Crossing the Line: Combining History and Mathematics to Answer "Why?"

When I was a student I probably asked the question why? too many times in a day. Sometimes, in math especially, the teacher could give me the answer to that question and I would still not understand (I’m looking at you, π, who decided what you were?) But there is an important tool teachers have at their fingertips to answer some of these questions.

• Why is a circle 360 degrees?  Because the Babylonians and other ancient cultures used a number system based on 60, and degrees is left over from that mathematical tradition.
• Why does the Pythagorean Theorem work, and…who was Pythagoras?  Well, Pythagoras was a Greek mathematician, and his proof using geometry proves this algebraic equation in a different way than showing them the equation does.
• Why do we need math?  There’s so many historical answers to this question. Point to the computer scientists and mathematicians that made it possible to go to the moon and have the computers we have today. Point to any of the many discoveries that have allowed us to advance as a society.
• Why do we have to do constructions? Well, other than constructions are an important tool for students to understand Geometry, point to the fact that mathematicians such as Euclid wrote entire books talking about and using constructions hundreds of years ago, and those books have been used and examined by mathematicians for centuries. It’s not just teachers trying to make Geometry harder- its teachers showing students where many of the rules in Geometry come from.

Combining history and mathematics gives teachers a unique opportunity. You get to cross disciplines (always a bonus!) and answer the students’ questions of why? It gives teachers the opportunity to show that math is not a stagnant, boring subject, but a subject that has been growing and changing for thousands of years. Combining these subjects also gives teachers the opportunity to show students that all their education is intertwined with each other. Showing students this gives them an opportunity to have a more well-balanced and well-rounded education. It allows students with strengths in different areas to find a way to connect their interests with classes they may not enjoy quite as much. If a teacher can show a student who loves history that mathematics is connected to history, and put what they are learning in that context, they’ve just opened a door for that student that may never have been opened.

Give that little background on Pythagoras at the beginning of class. Tell students about Babylonian number systems and about Hypatia and how she was killed for her work in mathematics. Cross the line that seems to divide subjects and give students the context that for some may connect ideas and bring a whole new understanding. And if it doesn’t help them understand the concept better, they’ve at least learned a fun fact, and one more fun fact never hurt anybody. 

Kristina Luczak

Teaching Motivation

     Thinking back to the days of elementary, middle and high school, I remember many of my teachers. All of them I would be able to recognize, some I would be able to recall their names, and still others I remember the class they taught and some important things I learned. The last teachers I mentioned have clear memories that define them as my favorite teachers, but hold the phone, why do I remember these teachers? What features or experiences did I have with them to hold this memory? After some thought, I discovered that every teacher I remember either guided me to a new way of thinking or motivated me through the way they taught.
      One of the most noteworthy teachers I had was in elementary school. She was my first-grade teacher that also taught second grade, and she was the teacher that recognized my skills in math. I still remember the day that she asked me to join the second-grade lesson and all the other second graders were so confused as to why I was there since I was a first grader. From that point on, I was in accelerated math classes throughout my middle school and high school careers. This teacher helped lead me to pursue a math major with plans to become a math teacher. I can firmly say that where I am now is directly related to that specific event and teacher. I had many other experiences with her throughout my first and second-grade years, but that day sticks will stick with me forever.
      Another teacher that had an impact on me was a high school teacher. She taught geometry and that class was particularly hard for me. I was well-versed in algebra  and found geometry to be more difficult for me. This teacher helped bring out my strengths in the class but what I remember most about her was that she showed me a new way of looking at people. I grew up in a very conservative family and let’s just say we have some strong views. Later in the year, I found out that my teacher’s sexual orientation was different than I expected, and this bothered me for a while. Throughout the year, she helped me appreciate her for being a great teacher and not focusing on our differences. From that point on I have been able to see people differently and I would say that she has been one of my favorite teachers. She also pushed me to take AP Calculus in high school and that was another big push to where I am now, in college.
     Throughout these experiences, I have learned some specific things. First, each of these teachers worked on understanding their students and using that they were able to create lifelong memories for me. I am so thankful for these teachers that God put in my life. Secondly, I found it interesting that these teachers and experiences I remember most were somehow tied in with mathematics. From that observation alone, I see why I pursued this field. The motivation I got from my teachers to pursue my strength in math have led me here, to SDSU: a Jackrabbit pursuing a Mathematics degree with Teaching Specialization.
      Thinking about these stories, I hope that you can go back and think of experiences that have motivated you as a person and as an educator. For me, I can only hope to model what these teachers did for me when I have my own classroom. With all the hardships of teaching, these memories allow me to push forward and see the greatness that can come from being a teacher. Without these motivational stories, I don’t know where I would be. In conclusion, I would like to give a shout out to all my past and future teachers! Thank you.

