Samantha Norrie

Big Idea

Calculus 1 is one of the biggest and most feared first-year university classes. Many students feel overwhelmed in Calculus 1 due to not sharing the same academic background as their peers, not resonating with the learning strategies presented to them, and struggling with the many life changes that come with beginning university. 

This lesson covers derivation. Derivation is often one of the first core concepts taught in Calculus 1. In this lesson, students will learn how to derive equations, why derivation is important, and its real-life applications. Often, students only learn how to apply the math concepts they learn during their first year later on in their degree. We believe that showing students the practical applications of derivation while they are learning the concept will help motivate their learning.

A geometric painting that only uses trigonometric derivations for lines by DALL-E

Still not convinced that derivation can be fun? The lines in this image were created by deriving trigonometric equations using the skills that we will be covering today!

Learning Outcomes

• Solve simple single-variable partial derivations
• Know how to derive trigonometric functions
• Plug in derivation equations into Symbolab and understand how to follow along with Symbolab’s step-by-step answers
• Describe at least one practical application of derivation

Evidence of Learning

Students will demonstrate their learning by completing a variety of active learning activities after doing some passive learning. Passive learning will be done by watching some videos on derivation. Students are not required to watch all of the videos provided. Multiple YouTube channels have been provided to allow students to easily explore different teaching styles. The active learning activities do not include a lot of derivative exercise sheets. This was done intentionally. While exercise sheets can help students learn, it is easy for students to cheat on them through the use of tools such as ChatGPT and Symbolab. This lesson aims to use the aforementioned tools positively by encouraging students to expand their learning by asking questions about content that they are interested in.

Activities

Watch

Before starting any of the hands-on activities, we recommend that you watch some videos on the concepts outlined in the Learning Outcomes section of this document. Please note that you do not need to watch all of the videos listed below if you already feel comfortable with some derivation concepts.

Here are some great math instructors on Youtube

• NancyPi (https://www.youtube.com/@NancyPi )
  • This is NancyPi’s derivation playlist: https://www.youtube.com/playlist?list=PL3j1ntBPCU_om5O1RBi5-vDRwVTvDwyeV 
• Dr. Trefor Bazett (https://www.youtube.com/@DrTrefor )
  • Definition of a Derivative Part 1 https://www.youtube.com/watch?v=hp046sLvQpM&list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m&index=18 
  • The derivative of Trigonometric Functions https://www.youtube.com/watch?v=QDKj-E-ICPo&list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m&index=26 
  • Derivative of Inverse Trig functions via Implicit Differentiation https://www.youtube.com/watch?v=fnVMT08u6fU&list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m&index=31 
• Khan Academy (https://www.youtube.com/watch?v=ANyVpMS3HL4&list=PL7B3AC52CD32D87A8 )
  • This is Khan Academy’s derivation playlist: https://www.youtube.com/watch?v=ANyVpMS3HL4&list=PL7B3AC52CD32D87A8  

Active Learning Activities

1. Play through A Journey of Blood, Sweat, and Derivation (https://h5p.org/node/1465369?feed_me=nps ). This quick game will help you gauge where you are with your derivation skills.
2. Plug a polynomial of your choice into Symbolab (https://www.symbolab.com). Take a screenshot of the answer you receive from the app.
3. Log into ChatGPT (https://chat.openai.com ) and ask ChatGPT about how derivation is used in the real world. Ask it four follow-up questions after you ask your initial one. Please take screenshots of your conversation with ChatGPT.

Here is an example conversation that I had with ChatGPT about how derivation is used in Computer Science:

Reflective Questions

Now that you have reviewed some derivation concepts and have practiced using derivation, it is time to reflect on your learning

• What have you struggled with the most during this lesson, and what have you struggled with the least?
• Did any of the videos or active learning activities resonate with your style of learning? 
• What do you think of Symbolab’s problem solver?
• What did you learn from your conversation with ChatGPT?

