The Last Technology Blog Post for Math 371 for Spring 2014

The students did their final presentations on Monday.  They had to create a video lesson over a statistics or probability topic, show us the video, and respond to the following:

·         Why you selected the particular math content for the lesson.

·         Which app or program you used and why.

·         What you learned while creating the lesson.

·         What you would do differently if you were to do it again or had more time.

The 11 students were divided into 4 groups.   It was very interesting to me that each group used a different technology for their lesson.  The following technologies were used:  Knowmia, Educreations, Camtasia, and a webcam.  Three of the groups presented with slides of material and audio added to the slides.  One group was brave enough to actually put themselves on camera and do a demonstration.

All groups did a great job and learned a lot—the most frequent comment was that it took longer than anticipated.  I think that one of their biggest takeaways from the course is the amount of time needed to use technology well in a math classroom.  I do think that this year’s class seemed to be more hesitant to embrace technology.  Several of them started the semester disliking technology and I think that they may feel the same way at the end of the semester.  This concerns me and is something that I need to think about before the class next spring—how can I convince them that technology can be very effective in a math classroom and maintain the philosophy that technology should not be used simply for technology’s sake?

What should you expect in this class in Spring 2015?

·         I think I am going to try to have students make an iPad app.

·         I am going to somehow incorporate my new Da Vinci 3D printer.

·         More blogging—and encourage them to think outside the box when they blog.

·         I want to figure out how to create animated lessons.

As you can see, it looks like I will be busy learning between now and January 2015.  One of the things that I love most about teaching is that I am always learning!

My Flipping Experiment

Greetings from Oklahoma!

  

My name is Keri Kornelson, and I'm in the math department at the University of Oklahoma in Norman.  And I can't escape the fact that I'm a technological newbie, at least when it comes to technology in the classroom.  But I decided to teach an inverted (flipped) class this semester, so I needed some technology to make it all work. 

The idea started simply enough.  Discrete mathematics is often the course where students get their first exposure to logic and proofs.  I decided to teach in the flipped model because I wanted to be present when students started trying to read and write the proofs, rather than letting them struggle through that on their own after I did the content delivery (a.k.a. lecture) during class time.  For example, they don't really need me to be right in the room with them when they learn the definition of an even integer, but they are likely to have questions when the time comes to prove that the sum of two even integers is always even.  

So, let me tell you what I'm doing.  I record screencast lectures and post them online for the students to watch before class time.  (Want more details?  I'm using a 22" Wacom digital screen and an open source whiteboard program called Open Sankore that also has recording ability.  After recording, I edit the videos with iMovie.)  I tend to make up some slides with definitions and outlines already in place, then fill in details and computations as I talk through the material.  I make 1-2 videos for each day of class and try to keep them under 12 minutes long.   

During class time, I focus on active learning and peer-to-peer engagement.  Students complete activities using the new material and often present their findings to the other students.  Since they are actually getting their hands dirty, a lot of questions come up.  They work together and often figure things out within their groups, but I'm also there to help.  

There are definitely some challenges.  It takes a lot longer to make a screencast video than to write a lecture.  It requires distilling the topic down to the essentials, creating just the right examples, making slides to fill in, and practicing both the script and the writing to be sure the final result will be clear.  Then, planning the class activities is also pretty hard.  Do you want to do group work, or individual?  Should they write on paper, or on the whiteboard today?  Is this topic better served by having presentations, or do they just need time to puzzle it out?  I'd definitely advise making core topic videos before the term starts and devising some class activities ahead of time that you choose from as needed.   

But now, at very nearly the end of the semester, I'm delighted with the results of the flipped experiment.  Students do watch the lectures ( I spent a long time worrying that they wouldn't) and they re-watch them before exams and while they are doing homework.  I even see the lectures called up on laptops and phones during class so they can review a definition or example.  While we are in class, I hear the greatest conversations.  They are talking to each other, drawing diagrams, testing out ideas, asking questions, answering questions, and just engaging in mathematical discourse.  They are learning how to learn math!  My work here is done.

Thanks, all, for letting me visit your discussion.   

By Dr. Keri Kornelson, University of Oklahoma

Isn't Technology Grand?

Hi Everyone in Math 371!

