Mathematical Problem Creation: How to Make Problems Real

In a Classroom Live 2.0 talk with Dan Meyer, the discussion dealt with mathematics text books, and the "pseudo" problem solving they require. Problems usually come out nice and even, information is laid out in an understandable manner (which is not how the real world works), and problems are forced into ridiculous situations. One example that I found particularly amusing (mainly because I have seen problems like this before) took a concept such as right triangles and the pythagorean theorem, and reduced this concept to a dog wearing a handkerchief, and how long one of the sides of the handkerchief would be if it were folded into a triangle. He had many textbook examples, but his point was that students see right through these fake problems, and begin to lose trust in mathematics.  

When problems are written and solved in such a simple capacity, people start to crow about the uselessness of mathematics. These types of problems can be put into the equation solver and figured out. Dan had received a Tweet saying that math was useless for this reason, and he was upset by this because the equation solver was not stressing the meaning of the math, just the solution. Dr. Scott Mcleod shared the sentiments of the Tweeter at a recent 1:1 conference I spoke at by reducing math to asking the AI on his phone for the answer. Dan points out in a pie chart that the answer is seen as the ultimate goal for most situations, when the process is just as important. This theory of just getting an answer simply skips a step in the important mathematical process, and I think that making better, more messy problems can alleviate this situation.

To help make problem solving more real, Dan suggests that that problems should not include all the numbers to start with. Numbers usually are not nice and neat anyway, and more than one solution is normally possible. He also showed some types of technology that he uses to help make mathematical problem solving more important. For starters, his smartphone has allowed him to take pictures on the go of any mathematical situation he comes across. He also uses Jott ("used" now because it does not exist anymore) to capture the situation with his voice and changing it to text so he can remember all of the context. YouTube or any other video site can be used to set up a real problem.

I use our text in class on occasion, but I would like to come up with better problems for my students to maximize their mathematical potential and show them that math is real...and not reduced to made up problems. I would use the techniques that Dan has outlined in the video and the technology he has suggested. After this phase has been enacted for a period of time, I would encourage students to find their own real situations out in the world to share with the class. This would not be an assignment with a deadline, because I want this to be natural, and not a stretch to find something. Many of my students have smart phones, or at least a phone that can take a picture. I would then set up a blog to display all of these questions after I have conferenced with the student presenting the problem. When students search for their own problems, it makes the learning experience more real to them. The problems would also relate to what interests each of them, adding a layer to the learning.

Credit given to reba@ghfoundation08 through flickr.com/creativecommons

Gaming and the Classroom: A Trip Down Memory Lane

Here is a topic I can really sink my teeth into! Games have been a part of my life since 1985 when my dad brought home an original NES. I still remember back when we first tried to play a two player game of Super Mario Brothers, and we could not figure out who this Luigi character was and why he was not moving. Being the genius that I was at age 3, it took me a half an hour to figure out that you had to plug in the second controller...

While I have learned from my video game mishaps, video games were a major part of my life up until the last few years due to my doctoral program. I still try to play, but lately I have not been able to even spare 15 minutes of a weekend. Just in case my readers are curious, I thought I would include a list of my top 10 favorite games of all time just so you can see where I am coming from. I love all of the Super Mario Brothers games, so I will leave them off the list since there are so many. In no particular order...

The Legend of Zelda: A Link to the Past
Super Metroid
Resident Evil 4
Bioshock
Mega Man 2
Fallout
Super Tecmo Bowl
Final Fantasy 3
Earth Bound
Chrono Trigger
Mike Tyson's Punch-Out!!
TMNT 2
Duck Tales
Secret of Mana
Banjo-Kazooie
Pikmin 2

OK, top 16 games...

In reading the commentary by Mihaly Csikszentmihalyi dealing with flow, a lightbulb clicked in my head as to why I like playing these games. As an experiment for my EIT class, I set aside an hour to play a game that I have never played before. I thoroughly enjoyed the first Bioshock game, and I had always wanted to play the second. Up to this point, I have not been disappointed. In fact, my hour turned into 6 in no time. The following is a look at most of the categories contained in the flow as related to Bioshock 2.


One of the major hooks that I enjoy about gaming is the story. I think about gaming as a more involved book. I am constantly wanting to know what will happen next. Bioshock 2 sucks you in from the start. As the player, you are basically alone in a vast city built underneath the ocean. There are other characters to interact with, but most of them are so far gone as far as sanity goes that not much talking is done. The city used to be a thriving community, but has sinse been left in ruin. The feeling of being on your own and exploring this unknown location is what does it for me. This is similar to how I felt about the first 3 seasons of Lost when the island and the places on the island were such a mystery. When looking at the parts of the flow, this takes care of the following categories:


Action and awareness are merged
Distractions are excluded from consciousness
Self-consciousness disappears
The sense of time becomes distorted
The activity becomes ‘autotelic’ – meaning it is an end in itself


Bioshock 2 is a combination of linear and open-ended exploration. I enjoy this about a game because while I feel like I can go almost anywhere and explore, I know what my main objective is keeping me on track. How I go about that objective is usually up to me.