To-do    

In your assignment submission, you should include

• Your polynomial derivation question screenshot
• Your ChatGPT screenshots
• Your responses to the reflection questions listed above

References

• “DALL-E,” 2023. [Online]. Available: https://www.dall-efree.com 
• “Symbolab,” 2023. [Online]. Available: https://www.symbolab.com
• “H5P”, 2023. [Online]. Available: https://h5p.org 
• “ChatGPT”, 2023. [Online]. Available: https://chat.openai.com 
• “Norco,” 2021. [Online]. Available: https://rawfury.com/games/norco/ (H5P artwork)

Reflections

I decided to generate an image for the Big Idea section. While adding imagery that is not necessary for the lesson can increase the amount of extraneous load the learners experience, the image I included helps set a creative tone for the lesson.

The primary goal of the Learning Outcomes for this lesson plan was to create a rubric that will help students develop solid foundational derivation skills while empowering them to take initiative. The learning outcomes of this lesson encourage students to practice basic derivation techniques that are taught in nearly all Calculus 1 classes while also pushing them to explore using tools that can help them work through derivative problems in the future.

I wanted to use a variety of different tools in the Activities section. For my passive-learning sub-section, I linked multiple math YouTube channels and their respective videos on derivation. I decided to include multiple channels and videos so that students could choose to watch the ones that best resonated with their style of learning as well as their current derivation knowledge. Doing this aligns with Merrill’s activation principle as it relies on students reflecting upon their existing knowledge.

I decided to apply Merrill’s application principle the Active Learning sub-section. I did this by creating multiple exercises that allow students to apply their learning in different ways. The first exercise is the most like a typical derivation worksheet exercise. I decided to make this exercise a quick game-based exercise to help make the traditionally dreaded worksheet a bit more fun! The next exercise forces learners to explore Symbolab. Symbolab is a great tool for learning how to solve a variety of math problems. While some calculator applications only give users the answers to their math problems, Symbolab provides users with step-by-step solutions. The last exercise pushes students to explore the practical applications of derivation by asking ChatGPT questions. I believe that having students explore derivation by themselves incorporated Merrill’s integration principle.
The Reflections sub-section wraps up the active learning portion of the lesson. It pushes students to reflect on the active learning they have done throughout the lesson. The students finish the lesson by handing in their screenshots and their answers to the reflection questions.

Module 5 blog post https://snorrie337.opened.ca/2023/11/25/module-5-reflections/

Module 5 comment https://kayleymcn.opened.ca/2023/11/24/blog-post-5-advanced-mutlimedia-tools/?unapproved=5&moderation-hash=2935de8524ed01d9eaaa2c254b3c95d4#comment-5

Module 4 blog post https://snorrie337.opened.ca/2023/11/25/module-4-reflections/

Module 4 comment https://edci337blog.opened.ca/2023/11/21/module-4/?unapproved=7&moderation-hash=ac10c23076ab473e9ff3342fdfc7b24d#comment-7

Module 3 https://snorrie337.opened.ca/2023/11/04/module-3-assignment-2-comment/

Module 1 and 2 https://snorrie337.opened.ca/2023/10/14/midterm-1-comments/

Duolingo is a video game learning support tool that I use quite frequently! On Duolingo, users can learn new languages through gamified learning. I have been using the app to help me learn Spanish over the last 10 months or so.

I’ve found that Duolingo incorporates Merrill’s principles quite well. The app allows users to practice their language reading, writing, and speaking skills in bite-sized lessons. By practicing these three language skills together, learners can practice and hone their knowledge in real world-like scenarios.

I think building an application for Historia could help improve the game! In addition to automating some of the repetitive tasks of the game, some graphics could be added to help further immerse students. I think some data visualization could also be added to help students keep track of their data.

CSC411: Information Visualization, a course on how to create effective data visualizations offered by the Computer Science department at UVic, implements constructive alignment and backward design quite well. Throughout the course, students iteratively work on a final project within small groups. This allows for the students to apply and practice the skills that they learn throughout the course.

I like the balance of active and passive learning in EDCI 337. I appreciate how all passive learning in the course is followed by multiple active learning activities. Having questions to answer, activities to complete, and blog posts to write after finishing the required readings for the course allows me to apply my recent learnings!