Taylor Davis

Stop Boring Students

Stop Boring Students

As a big sister, a tutor, and a nanny I am no stranger to helping with homework. I have helped in all types of classes. One thing I have noticed is that the person I am helping always seems uninterested. It is not that they do not really understand, but instead they just do not want to do it. Another thing I have noticed is that I always was and am helping with worksheets or problems out of the book,  and have never been asked to assist someone on a project, study for an exam or help with a paper. After a discussion in class I have begun to realize that the students understand what they are doing, they are simply just bored and tired of repetition.

Handing out worksheets and book problems are boring, never seem fun and by default students can become uninterested. Believe me, even some of the best students will become bored and unintrigued, and instead of changing it up, teachers continue to assign the same generic things. Once a student is bored, they mentally check out. They no longer want to come to class, and they start to become more interested in the minute hand on the clock, then what is going on in class. The homework they have is the last thing they want to do, and they will start to put it off until the last minute, or just copy someone else’s homework.  Turned off students will shut down in and out of the classroom. This can make a teacher’s job more difficult as they lose control over their students. A boring classroom is no fun for the students or the teacher.

As a future educator this is alarming to me. I do not want my students bored and looking forward to the end of my class before it even begins. There are a lot of different ways to assess our students that do not learn and grow from continuously using  worksheets. I understand that worksheets can be helpful and are a good way to assess students progress, but use them in moderation. Instead, try doing something more interesting to get the students involve in their learning. Teachers can use fun tools like Kahoots or online projects. Do activities, ask students questions in class rather than on a homework assignment. By doing interesting things like this, students become engaged in the class. It has been shown that students who are engaged and interested in class, will learn and retain more than a student who is not. Instead of continuously handing out worksheets, teachers should continuously change up their classroom’s learning tools to help assess students, get them engaged, and get them to learn and retain the material.

As a future educator and a past student, I know that just handing out worksheets or book problems will not work. Instead, change up your ways of assessment. Use fun activities and other forms to keep class interesting and engaging. Your students will appreciate it.

Ed Camp 2017

            Just this past weekend I had the privilege of attending my first ever Ed Camp here in Brookings, SD. I had many people tell me that you won’t regret going and they were correct. For those of you that don’t know what Ed Camp is, Ed Camp is a day of self-driven, high-interest professional development. It is a day to collaborate with teachers and future teachers of all grade levels. The best part is that you as participators get to choose the topics that are discussed that day. After a short introduction, you are asked to write down on a piece of paper what topics and ideas you want to discuss with other teachers. All of the ideas are then collaborated and you as a teacher participate to facilitate the discussion within the room. There are no presenters or power points, it is simply just teachers wanting to learn more from other fellow teachers.

            I learned more than I thought I would while attending Ed Camp. While in attendance, I was able to attend four sessions. The first session was Learning Management System (LMS) Practices/ Google Classroom. I found this session extremely interesting because as a college student we don’t always get to see the full side of a LMS. We discussed the pros and cons of Google Classroom and Schoology. I learned how many of the systems interlink with each other including Google Classroom and Schoology. I learned everything from inviting parents into the systems to working with cable companies to find low cost internet for you students who don’t have internet available at home.

            The second session I attended was Breakout EDU’s. Breakout EDU’s are becoming more and more popular to use in the classroom. I learned affective ways to use them in the classroom for all grade levels. I also learned about many resources that can help with regular Breakouts and online Breakouts as well.

            The third session I attended was Rich Math Tasks. In this session we talked about what a “rich” math task really is. I became informed of all the different resources that I have a choice on. From textbooks to online activities, as a teacher I will more than likely get to choose what the best resources are for my classroom.

            The last session that I attended was Applying and Interviewing for Jobs. This session was by far my favorite because I will soon be interviewing for jobs. I recommend to any future teacher to attend a session like this. I was able to discuss with a principal on the proper way to apply and interview for a job. The principal reminded us that the people we are interviewing with want us to do well and they want to help us. He gave us many tips to help us become successful for our first interview.

