggestions to make the work flow more efficient.

If you're headed to CUE 2015 in Palm Springs, come check out one of my two sessions where I'll use Google Forms and Sheets to capture, sort, assess, and discuss the rich thinking and data you can receive from students.

Forms,
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Des-man

Today, students had about 90 minutes to work on creating their Des-man. Des-man was the brainchild of Fawn. Desmos then teamed up with Dan Meyer and Christopher Danielson to create a suite of classroom activities, one of them being Des-man. I've done Des-man before, but not with the Desmos classroom. Let me just say, it's awesome!

As the teacher, I could see every students' work in real-time and display it up on the projector for all to see if need be. That's a really slick feature on top of the already amazing Desmos. It's like math euphoria! It was a blast to see students work 90 minutes straight, being as creative as possible with their Des-man (or Des-woman). After three weeks, Desmos became a very familiar tool for students because they used it with tasks like Barbie Bungee, Datelines, Hit the Hoop, Vroom Vroom, Stacking Cups, and more. I'd like to showcase a few creations for you. Enjoy!

Thanks Fawn, Desmos, Dan, and Christopher for a wonderful and creative math experience. Lastly, I want to thank my students. Today, you guys helped each other out, persevered, asked for advice, freely explored, had fun, and wanted to know more about functions, domain, range, circles, sliders, and more!

Desmos is great about asking for feedback. I have some observations and am curious. Maybe I'm missing something, but I noticed some features from the regular desmos calculator missing in the classroom. Maybe these are upcoming features:
Students couldn't duplicate functions. How come?
Students couldn't create (use) tables. How come?
Students couldn't create folders or text boxes. How come?
Students can't share their Des-man (email, link, etc.). How come?
As the teacher, I can't keep the Des-man (functions included) for each student. How come?
As the teacher, I'd love to have access to each student Des-man, especially if I want to send it to that student or share at a later time.
Thanks for listening, Desmos!

Des-manian,
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