I have found that the balance between active and passive learning has varied quite a bit in the courses I have taken for my Computer Science degree. The curricula of many math and algorithm focused classes involve a lot of reading and listening. I find these classes to be a bit difficult for me, as I am someone who likes to learn by working through many problem sets or coding problems.

My K-12 learning experiences involved a lot of active learning! I had the opportunity to be in a french immersion program throughout K-12. My french immersion teachers had my class and I complete many activities to ensure that we would be successful in learning French!

I think the assignments in CSC130: World Wide Web and Mobile Applications, a course that teaches students how to program websites, are a great example of scaffolding in learning. During the first half of the semester, the student learn how to write HTML and CSS code, which helps them create static webpages. Once they are done learning the basics of HTML and CSS, the students make a static website using the skills they’ve recently learned. The students learn how to use JavaScript, which allows programmers to add dynamic behaviour to their websites, during the second half of the course. At the end of the course, students create another website using HTML, CSS, and JavaScript.

My H5P object can be found at https://h5p.org/node/1465080

My lesson plan can be found here https://snorrie337.opened.ca/2023/11/25/module-4-learning-plan/ !

EDCI 337 Lesson Template

You can use this template (based on the structure of this course) to make sure that you create all of the connective pieces that knit a lesson together. You don’t have to use this structure, but your lesson should include most of these components:

Overview

A quick introduction to the topic of the week. Why is it important? How does it connect to the other topics in the course? Adding a video to this section can aid in creating a teaching presence in your course. 

(Keep in mind that this template is based on a real-life situation, where you’re building a lesson that is part of a course. For the purposes of this assignment, it’s not necessary to imagine the entire course and identify this lesson’s connection to the other topics in it. Although if you have some ideas about that, feel free to include them.)

In this lesson, learners will explore superposition and entanglement, which are two important foundational concepts in Quantum Computing (QC). These two concepts allow for Quantum Computers to solve problems that traditional computers cannot.

Lesson Objectives

What will learners be able to know/think/do by the end of the lesson?

• Define superposition and entanglement
• Put qubits into superposition using IBM Composer
• Entangle qubits using IBM Composer

Read/Watch

This is the content that will give learners the background knowledge to participate in the learning activities of the week.

• https://www.youtube.com/watch?v=mAgnIj0UXLY explains the basics of superposition
• https://www.youtube.com/shorts/pyMFz8f67FE explains the basic of entanglement
• https://qiskit.org/documentation/qc_intro.html further explains superposition and entanglement

Content

What additional content is required to prepare learners to meet the learning objectives of the lesson and connect the topic to the rest of the course?

• https://quantum-computing.ibm.com/composer/files/new IBM Composer allows users to explore creating quantum circuits without needing any coding knowledge

Application

How will learners apply their new knowledge and skills? What problem will they solve? How will they demonstrate their learning?

Learners will explore creating quantum states that are in superposition and that are entangled using IBM Composer. They will document the quantum states they create by taking screenshots and writing short reflections on them.

Reflection

Research shows that learners who can reflect on their learning are more likely to integrate and connect what they’ve learned to prior knowledge.

• While using IBM Composer, how were you able to tell if a quantum state was in superposition or not?
• Can qubits be entangled while not being in superposition? Explain why or why not.
• How can you tell if a quantum state is entangled? Some additional research may be needed to answer this question.
• What happens when a Hadamard gate is applied to a qubit? What happens when it is applied twice?

To Do This Week

A to do list helps scaffold learners, reducing the extraneous cognitive load involved in following a lesson. 

• Create three separate quantum circuits, all with different amplitudes, in IBM composer. Include screenshots of your circuits in your submission.
• Research Bell states and create one in IBM Composer. Include a screenshot of your Bell state in your submission.
• Answer the reflection questions above. Include your responses in your submission.

References

This is where you credit your sources.