There are clear goals every step of the way


Bioshock 2 has many ways of indicating your progress. For starters, you have a health meter letting you know your status. Windows also pop up indicating whether a goal was achieved or botched. This feedback is generally subtle, but enough to let you know how you are progressing.


There is immediate feedback to your actions


I will admit that the challenge versus frustration topic is one that I have mixed feelings about. Bioshock 2 is very forgiving, in the sense that your death does not set you back as much as you would think. If you run out of health, you are transported to the nearest chamber and are resuscitated with little penalty. While I do appreciate this, the difficulty can seem easy at times. On the contrary, any game in the original Mega Man serious would make most kids nowadays cry because of the sheer challenge. I have grown up in both eras and probably prefer the more difficult, but that may just come down to the type of person you are.


There is a balance between challenges and skills


As a teacher, I carry over my experience with games into the classroom. Students enjoy games being tied to their learning. I can say this confidently as a user of games for 7 years in the classroom. There are many challenging, problem-solving games that I like to use to get the students thinking. Some of these games include Liquid Measure 2, Bloxorz, and Cargo Bridge. These games are very challenging but fair, invoke large amounts of thinking to succeed, provide immediate feedback, are able to hold a student's attention. While I can tie each of these games into some sort of mathematical topic, they are not necessarily content specific.


This is one of my problems with gaming in education. When I want something specifically related to a mathematical topic, the games available are bland and boring. About the only one of the flow's bullet points hit in most of these educational games is the feedback. In looking at a previous post by Scott McLeod, I was embarrassed to see that the first picture of a game in this blog about "games sucking" is a game I use to try to hit computation standards. Good old Math Baseball! I don't know if there is anything terrible about Math Baseball, but it certainly does not invoke the flow out of my students. It is my hope that someone will create better educational games that students can get into and enjoy. 


As an avid, or formerly avid gamer, I fully believe in the power of games to provide a proper challenge, set clear goals, give instant feedback, and immerse students in a world outside of their own. I will continue to support gaming in hopes that others will catch on. What are your thoughts on gaming in the classroom? Do you see this as a viable learning tool for education? What are the views of individuals without a gaming background? I know a lot of my fellow teachers see games as educational fluff. 

3 Ways a Flat Classroom can Revolutionize Education

In order for education to change, innovations must be made that are initially slow to catch on, find their niche, and eventually turn the current system upside down. This idea was presented by Clayton Christensen in his book, Disrupting Class. The following are three ways that I see the the flat classroom, or global connectivity for all students, catching on through the context of education for my students.

1. Global Perspective

Living in a small town can be as pleasant as it is isolating. In a school that (most years) is 100% white, problems can occur with the unknown. Most of my students are not aware of what is possible outside of the walls of the classroom, and technology could open their eyes and put their thoughts to work. The ability to communicate and collaborate with a variety of people can expand their minds and broaden their viewpoints to see ideas in different ways.

2. Class Selection

I feel that our district does a great job with what is available to expand the offerings available to our students. We have a partnership with Hawkeye Community College as well as Project Lead the Way. One of our students has participated in various mathematics courses through Stanford University. However, so many opportunities still exist. This process of expanding education could occur with an obscure course that we do not offer, or an something totally independent from the district initiated by a parent or student. Educational opportunities have never been more readily available.

3. Making Learning More Meaningful

Within the walls of a traditional classroom, you can only make experiences so real. You can create fictitious projects that mimic real-life, but following through with all the objectives and details can be almost impossible. I want what is best for my students, and the idea of a flat classroom can make education meaningful. I have a project where we discuss the relationship between surface area and volume, and put it in the context of a food company. What size box should they make to hold the product necessary, but save money on production costs? Wouldn't it be great to actually work with a company to see what they are looking for? A flat classroom provides this experience.

These three ideas only touch the surface of the flat classroom. What are your ideas for implementation?

Credit given to ToGa Wandering through flickr.com/creativecommons

Maybe the World Really is Flat?

Do you remember learning about people from past time periods who thought the world was flat? The idea was that if you sailed too far, the ship would fall off the edge of the earth. This sounds silly knowing what we do in today's society, but as interesting as it sounds, the world being flat does not sound so far fetched. The concept of the world being flat was the overarching idea from Thomas Friedman's book, The World is Flat.

In a general sense, technology leveling the playing field across the globe is an interesting idea. People from underdeveloped nations can experience the world around them through communication with technology. Previously, technology was reserved for those thriving countries, giving an obvious advantage. With technology being more affordable and readily available, more nations are joining the party. When thinking about this from the perspective of a developed country, positives and negatives stick out. One of Friedman's thoughts was that with the advancement of technology in under-developed countries, economies could pick up to the point where there are more suitors to buy American goods. On the flip side, more jobs can be performed in other countries for less money than in America. This would clearly drive up unemployment, hurting our economy. Like in many situations, you must accept the good with the bad. 

