Thursday, February 8, 2018

Useful Technology in the Classroom

            Throughout high school classrooms, technology is being integrated more and more. In my education classes, we are learning about the do’s and don’ts of technology. The main point that I have taken away from this Technology for Math Educators course is that you need to make the technology you use in your classroom actually useful.
            Although technology can be a “fun” thing for your students to use in your classroom, if it is not challenging them, they will eventually just get bored. As a teacher, you need to incorporate technology that will be useful in your classroom. During our class time in this course, we have been assigned to teach about different mathematical apps that could potentially be used for our classrooms. Before taking this class, I might have said that it would be an okay idea to use most of them in my classroom. However, when I took a step back and actually thought about what the apps could do to help my students learn a subject I had a different thought on them. Most apps that I have reviewed wouldn’t actually benefit my students at all.

            Most of the mathematical apps that I have looked at for this class are apps that would just be “time consumers” in a class. What I mean by time consumers is that they are apps that won’t teach your students anything new, or even allow them to discover anything new. However, I have found some great apps that I intend on using once I become a teacher. Some of these apps include: Desmos Graphing Calculator, Geogebra Classic, and stats!. If you have never looked into these apps, I would encourage you to research ways that would allow your students to discover new things that you might not be able to cover in your lecture time as a teacher.

Thursday, February 1, 2018

Flipped Classrooms

              Many teachers are experimenting with the idea of flipped classrooms. Studies show that this type of structure causes more help to the students than harm. I have mixed feelings about flipped instruction but exploring new methods are important, especially when they hold proof of being beneficial to students. Flipped instruction is basically the opposite of the traditional lecture style of teaching. The lecture portion is done outside of class and the activities and homework are completed in class.

              I have some concerns about flipped instruction but overall think it is a step in the right direction. Many educators assume that every student has access to technology outside of the school setting. While this is true for most students, there are still some without access. Having flipped instruction would make it difficult for these students to watch lectures or other videos and online readings outside of class. Also, students already spend a large chunk of their time in class and may be unwilling to watch lectures made by their teacher on top of that.

              On the other hand, the flipped classroom method has many benefits. In the traditional style, students’ number one complaint is homework. When students are left to work on their homework at home without any aid, they tend to become frustrated when they come to something they don’t understand, resulting in them giving up. In flipped instruction, the students are with the teacher when working on homework and can ask for assistance when they get stuck. This keeps students from becoming discouraged and helps the teachers get a better idea of what their students are not understanding. Teachers can also give immediate feedback to students and can reteach material if needed. This style of teaching also allows for more discussion in class. Students have more opportunities to ask questions and the teacher can ask more thought provoking questions to expand learning.

              As with any teaching method, flipped instruction has its pros and cons. With our advancement in technology, this method makes more sense than the traditional lecture style. Having students watch lectures outside of class at their own pace eliminates the one size fits all idea. Students learn better through activities than through lecture and incorporating technology outside of the classroom allows more time for activities. Flipped instruction is the step in the right direction of reevaluating old methods and forming better ways to advance and support student learning.

Friday, January 26, 2018

Math: A Love-Hate Relationship

Over the course of my life, I have had my fair share of struggles when it comes to mathematics. It could be so frustrating when I would spend hours upon hours on a single question, with little progress towards understanding the material. However, there would be days I found enjoyment in math, solving problems that required a higher level of understanding with ease. As this cycle of attitudes towards mathematics continues in my life, I find myself believing this is the groundwork for having a passion, and in this case, being passionate about math.

To offer this idea in a different context, I sometimes compare my relationship with mathematics to my favorite football team, the Minnesota Vikings. They can have a great season with high chances of winning in the playoffs, but can also leave me frustrated, when they lose in a way only the Vikings can. The same goes for math. One moment I am ‘winning’ and the next I am ‘losing’, but, in the end, it still draws me in and I continue to be a fan of mathematics no matter the outcome. By understanding this idea of a love-hate relationship, it is easy to see how this applies to several areas of a person’s life, especially to his or her areas of interest.