            Overall, I recommend Ed Camp to all teachers, student teachers, future teachers, substitute teachers, and administration. You will not regret it. They also do drawings all day long so you may even go home with free materials for your classroom. It is a day filled with teachers who just want to improve their classrooms.

                                    Oh and did I forget to mention it’s FREE!!

By: Katie Murtha

A New Definition of Gamification?

So quite recently Taylor gave a talk in class about gamification in the classroom, and I was actually quite surprised. It seems as if I was used to a completely different concept of gamification than what Taylor presented to the class. It is not entirely strange that there exist two different definitions of gamification, and it did allow me to grow more used to the idea of gamification in the classroom.

Before I talk about the new ideas that I have thought of for gamification I’ll take a few sentences to explain the differences in what I thought to what Taylor knew. My thought of gamification was of applying the concepts of a game to the classroom. I’ll just start making analogies to World of Warcraft because it boils down game mechanics to their base state. In World of Warcraft you do quests, kill creatures and explore a world all for many different reasons. In the essence of World of Warcraft everything you do is to level up, all of the tasks are just to get the “ding” of the next level. Gamification is the process of taking that need for the “ding” of a level and applying it to the classroom. This entails some kind of progression in the classroom, homework gets you points as well as good tests and quizzes. In a perfect world, students would strive to do these things well in order to get that next level up. The way that Taylor knew and presented gamification is quite a different idea though. Taylor spoke on a classroom where games were used to teach topics, instead of lectures you teach through the games. One game that was mentioned was the use of monopoly to teach things like math and probability, but it doesn’t just stop there. With the advent of video games, there are whole worlds of lessons that could be learned through video games and applied to a classroom setting.

In concern to my own version of gamification, I frankly don’t like the idea of it. It has taken me a while to narrow down why I disagree with it, but I think it is because of the implication of why the student is learning. Is a student just speeding through material to get the satisfaction of the level up or are they genuinely investing in their learning? It comes with the same ideas of what we are doing currently in the school system, are students genuinely learning or are they just doing the busy work for the grade on the test and then forgetting the material?

This is in stark contrast to the ideas put forward by Taylor, in this form of gamification students learn by playing a game of some sort. Ideally, in this form, students use games that they want to play and from those games, they truly learn the concepts the game creators built into the game. I love this idea because I love games and I think they can teach a lot. I had heard a little bit about the application of video games in the classroom before Taylor’s talk, the forefront of it being Minecraft and its various applications. The thing that is more interesting to me though is the application of board games, it is one that I hadn’t had as of yet. Now that I’m thinking about it though, there are a list of games that I have that could be applicable to a classroom. For math and stats, I think the most applicable board game I could think of right now is Settlers of Catan. Catan is a civilization builder with great strategy, but underlying it all is mathematics for resource management and statistics for getting those resources. A quick one to learn and play would be Coup, in Coup there are a limited number of role cards that each player can have. The purpose is to call each other out on the other player’s role cards, it greatly helps if you know the probability of who has what. In addition to that though both are just fun games that people enjoy that you can really learn from.

I don’t know which of these is definitions is correct, or if it really matters at all. In the end, I think either way we would see student comprehension and that is what we are truly after. I just think that with the version of gamification that was presented by Taylor shows tremendous promise for classrooms and student learning.

A Trip You Can’t Top - Service Learning in Belize

After spending two college Spring Breaks at home on the couch, I decided that I needed to push myself out of my comfort zone and use college as an opportunity to experience new things. Last Spring, I learned about an opportunity to complete a ten-day course called “Educational Leadership in Service- Learning: Belize” through the College of Education and Human Sciences at SDSU. This Spring, I completed that course over my Spring Break with eleven other SDSU students and twelve Brookings community members. I never expected this trip to have such an impact on my life that I would shed a tear when I had to part ways with these amazing people who became like family over the course of this trip. Not only the people that I served with impacted me so greatly, but also the children, adolescents, and adults whom I met and worked with while in Belize. It has been eleven days since we have returned and I am still trying to process this life changing experience.

