Math and Fun: Not an Oxymoron in a Flipped Classroom

In middle school and high school, I heartily looked forward to science classes each day.  They were a chance to ‘experiment’ – to play, test, follow curiosity – and yet, somehow, through this, learn.  What a radical idea: the combination of natural interest and discovery and education!  But all sarcasm aside, teachers are testing more ways to make learning fun, memorable, and meaningful.  Labs need not be limited to a science classroom.  Indeed, flipped learning as a strategy for any class attempts to take advantage of technology to give students the best of both worlds: interesting lessons and non-drudgery homework in the form of class ‘explorations’ or other active learning strategies.  There is huge potential in using technology for this purpose, and as teachers, we can continue to learn by trial and error, using our imaginations (and the scope of the internet) to craft new lesson sequences and see what is effective.

Here is my attempt at creating such a lesson for a high school trigonometry or Pre-Calculus class learning about the Unit Circle.

Learning Objective

Students will be able to label the Unit Circle on their own, using intuition.  They will be able to identify the patterns that the trig functions follow.  Furthermore, they will be able to explain how we derive trig values from special triangles on a circle of unit radius.  Finally, when given a major angle measure, they will be able to return the corresponding sine, cosine, and tangent values, or vice versa, given trig values to match with angle measures.

Digital Resources for Flipped Elements

This lesson will work off of Bloom’s Taxonomy.  Students will begin with “homework” to do the lowest level of thinking to memorize the basic values of the unit circle.  They will have at their disposal multiple tech tools to do this, as students learn in a variety of ways.

Visual learners might want to utilize these programs on Desmos and Geogebra, which help students to connect the dots between shapes/spaces and trig values.

 

Desmos Unit Circle Exploration: I especially like the use of colors on Desmos – never hurts to make math prettier and more appealing!

 

Geogebra Unit Circle Exploration: Note how there is a slider which helps students visualize the effect of radian measure on trig value.

Students more inclined to numerical or algebraical thinking might want to use a chart (especially an interactive one like this), which shows patterns among trig values to ease memorization.

Clicking “Show” or “Hide” reveals the corresponding trig value in the chart, making this like a matching game.

The objective of this beginning stage is to gain comfort with the idea of radians, triangles inscribed in a circle, and the connection between angles and trig values.  At this point, students should develop a base knowledge of trig values in relation to certain radian measures, but I would not expect them to understand the significance of these values.

Active Learning Strategies – Interactive, Collaborative, Digging Deep

The next part of the blended lesson is the in-class work, which here will consist of active student participation in a “lab” to get to the root of the importance of the unit circle.  Students would work in groups, following a lab procedure that would lead them through activities looking at recognizing and questioning the qualities of the circle.  At sporadic points throughout the lab, I might draw the class together to make important points or to give them hints on how to proceed, but their background knowledge should give them the foundation to proceed more or less independently.  Finally, at the end, we would come together as a class to review our findings and discuss how this new material will benefit us in the coming unit.

How Will the Lesson Flow?

Using a flipped lesson sequence frees up time to focus on deeping students’ learning in class.  By intentionally guiding students’ focus from basic to more advance studies of the circle, my hope is that they will not feel overwhelmed by the unit circle and instead give each aspect of it its due diligence and attention; ultimately, this should pay off in gaining both a general knowledge and a more application-based ability concerning the unit circle.

Why Use the Blended Model for this Lesson?

The goal of this lesson is for students to develop an intuitive understanding of the unit circle in order to be fully prepared to deal with all things trig-related in the following units.  The unit circle is hugely important and often not covered in due depth.  It may seem that math teachers’ insistence on knowing by heart the values on the unit circle is overboard, but really – they are not deceiving you in telling you that knowing this material like the back of your hand will pay you back several fold as you continue in math.  More critical even than memorizing the values of the circle and a much more thorough way of learning the circle, in fact – is being able to derive these values.  From what do they stem?  How are radians related to measures of a circle?  How are trig functions tied to coordinate points?  How do we convert between trig functions, or even undo trig functions with inverses?  These are the deeper questions that students should be able to answer.

Featured image: Bob B. Brown

What’s Your Sine?

1. Learning Objective

Students will be able to find the derivatives of sinusoidal functions.

2.  Digital Resource(s)

Before coming to class, students will watch an online video that I will create of me proving \frac{d}{du}sin(u) = cos(u) and \frac{d}{du}cos(u) = -sin(u).