• “Qiskit textbook,” 2023. [Online]. Available: https://qiskit.org/learn
• “Composer,” 2023. [Online]. Available: https://quantum-computing.ibm.com/composer

I quite enjoyed using ChatGPT as a game simulator! While I think that not having any graphics (other than ASCII art) limits how immersive ChatGPT’s simulations can be, I still believe they can be great tools (and also very fun)! I think simulators like Benjamin Breen’s could be used to enhance lectures and readings in a variety of classes. I have included screenshots of my experience with Benjamin Breen’s simulator.

I have used ChatGPT as a learning tool! Whenever I’m practicing Spanish grammar, I ask ChatGPT to generate practice sheets for me. I also use ChatGPT to help me review different programming concepts.

I think ChatGPT can allow students to receive more learning support. In addition to answering student questions, ChatGPT can also help students practice for upcoming tests and assignments by making practice sheets for them.

While ChatGPT can be an inclusive learning tool, it is important to recognize that not everyone can access or benefit from using ChatGPT. The quality of information that ChatGPT provides greatly varies based on the subject material of the prompt and the language it is written in.

Despite being great learning tools, AI tools have raised many ethical concerns. One of them is copyright. Many artists are concerned about DALL-E using their work without their permission.

I found ChatGPT and Datawrapper to be particularly useful! ChatGPT allowed me to play through a variety of simulations while also helping me summarize my learning. Datawrapper allowed me to quickly see the data I provided visualized in many different ways. This allowed me to figure out which visualizations worked and which ones definitely did not! I’ve included a screenshot of a Datawrapper visualization I made.

While I will continue to use ChatGPT to help me reach my learning goals, I will not use it to make any important decisions, especially health decisions. As ChatGPT can easily present false facts as truths, I think it is important not to place too much importance in the answers it gives.

I hope that AI tools will produce less misinformation in a few years’ time. I believe this will have to be accomplished through the development of better safety and misinformation-checking tools.

I think adding animation to the Income Mobility data visualization helps captivate viewers. While the animation helps captivate viewers, I believe that it does make the visualization a bit harder to read at first. I think changing the visualization to being a static visualization would help improve its legibility.

While taking CSC411: Information Visualization, I had the opportunity to learn about data visualization techniques that can be used to misrepresent data. A few of these techniques include uneven spacing between graph ticks, not having percentage values add up to one hundred present, and using similar colors to connect unrelated data.

I also learned about effective data visualization techniques during my time in CSC 411. These techniques encompass using a color palette that aids in distinguishing unrelated data (and connecting related data if desired), clearly labeling crucial attributes, and employing varying font sizes to indicate the importance of information.

When designing a data visualization, it is important to be mindful of the color scheme being used to ensure that individuals with color blindness can still use them. Tools such as the Accessible Color Palette Generator (https://venngage.com/tools/accessible-color-palette-generator) can be used to generate accessible color palettes.

References

OpenAI. (2023). ChatGPT (Version 3.5) [Software]. Retrieved from https://www.chatgpt.com

Engage. (2023). Accessible Color Palette Generator [Software]. Retrieved from https://venngage.com/tools/accessible-color-palette-generator

Datawrapper. (2023). [Software]. Retrieved from https://www.datawrapper.de

https://www.datawrapper.de

My blog post for Assignment 2 can be found at https://snorrie337.opened.ca/2023/11/04/module-3/ and my comment can be found at https://addifowler.opened.ca/2023/10/27/assignment-2-video-for-a-learning-purpose/?unapproved=8&moderation-hash=90738c9b8e1053ecc33424b296a015d1#comment-8

I have included a screenshot below as my comment has not been approved yet 🙂

In Module 3: Storytelling and Creating a Video, I was able to learn about various storytelling techniques, how to use twine, as well as how to create instructional videos!

Video and Twine Projects

I decided to choose Quantum Computing as my video topic as it is my favourite area of Computer Science!

The learning purpose of my video is to provide viewers with a basic understanding of how Quantum Computing works. I also explain why Quantum Computing is so, so exciting and applicable to our lives. Over the last few years, “Quantum” has become a bit of a buzzword. I believe that it is important to separate fact from fiction!

