We Need to Keep Learning

Every spring semester I get to write the last blog post for Math 371, Technology for STEM Educators. I always title it, "What I Learned This Semester," but this year I want to be more specific about why educators need to keep learning. 

If we don't continue to learn, how can we ask our students to learn? As a teacher educator, I have always felt that modeling what I want our future teachers to do is the most important aspect of my job. How can we say one thing and do another? So I try to model good teaching, fair assessment practices, and being a lifelong learner. 

Last semester I did an action research project with collaborators from Georgia Southern University and the University of New Hampshire. We used a two-column proof software in our Geometry for Teachers courses at our respective institutions. We collected data through student surveys and the software. When it came to analyzing the survey data, I initially used a Chi-square Test of Independence on the pre-and post-responses to our Likert-scale questions. Our results weren't great, but we did have some low p-values. As I began to read more about statistics, I decided that a different test should be used because my sample sizes were too small for the Chi-square test to be accurate. So I kept searching for an appropriate statistical test and kept asking questions of my awesome colleague, Dr. Gary Hatfield. He even took my data to his class on nonparametric statistics and had them look at it to see if they could conclude anything from the data.

As I kept reading more about statistics, I found several tests that wouldn't work because they only worked for categorical variables that had 2 categories. My Likert scale had 4 categories, with 29 samples in the pre-survey and 20 in the post-survey. I finally converted the data from categorical to numerical, and then as I was reading some forum, someone mentioned a partially overlapping test. Then I Googled a partially overlapping sample and found a dissertation from Ben Derrick from 2020, where he created a new statistical test that seemed to fit exactly what I needed. He even created R code and I was able to perform the new test. We then got more results with low p-values. In addition, I did a paired t-test and Wilcoxon rank-sum test on the paired data, but these only resulted in low p-values for questions that already had low p-values from the new test.

This semester I went far outside my comfort zone and learned a new statistical test out of necessity for my research. I had to learn how to do some coding in R. And the best part of this experience was that one of my statistics colleagues asked me to send him the information on this partially overlapping samples test. He just got some data that he plans to use it on. My learning led to something that helped a Statistics colleague! Usually, the Math faculty are asking the Stats faculty for help, not the other way around.

How does this experience translate to help my future teachers? Well, I have shared this experience with them as they are required to do action research projects in their second semester of student teaching. They were able to see my first-hand account of my action research project--that the data you get doesn't always give the results you want, that you need to figure out how to analyze the data, and that a portion of the data doesn't give the whole picture.

A Semester Filled With Learning

By Allison Johnson

This semester has been full of learning. I have learned about a lot of different technology tools to potentially use in my future classroom. I have learned about a lot of different iPad apps to use. I have decided that I like having an iPad and being able to take notes on it so much that I am highly considering getting one. I also learned how to do things on a SMARTboard and Promethean board, which I was very excited about. Elementary-aged Allison would be so happy, I remember always wondering about how you work a smart board and I loved playing on it when I could.

This week we had a Desmos art project due. Desmos is an online graphing calculator. We had to create an image of some sort in Desmos. This activity was challenging, you had to graph a line and then just keep changing the numbers in the equation until it looked right. I was able to find some resources online to help, which was very nice. After I finished my activity, I sent a video of it to my parents. My mom said something along the lines of “that looks great, I would have no idea how to do that.” My dad is an engineer, so I often tell him about stuff we are doing in the classroom. I explained to him what Desmos was and what the assignment was, and he said, “wow calculators have come a long way.” I never even realized that neither of my parents have ever used anything like Desmos because I am so used to it, and I have been using it in a classroom since high school. 

Last week we got a TI-Nspire calculator. Our assignment with this is to learn more about how the calculator works and then teach our classmates how to do some math activities on it. For those of you who do not know about this calculator, it is a very advanced calculator. You can create shapes, make word documents, calculate, do derivatives, and much more that I have not figured out. I had no idea this calculator even existed and honestly, I do not know when I would ever use it. I do not foresee myself using this calculator daily because of how complex it is and how hard it is to figure out how to work it. This was another instance where my parents were flabbergasted by how far technology has come. They had no idea they made calculators this advanced and neither did I. 

Right now, in Math 371 we are working on a group teaching project. Each group got assigned a different learning management system. My group was assigned to Canvas. As of right now, I am not a big fan of Canvas. It took me almost an hour to figure out the settings and figure out what settings I needed to change for people to get into the class without the school having a license with Canvas. My classmates are also having issues logging into their accounts after they make one. I am having trouble getting things to show up where I want them. The feature to make quizzes was nice though. They have a lot of options for the types of questions you can ask and the types of answers such as true/false, multiple-choice, fill in the blank, essay, etc. 

Should Accounting be Considered a STEM Field in K-12?

