Flipping Out over Math!

With the dawn of virtual learning, it's been increasingly difficult to create engaging experiences for my students, especially in math. This year, I've taken on a dual role of digital coaching and instructing PreAP Algebra 2. What was I thinking?! 

I knew this year would offer challenges, not only in terms of rethinking instructional best practices, but also utilizing technology in a responsible way. I wanted to be "on the ground", so to speak, with the staff, but also find ways to help support them.

At our campus, we have shifted to a block schedule, with 90 minute class periods. That's a lot of Zoom, you might say! Isn't that too much for students?! 

While a 90 minutes block has it's challenges, especially for teachers with virtual learners, it also has the potential for deeper thinking. This year, I've decided to try something that I've only been reading about - flipping my instruction.

What can that look like?

1. 📽️Record and edit my content video using WeVideo. 
2. 💻Embed in Edpuzzle with questions to guide thinking and encourage predictions.
3. 💜Utilize the beginning of class as a "check in" using Google Forms (approx 10 min)
1. Instant data to provide quick feedback before diving deeper into content
2. A private space for students to share how they are doing
3. A fun space to get to know your students
4. Drop in a "this or that" to increase fun discussions
4. 📊Desmos Activities to expand thinking and build connections (approx 35 min)
1. Show videos and ask for predictions
2. Use sliders to build pattern recognition
3. Utilize multiple choice, but add "Explain your thinking" option.
4. Use Starter Screens as an exit ticket
5. ⏰Asynchronous Time with GoFormative (approx 45 minutes)
1. Students work on exercises at their own pace, seeking help when needed.
2. Provide students CHOICE: Stay on Zoom and treat like a Q&A, go to a virtual Breakout Room to work with a small group, or log off to de-Zoom, but still accomplish the task.
3. Give instantly feedback while students are working. Provide QUESTIONS not ANSWERS!

Samples:

• Google Form - Parabola Features
• Google Form - Applications of Quadratics
• Desmos Activity - Solving Quadratics
• Desmos Activity - Graphing Absolute Values
• Desmos Activity - Domain Restrictions

Remote Mathematicians

In this "new world" of remote learning, keeping students engaged in content can seem daunting. That feeling of not just sharing content, but making it easily accessible and engaging enough for students to stay connected, brings its challenges.
As a previous math teacher, it was tough enough helping students enjoy the content, so flexing the "creativity" muscle in the brain was a CONSTANT.

During this time, I thought I'd share my top 3 go-to strategies!

TIP #1: Encourage inquiry and self-discovery!

• Geogebra: This site offers Classroom Resources from elementary up to college courses. Students can explore theorems, visualize multiple cases, and then easily develop their proof. Geogebra even has built in activities with self-checks. Follow Tim or Steve on Twitter to see their creations.
• Desmos: Teachers can create a FREE account and send activities to their students. Use one that's already made or create your own! Explore transformations and how variables can affect equations.
• NEW UPDATE ALERT: Add a co-teacher!
• NEW UPDATE ALERT: Send customized feedback to students.

TIP #2: Increase the open dialogue by using open tasks!

• Which One Doesn't Belong: 4 boxes...which one doesn't belong? The best part - there is a reason EVERY SINGLE ONE doesn't belong. Bring the discussion into math and allow students to see there isn't just "one answer." Do you have gifted students? Encourage them to create their own!

• Copy/paste a puzzle and use THESE SLIDES! Share it with students so everyone can edit the same file. 
• Numbers Example (for Elementary up to High School)
• Open Middle Math: One problem can completely replace a worksheet! Students not only practice, but must use logic and reasoning to finish the puzzle. Available for K-12 students!
• PRO TIP: Share on a Google Slides or Keynote for students to respond. They can drop in recording to explain their thinking.
• PRO TIP: Use master slides to create text and image placeholders for students.
• PRO TIP: Attach an Open Middle or WODB problem to the "Focus" in a Flipgrid Topic. Ss can use the whiteboard mode to share their thinking with their peers! 

TIP #3: Using the tech in your tool belt!