I had two goals for this trip. The first was to learn about educational system and culture of Belize. The second was learn to be humble, optimistic, and appreciative. On just about every day of this trip, I became closer and closer to fulfilling these goals. We started our journey in Corozal, Belize and worked with children aged 2-14 that came from households with drug addict parents (see picture below). A retired principal in Belize puts on a vacation bible school program every Sunday for these children so that they are reminded that someone cares about them. I could see on their faces that these children were so appreciative for someone to give them attention and they jumped for joy when we handed each of them a new t-shirt. It was so fulfilling to spend time with these kids but so heartbreaking to watch them walk back to their dilapidated homes at the end of the day. We have so much and they have next to nothing.

Next, we traveled to Succotz, Belize which is a smaller town near the Guatemala border. The SDSU students spent their time at the Nazarene primary school and high school, while the community members helped repair a building owned by a local church. I thought most of my time would be spent working with the high school students in their classes, but we actually worked side-by-side with them while building a fence for the school’s sheep. I found the interaction I had with the students in this setting just as fulfilling as working with them in the classroom. They taught us how to use machetes and how to efficiently dig post holes by hand and we taught them how to communicate while working with a group to accomplish a task. I did get to spend some time in the classroom both teaching students how to sew and in a math class! Actually, myself and two other students got to teach a lesson on area and perimeter to a ninth grade math class. Students in Belize are only required to attend school until they are fourteen so these students chose to go to high school and were so eager to learn!

There are no public schools in Belize; there are only Christian schools that have a small tuition fee per semester. Students can earn scholarships based on need as well. At the beginning of each week, the high school students gather around the flag pole and have a ceremony where they pray, sing the national anthem, recite a pledge (my favorite line from this was “I am the hope of Belize”), and sing Christian songs. At the primary school, the teachers have devotions at the beginning of the week to pray. We got to observe both of these traditions. My faith is important to me so it was really cool to see that their faith is present in every aspect of their lives. These teachers were so dedicated to making sure that their students were set on the best track possible to live a good life in Belize. The principal was so passionate about introducing new skills to her students such as sewing, agriculture, cooking, and more. These students and teachers were truly inspiring!

This blog post only scratches the surface of the things I experienced while in Belize. I could easily write ten pages about it. I didn’t even get to the food, sight-seeing, laughs, interactions with locals, bus rides, and so much more! If you are an SDSU student or a Brookings community member and have the slightest interest in participating in something like this, go on this trip next year! It exceeded my expectations and I feel more humbled, optimistic, and appreciative as a result of this trip. I will forever cherish the memories and relationships I made while serving in Belize. Some of the Belizeans that I met have even added me on Facebook so it will be neat to stay in touch!

-Stephanie Schmidt-

The Equation for Becoming Teacher of the Year

     Recently in one of my courses we had the privilege of receiving a visit from the 2017 South Dakota, Teacher of the Year, Beth Kaltsulas. To our liking, Beth just so happened to be a fellow math educator at the middle school level. While visiting our campus, Beth was able to visit and present to many different content areas of the education department, and fortunately to our math class as well. Dr. Vestal gave a brief introduction and then Beth took the floor. Coming into our class she had up to three different presentations prepared to share with us young, future educators and you could feel the energy within her as she was realizing her reality at the moment.

     As Beth began speaking and sharing her experiences and stories, I found my mind wandering (sorry Beth) to the same questions over and over again:

• What did she do differently that set her apart to become teacher of the year? 
• As a young educator, did she set this as a goal of hers to claim this title one day? 
• Were there steps to follow to become the SD Teacher of the Year? 
• Is there an equation? (She is a math teacher!)

     As she shared her stories I began constructing what this equation could possibly be. It seems as if you might:

Take your four years of education, SUBTRACT at least two years of that education that didn’t apply to teaching, ADD a dozen lessons you learn within your first year of teaching MULTIPLIED by the number of students that prove your education courses wrong, DIVIDED BY the number of students that prove your education courses right, ADD the number of additional hours you need to spend outside of the classroom MULTIPLIED by the number of students who need your help outside of the classroom, ADD every single club and organization in the school MULTIPLIED by the hours spent chaperoning and participating in each of those, SUBTRACT your so called 8:00-5:00 job, ADD the expectation to teach all the standards MULTIPLIED by the number of classes you teach and those specific standards, while still SUBTRACTING the idea of teaching to the test while ADDING the use of technology any way you can while SUBTRACTING the fact that your school board has limited resources and walahhhhh! = Teacher of the Year. 