3. Active Learning Strategies

Once students have an idea where the equations come from, they can use the freed up class time to solve problems where they are asked to find the derivatives of sinusoidal functions.  One active learning strategy that I might employ is Numbered Heads Together.  I will split students into groups of three or four and have them collaboratively work on problems that I will provide.  One randomly selected student from each group will then provide a brief explanation of how their group went about solving the problem.  Students who would have difficulties solving the problems on their own will have the benefit of group members to help them out.

4. Lesson Flow

The video explains to students where the equations \frac{d}{du}sin(u) = cos(u) and \frac{d}{du}cos(u) = -sin(u) come from.  I will begin class by demonstrating to students how we can use these equations to find the derivatives of various sinusoidal functions.  The example problems will require the use of techniques taught in previous lessons such as the power rule, the product rule, and the chain rule.  After the example problems, students will be split into groups for the Numbered Heads Together activity where they will solve some problems in groups.  Finally, students will be given some homework problems to work on individually for the last part of class.

5. Benefit for Students

As a math teacher, I dislike presenting a formula or equation to students and asking that they believe it on blind faith.  I really believe that students benefit from seeing where formulas come from and why they work the way they do.  However, in many classes (especially calculus), there are simply too many equations to offer a formal proof for each one during class time.  By flipping this lesson, students are able to see where the equations \frac{d}{du}sin(u) = cos(u) and \frac{d}{du}cos(u) = -sin(u) come from, and I won’t have to use class time to prove the equations.  Instead, students can use class time to collaboratively work on problems where they will apply the equations.  This is preferred to having students work on problems at home, where they would not have a teacher or classmates to help them out if they get stuck.

Image credit: Creativity103

There can never be too many labs….

1) Learning Objective

Students will be able to demonstrate knowledge of cellular respiration through a tennis ball lab experiment through data analysis and graphing.

2) Digital Resources Used

The first part of the lesson would be the students on their devices at home watching a video that I created through EDpuzzle. The video would be an introduction and full overview of the process of cellular respiration, I would add checkmarks of questions that the students had to answer and they couldn’t skip ahead they have to watch all of the video. I most likely would not grade these questions but see it as a form of informal assessment for me to know where my students are at (it would all depend on where in the unit we are at). This would free up what would be classroom lecture time to insert a lab which I wish I could always do more of!

3) Active Learning Strategies

For me the best active learning strategies are getting students involved in a lab experiments in class. Currently I do not have the abilities to operate a flipped classroom so I can only do a small amount of labs, but in my opinion labs are one of the best hands-on and active way for students to learn content. The lab that I would do is a tennis ball lab that connects to cellular respiration. The students are in groups and they have to squeeze a tennis as hard as they can for 30 seconds take a rest and do it again. The students have to do this five times in a row and keep track of how many times they can fully squeeze the tennis ball. The connection is that over time your muscles fatigue with has to do with cellular respiration, glycogen storage, and anaerobic fermentation.

4) Lesson Flow

The lesson will flow in the direction of starting with the video and questions at home so that when students come into class they have received and reviewed the content, therefore they are ready to begin the lab. I would most likely do a review at the beginning of the class of content that pertained to the lab and then the rest of the class period would be devoted to the students lab time. A block class period would be perfect to also start a discussion and analyze the data however it could be done over a class period and a half or two full periods.

5) Benefit to Students

This format allows students to be exposed to the material outside of class so that by the time they come into class they know what they know and what they do not know. This allows time for more questions and one-on-one time with students in class. The content offloading also allows for more hands-on, minds-on activities in the class, which for me means LABS LABS LABS. Labs are wonderful opportunites for students to demonstrate their knowledge and learning in a more active format. It also helps students that struggle with learning content from a screen or a person another way to learn material.

Image Attribution: Allison Meier

LaTeX: Making Pi and You Look Prettier


I created a screencast about a very helpful STEM typesetting program called LaTeX.  I thought screencasting would be a helpful method for displaying this information because I could show some sample documents of LaTeX code and compare these to the final version in order illustrate how the coding process allows one to create such professional and well-formatted finished products.

I found CaptureSpace to be intuitive and easy to use.  I tried using the “draw” function to highlight certain parts of the screen while screencasting, which worked decently, save for slowing the video down a little and requiring extra time to erase the writing on the screen and turn the feature on and off.  I wager that this feature would come in handy particularly if I wanted to write math on the screen, for example.  I ended up making multiple takes to move more efficiently through my message and found it somewhat inefficient to have to re-record when I made a mistake.  However, in the end, I felt like the screencast turned out decently and conveyed the message I wanted.

