Using Internet Resources to Enhance Students Learning

Internet is a vast resource for both students and instructors. Every day, more tools, apps and content are added to increase our understanding and to enhance our learning. We usually find these resources whenever we need them. We not only need to know what we are looking for but also how we could use these resources in the most efficient way. In addition, using different types of learning activities creates a more joyful learning experience.

On this page, you will find some ideas that I explored in the past, and how I combined several different type of resources to support my students' learning in a variety of different ways.

Thank you for your interest to my page. Please feel free to contact me at selma@uchicago.edu if you have questions or comments. I would also be very happy to learn new ways that you use to increase your students' understanding.

GeoGebra Applets

I learned how to use GeoGebra well when I was teaching a course in the YSP Program at UChicago in Summer 2021. In this course, I and a co-instructor taught topics related to linear algebra and geometry to high school students. Considering their level, it was important to create active learning opportunities that they could explore with their TAs.

Since then, I improved some of those applets and created new ones for my students. I collected some applets here.

I also shared applets related to my courses in Canvas course sites. For example, I shared the ones about the formal definition of limit in a content page of Math 152 course while the applet about linear combinations of vectors(given below) is posted in Canvas Announcements of my Math 183 course site so that they can explore more about vectors and linear combinations while they were working on a homework problem.

Bringing Python, Mathematica and Google Jamboard together

After I learned about some image processing codes in Python, I have decided to create a fun activity that students can use in their multi-variable courses. This activity is about graphs and level curves of some surfaces.Besides the difficult of drawing these surfaces by hand, many instructors prefer not to talk too much about graphs of multivariable functions.

I have created the graphs and their level curves by Mathematica. By using Python, I have created puzzle pieces of level curves. For simplicity, there are only a few pieces for each plot but more pieces can easily be created by using Python. In addition, other interesting puzzles could be created by using Python and shared with students. For this purpose, Google jamboard was a good choice since students can log in and recreate level curves puzzle of a given surface. While completing the puzzles, they get to explore some features of surfaces and some important Calculus topics such as continuity.

A pdf document showing what these jamboards looks like is posted below.

When you click here, you can also go to the Jamboard and complete puzzles. In addition to graphs, there is an activity related to series. Students first try to answer the question and if they need a hint, they can complete the given puzzle. I kept these simple to emphasize the idea. Enjoy!

History of Calculus Quizzes

In Autumn 2021, I taught Math 152, the second course in the Calculus sequence. Most of my students already knew some Calculus topics before this course. At the beginning of the quarter, I have decided to give them an extra credit quiz about the History of Calculus. Learning more about people who invented/worked on topics that they usually see in a Calculus course and how these ideas develop create a more meaningful learning experience.

For this purpose, I first created a map that shows birthplaces of Newton, Leibniz, Euler and Clairaut by using Padlet. When they click on pins, students can read their MacTutor bigraphies posted at https://mathshistory.st-andrews.ac.uk/.

This padlet was shared with students in a Canvas Quiz. This quiz also had some questions that they could answer after reading their biographies. While some questions could be answered directly by reading a particular biography, other questions could be answered after reading all biographies.

2nd version:

I also posted an extra-credit Canvas quiz about the History of Calculus in Math 153: Calculus III course in Winter 2022. I changed the format and questions of this quiz. In addition to biographies, I posted an important article about the number e. This quiz was prepared so that students got familiar with the sum notation and series concept through the understanding of logarithm and number e. This padlet is posted below:

We can incorporate history of mathematics in many ways in our classes, even in advanced level of math classes. In this way, we also prepare students for doing scientific research, and they get more familiar with different ways of doing mathematics.

For example, students can

• examine the development of a particular idea;

• explore different ways that a certain proof method used in mathematics and write a summary paper or create a presentation;

• explore ideas/proofs that evolved into a new area rather than the original work;

• explore different aspects of works of a mathematician who contributed to many different fields and finding common ideas or themes that she/he used while working;

• create different, useful activities such as On-Line Encyclopedia of Integer Sequences,Math Genealogy project, or Erdos numbers.

I will continue updating this webpage with other activities that I created for my students. Thank you for your interest.

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