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

Class 10: Teaching with Data Visualizations

Quite often edtech tools are used by the teacher rather than the students and don’t do much more than make things prettier.

Think: Teacher at Smartboard as replacement for the overhead.

New digital technologies allows us to “see” information in new ways.

Think: Students analyzing text using Wordle

Many apps and websites can be a great tool to introduce the research method – form a hypothesis, gather and analyze data, revise hypothesis (as needed), draw conclusions, assess research methods. Working in teams students can easily pose research questions, run the data, revise and assess their research strategy. Students can quickly make and test predictions. They can then present and defend their conclusions to other classroom groups. All skills called for by the new Common Core standards.

In today’s class we will explore a sampling of free online data visualization tools that can be used in the classroom. Students will be asked to incorporate one of these tools into a lesson design.

GapMinder World: manipulate moving bubble graphs, select x and y axis from a variety of data sets

 NGram Viewer: online research tool that allows you to quickly analyze the frequency of names, words and phrases -and when they appeared in the Google digitized books. Ideas for classroom use Books Ngram Viewer.  For more advanced searches using NGram Viewer click here.

Chronicling America has digitized newspapers from across America from 1836-1922. You can search word frequency here.   Search Chronicling America and visualize the results across space and time at USNewsMap project

Bookworm: a collection of simple and powerful way to visualize trends in repositories of digitized texts.

  • Movies: dialogues of movie and TV shows
  • ArXiV: science publications
  • US Congress: bills, amendments, and resolutions (by political party)

Timelapse: is a global, zoomable video that lets you see how the Earth has changed over the past 32 years.

Metrocosm: All the World’s Immigration Visualized in 1 Map

Combine multiple online tools for research: For example, Black History in America:
Map of White Supremacy mob violence here
Mapping the “Negro Travelers’ Green Book” here

Assignment

Choose one or more of these digital tools (or use a favorite our yours) and blog about how you would use it in an activity, lesson or unit. A few things to keep in mind:

  1. Be sure you design a lesson that allows your students to be using the tool
  2. Be sure to include an embed of the tool (if possible) or at least a screen shot.
  3. Blog post due: 3/30

Image credits:
Header: AdobeSpark public domain
Insert: Teaching with a SMART Board / Flickr

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

Sample write up: Where I’m from

This  is a model blog post that demonstrates a write up for the Blended / Flipped Lesson assignment. Bold face is your assignment. Followed by how I would have written it up.

This write up is based on a lesson I used at the beginning of my Alaskan History and Culture course in the MAT program at the University of Alaska SE in summer 2016. See my assignments here:  Where I’m From and Google MyMaps lesson: Place

Here’s the work done by Jimmy Andrew – one of my students from a Yup’ik village of 300 people – Kwigillingok Alaska.

Learning objective – content and or skills students will know or be able to do by end of the lesson.

This was the second class of course and it served multiple objectives:

  1. My primary objective was to introduce the idea of place-based education with a poem and personal reflection on a place they were already familiar with. (later they would learn about another place – Alaska)
  2. I wanted to give the students a relatively simple tech-based assignment (Using HaikuDeck and creating a WordPress post) to build confidence for more elaborate tech assignments later in the course
  3. I need to free up class time so that students could get individually logged into their new WordPress accounts

Digital resource(s) you’ll use for flipped / blended elements.
Note: it’s not necessary to develop the digital elements – you can just describe them.

  1. I designed and posted the lesson to our WordPress blog so that everyone had access to assignment and resources.
  2. I made a few how-to videos describing how to create a Haiku Deck account, create a presentation, and embed it in Word Press.
  3. I made few how-to videos on using Google MyMaps
  4. I reused a collection of how-to videos that I had created for how to use WordPress

Active learning strategies employed with freed up class time.

Students used the time to read the poem for inspiration and get to work designing their own personal “Where I’m From.” Others elected to try the second design option using Google MyMaps using a lesson called Place. While the Haiku Deck approach was more visual poetry, MyMap used geographic tools and a spacial approach to design a Google map tour. Once I was done meeting with individual students to create their WordPress accounts, I was free to move around getting to know students better and assisting them on specific questions.

How the digital resource integrates into other instructional elements of lesson – what’s the flow of the lesson?

The digital content was created and posted to the web in advance. At the end of the previous class I asked students to read both lesson options (HaikuDeck  and MyMaps) in advance and think which lesson they want to try and how they will respond. The day of the class, most of our 3-hour session was spent with students working with HaikuDeck or MyMap. Then they began turning their work into their first blog post. Many students were excited to “show off”  their creations with one another.

Benefit for student content mastery, collaboration or learning workflow – Why is it worth it flip / blend some of the content.

Using these digital resources enabled students to begin the course with an easy “tech skills win.” Every student was successful in completing the assignment and posting it on WordPress. I was able to re-use my WordPress how-to videos originally made for another course. Along with the how-tos for HaikuDeck and MyMaps, I was freed up to handle the management of new WordPress accounts and spend some one-on-one time with all my new students.

Class 8: Flip content means more time for student interaction

Introduction

From Are We Innovating, or Just Digitizing Traditional Teaching?

“A few months ago, I noticed an increased amount of discussion around the notion of blended learning. Many of these conversations started on a similar note: “We’re blended—all of our teachers use Google Classroom.” However, in probing further, I often discovered that these tools had merely digitized existing content and classroom procedures.

Instead of filling an inbox on the teacher’s desk with packets and worksheets, students now completed the exact same procedures online. Rather than write homework assignments on the board, teachers posted them to the students’ digital news feeds. While blended learning brings with it the promise of innovation, there is the peril that it will perpetuate and replicate existing practices with newer, more expensive tools.”

Flipped and blended learning can easily fall victim to edtech’s fascination with faster. Better. Shinier. Instead, we will utilize our new skills in digital content creation to design a lesson that utilizes additional class time to foster greater student interaction.

Class overview

Class will begin with a brainstorm session where we consider how we can use flipped and blended resources to enhance classroom interactions. After pitching some ideas to one another, students will get down to developing an outline of how they could design an activity, lesson or unit. Those designs will be incorporated into a blog post due 3/23.

Note: Some class time will also be devoted to updating our critical thinking design project and previewing iBooks Author which will be used for showcasing our lesson.

Assignment

Next week (3/16) there’s no class because of  break. Students have two assignment due when we return. (3/23)

  1. Be prepared to give a 5 min demonstration of your critical thinking lesson.
  2. Complete your flipped / blended model lesson as a blog post.

See my sample lesson blog post here

Flipped / blended model lesson should include the following elements. See sample completed assignment here.

  1. Learning objective – content and or skills students will know or be able to do by end of the lesson
  2. Digital resource(s) you’ll use for flipped / blended elements. Note: it’s not necessary to develop them – you can describe it.
  3. Active learning strategies employed with freed up class time (follow this link for lots of ideas)
  4. How the digital resource integrates into other instructional elements of lesson – what’s the flow of the lesson?
  5. Benefit for student content mastery, collaboration or learning workflow – why is it worth it flip / blend some of the content.

 

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