• Keynote (on the iPad): While it is similar to Google Slides, Keynote on the iPad takes the advantage! A fantastic mathematician and edtech enthusiast, Morgan Cave, on the team I work on got me into this app, and there is NO turning back! As an Apple Distinguish Educator, she's continuing to push outside the box for how Keynote can be used to explore all concepts.
• Built in shapes (including 3D ones with the latest iOS update!)
• Drop in just audio to explain thinking.
• Utilize the Drawings option with multiple colors to clarify steps. My favorite? Use the "Line Draw" animation so that students can visualize their work (and steps) come to LIFE!
• Use backgrounds and "locking" to prevent students editing important information.
• Templates from Morgan Cave: Shapes Hunt, Alpha See Say Draw, Numbers See Say Draw
• $FREE Apple Books: 20 Keynote Creations & Keynote in the Classroom
• Google Slides (for Chromebook): 
• Use master slides to create template responses with placeholders.
• Ss can drop in pictures, links, videos, text, animations, and MORE all in one place.
• Collaboration feature for discussions or group work is PERFECT! With the editing history, no work is lost and students are help accountable for their contribution.
• Google Sheets (for Chromebook): Check out these helpful resources and templates using the "ugly step sister" of the G-Suite family!
• Eric Curts' Blog
• Create a digital breakout activity with if-then formulas!
• Math Learning Apps:
• Digital manipulatives for the WIN!
• 100% FREE!
• Includes annotation feature! 
• PRO TIP: Ss can screenshot their creation, and drop it in Seesaw or Keynote to add audio!
• Flipgrid:
• Whiteboard Mode = PERFECT for explaining work.
• Drop in a video, picture, and/or links in the Focus for your Topic.
• Students don't want others to see their face? Use Pixel Mode!
• Check out their Disco Library for Topics ready to go!

A "functional" Transformation

One of the biggest topics in a secondary mathematics class is function transformations (horizontal/vertical shift, compressions, stretches, etc.) Usually students will memorize the rules rather than understand the reasoning. I needed a way to enhance the lesson to allow students room to investigate these concepts and draw their own connections and conclusions - time to spice things up with technology!

Topic: Intro to Transformations

Essential Question: How can I transform ANY function?

Materials:

• Desmos Activity - Make a copy if you'd like to make some adjustments! (link)
• Student Notes - Google Slides (link) Click [Use Template] to make your own copy in your Google Drive.
• 1 device per 2 students - I recommend a Chromebook/computer.
• Recommendation: a Google Classroom to share the notes with each student.

Student Notes (Google Slides) Preview

Teacher Notes:

1. Assign the notes in Google Classroom where each student gets a copy.
2. Go to teacher.desmos.com. If you don't have one, create an account! I recommend with a Google Account to make the sign-in easier.
3. Open the Desmos Activity (Intro to Transformations) above. 
4. Click on the teal [Create Class Code]. This will need to be copied on Slide 1 in the Google Slides. This is how students will access the activity.

   

   Desmos Activity (Preview)

5. Students will partner up and bring their computer/Chromebook. Each student can login so that everyone answers the activity questions and can take screenshots to add to their Google Slides for their notes.
6. Encourage students to take their time exploring each transformation carefully. They may struggle understanding shifting left and right. I related it back to the distance formula - (x - 3) moves RIGHT 3, not LEFT. 
   
7. The Exit Ticket/Reflection piece is on Flipgrid. Create a TOPIC in Flipgrid where students can respond.
8. TIP: I created a topic for EACH UNIT in my class so that students could see how their questions and reasoning improved as the unit continued. 

My Reflection:

• Since the remaining of the year (and future mathematics courses) depended on this lesson, I felt strongly about student exploring it on their own. I tried teaching the rules one year and it only set them up for failure later. 
• I'm currently reading Shake Up Learning by the infamous Kasey Bell of Texas. In her first couple of chapters, she stresses the importance of integrating 21st century skills into as many lessons as possible - hence, shake things up! Students will be asked to analyze critically and shoving rules in their faces wasn't accomplishing this and was NOT preparing my students for their future careers. Careers where thinking on their own and creating their own connections would be a requirement.
• One of my biggest fears with "shaking up their learning" is that my students won't learn the concepts "correctly". What if they misunderstand and I don't catch it?! In my mind, technology allows me to assess formatively more often, therefore I can check understanding frequently. When my concern of "learning incorrectly" snuck in to my mind, I forced myself to remember Jo Boaler - making mistakes is a learning opportunity. Even more so, making mistakes will make their brains grow. 

"Transform" your Mind to "Transform" your Students

Algebra 2 can "stretch" the student's brains, because it truly extends what they've seen in new ways. I believe that this course has new topics that students haven't seen, but much can be built on their foundation from Algebra 1 with the help of inquiry-based strategies.

