Friday, June 3, 2022

When Math Gets Artsy.... Update!

In 2020, Covid-19 shut down our schools before I could take on another chance at one of my favorite projects. Check out my original blog post here

Then, in 2021, I had taken a job with an online school and didn't teach content that was applicable for this project. So again, I mourned the loss of another shot at this. 

Bring on 2022! The excitement and anticipation I had for this project was borderline insanity. I counted down the days until we could start all spring. I just knew that my group of students was going to absolutely crush it. A few changes to note from 2019 to 2022:

1. A more detailed attempt at a rubric. I wanted this project to be purposefully open ended with very little restrictions. Check out the 2022 rubric here: Desmos Art Project Rubric. Rubric writing is something I am still working hard to get better at. Students seemed to really understand the success criteria and I had very little confusion or questions arise about the rubric. 

2. We started the week long project with a full period of exploration in Desmos. I wanted to put out as many fires as possible before they started so they could really focus on the mathematics and the creativity could flow with out roadblocks. We covered all kinds of logistical tools and components in Desmos and I just let them explore and ask questions. This helped tremendously and I believe led to an increase in the quality of the projects turned in.

3. A Padlet for posting projects so that students could view each other's finished projects. They absolutely loved being able to see each other's projects and I do think that the fact that they were responsible for posting their project for others to see led to an increase in quality as well. The Padlet helped me stay organized and made for quick and easy sharing with colleagues and parents. 

So here it is, my 2022 Desmos Art Projects:

 2022 Desmos Art Projects Padlet

I could not possibly be more proud of my students. The work they put in and the amount of effort and grit they showed along the way to make the best possible version of the picture or image they could was beyond inspiring. 

4. After the project was over I asked them to complete a survey about the project and their experience. Here is the survey: 2022 Desmos Art Project Reflection. The results were almost as heartwarming and exciting as the projects for me. Here are a few direct student quotes from the survey: 

"I liked that creativity was important in this project which isn't the “usual” in math class, so that one thing i enjoyed."

"I liked the freedom and creativity and that there weren't really any rules that came with the project. It was easy but hard at the same time depending on what grade you wanted to get."

"I liked how challenging it was, some parts were harder to understand; especially the shading. I will say, I restarted like five times before I just stuck to a basic picture I knew I could create."

"I had a lot of fun figuring out how to move each line to match up with other lines. I was thinking about doing more for fun on my own."

"I enjoyed the process of moving around the different functions to perfect certain parts of my project."

"It was a fun way to review and get more practice on this units material."

Wednesday, May 4, 2022

Six Terrible Words to Say to Your Child

 Me: "Great job this chapter! You really did a fantastic job grasping some tough concepts. Way to persevere!"

Student: "Yeah. Thanks. I mean, I am glad I got an A on the test but it was kind of a waste of time. Even my dad said I am never going to use this stuff."

Me: "What do you mean?" Holds breath... knowing where this is going...

Student: "Just like this stuff we learned is pointless, ya know?"

Me: "I don't think it's pointless. I would imagine that many other professionals who regularly use this type of mathematical thinking don't see it as pointless either. Do you want to discuss applications of any of the concepts we learned about this chapter in more detail?" 

Student: "No not really. But have a good day!"

Me: "You too!" (fakes a smile while dying on the inside)

This was one of my conversations with a student last month. It's been a few weeks and this conversation is still frustrating me. It's not really bugging me from a teacher stand point (I think I am just numb at this point to the question of "when am I ever going to use this?") but more so from a new parent perspective. 

This student's parent said "You're never going to use this". Six terrible, dangerous words. I would imagine that underneath those six words the child heard much more. For example:

"You're never going to pursue an advanced STEM degree where this type of thinking and knowledge is needed."

"You're not the type of person who is going to find value in these complex problem solving skills."

"You have limits and boundaries to what you are capable of and it does not include advanced mathematics."

"I know more about what you will and will not want to study some day than you do and I am telling you what you can or cannot do."

I taught for almost ten years before becoming a parent. During that decade I tried really hard to never judge anyone's parenting. How do I know what it's like? Sure, research says xyz about child psychology and building confidence and blah blah blah but I have never truly been able to view education through the eyes of a parent.