    Thank you so much for having me as a guest blogger this week.  My name is Rachel Harrington and I am writing to you from Corvallis, Oregon.  I am an associate professor of mathematics education at Western Oregon University.  On Fridays, I work from a coffee shop in my hometown and do virtual office hours through Google Chat.  Isn’t technology grand?  I have never actually met Dr. Vestal, but I talk to her regularly via Facebook.  She is a friend of a friend who did a virtual introduction.  Our friend in common knew we did similar work and thought we should “meet.”  Again, isn’t technology grand?

    I have read the past entries of your class blog and see that folks have used it to summarize their personal experiences with technology and also a chance to review how they explored technology tools in the previous week’s class.  So, continuing with that theme, I thought I would use this opportunity to share how I used technology in my professional work this week.

    On Monday, I had a Skype call with four other researchers from Ohio, Oregon, Michigan and Virginia.  We are in the final stages of a collaborative paper that synthesizes all of the research written on Technological Pedagogical Content Knowledge (TPACK) over the past 10 years.  TPACK is the idea that there is a special type of knowledge that teachers hold that helps them to integrate technology into instruction.  Essentially, it is the idea that you can be a good math teacher, but never use technology OR you can be skilled at using technology, but have no idea how to teach math with it.  Having a solid TPACK means you know how to do both—you know how to teach math with technology.  Math 371 is helping you to develop your TPACK!

    On Wednesday, I taught my math pedagogy class.  In that class, everyone has an iPad and we do a lot of our work using them.  My students are currently investigating a common problem or misconception in mathematics and researching an app that claims to address that misconception.  They are going to write a critical review of the app based on their research.  There are so many apps out there for teaching and learning math and it can be really easy to waste your money $.99 at a time.  I’m glad you are getting a chance to do critical analysis in your Math 371 class.  This will pay off (intellectually and fiscally) down the road.

    After I finish up this blog, I will start work on an eBook that I am writing with my colleagues at the Center for Algebraic Thinking.  Three years ago, we took all of the research since 1970 that has been written on teaching and learning algebra and compiled it into the Encyclopedia of Algebraic Thinking.  Our next step is to convert it to an eBook.  If you find that you are going to teach a lesson on Negative Numbers, and you don’t know where to start, consider going to the Encyclopedia.  It has ideas on good problems to give, places where students struggle, and tips for teaching.  One more thing that you might like:  we have developed 20 iOS apps to address common problems in Algebra and they are ALL FREE!  (Well, one costs $.99, but trust me, it’s good!)  They are on our website and also on iTunes.  Just search for Center for Algebraic Thinking and you should find them. 

    Thank you again for giving me the chance to share how I have been using technology this past week.  I will keep following your blog because it is giving me good ideas to use in my own teaching!  Thanks for reading—I think I need to get back to my coffee and pie.  


Rachel Harrington, Western Oregon University

Math Technology Reflection

Since we did not have class last Tuesday I will reflect on things we have discussed throughout the semester this far.  The first thing that comes to mind when thinking about what we have discussed and learned is how much time it takes to learn the technology that surrounds us in the classroom.  Spending time with the SmartBoard and the Promethean board has been invaluable.  Some day as we venture out into our own classrooms, the majority of us will have these tools to help teach the content to our students.  Preparation is going to be vital in ensuring that we deliver a smooth, effective lesson.  Technology is very frustrating for me, but a big reason for that is because I have not spent the time with it to get comfortable.  This class has opened my eyes that I will indeed need to prepare for a learning curve in the use of technology.

Some other valuable tools learned are the computer applications Desmos and GeoGebra.  I am sure that there are numerous other applications out there that are effective as well.  Again, learning about how to use these apps opened my eyes that there are a lot of great tools out there to be found to help teach the content; we just have to be willing to search for them.  The capability that was so appealing about these applications was their graphing abilities.  They are very user-friendly and quick to use.  That capability really helps us visualize what various functions look like on a graph.  I cannot remember if Desmos or GeoGebra can graph in 3-D, but I know there are many 3-D graphing tools online.  I wish I would've had those throughout my Calculus classes.  Being able to see the 3-D graphs would have helped vastly in figuring out what the functions looked like instead of trying to see that by attempting to draw out a 3-D graph.  If used correctly, the tools found online can really enhance a student's ability to comprehend the information being taught to them.

The book we are reading has also helped make me aware of the obstacles technology brings along for students. The technology in our world makes communication available at all times.  This is a great thing for friends near and far.  It is, however, negative for unwanted communication with people that do not get along.  Bullies can reach their targets at anytime and from anywhere.  As teachers, it will be important to encourage students to positively use the luxury of technology and to report any misuse.  