Transformed functions showcased in the Olympics

Transforming functions has a huge impact in the real world, because let's face it, how often do you see a Parent Function staring at you on a day-to-day basis? (Yes, it's okay if you said never...) However, once you transform them using a variety of operations, you've created something incredibly useful and underrated in classrooms today.

I wanted to share this lesson involving inquiry-based instruction that depends on student's to explore the various rules and see them in action using Desmos.

"Millions saw the apple fall, but Newton asked WHY!" -Bernard Baruch

Check out this Desmos Teacher Activity that I created! If you haven't used Desmos before, I highly recommend it! It allows students to explore various cases in mathematics within seconds. Students can make connections instantly and feel free to investigate freely.

In the Desmos Teacher Activities, you can:

Teacher Options

1. Select your own "Pacing." This is especially helpful for those courses where chunking is crucial to student success.
2. Select the "Pause" to make connections as a class and bring the group together for a quick formative assessment.
3. Select "Anonymize" to help students share their answers in a stress-free environment. 

Screenshot from a Statistics Desmos
Activity where they were asked
to create a line of best fit.

While you're running the activity, you can determine if students have answered all the questions and leaves you free to assist students as necessary. The grayed-boxes in the picture would help be assist students that are struggling and need additional support with questions or encourage them to work with their team to brainstorm.

I've included some screenshots of previous activities that I've run in my Statistics course as well. The picture below shows my students creating what they believe is the "best-fit" line before we discover how to actually determine the real best-fit.

I can't stress how important it is for students to make predictions first before revealing anything. I couldn't count how often my students surprised me with their intuition and mathematical connections before I shared the "real" answer.

Screenshot of Anonymized Students
and students' Progress

The hardest part of Inquiry-Based Instruction that I've found is allowing your students the freedom to explore and knowing that they WILL discover it on their own without you. I get very tempted to step in, show them the steps, and then have them practice. However, I PROMISE, they will have a firmer grasp if you give them the chance.

Inquiry Based Benefits: My Favorite 5!

1. Nurture students' passions and natural curiosity
2. Increases engagement by relating the content to them personally.
3. Teaches perseverance through tough problems
4. Encourages students to take responsibility for their own learning.
5. Allows students to ask deeper questions.

Interested in learning more about Inquiry-Based Instruction? Wanting to become a teacher?!

Consider the UTeach Program and its sister programs across the United Stated. I am an alumni of the Teach North Texas program at the University of North Texas.

Pieces of my Heart

Check out Desmos Art for more!

For my final post in the Mathematics Series, I want to share one of my favorite projects. (Don't worry...just taking a break from the math to begin a new series)

Piecewise functions can be drag and cause students to break into pieces themselves. To me, piecewise functions can be the most useful ones in all mathematics. I usually explain to students that these are thieves - stealing pieces of functions that it needs or finds useful.

"To me, mathematics, computer science, and the arts are insanely related. They're all creative expressions." ~Sebastian Thrun

One of the BEST projects that I've done for my students is creating a "piece" of art using only piecewise functions. Not only do I get to see my students creativity come to life, but I also can determine their level of understanding of this topic. The project requires...

• Knowledge of Parent Functions
• Knowledge of Domain and Range
• Knowledge of restrictions that apply to different functions
• How to utilize inequalities for shading

Instead of focusing on graphing these functions and writing their equations on a worksheet, students are practicing these skills digitally but also engaging in other digital skills. Students loved coming to class to create a picture using maths. They were constantly surprised about how maths could fit into the pictures they were creating. Students were driven to reach beyond functions we've seen and create new ones (circles, ellipses, and trigonometric function). At the end, students shared their work and voted on their favorites to be featured on our class Twitter page.

Project: Pieces of Art

Directions: 

1. Students work with a partner to complete the activity in Desmos. This will help them discover and learn Piecewise Functions. This activity walks them through how to create different functions using Desmos.
2. The last slide of the activity provides a link to the Desmos website for students to get started with their creation.
3. A rubric is included below that uses Google Docs (paperless we go!).

👍TIP: Have students create a Desmos Account! This way they can save their work each day and then email you the picture at the end of the project!

👍TIP: Use a Google Form for student submissions. Then you have all the links in one place and your email is less flooded!

Materials:

• Student Activity in Desmos (Click me!)
• Piecewise Art Rubric (Click me!) 
• Example of a Google Form for student submission (Click me!)