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

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: clotheslinemath.com

Floor,
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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,
726