Although it is interesting to consider how math is a love-hate relationship, as a future math teacher, I cannot let the thought end there. The posing question to be asked is what is the student’s relationship with math? I cannot count how many times I have heard the words ‘dislike’ and ‘math’ uttered in the same sentence. It appears to be the frustration that is most notably expressed when using mathematics, and understandably so, for it is a challenging subject. Frustration is a normal outcome when going through challenges, but, by persevering through these difficulties, one can succeed by learning from his or her endeavors.

The goal is not to make the student ignore their frustration, but rather to help him or her develop that balanced relation with math through recognizing its potential. One possible way to achieve this may include a lesson directed at a student’s interests to help with broadening their understanding of certain applications and uses. I believe it important to share one’s own difficulties with math as well as the success and enjoyment. When only the success from experience is expressed, it can be displayed as to not having failure in math, when we all know that is not true. By letting students know everyone has those ups and downs, it allows for the students to realize we all have frustrations with math, creating a mutual understanding and connection with the students. Having this common ground may help students to reconsider their feelings towards math and move from frustration to being interested.


I know I will always have this “love-hate” mentality towards math, and, therefore, I know my students will experience one or both feelings towards math as well. Knowing where the students stand and how I can relate to those situations will not only benefit my students’ appreciation for mathematics, but also develop my path as a teacher.  

Thursday, January 18, 2018

Try Something New!


Living in the Digital Era, we see many uses of technology in the classroom. For many students, technology is used during every class period. Whether this be writing on a Smart Board or looking something up on their phone. Educators cannot shy away from the fact that technology is becoming a big part of the classroom and it is benefiting our students as well. 

Some teachers are reluctant to use technology because they are afraid that they will not be able to use it or that something will go wrong with the technology during their lesson plan. There is some very useful technology that is easy to use but that can also greatly impact our students. If you feel uncomfortable using technology talk to your school’s digital coordinator. They can show you in a matter of minutes how to run certain technology. You will also find that your students often know more about technology then you might. Ask the students if they know a simple solution to the problem. My sixth grade teacher designated someone to be tech helper for the semester.

Some teachers also believe the old saying that, “If it ain’t broke don’t fix it.” These teachers are unaware of the advantages technology can have on their students. It is not only enjoyable for their students but is also a different way to expose students to the content. I encourage these teachers to communicate with other educators in their field to find an easy way to incorporate technology into their classrooms. After you find a few programs that work for you, be proactive in learning about them. Find different ways to incorporate them into your lesson plans. This is also beneficial because your students are already familiar with them.


My goal for the readers today is to try a new technology in your classroom. This might be one of the first pieces of technology you have used this year or might just be something different for your students. Either way you are guaranteed to learn from the experience and share that experience with other educators. Don’t be afraid to try something new!

Friday, January 12, 2018

It all began five years ago…

Five years ago today I started this course blog for Math 371: Technology for Math (STEM) Educators.  I am happy that I did it and am looking forward to another great semester of this class.  I am also glad that my students in that class wanted me to continue using the same blog each year so that we could look back on the changes in technology over the years.

Each spring when I teach this course, I do it differently, partly based on what the students want to learn and partly due to changes in technology.  So I find it fitting to use this quote from Robert John Meehan on course management system page, "Life as a teacher begins the day you realize that you are always a learner."

On the first day of class, I told the students that I am not always going to be the technology expert on certain technologies and that we are all learners in the course.  Each semester I learn new things and hopefully they learn new things.  Ultimately my goal is to make our math pre-service teachers good consumers of technology. In particular, I want them to be well-versed in Technological Pedagogical Content Knowledge (TPACK) and understand that technology should not be used for technology’s sake, but technology needs to enhance student learning.

One significant change that I have made over the past five years in this course is that I now ask students to tell me what they want to learn about. There are some things that we will do regardless of their suggestions, but I like giving them choice in what we do.  Some things that they suggested for this semester are: math typesetting, online grading systems, online homework, 3D printing, Excel, and interactive whiteboards. Other topics will include copyright laws, blogging, and teaching with the TI-Nspire.  We will also work with iPads and how to utilize them in math classes.

I am looking forward to another semester of this course and I am certain that I will learn a lot!

Friday, April 28, 2017

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

Friday, April 21, 2017

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