Math 371 Technology for STEM Educators

As always, I feel like this semester has flown by. Part of it going by so fast is because it has been so busy. In February I was able to attend the Association of Math Teacher Educators conference in New Orleans. I presented some of my research with my colleagues Orly Buchbinder, University of New Hampshire, and Tuyin An, Georgia Southern University. I met them through the Geometry for Teachers (GeT) group, coordinated by the University of Michigan. At the end of February, I was able to attend the Research in Undergraduate Mathematics Education conference in Omaha. Several of us from the GeT a Pencil community got there early and were able to gather and talk about writing chapters in an upcoming book and the work that we have already done. As a first-time attendee, I enjoyed the RUME conference, and I hope to go again next year. Again, I co-presented with Orly and Tuyin about our FullProof project. We had a lot more people in the audience, thanks to our GeT community. The GeT commu...

It's that time of year again when finals are starting to roll around. Students are getting anxious and are studying more than ever. On average, college students take anywhere between four to six classes each semester which leads to about three to five finals at the end of the year. My questions for you are: should colleges have finals, should the finals be cumulative, and when should they be given.  To answer my first question, I think that colleges should have finals. Finals are a great way to see if the student should really pass the class or not. Without finals, a student may slide through the year by cheating on homework and studying enough for tests to remember the information for a small period of time. Having finals makes the student learn the information well enough to the point where they will still remember the information months later. At that point, the student has embedded the information into their brain and will most likely remember it for a ...

Coding can be a useful tool in a classroom but isn’t as widely taught as some people may think. Coding is essentially the process of writing commands that a computer follows to carry out a task. The skill of coding is useful in creating many applicable things we use every day like video games, websites, applications, and much more. So, how can we teach and use coding in the classroom? Coding, by its nature, requires a certain threshold of patience and problem-solving to be successful, two very important things to have and learn when entering the real world. There is a lot of trial and error that goes with coding, and being able to stomach that is important.  Coding also improves a student’s knowledge of how a computer works. When going about their everyday tasks, people that know and understand code can see the various background processes that go into a computer and can see that some websites or social media are coded in a way to make you use their apps as much as possible. This...

Many schools use online learning management systems for homework and class material. They make it easier for teachers to have all notes, assignments, and quizzes in one place. However, since the pandemic moved classes online, homework has also moved online. Through the LMS and online homework system, class data is at the teacher's fingertips. For me, that begs the question, are students better off with online homework? There are many different LMSs and homework systems, so teachers and school districts may stuggle picking out the one they think would be the best for their class. The homework system could vary from class to class even. For example, my high school math teachers use DeltaMath for Algebra I, II, and Geometry, but use Webassign for Precalculus and Calculus. My school also uses Google Classroom as the LMS, but other schools use different ones like Microsoft Teams and Canvas.  However, almost every teacher did homework differently, even if they use the same LMS and homewo...

Whiteboards in my opinion are amazing for doing problems. I myself carry multiple mini whiteboards that I’ve gotten from Amazon and have handed out many to my peers. These whiteboards were great tools when doing math homework or even other classwork. Whiteboards made it easy to fix small mistakes versus having the annoying smudge marks on paper when you make a small error. Coming to SDSU, at the AME building, even the walls are whiteboards! Many professors put students in groups and send them to the board to solve problems. Did learning from group board work help students learn? Group board work is a great way for students to communicate and problem-solve as a group. As some students struggle, they may glance at other groups’ boards to see what they are doing wrong and learn from the mistakes that they could’ve been making. There are many times when students do a worksheet for the day during the class period and later it is assigned as homework if it is not completed during the class...

Technology has changed the way we teach and learn mathematics. We as educators are not restricted to just using pencil and paper anymore because of the wide variety of new technologies that have been developed. These technologies allow us to graph functions that would be impossible to graph by hand, create interactive activities for students to complete, and so many more things. One major player in the development of math technology is Desmos. The power of Desmos is unmatched, and the opportunities are endless.   One major function of Desmos, which is probably the most used function, is graphing. Desmos allows you to graph pretty much any function you can think of, including trig functions, exponentials, circles, conic sections, polar and parametric equations, and more. Desmos also has a section on statistics, where it is able to graph things such as linear regression and histograms. In addition to just graphing equations, Desmos is able to plot lists of points. Desmos can be a ver...