From here, I envision using screencasting to create mini-tutorials similar to those on Khan academy: as supplements to class instruction or resources for students to explore extensions to material in class.  In a math class, rather than interrupting class to use technology, perhaps I would create a screencast to display what I would have in class so I can focus on the central material in class without losing the benefits of using technology as a visual supplement.

Featured Image: chucka_nc

An Ode to Not Answering the Same Question 1000 Times

I like the idea of building a set of classroom reference screencasts to answer questions that always come up. For example, how to correctly use semi colons, or how to use whatever program I’m asking them to work with. Slidecasts would also be ideal to for students who are absent, or, since I don’t lecture often, I could make them to review certain topics before a test. However, I will also have to put this information together in other ways so students without access to technology can view it. While it is a good resource that will save me some time, it’s not an ultimate solution.

I see many cool possibilities for student screencast assignments. Student how-to videos can potentially have a bigger impact on their classmates than teacher instruction, and students benefit not only from learning the content, but also up their tech literacy in the process. Language arts isn’t the most friendly subject for screen casting, but I could see grammar, research or figurative language explication topics working.

Despite all the good, there are some challenges around technology access that could potentially complicate the process. Screen casting necessitates a quiet space to record, and if everyone is in the classroom doing this with laptop cart computers, things are going to get pretty loud. Also, with the shift from Macbooks to Chromebooks in most schools, the quickest and easiest way to do this is no longer possible. In a school like mine, where there are no laptop carts, this is not going to be possible at all.  I think it’s a great tool, but may be better used as a project option than as a required activity for the whole class.

I made a screencast that explains how to use parenthetical citations in essays. I chose to do this because I am eternally doomed in Tartarus to answer this question over and over without a single student remembering what I say.  It was pretty easy to do, and I would definitely use this tech tool again for review or some short little explanation like this.

Featured Image Credit: Psychedelic / Abstract Cat by Callum Hoare on flickr

 

Inequalities with Desmos Graphing Calculator

I used CaptureSpace to record an instructional video on how to graph inequalities with Desmos graphing calculator.  I thought using CaptureSpace was a fairly straightforward process, which isn’t how I normally feel after using a program for the first time.  I was easily able to record my video and upload it to the UP media page.  In the future, I could see myself using a screencast to explain to students how to use technology, such as the Desmos graphing calculator or even certain functions on a Texas Instruments calculator.  I could also use it show mathematical proofs for things that I don’t have time to prove in class.  For example, if I want my students to know that the derivative of sin(u) is cos(u), but I don’t have time to show a formal proof in class, I could give them access to a screencast of me proving it.

One thing I don’t like about screencasting is how difficult it can be to fix mistakes.  For example, when I re-watched the embedded video, I realized that I made a mistake at the 1:33 mark – I said the circle had radius 4 when I meant to say that it had radius 2.  This was a small mistake, so I just let it slide for the purposes of this assignment.  However, if I was sharing a video with my students, I would not want them to be confused by a mistake on my part.  Therefore, I would probably have to go back and re-shoot the entire video just to fix one mistake.  And then if I noticed I made a mistake in the re-shoot, I might have to record yet again!

Featured Image: Sykez Tom

Poetry Annotation: The ‘Sickest’ Way to Read Poetry

For the life of me, I don’t know how I’ll integrate screen captures into my instruction, but at this point in time I think it’s worthwhile especially as more and more schools go 1-to-1 with devices. I wish this was usable on the iPad though.

You’ll definitely see how janky my control over the writing tool is as you watch my video, but I suppose that was a learning experience. So enjoy listening to my awful, sick voice try to explain annotation in a format that flat out does not work.

 

Featured image by Felix E. Guerrero

Stuck in a Slope? Let’s Find a Way to Intercept That and Get Out.

So, in the video below, I recorded a mini-review about the parts of y = mx + b, or slope-intercept form.  What I hope to achieve here is that people who watch it can get a better understanding of what and  are asking for when they look at y = mx + b.  I also hope for them to be able to plug the slope ( m ) and y-intercept ( b ) correctly into the formula if given those numbers and/or be able to tell which is the slope and which is the y-intercept if given the formula, like y = 4x – 5 for example.  In this case, they would find that m = 4 and b = -5.