Until now. Granted, I am only 18 months in. I am far from an expert here. But I hope that my daughter never feels like there are limitations on what she can accomplish. I hope that I always choose to speak to her and about her current and future educational experiences with genuine curiosity and excitement for the content she is learning, whether I find it useful or not. I hope that I never make comments like that parent made. 

I don't really care what the content is. Ceramics? Shakespeare? The water cycle? Dividing fractions? The complex structure of the human heart? Making paper snowflakes? All learning has value. All content has it's place and time in a child's development. I hope I never squash her desire to learn for learning sake. Not everything taught in school has to be relevant to the "real world" or the perception of what the real world is or is not. Not everything taught in school has to have explicit purpose some day for all students. But the ability to learn, to problem solve, and to acquire new passions and interests should be celebrated and encouraged every day. 

And it is for this reason that I want to say... 

(image taken from here)

To all the teachers out there who work day in and day out to make sure that school is a safe place for children to thrive, explore, and learn.... We celebrate you! You are needed! 

Thursday, April 7, 2022

Desmos Day of Exploration


I finally made a Desmos activity. It may not seem like that impressive of a feat to most people, but I have started and surrendered so many times. My teacher.desmos account is really a graveyard of whole hearted but half finished attempts. I never really knew whether it was a lack of desire or a lack of skill that prevented me from finishing the task but this week my inspiration to create the vision I had was through the roof and I was determined to make this work. 

And work it did. It was an incredible day. One of those days that feels almost illegal to not document or celebrate.

So cheers, to a completed Desmos activity and an instructional win full of student connections and exploration!

Students have been working with linear, quadratic, and absolute value functions with a focus on transformations from the parent function. Mix in a little systems of equations (graphing only right now) and here we are! I'll be honest, the actual creation of the activity was pretty easy. There are 4 challenges, each challenge with a clear set of requirements for the functions they had to write and a target intersection point. This was SUPER open ended which allowed for some rich comparison conversation and a lot of notice/wonder type whole class and group discussion. 

Teacher Dashboard View:

The really impactful part of this lesson was projecting the teacher dashboard view for students to see. There was such a wide variety of ways students completed each challenge and being able to quickly pull together different subsets of answers was really powerful.

Students were really engaged and motivated to figure out functions for each challenge. Creating the "need" for students to understand and use those transformations was really key. Even some of my more disengaged and less motivated students were finally asking me, "Hey Mrs. Bell, how do I make this thing go to the right? I am too far left." BEAUTIFUL... so let's talk about everything we've learned the last two weeks.... Better late than never! Maybe they just needed an actual reason to move their dang parabolas around finally!

Here are some awesome examples of each challenge and the functions students' created.

Student Work Challenge #1: 

Student Work Challenge #2: 

Student Work Challenge #3: 

Student Work Challenge #4:

Been hesitant to finally create that Desmos activity? Here is your push to do it. New things are hard. After a decade of teaching and plenty of Desmos specific training, I finally did it. Now is always the best time to push ourselves out of our comfort zone and grow as educators! 

Tuesday, March 10, 2020

Explore, Discover, Inquire: An Attempt at Inquiry Based Learning

I love the idea of inquiry based learning. I found this incredible graphic here to describe 10 reasons why teachers should be using inquiry-based learning in the classroom.

Phenomenal, right? Why would you NOT want to use inquiry-based learning in the classroom?

Let's be real for a second. There are just times when students cannot simply inquire their way through something. For example, the Quadratic Formula. I'm sorry, but no 15 year old is going to have enough grit or perseverance to ever come up with that bad boy.

Image result for quadratic formula meme

I am very selective with when I use inquiry in my classroom, cautiously only choosing content that students have plenty of background knowledge with so that they have an entry point to their exploration. I never want to have so much self guided inquiry that students shut down, give up, or feel like they have no idea how to begin. For 10th grade Geometry, finding the area of a polygon is the perfect opportunity for students to find success with an inquiry-based activity. Prior to this unit, students have had instruction on trigonometry, Pythagorean theorem, special right triangles, interior angle sum of polygons, and area of quadrilaterals, triangles, and trapezoids. With all the tools in their toolbox they need, students were ready to start exploring how to find the area of regular polygons!