By Hunter Hanson

Accounting is becoming more and more technology-savvy with each day that passes by. Right now, in the United States, legislation has introduced accounting to be considered part of the sciences, technology, engineering, and mathematics (STEM) field instead of being in the business field in K-12 Education. Accountants are responsible for recording the financial transactions of a business or organization. The accounting process includes summarizing, analyzing, and reporting financial statements. All businesses need an accounting professional to do their finances, which makes them in high demand in almost every economy today. STEM provides some of the fastest-growing jobs related to cloud computing, engineering, mathematics, and sciences.

The legislation would allow STEM K-12 grant funding to be used to help with accounting awareness and education. The activities would promote the development, implementation, and strengthening of programs to teach accounting. The goal of the bill is to help increase access to high-quality accounting courses for students in high school who would like to go into the accounting field. If passed accounting still wouldn’t be considered a STEM field at the post-secondary level, but if passed would strongly help it to become one.

The American Institute of Certified Public Accounts (AICPA) has wanted this bill to be passed for some time now because their argument is that there is a clear and logical overlap between accounting and technology. As the profession has become bigger than ever, CPAs have become some of the biggest leaders in the technology field with many having to manage and analyze big data and help with data security every day working alongside information technology (IT) professionals. Business professionals and accounting firms are looking for more tech-savvy CPAs and accountants, which increases the need for more technology classes in the field. Overall, accounting is a great profession, with many opportunities in the field, and time will tell if accounting will be considered a STEM field. 

Online Homework

By Melissa Christlieb

Have you ever been assigned a homework assignment online? Or have you ever assigned your students online homework? Online homework is being implemented more and more in education each day. So, what are some pros and cons of online homework?

Let’s start with some pros. A major pro of online homework is the flexibility that it allows. Students have complicated schedules and are involved in more things than just your class. Having homework online allows students to learn when the time suits them and the opportunity to work in a different environment than a classroom. There are so many resources online now to help with homework and understanding. Online homework can be beneficial to students who are shy or do not like to talk in the classroom. Having discussions posts online gives those students a way to communicate what they are learning in a way that is comfortable for them. As a student, one aspect of online homework is that immediate feedback is provided in most cases.

Next, let’s talk about some cons with online homework. When assigning online homework, you normally have a bank of questions to pick from. This can cause teachers to assign too many problems because it is easy to assign them to students. Too much homework is a huge problem. With having homework online, especially with math, the websites want the answers in a certain way. This can be discouraging for the students if they doing to problem correctly, but the online website wants an answer in a different form. This recently happened in one of my tutoring sessions. After the third problem that was incorrect because of a formatting issue, the students felt very defeated and like they were doing everything wrong. However, if they were to turn in their answer on paper to the teacher it would be correct.

Overall, there are many pros and cons to online homework. Online homework can make tasks much simpler and more accessible to do anywhere students want to learn. On the other hand, online homework might be discouraging to students if simple formatting mistakes occur and continue to get problems wrong. So, would you use online homework in your classroom? 

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.

CODAP-Common Online Data Analysis Platform

By Allison Johnson

Statistics in middle school and high school is often not considered a priority standard and can sometimes be overlooked by the teacher or skipped if the class is behind. Most teachers also do not feel comfortable and confident enough to teach statistics. There are many resources online for teachers to sharpen their statistics skills and better prepare them to teach the lessons.

The traditional way to learn statistics is to use Excel. Excel does have a lot of nice functions and options. It is easy to calculate the mean and median and other numerical values in Excel. The graphing functions in Excel are not so good. The graph function in Excel is not easy to manipulate and it is hard to easily change what is on the x-axis and y-axis. This week in class we learned about a program called CODAP. CODAP stands for Common Online Data Analysis Platform.

I found a lot of things in CODAP that I liked. You can easily rearrange the way the data is sorted by clicking on the title of the column and choosing how you want it to be sorted. It is also very easy to make graphs and customize them. In CODAP when you make a graph you drag and drop exactly what column of data you want on the x-axis and y-axis. You can also delete the data from the graph and drag a new column onto it to make a different graph. You can choose what type of graph such as line graph, bar graph, pie chart, histogram, box plot, etc.  You can adjust the settings on the graph. You can also easily hover over points in the graph and get their exact value.

There are a lot of functions and features to the graphs that Excel does not have that CODAP does have. In Excel, you cannot easily customize and change the graph by dragging and dropping columns. In CODAP you can also make a line of best fit and it will tell you your r^2 value and the equation of the line. Just like Excel, CODAP can also find the mean, median, standard deviation, etc.

Technology is a very useful tool when learning statistics. Personally, I never used Excel until college. In my college statistics class, I had to completely learn how to use Excel. I wish I would have been introduced to it in high school or middle school so I would have a better understanding of what I can use Excel for and how to use it. When teachers are teaching statistics concepts in middle school and high school, I think it would be very beneficial to use either Excel or CODAP. Using these software programs can be a great learning tool to better understand statistics. 

Floop: An innovative way to give feedback!

