March 2018 – Kaz’s Blog

March 18, 2018March 18, 2018

Create a Multimedia Enhanced Student Activity

Learning Objective:

Understand how the graph of $f(x)$ changes under the transformations $pf(x)$ and $f(qx)$

Task

In pairs, create a screencast that demonstrates your understanding of how changing variables $p$ for $pf(x)$ and $q$ for $f(qx)$ changes the graph of $f(x)$ . The graphs should be transformed using sliders and the graphing tool on www.desmos.com and the screencast should include audio commentary by both students.

Instructions

1. Go to Desmos Graphing Calculator and learn how to create sliders to change the values of variables $p$ and $q$ .
2. Investigate how changing $p$ for $pf(x)$ and $q$ for $f(qx)$ changes the graph of $f(x)$ by testing various functions (for example: linear, rational, quadratic, cubic, exponential, logarithmic, trigonometric, modulus). You will need to test a wide range of values for $p$ and $q$ and take notes on when and how the graph changes.
3. Once you understand the effects of $p$ and $q$ , you are ready to create your screencast. Plan out what you want to show and a script for what you want to say. You can watch a sample screencast that I created for this task at the bottom of this post.
4. Be sure to check the assessment rubric so that you know what you should include and how you will be assessed.
5. Submit your screencast as a .mp4 video file to the assignment on our Google Classroom page.

Assessment

Criteria	No Marks	Partial Marks	Full Marks
Use of Desmos and Sliders	Does not contain sliders	Sliders are used but do not change the graphs correctly	Sliders are used correctly and effectively
Understanding of Transformations	Little to no understanding of how $p$ and $q$ transform the graphs is demonstrated	Some understanding of how $p$ and $q$ transform the graphs is demonstrated	Strong understanding of how $p$ and $q$ transform the graphs is demonstrated
Depth of Investigation	The effects of $p$ and $q$ are not investigated	The effects of $p$ and $q$ are investigated but in a general sense	The effects of $p$ and $q$ are investigated for different ranges of values such as $p<0, 0<p<1, p>1$
Audio Commentary	Both students do not present or the audio is difficult to hear	Both students present but the investigation results are unclear	Both students present and the investigation results are clear and the commentary is effective

Resources

Desmos Graphing Calculator
How to use Desmos Sliders
How to make a Quicktime Screen Recording

I recently taught a unit on transformation of functions with my Grade 10 Math class and although I used an inquiry-based activity with a worksheet for them to fill out and demonstrate their understanding, I felt that there was room for the students to investigate on their own rather than completing a task just to fill in an answer. When I developed my own enhanced lesson, I realized how much understanding is needed in order to present on a topic and therefore felt that having students create their own presentation in the form of a screencast would require them to have a strong understanding of the learning objective. In the activity, I had students use Desmos Graphic Calculator which they are familiar with from other lessons, and get “hands-on” with the slider functionality which allows them to see how changes they make effect graphs in real time. I provided a sample screencast for students to refer to so they have an idea of what is expected. At first, I was undecided about providing this as I feared students would simply copy the format and all the submissions would seem the same. However, I have found from experience that when the task is too open-ended with little guidance or structure, students have a more difficult time reaching the learning objective. Also, this task requires much more investigation than the sample I provided which force students to have to inquire further. Finally, I provided a rubric on how they will be assessed so that students are aware of exactly what is required for the task. Some of the descriptors are also my way of guiding the students what exactly they need to be considering when studying this topic.

March 17, 2018March 18, 2018

Week 10 Activity 4 – Experience with File Storage Sites

Here are some of the file storage systems I have used and some thoughts.

Google Drive and Google Backup and Sync
15GB – Free
100GB – $1.99/month
1TB – $9.99/month
(not sure if the CDN prices are accurate as I am in Japan)

This is what I currently use to backup all of my data because my school is a Google for Education school which means we get unlimited storage space. This is quite a nice perk because it means I can keep everything on my computer backed up in the cloud and not have to worry about choosing what to sync or reaching capacity. All of the school’s file sharing and storing for students and teachers is done on Google Drive.

Google Drive is my choice. I’m sure most people are familiar or use Google Drive or some other file syncing system but here are some features which you may not know about:

With the app downloaded on your computer, Google Drive becomes a folder on your Windows Explorer or Finder which you can drag and drop files into or browse seemlessly without waiting for pages to load (as with the browser version). The folder is continuously synced so whatever is in the folder is what is in the cloud.
Recently, Google launched Google Backup and Sync, which not only syncs your Google Drive folder but has the option to sync other folders and files on your computer. For example, you can Sync your desktop or your Photos for MacOS backup file.
If you right-click a file in Google Drive (on the browser), you can “manage versions” which allows you to download or go back to a previous version of a file. This has saved me many times when I hit save and close on a Word doc even though I didn’t want to save the changes I made.
You can share files and folders very easily with other people who have a gmail account.
The mobile app also allows you to access everything. Google Docs, Sheets, Slides look fine but other files such as Microsoft Word, Excel do not always display correctly.