My colleague, Dr. Matt Biesecker, decided to play with ChatGPT as he was preparing the Probability & Statistics final exam.  He asked ChatGPT, “ What is a good exam problem involving conditional probability? ” Below is his exchange with ChatGPT: ChatGPT:   A jar contains 5 red balls and 5 green balls. A ball is drawn at random from the jar. What is the probability that the ball is red, given that it is not green? Dr. Biesecker: What is the solution to the problem you told me about ? ChatGPT:  The solution to the problem is that the probability that the ball is red, given that it is not green, is 4/10. Dr. Biesecker:  Could you explain your solution to me? ChatGPT:  The solution to the problem is that the probability that the ball is red, given that it is not green, is 4/10. This is because there is a 4/10 chance that the ball is red, and a 6/10 chance that the ball is not red. Dr. Biesecker:  I think you are incorrect, because if the ...

Making math fun for kids, rather than work is a huge task that a lot of math teachers have taken on over the years. “When am I ever going to use this?” “Ugh! Why did our math teacher assign so many problems?” “Math is so boring.” These are all comments I have either heard during my time in grade school or personally said myself. I am sure teachers are getting sick of hearing it, as I am sure students are tired of doing textbook assignments with no color or taste. Well, there is a solution to that: gamification. Gamification, in the classroom, is the incorporation of games into learning which allows teachers to better engage students.  Math is one of those subjects that students typically either understand or don’t. For those that don’t understand it, it is typically because they fail to find interest or appreciation of the subject. Using gamification when teaching math allows the students to see math in a different way, a more fun way if you will. Studies have shown that within cla...

With the introduction of more and more technology into our lives, classrooms have adapted to this change of technology over the years to better suit the students, which has led to many cool programs, apps, games, and practices being used in the classroom.  It has also led to some controversy as math calculators and help tools become widely more popular as every day passes.  But why, and what are the effects of using these calculators?  In the year of our lord 2023, there are dozens, if not hundreds of different math calculators and math help tools available to anybody with a computer and Google.  Typing in simple phrasing like “polynomial calculator”, “integral calculator”, and “inverse calculator” into Google can give a student many results that are not only helpful, but some consider to be downright cheating.  In my humble opinion, math apps and calculators are fair game, just as long you don’t use them just to get homework done, but to actually learn the ma...

Many math teachers might struggle with finding the right problems for their students to work on during class. For new teachers in particular, this task may seem daunting or nearly impossible to do. However, at the South Dakota STEM conference, Sharon Rendon did a presentation that provided tools to help ease this process. The presenter talked about five practices that a teacher can use to help find problems that would help develop math discussions that are productive, not destructive. The five practices she mentioned are anticipating, monitoring, selecting, sequencing, and connecting. First is the anticipating step. In this step, the teacher should do the problem themselves to try and make sure the problem is appropriate for the students. The teacher can use their technology to see if they want students to use specific websites like Desmos for coming up with the solution. Another part to this step could be anticipating what the students might get out of the problem or reviewing wheth...

We have all experienced the struggle in math class, whether it was you struggling or seeing someone else in the class struggling. There’s just too little time in class to learn all the material for the day and to also practice it too. Then to add to that stress, having the homework and not knowing how to do it after you get home for the day. Many parents even struggle when helping their child with their math homework because it's been years since they've done it. This is where the idea of flipped learning comes into play. The idea where you spend around 15 minutes outside of class learning new material then going to class the next day to fortify and build upon that knowledge through activities in class. Flipped learning is a good way for teachers to know who is struggling and have the time to help them in class while the students work on activities or worksheets. The outside learning portion should only really need to be around 15 minutes because of the attention spans of the...

As we start this semester of Math 371, we are just beginning to learn about the vast list of technological resources out there for teachers. As we continue through the semester, we will master how to use technology in our classrooms to improve students learning, but as teachers, we need to ensure the technology we are implementing into our classrooms isn’t harming our students. While learning about new technology resources, Dr. Vestal posed a question along the lines of “Do you think technology grants more access to students?” My initial response to this question was “Yes, it definitely does.” I went on to talk about how technology allows students to do so many new things that students in the past weren’t able to do. For example, over the last few years students learned how to do school over Zoom, something that our parents never would have dreamt of being able to do. Students now can use online math manipulatives, graph equations on Desmos, watch videos over subjects they are confused...

Unless you have been living under a rock for the last month, you have likely heard of ChatGPT and the concerns that teachers have due to this software. I understand these concerns for teachers who assign writing projects, which I do, but can a student use ChatGPT to write a research paper? Since we are getting ready to discuss copyright in the Math 371 class, I wondered if ChatGPT was smart enough to not use copyrighted material. I decided to ask an SDState librarian who is the resident expert on copyright, Elizabeth Fox. Another concern I had is whether ChatGPT would produce a bibliography. Fox asked it “I need 5 peer-reviewed articles on artificial intelligence.” ChatGPT produced a list of 5 articles. It gave her a list, but the links to the articles didn’t work and when she searched databases for these articles, the articles did not exist. Therefore, I am not convinced that ChatGPT could write a good research paper with citations and a bibliography. Fox said that she thinks that C...