In groups of 4, students were given a regular hexagon with a side length of 6. Of course I used my favorite dry erase mats. 

They were instructed to work together, using whatever mathematical tools necessary, to find the area of the hexagon. Here are some of the creative ways they split up their hexagons...

After students found the area (which by the way, almost every group was able to!), each group presented their strategy to the class.

After each group presented, we asked the class the following questions: 

1. How does this method compare with your method? What's similar? What's different?
2. If you had to find the area of another hexagon, would you change your method and do this one instead? Why or why not?
3. If you had to find the area of a heptagon, would this method still work? What about a octagon?

It was an awesome day and will lead beautifully into a more formal strategy for finding the area of any polygon as well as the formula using the apothem and perimeter. You could literally have checked each box from the graphic organizer above today. All the things happened. When inquiry is done right, it's a magnificent tool. 

Kudos to my student teacher, Ms. Schmidt for all the set up for this activity. She's half way through her student teaching and totally rocking it like a seasoned pro. I am so excited to see where her career takes her. If this is the beginning, I can't even imagine what's next!

Sunday, January 12, 2020

Traffic Light Class Activity

There's always certain topics that make me a little nervous to teach. Big topics. Those topics that you know your students need to understand, not just to be successful on this chapter or this year, but for all math every year after this year. It's a big responsibility to be the first teacher to expose them to a new idea, solving strategy, etc. It's sort of like laying the foundation on a house that you know others will need to build upon and the pressure to build a strong foundation can sometimes feel overwhelming. 

One of these topics for me this year is completing the square. I am especially anxious every year to teach this because it's a topic that I didn't understand at all when I was in school. It wasn't until college when I fully understood why we complete the square, when we complete the square or mathematically what the heck we're doing when we "randomly" add this "magic number" to both sides of the quadratic equation. I want to make sure that my students aren't just memorizing a bunch of steps but rather understanding the entire process with the end goal the focus of every step. 

After some good teaching days we were ready to practice but it was apparent that the level at which students were grasping this new idea was dramatically widespread. I needed an activity that would allow them to practice at a level that they felt comfortable, but would also challenge them to keep working on harder problem types. BOOM! Traffic Light Activity. Here it was...

The idea behind this activity is to create a variety of problems at different difficulty levels. Student choose the level they want to work at with the flexibility to change as needed. The cards are placed in my favorite pouches and spread all over the front of the room. It's organized chaos.

For this activity, green cards were worth 1 point and included completing the square problems where a=1 and the answers were nice rational numbers. Yellow cards were worth 2 points and included problems where there was a GCF involved (a is NOT 1) but still had rational solutions. Red cards were more challenging problems that sometimes had a GCF, but did NOT have rational answers, requiring them to simplify their answers in radical form. 

Students were told they needed to complete 8 points worth of work and they could be done for the day. Students got to choose how they wanted to earn their 8 points, with a mixture of easy, medium, and hard problems types. You could do more easy problems, or less hard problems. The choice is yours! The nice thing about a number like 8 is that you can't just do all green (there were only 5) so it forced students to at least try one or two of the harder ones to achieve 8 total. 

Many students got a little excited at the idea of the less work option, but when they realized they weren't quite ready and needed to go down a level, they just walked up to the front of the room and tried a level easier. There is lots of flexibility to allow students the ability to self asses where they are at, and change as needed with the goal of working up to the red cards. 

I wrote the answers on the back of the cards so that students could self check as we go. Our class culture involves almost daily conversations about how the answers are not the only end goal. Understanding how to arrive at the correct solution and being able to articulate a variety of solving methods with regards to efficiency, visualization, connections to previous concepts etc. is the bigger goal. When the answers aren't secret, students don't obsess over copying them with out doing the work. They know that I look for evidence of student thinking, not just answers.

There are so many ways to incorporate a traffic light activity in math content! This semester I have a student teacher again (TALK ABOUT A BLESSING) and she was so helpful in creating all these problem types. Seriously, can I have a student teacher like her every semester!? I am so lucky to have won the student teacher jackpot this semester! Boise State sure produces some top notch future educators.