Blended Learning in Mathematics, I’m not the only one doing it!

This week we were asked to explore an aspect of online/blended learning that we are interested in. As I am working on building a blended Calculus 30 course, I felt this would be a great time to read into how others are structuring blended learning of the mathematics variety. I should also warn you, this is a long post but, if you get through it, you will find my favourite definition of blended learning (thus far anyways).

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Photo Credit

In my searching, I found a series of articles written by Birgit Loch, Rosy Borland and collaborative authors Liam McManus and Nadesda Sukhorukova for the annual ASCILITE conference. Their papers discuss a variety of ideas, implications and challenges around creating a blended mathematics course. In their first article, The transition from traditional face-to-face teaching to blended learning – implications and challenges from a mathematics discipline perspective (Loch & Borland, 2014), the authors discuss how mathematics is often overlooked for moving to a blended format for three reasons:

  1. Limited resources and cramped curricula.
  2. Instructor reluctance to move from the traditional “chalk and talk” as they have never experienced an alternative method of learning.
  3. The belief that mathematics is different from other disciplines and it doesn’t need to be re-invented through another method of instruction.

I have to admit, I am not going to argue any of these points but I may use them to help plead the case for blended learning. We have discussed in class about the cramped curricula and, to me, that is the ultimate reason why we SHOULD be moving to blended learning, allowing our students a better opportunity to have access to the teachers to help them with their learning. What better reason to try something new as “I’ve never seen anything else done”, I hardly think that “this is how it is has always been done” is a good enough excuse to not move to blended learning. And mathematics is definitely different than many other disciplines, Loch and Borland mention that mathematics is “complex due to the visual nature of the discipline” and recognize that the digital typesetting of mathematics can be difficult for students and instructors to communicate in short response times. With applications such as SeeSaw and FreshGrade where students are able to post pictures of their work, I’m not sure that this is completely valid, although I definitely think that timely feedback is still a challenge digitally. They also discuss the technology requirements for both students and instructors as well as a fear that by focusing on the online submission of assessments, “the development of deeper mathematical understanding that occurs during practice may be impacted as students may be ‘doing’ less mathematics because they no longer write it out” (Loch & Borland, 2014).

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Micaelamolinagt, Aula Invertida, CC BY-SA 4.0

Loch and Borland go on to discuss the use of the flipped classroom and how it has developed a more active classroom, where students are able to “do” mathematics with the support of the instructor as opposed to this time being used for lecture. This allows for the concepts to be developed deeper. Within the flipped classroom, they recommend using audience response systems (such as Kahoot, Mentimeter, or Plickers) to help gauge student understanding and misconceptions but they question whether students with low prerequisite knowledge are truly capable of learning in this manner. Interestingly, they found that students that were in active learning classrooms were 1.5 times less likely to fail than those in traditional lectures (Freeman et al, 2014 via Loch and Borland, 2014).

While in the classroom, Loch and Borland discuss “board tutorials” where students work a problem together on a whiteboard, effectively “doing” mathematics together and collaboratively. This comment made me think back to my undergrad and Math 223 where we would often go to office hours and have our professor, Douglas Farenick, find us a large chalkboard to work the problem as a group. This course was one that challenged my thinking and caused me to struggle in mathematics (something that was new to me at the time) but when asked for help from a student, I look back at that and try to emulate it, as I find it was one of the most useful exercises I have done (thank you Doug if you read this).

The article is summed up with seven questions that the authors feel need to be further researched:

  1. What can we do to ensure students engage with both online content and classroom activities?
  2. How can we encourage school leavers enrolled in first year mathematics units to self-regulate their learning?
  3. How can we build in redundancies, eg. enable students to recover if they have not watched a video beforehand or have not attended class?
  4. What technology is needed to enable effective online communication and collaboration to support learning in Mathematics?
  5. What technology is needed to support deep learning of mathematics? What new technologies might be on the horizon? What impact can learning spaces have on student engagement?
  6. On a departmental level, what is the best approach for supporting teaching staff (including sessional staff) to develop and implement innovative pedagogy approaches, promote digital content creation and use technology to enhance learning and teaching outcomes?
  7. How do we measure the success of a flipped classroom?

The second article by these authors, Implementing blended learning at faculty level: Supporting staff, and the ‘ripple effect’ by Borland, Loch and McManus (2015) discusses question #6 above and the supports needed to implement blended learning at an institutional level and discusses many of the common themes that come up in our #eci834 discussions such as cost, accessibility, and professional development. What really jumped out at me from this article was the definition of blended learning that they chose to follow:

“an understanding of blended learning as being an approach which increases opportunities for students to engage with content and resources online in order to make more time available in face-to-face classes for active learning” (Borland, Loch, & McManus, 2015)

This definition really resonates with me, I value the face-to-face connections that I make with students and I like that their focus was to increase the effectiveness of this time, taking the lecture out of the face-to-face sessions and focusing on the student and their needs.