Dropbox
2GB – Free
1TB – $9.99/month
I use Dropbox as a sub account. It works just fine and I don’t know if it does anything more or less than Google Drive. I do know that some of my app on my phone (like 1password) can link with Dropbox and backup the contents automatically.

Flickr
1TB of photos – Free

Box.com
10GB – Free
1TB – $9.99/month
I setup an account and tried it for the first time. It works very much like Google Drive and Dropbox.
One interesting thing I found was that you are able to create a new Microsoft Word, Excel or Powerpoint file right in the browser. I knew it was possible to create Microsoft Office documents from office.com but I found it interesting that this option was available from a third party.

March 9, 2018March 11, 2018

Create a Multimedia Enhanced Lesson

Lesson Objective: Find the domain and range of a function from its graph.

We have learned that certain relationships between two variables are called functions. If a relationship is a function, then for every input $x$ there is only one output $y$ .

The domain is the set of all possible values of $x$ for a function. It is a set so we use set notation such as $\{x>0\}$ .
The range is the set of all possible values of $y$ for a function. It is also a set so we use set notation such as $\{y\ne0\}$ .

Example 1
Example 2
Example 3
Example 4
Video

Example 1:

Find the domain and range of the function with the following graph.

Domain:

$Domain: \{x>-3\}$

Range:

$Range: \{y>-2\}$

Example 2

Domain:

$Domain: \{x\in\mathbb{R}\}$

Range:

$Range: \{y\leq2\}$

Example 3

Domain:

$Domain: \{x\neq4\}$

Range:

$Range: \{y\neq-2\}$

Example 4

Domain:

$Domain: \{x\neq-2,x\neq2\}$

Range:

$Range: \{y\leq-1,y>0\}$

Video

Homework:
Question #2 on Page 387

When I first started thinking about this assignment, I thought of topics that my students have struggled with in the past and Domain and Range topped my list. It is a difficult concept that diagrams in textbooks just don’t explain effectively. To enhance student learning, rather than relying on text and diagrams, I drew graphs of the function and domain/range on Desmos and used the animate feature with some Math tricks to show how the domain can be visualized. In addition to creating graphics using screenshots, I used GIPHY Capture to create short gifs for the lesson so the students can repeatedly watch the process. The minimal use of text is intentional so that students can try to develop understanding through visuals but I also added a video with explanations for students who need further support. To create the video, I used the screen recording feature in Quicktime, then used Handbrake to reduce the video file size from 113.3MB (.mov) to 7.2MB (.mp4). Finally, I uploaded the video to YouTube and embedded the video in the lesson. Quick LaTeX was used for all the Mathematical formulas.

The font used is Libre Franklin (a sans-serif font) for ease of reading and there is high contrast between the font and background colors for better comprehension and reading speed. Headers and lists with hyperlinks to anchors on the page are also used as organization tools (Webster, 2014). Domain and Range is a deep topic but this lesson focuses on one small chunk without extraneous elements in accordance to Cognitive Load Theory (Webster, 2010). I used interpretive graphics (Clark and Lyons, 2010) to show the relationship between the graph of the function and its domain and range. The gifs are provided so that students can learn at their own pace and watch an example over and over again until they understand, based on the Segmenting Principle (Mayer, 2014). The positioning of the diagrams, such as the static domain image shown directly below and the static range image shown directly to the right of the animation as well as the positions of the equations for the domain and range, are based on the Spacial Contiguity Principle (Mayer, 2014). I used narration for the video with no words on screen to avoid split attention and overloading the visual channel as prescribed by the Modality Principle (Mayer, 2014).

References

Webster, K.S. (2014). Text Design for Online Learning. Retrieved from
http://courses.olblogs.tru.ca/eddl5131-jan17/week-2-text/text-design-for-online-learning/

Webster, K.S. (2010). Graphics for Learning. Retrieved from
http://www.youtube.com/watch?v=K5yd_M2xe78

Clark, R.C & Lyons, C. (2010). Three views of instructional visuals, In Graphics for Learning: Proven Guidelines for Planning, Designing and Evaluating Visuals in Training Materials. San Francisco: Pfeiffer, 15-28. Retrieved from
http://site.ebrary.com.ezproxy.tru.ca/lib/trulibrary/reader.action?

Mayer, R.E. (2014). Research Based Principles for Multimedia Learning.
Presentation given at Harvard University, 5 May 2014. Retrieved from
https://www.youtube.com/watch?v=AJ3wSf-ccXo