Could the Future of Math Education be Desmos?

By Sydney Stapleton

This past week our class created Desmos activities, which are digital mathematical experiences that aid students’ learning by modeling and using multiple representations to show concepts. While exploring Desmos to make an activity, I am amazed at the tools and abilities it offers to help teachers visualize the learning concepts for their students.

Desmos was started by a Yale math and physics major and now CEO, Eli Luberoff. Like most, if not all, secondary students, Eli grew up utilizing a graphing calculator. With the wave of technology in the world, it makes sense that we would see people create software that can do the graphing on a bigger screen, like a computer. Desmos now has not only a graphing calculator tool, but a scientific calculator, four-function calculator, matrix calculator, geometry tool, and test practice as well. SInce Desmos is specifically for educational purposes, it strives, “to build a world where every student learns math and loves learning math, where a student’s access to the power and beauty of math doesn't depend on their place of birth, race, ethnicity, gender, or any other aspect of their identity” (“About Us”). Desmos holds strong principles in creating equity for all learners. As the software and team of people expand, Desmos works hard to listen to its users to keep bettering the free service for everyone.

Desmos activities are a great resource for formative or summative assessments. There are activities geared toward helping students self-teach a lesson or introduce the topic based on their previous knowledge. Desmos activities can also be purely used for students to practice, as a great at-home resource to assist homework assignments. Teachers can create activities applying minimal to more complex coding and Desmos graphs. A benefit of using code is that the teacher can set up a code to provide students immediate feedback. Another significant benefit for teachers is that you can assign pre-made activities that contain a more professional feel. This ability is great if a teacher finishes a lesson early and wants students to stay productive and practice the concepts.

The newest addition to the Desmos software is a sixth through eighth-grade Algebra I curriculum. This curriculum will be fully available to schools in 2022-2023. This curriculum includes daily Desmos activities ranging from first-day introductions, exit tickets, and unit assessments.

Our country had to adapt and come up with solutions to online teaching during this pandemic. Online schools or flipped classrooms are definite candidates to implement the Desmos curriculum. With more and more schools emphasizing technology in the classroom and quickly increasing amounts of one-to-one districts, Desmos’ software in addition to the Algebra I curriculum has the potential to be instrumental in a shift in mathe education. Depending on the magnitude of implementation that Desmos’ curriculum gets, there may be more grades of curriculum available in the future. The possibility of using Desmos to teach all students mathematics across the country is an interesting concept to ponder.

Source:

“About Us.” Desmos, https://www.desmos.com/about.

Formula Sheets for Exams

by Emily Siemonsma
        In high school, the importance of memorization is stressed in almost every class. Even in some college courses, memorization is the only way through the class. However, memorization has never been a strength of mine and I am sure many other students agree. Memorization takes up so much time and honestly I forget eighty percent of the material right after the test if I force myself to memorize terms or methods. Learning is about gaining a deeper understanding of the subjects you are introduced to. Thus, I believe that memorization needs to become a thing of the past, especially in the math classroom.
        Once we say goodbye to memorization, we can start discussing allowing formula sheets in the math classroom. I think that formula sheets make perfect sense in the math classroom. When someone is working as an engineer, teacher, or mathematician, they will probably look up most formulas. Memorizing formulas for an exam is a waste of time because students will likely be more concerned with remembering the formula than understanding the question. Also, students will probably forget the formulas after the exam anyways.
        Most formulas will not give away answers to students, but instead, help check that students understand the concepts. If a student does not know what to plug into a formula then they probably do not understand the concept, but if they know how to use a given formula and can explain their answer well then there is nothing wrong with giving them the formula.
        If a teacher is concerned with students not understanding where formulas come from, then they should quiz them on how to come up with a formula. But when it is time for the exam, save your students some time and give them a formula sheet. Students should not have to stress about remembering every single equation perfectly, they should get to spend their time deepening their understanding of the concepts taught.
        In my statistics class this semester we are given a formula sheet. It is very helpful especially because there are lots of formulas to remember for statistics. Before every exam, I review every formula and make sure I understand how it works and what it is for. I honestly could probably go without some of the formulas on the sheet, but it brings me a sense of security. I know that I can stress more about understanding all the concepts rather than making sure I know how to write out an equation.
        Overall, it is up to the teacher if and when students get formula sheets. I understand that there are some situations when formula sheets are not necessary. However, most times memorizing the formulas is not going to make the student a better mathematician and in these situations, I am an advocate for formula sheets.

Mass Customized Learning - Effective When Succesful but Very Difficult to Execute

    While technology has opened up a variety of opportunities not only in the math classroom but in classrooms in general, it runs the risk of leading to a disconnect between teachers and students. Coming from the Harrisburg School District in high school, the first district in South Dakota to adopt Mass Customized Learning or MCL, I feel as though I have gained a unique perspective on how teachers who are either forced to use too much technology or teachers who aren't prepared to use technology can lead to a classroom environment with the teacher almost completely uninvolved. MCL provides the potential for strong student-teacher interactions with teachers being readily available to help students who have already gotten an understanding of the material. The teachers need to understand that they need to make sure they are still actively involved to not lose their students' attention.