I applied a few of Mayer’s principles of learning in my video. I incorporated the personalization principle by not using any unnecessary jargon and by focusing on using a conversational tone. I also applied the interactivity principle by asking viewers a question at the beginning of my video. Lastly, I made sure to use the split-attention principle in my video by making sure that any visual content that I used supported my narration instead of taking away from it or overloading viewers with too much information at once.

One of the critiques that I have for my video is that the stories that I use are quite short. They are more like short analogies than complete stories. While I think they help the audience visualize topics introduced in my video, I think they could be improved upon to help further improve learning outcomes. Despite them being quite short, I found myself intuitively trying immerse my audience in Quantum Computing by showing them why the subject is interesting instead of directly telling them. I think this reflects on which storytelling techniques have impacted me throughout my degree the most. I believe that it is easier to show why some Computer Science concepts are important through immersive demonstrations and analogies than it is through full-fledged stories. This does not mean that the former are better, though! This assignment has made me wonder if I have been limiting my growth as an educator by not using more detailed stories when explaining new Computer Science concepts.

I tried to apply the learnings from my Assignment 1 feedback in my video! Instead of recording my audio in one take, I took multiple recordings for each section of my video. I also tried to not speak so quickly. I think I still need to work on this, but I did notice myself slow down a bit more while recording my audio!

While I did make some mistakes while recording my audio, I believe that it was the easiest part of the video making process for me. Having a script already made allowed me to focus on reciting my script instead of on how to explain different concepts on the spot. While it is still hard for me to listen to my own audio recordings sometimes, I think experiences like these are helping me gain more confidence!

I want to use more props next time I record a video! I have seen others use props such as donut pillows and balloons when explaining Quantum Computing. I think adding fun props to educational videos helps make the content being presented less intimidating and more fun!

My video can be found at https://vimeo.com/user210622551 !

My twine story can be seen below. I used Figjam to help show how my Twine passages are connected.

Reflection Questions

During my first lecture on Quantum Computing, the lecturer told us a story to help demonstrate to us how one of the algorithms he was using works and why it is important. I quite liked this technique as I believed it helped the class get a good grasp of why they should be learning about Quantum Computing before learning about the math behind the algorithm. This lecture made me want to pursue doing research in Quantum Computing.

I found Malcolm Gladwell’s TED talk to be quite compelling. I appreciate how he described the characters in his story. I believe that doing so allows his audience to relate more to aspects of his stories while also gaining better context of what he is describing.

When I tell stories, I like to show my audience aspects of my stories instead of telling them. I think this helps my audience immerse themselves in my stories while also drawing their own meaning from them. I also try to end my stories with a positive take or a lesson I learned from them (when appropriate)!

My script for my video is below:

Before I start talking about Quantum Computing, I want to ask you to compare two pieces of technology: cars and submarines.

Both are useful pieces of tech, but they’re not great at doing each others’ jobs. The same can be said about classical computers, which are the computers that we use today, and quantum computers
So, why are classical computers and quantum computers so different?

Classical computers and quantum computers are different because they speak different languages

Classical computers use bits to communicate. A single bit can be either a zero or a one. Bits can be visualized as a light switch that can either be on or off

Quantum computers use qubits to communicate. Unlike a bit, a qubit can be a zero and a one at the same time. qubits can be visualized as a light switch with a dimmer. It can be completely on (and have a value of one), completely off (and have a value of zero), or it can be somewhere between one and zero.

How can this be?
The value of a qubit is dictated by probabilities. For example, a qubit can be 50% zero and 50% one, or 75% zero and 25% one. There are infinitely many possible probability combinations, the only criterion is that a qubit’s probabilities must sum up to 100%. Qubits that are not 100% guaranteed to be either zero or one are said to be in superposition. Superposition is what allows quantum computers to work their magic

Qubits can be extremely powerful. Their superposition allow us to quickly solve problems that either take a long long time or are impossible with regular bits.

