We did it--classes are done for this crazy year!

I always get the privilege of writing the last #Math371 blog post of the semester. I like to reflect on what I have learned while teaching this course that semester. While I will do some of that, I will also reflect on things the students have shared throughout the semester.

For the past 2 years, I have asked the #Math371 students to create a Desmos Activity Builder. This year I decided to make that task more formal and give them a list of items that needed to be included in their activity. I got feedback on the activity before I assigned it from Mark Kreie, Brookings High School math teacher. He was very helpful and offered great suggestions. I feel like this was one of the most successful assignments this semester. The students did a great job and many of them are now excited about using Desmos in their classroom. After they created their activity, they also had to reflect on the experience. Here are a few excerpts from journal entries:

• I think it would be good to use this as an interactive lesson in the classroom versus as a homework assignment. It facilitates lots of group discussion and it allows the opportunity to correct student misconceptions immediately.
• I decided that this tool is best utilized not as a method to teach new material to students, but a way to find entertaining new ways to show the new material that has been taught.
• Creating an activity for a classroom was rather fun to me. I felt like I was playing teacher and thinking about my students and how this kind of stuff would make the most sense to them. For me, that was really fun to experience the work teachers have to put in to make a good activity.

Another project that I improved for this semester was the group teaching project. I divided students into groups, assigned them a Learning Management System, and they had to create a video lesson, a homework assignment, and a quiz in their course that they created in their LMS. This assignment wasn’t without issues as I assigned one group Moodle and we discovered that it involved downloading software so I switched them to a different one, which also didn’t work well. They finally decided that they wanted to use Edmodo. In general, this was a good assignment as they had to figure out their own LMS as a teacher as well as understand the other groups’ systems as a student. I feel like we all learned something from this project. In their reflection on this project, some students said:

• Overall, I liked being able to experience the different system in this project. Before I worked on this project, I had only used Google Classroom. I liked being able to see the pros and cons of each different management system as the student’s point of view. This is only going to help me make a better choice for my classroom in the future.
• Nevertheless, the LMS project made me ponder about what I like and dislike in LMS and gave me appreciated experience with using a system from the perspective of a teacher.

Despite the pandemic, we had another great semester in #Math371. We all learned new things and had fun in the process—well, at least I did. I always feel so lucky because SDSTATE has awesome students! I can’t wait to watch them grow and become great math teachers.

Should Calculators Be Allowed in the Math Classroom?

This is the age-old question that all mathematics educators have been faced with. They might not have referred to the modern-day calculator but rather an equivalent item of assistance for the era. In fact, in early mathematical history, the abacus was used to aid in calculation. Eventually, we had the slide rule, then the handheld calculator, and now we all have calculation apps embedded into our smartphones. All these tools have made mathematical calculations easier. If they were never allowed, how many mathematical discoveries would still be undiscovered? This being said, there are pros and cons to allowing calculators in our classroom.

One of the main advantages to implementing calculators in the classroom is that it allows for students to solve more advanced problems. Online graphing calculators such as Desmos and GeoGebra, are quite powerful tools. There are so many ways to implement sites like these to allow students to explore different aspects of graphs. GeoGebra is especially valuable when teaching geometric theorems as it provides students with visual aids. Another pro is that it gives students opportunities to connect algebraic expressions with the graphical representations of those expressions. It really comes down to student mastery and understanding. Calculators should be used when students have shown us that they have mastered the skills a calculator can do for them.

One of the biggest downsides of calculators is that because calculators are so powerful students can easily use them to cheat on exams. Many of the TI graphing calculators can be used to store notes and formulas that we wouldn’t want students to use on exams. Another big downside is that it can give students an easy way out. Many concepts can be figured out with a calculator, but students need to know how to do them on their own because they are building blocks for bigger and more complicated concepts. Many professors at SDSU take the approach that “If we let our students use calculators for everything, they won’t know how to do the math on their own”. This is a valid point, but I would argue that if we are using calculators in a valuable way, students will still gain conceptual understanding.

I hear a lot of older teachers say things like:

• “calculators have hindered students because they don’t work as hard as students used to.”
• “This new generation is too addicted to technology.”
• And my personal favorite: “What happens when technology fails, and you can’t figure out what to do?”

While I agree and fully believe that students are not thinking as critically as they used to, I don’t think we can solely blame this on calculation tools in the classroom. Our main goal as math educators is to promote mathematical understanding. It doesn’t really matter if our students can perform mathematical process after process if they don’t know where it is coming from. Technology can be used in both good and bad ways, and we have to learn how to teach our students knowing that they will be thrown into a technology-oriented world. The notion that students of today must have it just as difficult as we did is quite frankly ridiculous. Society evolves. That’s what it does. Shouldn’t the way we are educating our future generations adapt to the era we’re living in? It’s time we stop churning out human calculators and teach our students to learn for understanding.

So in conclusion, calculators are wonderful inventions that have allowed for some of the greatest mathematical discoveries. We would be depriving our students of valuable knowledge if we didn’t allow them to learn how to use technology in a positive way. In all things, it comes down to balance. I believe that teachers should continue to allow students to use calculators in the math classroom. However, policies need to be created and implemented to prevent cheating and create problem solvers and critical thinkers.