The third article, How to engage students in blended learning in a mathematics course: The students’ views by Loch, Borland and Sukhorukova (2016) addresses questions #1 and #3 from the above list, and do so from the perspective of the student. They state that students in blended learning courses need to be self-directed and self-regulated learners (they could use the skills from Twana’s post on online learning success strategies). Students in this study stated they like the face-to-face sessions because they were able to ask questions and gain further clarification on topics and it was found that students reacted positively to interactive and technology-enhanced classrooms where they were able to contribute in discussions with their peers (Donovan & Loch, 2013 via Loch, Borland, & Sukhorukova, 2016). Students were also honest, stating that they do not always watch as many recorded lectures as intended or even never watch them at all, students cannot be forced to engage in teaching activities of any sort if they do not want to. I appreciate this very open, honest, and abnormal statement in the article as too often we focus on being able to reach every child when, we know deep down, some are just not ready to be reached.

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via GIFY

An aspect of a blended course that I did not think of until reading this article was the ability for the instructor to incorporate additional information on the “why” we are learning this, with students in the study stating that they enjoyed being able to get deeper into why we focus on a specific concept and its general use outside of the grading scheme for the course. This is a common question in my classroom and I like that blended learning provides a non-mandatory platform for students to pursue their interests in this way to gain a deeper understanding.

In discussing the motivation for watching videos ahead of class time, a variety of ideas were provided. The one I disliked the most: providing marks for watching the videos. Signing in to watch the videos does not mean that students are actually “watching” the videos, they can hit play, mute, and walk away, never gaining the understanding they should and receiving grades that do not reflect their understanding accurately. The one I like the most: recap the content at the beginning of class, using one or maybe two examples, and provide a plan for each class so that students know what they are missing if they have to. Recapping with a couple of examples helps instructors know where their students are in their understanding and allows for further instruction, if necessary, before the daily task is started.

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via GIFY

One major fault in blended learning as addressed in this article is that math is very hierarchical, constantly building on the content previously learned. If, when watching a video example, a student does not understand an early step, the entire video is lost, as is the time dedicated to it. This is something to consider in making videos for a blended learning course as you need to ensure you are being detailed enough that the weakest student in the class will be able to follow along, an perhaps may need to provide a review of prerequisite knowledge to help all students ensure they are confident in their solutions.

If you are still with me, congratulations, this has been a very long post and I am not quite done yet. In reading this, I am inspired to change not just my Calculus 30 course but by other mathematics courses as well, although I will wait until the fall semester to ensure I have had the time to adequately prep and organize my ideas in a meaningful and effective manner. In general, this is how I think I would like to set up my classes:

  1. Flipped classroom: Students are required to watch video of the examples with notes to follow along with before coming to class (such as how Ashley has described she runs her flipped classroom).
  2. At beginning of class, have a Plickers activity to determine how students are doing. This will require them to tell me if they are confident, need some clarification, or have no idea what happened.
  3. One to two examples on the board, so I can gauge where my students are. This will be followed by students asking specific questions on their current misconceptions.
  4. Group “Board Work” where students will be given a enrichment question and will need to come up with a solution collaboratively. I would like to play around with a presentation method similar to the interactive notebooks that Andy uses in his class, with some modifications.
  5. Work time for an practice questions. Or more time for enrichment. I am a firm believer in not everyone needs the same amount of practice to understand a concept and therefore do not require them to do all assigned textbook questions.

Well, I think that is it that I have to share, what do you think about this set-up for high school mathematics classes? Have you done something similar to any of the parts? What do you think of the findings of the articles? Let me know in the comments!

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Feeling Alone on Audio- Island

This week, we were asked to reflect on Tony Bate’s chapter on the different types of media that can be used in the classroom. Initially, I thought I was right on board with many others such as Kelsie, Ashley, and Liz and that I prefer and learn best from text but as I was reading through the various other posts by our eci834 classmates, I realized that maybe I learn better through audio than I had thought.

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A Song of Ice and Fire via Flickr user Jemimus

I would like to address what Bates calls the unappreciated medium of audio. I love audio, and not just of the musical sort. About 2 years ago, I was encouraged by my sister-in-law to listen to the podcast Serial (Season 1) and I was very tentative to jump on board, I didn’t think that I would like just the audio. I had always had text in front of me before, I was sure I wouldn’t want to just listen to someone talk. The long, and uneventful drive from my home in Kipling to Regina that I was making at least once a week for classes was the reason I decided to try it out…and I LOVED IT! Now, it is a very interesting, even addicting, story (you seriously need to listen) which probably helped keep me interested but it made me think that this might be a good way to stay more up-to-date on my growing “to read” list. So, I downloaded Audible and decided to tackle a massive series, A Song of Ice and Fire by George R.R. Martin, all 201 hours, 41 minutes of it, and my love of audio was fully confirmed. Since finishing what has been published of that series, I have started to listen to some of the more classic works on my list, The Prince by Niccolo Machiavelli, Frankenstein by Mary Shelley, and I am just about finished The Divine Comedy by Dante Alighieri.

My love of audio goes further than just listening to content. I find I focus better when I am listening to something, even if I am trying to read. While reading Bates’ Chapter 9 for this week’s class, I was listening to Spotify’s Intense Studying playlist., it helps keep me focused and minimizes the distractions around me.

