Visuals and Manipulatives

I have often used manipulatives in classes to help students understand things. These often included building models for geometry, or giving students instructions to discover that the inverse is a reflection along the line y = x. I have recently been giving a lot of thought to these.

I find that students learn more on days when they have more visuals, or have more hands on things they can manipulate. I have been working with Geogebra and Desmos a lot this summer to build models for my classes in the fall. My original plan was to have this as the home page for our class on our LMS. It would change regularly, and I would have one for every topic.

As I continue to build these this summer, I am realizing how hard this is. How do I build visuals for solving radical equations? We later discuss using graphs to solve equations, so I don't want to introduce that method quite yet. So how can I help students visualize what is typically a very difficult topic?

When I teach Geometry in Fall 2019, there will be so many of these visuals and manipulatives. However, subjects like Algebra are not as easy. Students in College Algebra really benefit from this type of learning (at least in my experience). However, it seems that this is the class it is the most difficult to build these for. Probably why students think it is so difficult of a class.

While there are some challenges, I do hope to have a full set of visuals for College Algebra, Statistics, and Calculus I by the end of the fall. Once those are completed, I hope to move to Precalculus, Calculus II, and Calculus III. As I continue building these, I will slowly update the rest of my website with the appropriate videos, visuals and manipulatives, and activities and problems that I find helpful.

Flipping the Class

I have flipped classes in the past, but really want to change how they are done. In the past, students would watch videos or read the book, and then do an activity in class or have class discussion. However, I never knew how to handle these activities. 

When I first started, I tried to have only participation grades, and not collect the actual work. If I did collect work, it wasn't graded. However, even with a participation grade, I found many students not actively engaging in the work, or not really trying or concerned about doing the work correctly. 

To counteract this, I started grading these activities for a small percentage of the overall grade. This also didn't work, since students were extremely concerned about finishing before class was over or whether it was correct. It resulted in a few students actually doing the work, and the rest just getting the answers from them. In addition, it was a ton of grading and extremely time consuming.

This past year, I tried a nice balance. The grades were 70% participation and 30% came from 2-3 randomly selected problems in the activity. However, it was difficult to select the problems, especially if I didn't want to penalize them for not finishing in class. Some students work slower than others, and they shouldn't be punished for this. 

This year, I hope to do something new that I think will work. Students will work in groups that are randomly selected and different every day. This will (hopefully) prevent the select students from just relying on the rest of the group to do the work for them. Towards the end of class, each group will be responsible for presenting the complete solution to a set of problems. These will be randomly selected, and the group will not know which ones they are responsible for until the end of class. In addition, there will be 1-2 problems turned in for the entire group, rather than individually. 

My activities will be different as well. I want to break them into three categories: Getting Started, Main Course, and Let's Keep Going!. The first of these will be basic skill building exercises to make sure all the students understand the basic ideas of the lesson for the day. The second will be a variety of problems that are slightly more involved, as well as the problem(s) they will turn in for the day. This will typically be some kind of puzzle they need to solve using the particular topic. The final section is slightly more in depth and is really designed for the more advanced students. No one will be penalized for not getting to that section, or doing it incorrectly. It is just to extend a little bit to keep those students interested. I hope to have at least one group get to this section each class, so it can be discussed in closing for the end of class.

I hope this will relieve some of my grading, as well as keep students engaged. It also allows students to instantly have the answer keys to these activities. In addition, students may present a problem they had done incorrectly, which can be a great place to start a discussion in the class!

My Goals

A few days ago, I woke up with several new ideas I wanted to put into action. While some may be easier than others, I do hope to implement them all within the next year and a half. The first step in this is getting my website up and running. I thought it would be appropriate to start this site by listing my goals for what is to come:

Goals for my website:

This website is very much still a work in progress. I hope to go through and add content every day to at least one of the subjects listed. Most of the materials are already completed. However, they are taking time to add to the site. I hope to have at least most of it done before the new semester starts. I hope to slowly add more classes in the future as well. I also hope to keep updating the material as I do new things in my classes.

Goals for my blog:

For this blog, I hope to give weekly posts. These may be over what I have accomplished that week, or what I have been thinking about that week. It may include a new idea I had in a class, or how something played out in class different than I was expecting. I hope to use it as a place where I can go back and reflect on how I am growing.

Goals for my YouTube:

As of right now, my YouTube channel primarily consists of videos for various courses that I have taught. I hope to grow this to include a variety of other random topics that may be of interest as well. While I have ideas of how I want to do this, I don't want to put them in writing just yet. I hope to learn more graphic design in the next year to update videos with animations, rather than just handwritten notes.

Goals for my social media:

I am usually not a big poster of social media, so this one may be harder for me. However, I hope to regularly update my social media accounts with things I am working on, or things others have done that I find interesting or helpful. I hope to actually seek out videos and articles that I enjoy to share with the world.

Goals for my teaching:

My teaching has always been very student-focused, rather than long lectures. I hope to continue that process, and expand on it. I am creating hands-on visuals for all of my classes to play with to help them understand topics. These include activities on Geogebra and Desmos that they can manipulate to hopefully better understand the topics. I want to give regular anonymous surveys to the students to see how these are helping, and what I can do to help them even more.

Other goals in life:

I want to listen to others more. Something we are all guilty of is having our ideas of how things should work, and seeking out the research to support those. I want to be more open in my teaching and my online presence (this site, YouTube, social media, etc) to other ideas. I want to reach out to others more to see what I could do differently, or what I should do more of.