Annamarie Dobbs

 

Technology, Mathematics, and Grading

     As a future educator, there are a lot of things I am learning that are important in the teaching world that I never really thought about before. One of them is grading, and relating to that, homework and assignments. A teacher's job and goal is to help their students. Help them learn and achieve their goals in the class. The way we assess their progress is through grades. So a big question is, what type of homework should teachers give so that the grades reflect student progress?

    When I was considering this question, I thought back to assignments I had in high school. Some teachers would load us up with homework that wasn't very meaningful, but it was worth a large part of our grade. We did whatever we had to do to get it finished. This means our grades probably didn't reflect how well we learned the material. But then I thought of the stimulating research projects I did in an AP English class and writing the research paper for that. The paper was worth a lot of our grade, but I loved writing the paper and I learned so much from it. This was a perfect example of an assignment that returns an accurately reflective grade. 

    As I started college, many of the assignments were more along those lines. The assignments required us to demonstrate what we learned and sometimes give our own unique understandings on the subject as well. For example, in a Calculus I class, our professor put us in groups to solve a few questions. This way, we learned from the different perspectives of our group members as well as practiced the skills we needed. 

    Of course, teachers can't always give in depth assignments like this to constantly stimulate our minds so much. It would be hard on students and would create a lot more time needed to grade the assignments for teachers. But what I learned from my experience and from classes I have taken, short answer questions are almost like the sweet-spot of an assignment. It is harder to cheat on short answer questions that require an opinion of a student.They don't require such in depth thinking all the time, but they are a more accurate way to gauge how well a student has learned something in a quick three to five sentences.

    Another huge factor that teachers must consider today is technology. Should they give assignments online or not? This decision has big implications. If they don't give assignments online through a program like WebAssign, they will have to grade the assignments themselves, which is always something to consider. However, there is always the risk that if they give an online assignment, the students will cheat to get it done instead of just doing it themselves. For myself, I know that I will do online homework, but if I am running low on time, I will look up the answers and just do the problems later when I have more time to make sure I understand them. I think if students did that, it might be fine. However, there is now way for teachers to guarantee that their students will do that, which leads back to the question of an accurately reflective grade.

    In the end, I think it must be left up to the teacher's discretion. They know their students best. They should be able to assess what their class would be capable of handling, the best way of assessing them, and helping them practice their skills. Hopefully, with the knowledge from a relationship with their students, teachers would be able to give relevant assignments. This way, teachers can grade accurately and give their students meaningful homework that they may be more willing to do.

Kaia Erickson

Is Technology Making Students Lazy?

by Halle Gronlund    

     With the use of online homework, zoom, online instruction, and social media, the world of education has turned to the use of technology during this unprecedented time. At the start of the pandemic, we had no other option than to turn to technology to help us continue learning and teaching. We would have struggled without our current advancements. Now with students waking up 2 minutes before class, lying in bed during class, and cheating through online homework, it begs the question: “Are students lazier because of this technology?” As we navigate our way back to a “normal” post-pandemic world in the next few months, we will see the effects of the pandemic in our education.

     Technology has not always been a controversial topic in education. We talk to our parents and there was no such thing as cheating or online homework when they went to school. They didn’t have the websites to look up a problem when they got stuck or text a friend to send them the answers. They did the work on their own, for the most part at least. With the developments of technology even before COVID-19, students get stuck on a problem for 30 seconds and the first thought in their head is to look it up on the internet. And that is being generous on some occasions, some students don’t even try for themselves and look up the answer the minute they get the assignment. We wonder why homework grades are soaring and test grades are plummeting. With COVID-19, I feel as if this is only worsening. Time management was given to students to figure out on their own. They received a list of assignments for the day and they weren’t given a certain time to do it. This led to procrastinating until the last moment and only having time to look up the answers to turn the assignment in on time. I can only imagine the student would see how easy this is and never want to do another assignment on their own, even after this pandemic is over.

     Zoom is great. Great in a pandemic when you have no other option than to record lectures for students to watch at a given time or whenever the student found time. Great for meetings with people across the country. Even great to catch up with family that lives states away. It’s not great for when students are too lazy to get out of bed in the morning and jump onto class 2 minutes before it starts. It’s not the teacher’s fault, but the responsibility lies within the student. Students have found a way to make life “easier” in a pandemic. I mean I would love to lay in bed, watch class, take notes, and understand what is going on, but that’s just not how it works most of the time. No teacher is watching you making sure you are paying attention, so many students do not pay attention. There are so many distractions to take your focus off class that aren’t present when you attend class in a classroom. Don’t get me wrong, some students need zoom as their only way to learn in this pandemic, but some students are abusing the system because they are too lazy to walk or drive to class.

     To wrap things up, I think technology is super useful when it is used right. But I also believe students are not using the technology in the way it is supposed to be used. Students are only using it to make their lives the easiest they can. Without the educational technology created, the pandemic would have been even more of a mess. But as students, educators, and parents, we need to reflect on how we are using the technology given to us.