By Melissa Christlieb

On Friday, February 4th I attended the SD STEM Education conference in Huron, SD. During one of the presentations, we learned about the website named Floop. This website is a tool for teachers to use when grading and giving feedback to students online.

With this website, teachers are able to make assignments for students and the students use Floop to turn in the assignments electronically. On the teachers' side of this website, you are able to insert comments, write on the assignments, give audio comments and see who has read and replied to your comments. If a student replies to comment it will flag the assignment as if they just submit something. I think this would be very helpful for teachers so that a student's comment does not go unseen. As a teacher, you can select to see who has turned in the assignment and who hasn’t. Floop also keeps a bank of your previous comments made which can be reused for different students.

This website is able to be accessed on a mobile device, iPad, tablet, or computer. This makes it super easy for students to take a picture of their assignment and upload it to Floop. In Floop students are able to peer review their classmate's assignments anonymously, and it also gives them prompts for giving feedback to others.

Another thing that was talked about during this presentation is what descriptive feedback is. Descriptive feedback is more than just saying ‘Good job!’. It is giving thoughtful responses to questions and engages with students about the work they have completed. This includes positive feedback on their work as well as where they might have made a mistake or could improve their work.

In math education, this website can be very beneficial because students can get feedback from the teacher or their peers immediately. Students are also able to have conversations with their teacher in the comment section. Floop allows grading to be done in a timely matter and allows teachers to give descriptive feedback to more than one student easier. 

Should students be forced to work in groups?

By Emily Siemonsma

Group projects are a huge part of high school, college, and people’s careers. However, does group work really create a better individual learner? In the long run does group work in school create better members of society.

It cannot be denied that teams are a necessity to society. Think about a team of doctors. If someone calls 911, EMT’s will arrive, then the patient will meet nurses, doctors, and so many other people to help take care of them. If all the members of this team had not learned how to work with others leading up to them taking this job, that could be detrimental to the patient. Another example is a sports team. In basketball if one person hogs the ball and tries to play the game by themselves, the team probably will not win. The athletes must learn how to play with each other and be confident in each other.

When group projects function as they are supposed to, the outcome is wonderful. Students learn how to better interact with their peers. Students learn how to delegate tasks to one another. And students find ways to overcome social challenges with others. Specifically in the math classroom, students can gain knowledge from peers in group work and do not feel as much pressure to know the answer to every problem because of the help of their group members. Additionally, group work in the math classroom can inspire students to possibly dig a little deeper, because they are encouraged by their teammates. Most importantly they become better learners.

There are a few issues today however with group work. It does not work very well online. Whenever I try to host a meeting over zoom, it feels like less gets done than what normally would. Also, trying to come up with a project idea online takes way longer than it needs to. Even if groups can meet in person it can still be difficult. I remember dreading group projects in high school. I always felt like half of us ended up doing all the work, and the other half did nothing.

Thus, for groups to be effective, teachers must do their best to keep students accountable. Students will put effort into their group if they feel passionate about what they are learning, so whenever it is possible teachers should encourage students to pursue topics that excite them. If students excel in group work in school, they will likely perform well in groups throughout their lifetime. This is important because in the real world no one can learn alone or work alone.

Technology Makes Breaking the Law Easier than Ever Before

by Sydney Stapleton

Technology advancements have created the ability to share information within seconds. New high speeds of data, Wi-Fi in nearly every building, and more technology available than ever before allows everyone to publish and distribute content. This generates the perfect storm for violating copyright and fair use laws. Educators need to educate themselves in order to protect them and their school from getting involved in lawsuits and paying large fines.

This week in class, I was taught, for the first time, the rules and vital fine print statements pertaining to copyright and fair use laws. Before reading any information on copyright, I assumed it was similar to how you must cite your sources to avoid plagiarism. While some aspects, like citing the source, are still relevant there is much more to it than that.

While discussing during class, it was clear there are many misconceptions surrounding what is permissible without breaking laws. The fair use doctrine can cause confusion, due to the fact that it permits unlicensed use of copyright works in certain circumstances. The doctrine is beneficial to educators since the instructional purpose within a classroom falls under an acceptable circumstance. An important tip is that the instructional purpose must be applicable to the content the students are learning, factual, and only presented to the students in the classroom. As a general rule of thumb, as with most things, you should always error on the safe side and never use somebody’s work without their permission.

Why are students not being taught proper copyright laws from the time they are able to use works of any sort from the internet? Explaining and showing students why it is important to apply the creative commons licenses tool when searching for images on the internet is a prime example of an introduction to copyrights even elementary kids can understand and implement. I have stated that educators face the responsibility of preventing misuse of copyright works, but so does nearly every employment position in any job. This means that students have a right and responsibility to know copyright laws and should be taught and then held accountable for not breaking them.

In the long run, technology is going to be more and more a part of the learning experience at any education level. My guess is that the ability to break copyright laws will go up hand and hand with advancing technology. It is important that educators and curriculums find a way to educate students on what copyright is and how to protect not only others’ work, but theirs as well.