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Academic reading process Photo Credit: Nina A.J. Flickr via Compfight cc

Even though I enjoy audio, when I comes to what may be considered more academic reading, I still think I prefer text. Andrew‘s approach of which medium is the best for him is probably closest to my overall views of media. It depends on mood, topic, and the quality of the resource. Liz mentioned that she often writes and highlights all over text that she reads and I do the same. Last semester I took EADM 814 and found that I had notes, questions, and definitions jotted everywhere to ensure that I understood the cases we were studying. In this course, I struggle not to print the textbook readings so that I can make my notes in the sidelines. Luckily, I have found that Evernote is helping me break free of my not so eco-friendly habits.

Video is, of course, an amazing media to use when teaching as it can incorporate the audio and the text features along with visuals. Angela and Chalyn describe the way that video integrates all of these mediums.

What do I use when I teach? I use a blend of all three. I agree with Jannae that in teaching math, especially at the high school level, there is a need for text in the form of mathematical symbols. But I also describe what I am doing in each step of my work as we go through examples and I encourage my students to do the same. Bates references this stating that “explaining or ‘talking through’ materials presented through text, such as mathematical equations, reproductions of paintings, graphs, statistical tables, and even physical rock samples” can be “particularly ‘potent'” (Bates, 2015, 7.3.2). At the end of a concept, I try to incorporate a video that is well done and applicable. Much like Logan, I think I integrate both the text digitally on my SMART Board and the audio in the form of lecture and video.

It seems I am a part of a very small group of audio-lovers. Are you tentative like me to jump in or have you had a bad experience? Would you consider it for the “right” topics?

Rapping Math Concepts – WSHSmath Video Review

For this week’s blog, we were asked to either critique a unit of instruction done by someone else, or to use one of the content creation tools that we discussed to create our own content. I have decided to do both.

Like Andrew mentioned in his post Crash Course – 7 Thumbs Up!, I also like to use videos in my teaching for both learning a new concept as well as for review. I am a huge fan of the Crash Course videos as well as I use historyteachers as they present the information in a unique manner and give students another perspective or way of viewing things that help the importance of what we are discussing sink in.

As a math teacher, finding videos that are not super cheesy but that are mathematically sound is not an easy task. I also try to stay away from videos that fall into the “math is not cool” or “wow that person is a nerd” stereotype such as Mathmaticious. That is why I was pumped when I stumbled across WSHSMath‘s channel. They only have 7 videos but they are QUALITY. They are created by a group of teachers at Westerville South High School in Westerville, Ohio. The next video that I will be using in my classroom is the factoring video.

I love that they remake popular songs and sing/rap about mathematics concepts. This is Teach Me How to Dougie by Cali Sway District, but they also use Yeah! by Usher, Gettin’ Jiggy Wit’ It by Will Smith and Call Me Maybe by Carly Rae Jepsen. They have their students in their videos as well. I find that this helps my students relate more as they can see people their age involved and engaged in the content (not to mention, some of them have some sweet dance skills).

These videos are catchy and educational, I will often hear students in the hallways humming the melodies after watching the video in class. (I am sure they are not thinking the “math lyrics” but a teacher can only hope!)

So, how hard would these be to recreate by the “average” teacher?

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Photo Credit: ToGa Wanderings Flickr via Compfight cc

Personally, I do not have a singing voice nor am I very good with the remixing of the lyrics. To recreate an entire song would probably take me weeks or months of trying to make it work and sound good. I would say that these three gentlemen are masters of the parody of lyrics, but, that doesn’t mean it is out of reach for the average teacher, just maybe for me.

Their students are amazing. I am pretty sure that I could convince my students to join me in making a video such as this if I had the right “motivation” (which could be as simple as a candy at the end). If you are passionate about your project, I think that most teachers would be able to gain a dancing posse for videos such as these.

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Screenshot from Urban Dictionary

So what about the graphics? This is where I am going to try to out a new tool! I am going to try to recreate some of the graphics in the video Teach Me How To Factor (above).

The Difference of Squares example

I did not rap, but I did go over the example in a (not very catchy) way. The graphics were not very difficult. I used SMART Notebook and SMART Recorder to take the video.

Overall, I think that this would be an achievable goal for many teachers. And, knowing how my students react to these videos, I think that it holds a lot of value for students. It is not a lesson in itself as many of the videos glaze over some of the key things that are needed for understanding but as a review, I feel that they have done an amazing job of their videos!  What do you think?

When I started to recreate the graphics, I really tried to used Screencastify but it repeatedly froze my computer for some reason. I will try again in the future but for now, I will settle for using SMART products instead of more “open” options. I am also very intrigued by Audacity for my Social Studies classes I did record myself reading out of a mathematics book that I own A Curious History of Mathematics by Joel Levy and will probably be playing around with that in the near future.

UPDATE: I have figured out Screencastify and have made a how-to video of me uploading files to Canvas in the modules. More work to come on organizing the course!