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    Visualization in Precalculus and Calculus with MyLab Math

    By Aaron Warnock

    “I’d rather sing you a song than draw you a picture,” is what I’ve been telling my math classes for almost 20 years now. I’ve always enjoyed music (I was one course shy of a Music minor) and I always enjoy an opportunity to sing. Even in my math classes, I would sing the quadratic formula to the tune of “Pop! Goes the Weasel” – something which my students always enjoyed.

    When it comes to drawing however, that is a whole other matter. My stick figures are embarrassing, so you certainly don’t want me to draw complicated 3D figures in Calculus. If only I could sing about washers and cylinders for volumes of rotation in Calculus; unfortunately, a picture is better than a thousand words, or songs, in my case.

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    Building community in the online classroom with Affinity Groups

    By Aaron Warnock

    We’re all familiar with trends coming and going in higher education; we’re also used to seeing a lot of research too. How do we know what’s really worth it?

    Throughout my years as a professor, one subject that has garnered significant research is building community in the classroom. Building community is a valuable tool for improving equity. When I began teaching online, I found it to be far more difficult to achieve.

    I would assign students to groups in my Learning Management System (LMS) and encourage them to work together on a weekly Relevant Application assignment (to see how the mathematics we were doing realistically applied to the world around them). These group assignments were regularly met with resistance from students – citing, “I took an online class so I wouldn’t have to work with other people!”

    This attitude is one we can’t afford to tolerate, especially as our world increasingly becomes digital, and more people are working in teams with folks from around the country and the world virtually.

    What can we do about it?

    A few years ago, I attended a talk at InstructureCon (Canvas developers annual conference) on creating Affinity Groups for students in online classes. I loved what I saw; implementing their strategies eliminated complaints from students about working in online groups.

    How Affinity Groups work

    As in many online classes, at the beginning of the quarter my students are assigned to post a short biography to a discussion board; in this post, they introduce themselves to me and the rest of the class. They are asked to discuss their educational goals, hobbies and interests, as well as something unique about them.

    When I read their submissions, I make notes of hobbies and interests of all the students. As I see trends of topics being mentioned 3 or 4 times, I list them as a potential group category. I then create a group set, and name the groups based on the categories that stood out for that particular group of students.

    It’s fun to belong

    Almost every quarter I have “Parents”, “Binge Watchers”, “Gamers’, and “Travelers” to name a few, as recurring group themes. You can even add alliteration for more flare, like “Proud Parents” or “Great Gamers”. It is fun to keep an eye out for those unique groups that surface in a given quarter. One quarter we had “Anti-Coffee-ers” for example – a group of students who surfaced declaring their dislike for coffee, or “Foodies Forever”.

    A tight knit group

    I choose to cap the groups at 5 and create more groups than necessary, because I don’t know exactly what students will be drawn to. Lastly, I always create a “z. None of the Above” group, as an option for students who don’t identify with any of the other group. In Canvas, you can simply rename the groups while you’re creating them. In Blackboard, after you’ve created your Self-Enroll Group Set, you’ll have to go to each group individually and rename them by selecting Edit Group.

    Freedom of choice

    At this point, I ask students to self-enroll in the groups of their choice through my LMS (both Canvas and Blackboard have the option for students to self-enroll). Note: If your LMS doesn’t allow for this action, there are other ways you could use to have for your students choose their group, like a poll or survey where they choose one option.

    No one is left behind

    Once the given deadline has passed for choosing a group, I put those who haven’t selected a group into the newly created “Non-Responders” group and encourage them to choose a new name amongst themselves. Not surprisingly, that group of students tends to not succeed as well as the others. I also check for groups with just 1 or 2 members, and combine them, getting creative with the name – like “Binge Hikers” (combination of “Binge Watchers” and “Hikers-R-Us”). Lastly, I delete the groups that didn’t attract any students; now you have students in groups with similar interests.

    A little change makes a big impact

    This may seem like a small distinction from randomly assigning groups, but it is fascinating to me how the knowledge that they are all parents, or they all like to cook, helps them to engage with each other more effectively and actively. Rarely do I get any resistance from students saying they don’t want to work in groups anymore.

    My focus here has been on how to design groups to help encourage students’ engagement. Two other great resources for strategies for effective group work are these Duke University and Carnegie Melon University articles. You can also learn more about the importance of student engagement in survey results from the National Survey of Student Engagement (NSSE), as well as other research done by National Academic Advising Association (NACADA).