     Well as with anything else in life, I realize the answer to most of these questions was not what our math brains want. There is no one answer, no process and procedure to follow, no problem to derive and make logical sense of, and of course, no equation. Before I continue on, I want to make it clear that I am not writing with the mindset and intention to figure out how to become Teacher of the Year one day. Beth was awarded this honor for a number of reasons, and I am sure she would say there were also a number of teachers that could have also received this award. My ideas in this blog are not to minimize this award to a simple procedure to follow, knowing that would belittle the teachers that have dedicated themselves to being great educators, and great people, but rather to highlight some of the attributes all great educators have.  

     Beth shared much of her own personal philosophy and mantras for teaching, some of which I too hope to implement as a future educator. She had philosophies on homework, use of technology, testing, quizzes, just about everything and you could tell her years of experience have equipped her well for each of these pieces. As she continued sharing I found an overarching theme within her teaching style that I felt covered all that she had mentioned: Welcome Change. 

     Beth is not a stagnant educator. Just about every story she shared included the idea of her needing to change, adapt, or alter something. She was willing to change for her school, for her administration, for the technology uprise, and for her students. Beth constantly seemed to be striving towards always being able to answer the question, “Is this the best for…?” while never inserting her name at the end of that question or fearing the work, time, and effort that these changes may require. 

     Her principal needed her to teach a special education class, in which she had no experience or training. She welcomed the change. Technology has vastly changed and enhanced since she became an educator. She welcomed the change. The idea of a flipped classroom came prominent and popular within the education world. She welcomed the change. She found many students struggling with math and felt the need to start a Math Academy. She welcomed the change. And now, after receiving Teacher of the Year, she’s being asked to speak at a number of conferences, seminars, and to all types of classes. She’s welcoming the change. 

     I recognized this trait within her from only listening to her speak for about an hour. It is clear, that to be this type of educator, we as teachers need to always be searching for what’s best. Allowing ourselves to lay down our own personal mantras and philosophies when needed. Always willing to learn from others, and implement accordingly. Always searching for new and better, while keeping what is good. Always welcoming change. Thank you, Beth for teaching us future teachers. Thank you for sharing your experiences and time in order to better the education world around you. Thank you for welcoming change at whatever cost to make things better for others, and for allowing us to learn from your example.  

By Bailey Jorgensen

Why We Need to Rethink Our Approach to K-12 Education

     My 13 year-old son has been sick this week.  He has a soccer tournament this weekend and wanted to play tonight so last night he decided he would go to school for part of the day.  This is what he said to my husband, “Playing soccer is easier than going to school.  If I can go to school, I can play soccer.”

     While I found his comment amusing, it also made me sad. I think he was saying that sitting in school all day in classes is hard for him. Knowing how active he has been since he was little, it doesn’t surprise me.  Even now when he watches TV, he is either kicking a ball or throwing a ball—never sitting still unless he doesn’t feel well.

     Last week, he asked me if my classes were the same every day.  I said that it depended on my class, but one of them was never really the same any day.  He then said that he doesn’t like school and thinks it is boring because his classes have the same structure every day.

     This is why the concept of Personalized Learning is very intriguing to me.  Personalized learning allows students some freedom in how they demonstrate their learning of specific learning targets.  I was fortunate enough to go on a trip to Chaska, Minnesota to visit a district that has personalized learning. The middle school we visited was so interesting and you could see how much the kids loved school. 

     This week I watched a webinar on the Global Math Department called Pathways to Learning, which was presented by one of our alumni, Carla Diede.  Carla teaches at Harrisburg South Middle School in Harrisburg, SD and it was so interesting to hear how she uses personalized learning in her classroom. 

     After this recent exposure to personalized learning and listening to my child, I firmly believe that it should be the future of education.  Kids are different so why should they all have to demonstrate learning the same way.  Giving kids choices empowers them to take ownership of their learning.  When listening to the panel of 6^th graders in Chaska, all I could think about was how mature they were and how much they understood about themselves as learners.
     So have I embraced this idea in my own classes?  Not entirely, but I am making baby steps. In my Math 371 course, each student is presenting a technology topic that interests them to the rest of the class.  I also give them choices when creating their 3D projects, their Desmos art projects, and their teaching lesson.  I guess maybe I am better about giving students choices than I thought.  Offering options to students is going to make them better decision makers and problem solvers—ultimately those are the skills needed for the workforce.