After learning and messing around a bit with screencasting, I saw some benefits and a few struggles, but that can easily be overcome with perseverance and determination.  I am also very happy to finally figure out how those people on YouTube do those “How-To” videos that involve going from screen to screen.  Always thought that those people had a really good recording camera that was set up on some sort of amazing tripod and they created the video from there.

Anyways, the biggest benefit I can see is that screencasting can be very useful in filling in any holes that a lesson(s) could have had since, as we know, class time can be quite short (55 – 90 mins) and that not everything can be covered in that span of time.   Another benefit is that after the video is made, it is now a semi-permanent resource that can be accessed by one’s current students and future students if one was to teach the same lesson again.  Another benefit is that the application is easy and free to use (as far as I know) that one does not have to buy much equipment (except maybe a microphone).

The struggles I found are just some personal struggles that I feel like some people share with me.  One struggle is that, even with a script, one can still say too much or too little.  In other words, one can go off-script at times.  Another is that If one is really nit-picky about their recording, then he/she would probably restart every time he/she makes a mistake.  Another struggle is that the “attached” recording equipment can be faulty at times and one would not find out unless they do a test run or until the end, depending on the type of person one is:  “being prepared” or “power on through”.  I would make a new recording for the video down below, but I wanted to show where these struggles can pop up.  And like I said earlier, all of these can be remedied by staying determined and having the motivation to make a good lesson video for one’s students or for the people of the world.

So, I can see myself using this in the future definitely.  It was a lot of fun, though I did not enjoy hearing my own voice coming out of the speakers.  The idea of making these was challenging.  You know, making sure all the basis were covered, my “recording room” was quiet enough to record, my script was a draft of what I wanted to say (Reminder Points), and so on.

Enjoy the video! Hope you learned something or laughed at my mistakes!

Featured Image: Wikimedia

Screen-Recording-English-Paper-Research-Absolutely-Wild-Fun-Tyme!

I did my screencasting assignment on showing how to do research from the UP databases. At first I wanted to do multiple videos, however that desire quickly changed. I realized how scattered that would be because doing research on the internet involves going back and forth to certain websites. So I decided to just make one long video that comes out to be roughly around 3 minutes. After a few takes, I realized how awkward I seemed to be while just being a voice while talking over a website. This was just something I had to get used to. Quicktime makes it incredibly easy due to its user-friendly-ness, so that helped out a lot.

I have learned that there is so much use in screencasting. I feel that I would have understood how to do research at UP if I just saw a ten minute video online on how to use the databases rather than going to an hour and a half class on how to research. Also, when trying to find my “embedded” code in order to put the video on this blog, I went to different videos on YouTube to see where the code was. The multiple advertisements I saw while searching for the code seemed to be all screencasted. It was here when I realized just how much everyone uses this tool. I think this is an immensely useful tool to use. I would definitely encourage teachers to know how to use screencasting because they can convey things to students via video in a much more applicable way than talking.

Here is my screencast video about doing research at UP!

Featured Image is called “Typewriter” by Charlene N Simmons

What is a Nearpod, you may ask?

Instead of Screencasting for my students, since earlier in the year my kids did a Screencasting activity for social studies, I thought I would screencast something that teachers could use in their practice that is related to technology.  Earlier in the year during a PD on Smartboard activities, I was introduced to this great website called Nearpod, which is a website that allows you to create interactive PowerPoint presentations that students follow along with on their own devices.  The one major hindrance for this resource would be that students would need their own device, like a Chromebook or an iPad in order to be able to participate in the lesson.

Nearpod is a great tool for increasing student engagement because there are lots of interactive slides that you can build into your lessons, while also teaching students any concept that you might come across in your curriculum. I just thought I would share it with you guys, especially those of you who are secondary and may use PowerPoints  a lot and are looking for a way to get your kids more engaged.  In my Screencast, I show the viewers what a Nearpod lesson looks like both from the perspective of a student going through a Nearpod lesson, as well as what a Nearpod lesson looks like from the perspective of a student.

As for Screencasting, like I said earlier, the tech coach at our school came in earlier in the year and taught our kids how to use Screencasting to talk about these PowerPoint presentations that they all put together on Google Slides that showed what they had learned about the Revolutionary War up to that point.  They then posted their Screencasts to some website that they all had access to using their district Google accounts that were then accessible by QR codes that their parents could scan with their phones during a Tech Night that the school hosted in December.  I would love to do another Screencasting activity with my students, I just don’t know when we will have time before I’m done student teaching.

 

Featured Image Wesley Fryer