    In theory Mass Customized learning is a modern idea where students can learn at their own pace with teacher-prepared lessons given to them in advance. The goal of this is to provide students the ability to take more or less time on a given subject and to have the teacher there as a constant resource for students to get one-on-one instruction from should they struggle with something. When Harrisburg chose to adopt this policy they really had no examples to go off of so the resulting program essentially had the opposite effect. Students instead had no motivation because of the lack of hard deadlines and many teachers thought that they were helping students to think more independently by not helping them when asked. I was in this program the second year after its introduction so they did not yet have a chance to figure out what to do. By the time I had graduated almost none of the policies I started with were still in place.

    During my Freshman year of high school, I would say I interacted with my math teacher in particular about three to five times a week, once for a weekly check-up on my progress in the class, and the other times to ask to take exams. Whenever I went to class I would either watch a video or take a test. The tests were graded with no explanations as to what you did wrong and you would retake the same exam as many times as it took to pass it. Normally I would simply write this off as a teacher who simply isn't doing their job very well, but this was the department-wide standard at the school. With the videos the same problem occurred, if you had a question you would simply be referred back to the notes or the video until you figured out the issue on your own. This was once again a department-wide standard to promote independent learning. Finally, as I mentioned earlier there was a weekly meeting in which instead of getting help with issues you had, the teacher would simply tell you whether or not you were at the recommended pacing for the class. To me, this is an example of how technology can be misused very easily to make almost every student upset with math.

    Thanks to myself and a few of my friends, these practices were changed the following year to make things better for everyone. Instead of giving the same test until you passed, you would get an explanation of what you did wrong and receive a similar test with different questions for your next attempt. Each day in class, teachers would give a small lesson based on the content of the scheduled pacing to ensure people understood what was going on, and the weekly meetings were removed. By bringing teacher-student interaction back into the classroom, the environment was improved greatly for everyone. I saw my personal stress and anger towards math greatly reduced, and I was able to understand things much better. Everyone also enjoyed the new system much more. Students were able to use teachers as a resource when needed and to learn the material at their own pace. This change happened largely due to voluntary student feedback, not feedback asked by teachers. Because of this, I feel it is very important to make sure you know students' thoughts when any new system is introduced, but especially one so focused on student's individual learning.

     Technology is a vital part of the classroom these days with almost every school district I have seen having computers either readily available or individually assigned to students. What can come from this is either an enhanced experience where students can understand the material before coming to the classroom and use the teacher as a resource to better understand what they are supposed to be doing. While this seems good in theory, the execution is very difficult and can take time to be done correctly. Fortunately, now there are far more examples and learning strategies for MCL in particular so a situation like this does not happen again. However, it is an example that can be used to show how important student feedback is when introducing a new style of learning.

Pros and Cons of Gamification in the Classroom

By Hunter Hanson

What is gamification in the classroom? Well, gamification is about transforming your classroom environment and regular activities into a game. The teacher can do many things with gamification to try and get students involved with what they are teaching. They can use a leaderboard with students getting points each week as they progress throughout the year. This can be achieved through either effort from the student, the attitude of the student, or even how well the students perform in the activities. It can be a great tool in the classroom with many pros but also has some cons as well. Some gamification websites that you can use as a teacher include Kahoot, Quizlet, Gimkit, and many others.

Pros

One pro of gamification is that it creates enthusiasm in the classroom. Gamified learning can help students that may struggle with certain subjects in school like math. By gamifying the subject, you can make the students more excited and competitive while learning at the same time. Another pro of gamification in the classroom is that it provides instant feedback. Students after completing certain tasks on the computer can see how they did with instant feedback such as scores and rankings among students. This can help push students to do better with trying to get a better rank in the classroom. The last pro I would like to talk about is social connections. When gamifying a classroom, you can put students in different teams and have them work together which can help students who may have trouble connecting with other students socially. By playing games it can allow students to loosen up and interact with each other.

Cons

One con of gamified classrooms is badges. This is a reward system based on the skill level of students, leveling up as they progress in learning and receive badges along the way. One example of this in the classroom is with the program Khan Academy, the more time you spend on the platform doing problems and watching videos you receive points to earn badges. One con of this method is that ranking students may make some students not feel as smart as their peers, who have more points and badges than them. Another con of this method is with false learning, where students may think that they are understanding the material, but later they find that they just knew how to do those problems well. Some other cons of gamification in the classroom include decreased attention span of students. When playing games in the classroom students may not want to engage in the game and would rather talk with other classmates and not participate. The last con I want to talk about is student assessment. What I am referring to is how much are the games really tying into the curriculum of the classroom. It can be hard at times to make the classroom fun and exciting while at the same time staying on track with course materials and teaching it to your students properly.