Unfortunately qubits in superposition are extremely finicky. In order for a qubit to be in superposition, it must be super super cold. This is why quantum computers have such huge fridges. If a qubit gets a little too warm, it may stop being in superposition, meaning that it will take a value of one or zero. This process is called decoherence. Qubits can also experience decoherence if they’re not given any instructions for a long period of time or if another qubit near them disrupts them.

Researchers are working hard to create techniques that help prevent and eliminate decoherence. The quantum computers we have today are known as Noisy Intermediate Scale Quantum computers, also known as NISQ computers. This means that we have to expect and account for decoherence when working with these computers.

So, if quantum computers are only semi-reliable, what can they actually do?

Quantum chemistry is currently one of the most promising fields that involves quantum computing. With classical computers, only compounds with only up to 15 atoms can be simulated. Thanks to the computational power of quantum computers, this limit can be surpassed, which will help with the invention of better drugs

Quantum machine learning is also a hot topic. Powerful AI models such as ChatGPT currently only use classical computing power. Imagine how much more powerful and efficient ChatGPtT could be if at least part of its AI brain was quantum.

Lastly, quantum computers can help us deal with optimization questions such as what is the most optimal way for factory machines to work in tandem as well as various complex traffic and mapping problems? These problems may not seem too difficult, but they can get hairy pretty quickly, which causes classical computers to stumble

Thank you for watching my presentation!

Here are my comments for midterm 1!

Module 1 https://usunghiro.opened.ca/2021/05/04/test-post/#respond

Module 2 https://rsim.opened.ca/2023/10/13/accessibility-and-design-principles-through-infographics/#comment-4

I have added photos of the comments below as well!

• good! I can’t seem to figure out how to modify my published comments 🙂

In *Module 2: Design Principles for Effective and Accessible Multimedia*, I had the opportunity to learn more about accessible design and to reflect and learn from the accessible design mistakes that I have made in the past. By using the WAVE accessibility checker tool, I was able to learn about the accessibility weaknesses in my WordPress blog. One of the main issues that I discovered by using the tool was the lack of high-contrast text on my site. This surprised me! When I first made my WordPress site, I made sure to choose a theme that I thought was accessible. Running the WAVE accessibility tool showed me that I need to make sure to not only use my own judgment when designing websites. I plan on using WAVE to test future web development projects of mine! 

WAVE also made me realize that I did not add any alt text to the screencast that I made! In addition to forgetting to add alt text, I also forgot to add captions to my screencast. While it is possible to auto-generate captions, the results can sometimes to so-so.

I made my infographic about the five stages of language learning! I focused on simplicity while creating my infographic. I did this by using a limited colour palette, and by using simple imagery. Using a limited colour palette and simple imagery helps reduce the viewer’s cognitive load by ensuring that they do not have to concentrate on mapping colours to different ideas presented in the infographic.

I found Canva to be very helpful while making my infographic. Being able to view many different templates allowed me to explore and come up with many different ideas for my infographic. I also found Canva’s recommended images to be very helpful. The images that Canva recommends are based on the images that have already been added to an infographic. This helps users keep their images consistent, which in turn leads to their infographic being simplistic and legible!

While graphic design is visual, I think that it is very possible to make graphic designs accessible for those with visual impairments! This can be done by adding alt text to designs and by ensuring that they can be read by a screen reader. If one is using code to create their design, they can ensure that a screen reader can read their design by using the appropriate HTML tags in their code. HTML is the programming language used to design the ‘skeleton’ of a website or design. How the website or design is styled or reacts to user interaction is determined by other programming languages that are put on top of the HTML.

To me, inclusive design is the practice of designing for real people. During my first two years of studying Computer Science, I found that it was easy to forget that the ultimate goal for the code that I was writing was for it to be able to help *real* people! I think that this happens to many students early on in their degree as most of what we focus on is getting comfortable with the algorithms and math used in Computer Science. After completing some co-ops and learning about web development, however, I realized that inclusive design should always be the main goal of anything that I create. Including design classes early on in Computer Science degrees would be incredibly beneficial.