Overall, it has been great to have the opportunity to learn about the numerous tools that are available to us as teachers and to get the chance to play around with the Nspire, Ipad, SmartBoard, and Promethean board.  As we venture out into the world of teaching, things will continue to change and time will need to be spent in figuring out what the technology that surrounds us is capable of doing.

“It’s Complicated”

In Math 371 we continued to discuss a book that we decided to read called “It’s Complicated” and we also continued to play around with Excel.

            In the book discussion we talked about two chapters of the book. These chapters were about bullying and online predators. We did not focus on the chapter about online predators as much as the bullying chapter. As future educators all we can do is teach our students about Internet safety and how they shouldn’t talk to strangers online. We focused mainly on the bullying because as teachers, that is something we know we are all going to have to deal with. The definition of bullying stated in the book, which came from Swedish psychologist Dan Olweus, is constructed with three components aggression, repetition, and imbalance of power. In this book they interview teenagers about different social issues and uses in technology. Something that stuck with me was the fact that many of the people they interviewed mentioned how when they interacted with their peers they rarely used the word bullied. They would use words such as “prank” and “drama” etc. to describe their different acts. It was said that the adults use the word bullied much more loosely then the children/teenagers. As future educators or even as current educators I believe this is something we need to keep in mind when we see students giving each other a hard time, or what we might see as “bullying” might just be a way that they interact with their peers. We have to insure that we make our classroom as comfortable as possible so that if students are actually getting bullied that they will be able to come and talk to you about it.

            Now to mention what we did on the technology side of things for our classroom we continued to work with Excel. We practice with the graphing some more and how to switch different axis. We also tried to a couple other programs to see if they were compatible with the SMARTboard. It turns out that not all sites are very SMARTboard friendly so as future teachers, that is something that we are all going to have to be aware of when it comes to us planning our classes. Also one of my fellow classmates was telling us about how he was playing around on Geogebra and learned how to do some other things with it, that just goes to show that as you become more comfortable using programs and certain technologies you can learn more things about them and use them in an even better way. When a teacher knows how to effectively use the technology they have it makes it an even better experience for the students. 

By Lindsey Jarman

Excel and GeoGebra

In Math 371 we spent the day working with Excel and showing its uses in the math classroom particularly with statistics. From working with it, I realize Excel does have quite a few uses in the math classroom setting. We spent time working with the probability and statistics section which worked quite well especially for calculating average, median, mode and all sorts of other types of statistical data. It also had a variety of different charts useful to plotting data. Another uses of Excel is the spreadsheet. The spreadsheet allows students to create formulas that are useful for data. The students can just develop an equation and then copy and paste to put different values into it which make it easy to solve equations. However as a teacher, it is much more useful for students to solve equations themselves and when equations are used it is much more useful to see the graph which Excel cannot do. 

This is one of the major reasons I find GeoGebra to be a better tool for a teacher than Excel. GeoGebra contains both a spreadsheet and a graphing section which allows the formulas to be shown on a graph. This allows students to visualize the concept which is a huge advantage over Excel. The spreadsheet section on GeoGebra does almost all the things the Excel version does that are useful for doing mathematics. I personally found the Excel spreadsheet a little bit easier to use but not enough for me to want to use Excel more due to GeoGebras many other uses. The graphing by itself creates a huge advantage as it allows points to be plotted to create different shapes and figures while also doing a variety of different manipulations to the object such as measuring, translating, dilating, reflecting, and much more useful concepts especially in Geometry. Also after more experimenting with GeoGebra I realized that it does have a slider tool which can be extremely effective for showing how certain changes affect the graphs of lines and other equations. I could find this especially useful when teaching trigonometry as students struggle to understand how different values affect the graph of sine, cosine, and tangent graphs so by using the slider, you can show how different values affect the graph.

Therefore, while Excel and Geogebra both have good uses in the math classroom, GeoGebra’s larger variety of mathematics related concepts gives it a huge advantage in my opinion over Excel. Excel's ability to create formulas seems like a great tool but really I do not see as many uses in the math classroom. The formulas allow students to receive a variety of answers quickly but in the math classroom the process is more important than the solution so it does not have too much of a use. GeoGebra also has the same spreadsheet feature even if it does not have all the same features but the graphing portion of it just makes it a better option to use in the classroom. Plus GeoGebra has an app which allows it to be used on portable devices such as iPads. And one final remark on this concept is that GeoGebra is free to download. Free programs are always a bonus and GeoGebra definitely gives good value for a free program.

By Jayden Streifel