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    Classroom engagement: A New Year's goal checked off!

    By Aaron Warnock

    I attended college in an age of lectures. You know the student lecture mode. You go to class, listen to your professor lecture for an hour or more, frantically take notes, and then hope you can make some sense of those notes while trying to do your homework.

    When I became a professor, I didn’t know much else to offer. Group work was popular, so I did incorporate group work assignments, usually as a review activity before an exam. My daily routine though, continued to be mostly lecture. I would call on students to answer specific questions – I tried to move around the room so everyone had a turn. It felt “fair,” but I’m sure it didn’t help those students who had math anxiety. It didn’t seem like enough.

    Some of my colleagues across campus were using “clickers” so students could answer multiple choice questions during class. But because I was teaching a math class, I didn’t want multiple choice questions – I wanted the students solving and answering questions on their own, not guessing from a list of choices or working backwards. Think – Pair – Share was another technique I tried with relative success, but inevitably I still had up to 1/3 of the classroom sitting there quietly, not talking to anyone.

    Along came Learning Catalytics: my classroom would never be the same. Learning Catalytics is a classroom response system that students can log in to with their phones or other web-enabled devices. Instead of just multiple-choice questions, there are 18 different question types.

    This includes mathematical expressions, multiple graphing options, direction (think vectors), short answer, and many more. It was also quite simple to create my own questions directly from my notes for class, or I could choose from a vast library of existing questions already available.

    I used to walk around the room while students had a practice problem to work on, seeing a handful of their work and having a vague overall idea of how the class was doing. Now I was able to see the responses from every student in one summary at my computer.

    The real game changer though, came with the seating chart. It’s not assigned seating for the students per se; it is set up that they click on the seat they’re sitting in when joining the class session. While students are working and submitting answers, I’m able to see which areas of the classroom are struggling more (due to an increased number of incorrect responses). Now I can focus my “wandering” time with the students who are struggling with this topic, right now.

    The real beauty with the seating chart though, comes with the ability to assign the students into groups to re-work a problem after discussing it with each other.

    Let’s assume the “correct” responses are somewhere between 30% and 70%. With the click of a button, I can assign the students into groups of 3 for discussion and resubmission. There is even an option that students are group by “different” answers. This disperses the 30% or more of correct answers throughout the groups, so you can be almost certain that every group has at least one member who answered correctly.

    Students discuss with each other and demonstrate how they solved the problem, and then they resubmit their answers. I regularly see the correct response rate to a question go from something around 40% correct to 80 or 90% correct – and I haven’t said a word! The change is from students working together.

    My class is busy: students are moving around, getting their blood flowing, and everyone is engaged. Each person’s device tells them the name of the others in their discussion group and where they’re sitting with respect to them. I tell the students, “If you have their name, they have yours – don’t be rude! Get up and talk to each other.” Gone are the days of 1/3 of the class sitting quietly after you’ve asked them to “discuss with a neighbor!”

    If the response rate is below 30%, depending on the topic, I might step back and do some more class discussion, as obviously the topic is not clear enough to them. If the response rate is over 70 or 80% correct, it’s probably worth moving forward, rather than spending the time to redo the problem in groups.

    However, even in these cases, all the aggregated responses can be shared on the screen, including the incorrect ones. As a class, we’re able to discuss some of the errors made in the room, and how to avoid them, without any individual student being singled out.

    Last term in my Linear Algebra class, there was a simple definition presented – I thought it was as straightforward as could be. I threw a simple concept check in Learning Catalytics expecting overwhelming correct answers – and to my surprise, less than half the students got it right. It was clearly time to review it again. It felt so good to know quickly that we needed to spend some more time on that topic.

    Gone are the days of being unsure during class how well my students are grasping the topic of the day. I can find out on the spot and give them opportunities to actively work together to learn the material. Students are engaged, excited to come to class and interact with each other.

    Is it a time investment in class? Yes, it is – but it’s well worth it. And for those doing Co-Requisites, what better way to help pace your pre-requisite content being covered. Topics with high correct response rates mean you are free to move along! And those with less, you’re able to spend more time on. Thank you to Learning Catalytics for helping transform my classroom!

    Here’s a very brief video overview of what Learning Catalytics can bring to your classroom. And click here for Training and Support materials if you’d like to engage your students with Learning Catalytics.