Education also feels the effects of a flat world. My students live such a sheltered life growing up in small town Iowa. Sure, there are advantages, but from a cultural standpoint, being naive is an understatement. I have been teaching long enough to know a few classes of students who have graduated, and I frequently hear comments dealing with the adjustments to places that are more diverse than small town Iowa, but not really that diverse in the grand scheme of things. Take places like Cedar Falls, Iowa City, and Ames. Many of our students go to these universities, and believe it or not, there is a culture shock upon arrival. The college transition is difficult, but I am referring more to the variety of individuals. I would like to find a way to broaden my students' horizons before they graduate, and what better way than with the flat world concept.

Another way the flat world can aid my students is through the enhanced of understanding what is actually available to them after high school. Living in a small community does not do much for the students when thinking about future careers. They have very few ideas as because they do not know what is possible. I had one student who was interested in applying for an Ivy League School. To be honest, I did not even know what it would take to get accepted, but I was sure he would need to get started as early as middle school. This idea can now become a reality. We can collaborate with different schools online, and iTunes has different classes available through the iTunes U program helping with the experience. Even if a student did not want to go to a school like this, the idea of free learning is amazing (hopefully my educational job does not get outsourced...but that is a possibility just like the rest of the job  world).

From a smaller perspective, I often pull back and think of our community as a mini world itself. Even in this context, the flat world idea has made education and learning equal to all. I talked about this briefly in a previous posting, but the gap between the haves and the have nots has shrunk in the past few years through technology. People tend to think that in a small community, most of the students and families are of the same socioeconomically. I would disagree. We have quite a range in family income, which can limit opportunities for many students. With the rollout of our laptops and Internet available at our school at any hour, the opportunity to learn has increased. Students still have to take the initiative, but the fairness has increased.

Now that the world is flat again, we as educators have to take this to our advantage, and make sure our students do not fall off the edge. We need to show our students the possibilities of a flat world and let them explore. Teachers and other educators are the captains of the educational ship. Hopefully, we can steer away from what has been done and sail off into the unknown, improving education and the student experience along the way.

Credit given to Maciej clubfoto.lu's through flickr.com/creativecommons

A Commentary on Scott McLeod's Opening Remarks at the Iowa Education Summit

I enjoy reading the Dangerously Irrelevant blog because of the challenges made to school districts by the author to improve on our practices using technology. Sometimes I walk away feeling overwhelmed or even a little angry, but the comments made by Dr. McLeod are always (in my opinion) with the future of our students in mind. The following is a look at a few of the comments made by Dr. McLeod at the Iowa Education Summit with my thought.


Dr. McLeod:


...we'd teach students how to properly maintain and manage those computing devices rather than removing user privileges and locking down the ability to change any settings


My Comment:


I agree with this, because the more you attempt to lock something down, the more the students seek ways around it. I am not saying that our district does not lock things down...they do mainly for liability reasons. I think if Dr. Mcleod is leaving anything out, it is the legal aspect. That being said, we have allowed cell phones out of lockers for four years now. That has been a big help because students are not constantly trying to sneak them. They know the time and the place. It has been so successful that I do not say anything when they take the phones out of their pocket and use them in class; whether to look something up, send a text asking a question, or to use the calculator. Our laptops do have some items lock on them, but they are always open for debate. If it can be used for an educational purpose and that can be conveyed by a teacher or student, the locks always come off. 


Dr. McLeod:


...we'd find out the exact percentage of our schools’ families that don’t have broadband Internet access at home rather than treating the amorphous ‘digital divide’ as a reason not to assign any homework that involves use of the Internet


My Comment: 


By my rough calculations, the amount in our middle school without any Internet access at HOME is 15-20 percent. That is not a large number, and when you factor in the library, hanging around the school, or going to a friends, the percentage drops to about 5. Most of that conversion from 20 percent to 5 percent comes down to responsibility. Yes, you may have to go a little out of your way to get the Internet, but not everything in life is easy. The only students that are tough to accommodate for are the country students who ride the bus and live so far out in the middle of no where that satellite is their only choice. Satellite Internet is often slow and expensive compared to other options.


With 5 percent of our population not having any Internet access, can you still work outside of school using technology? My answer is yes. Make accommodations to the other 5 percent. Just because they do not have Internet does not mean the computer is useless. They could still use iMovie or anything else they have already on their computer. Another option is to write a grant that could fund an Internet connection for a year for a few students. I have not done this, but I am running out of items to write grants for and I always thought this would be a good option. 


Dr. McLeod:


...we'd recognize the power and potential (and limitations) of online learning rather than blithely assuming that it can’t be as good as face-to-face instruction


My Comment:


I did a form of online learning last year in my classroom. Students had to only communicate with peers and myself through the use of a chat. All work was done online. This was a great experience, but I always had to be in the room and the students could not relocate around the school or stay home for legal reasons. We did 10 units this way where one group was in the traditional setting and the other used online learning. Without involving the inferential stats, the means for all the posttests combined were .1 off out of an average of 10 questions. I thought this was pretty monumental and I hope we can expand on this form of learning. 


Dr. McLeod:


Here in Iowa we're currently spending less on school technology than we did a decade ago


My Comment:


I am not sure about this one. He probably has some statistics to back this up, but in general, technology costs a lot less than is did 10 years ago. I know in our district 7 years ago, we had quite a bit of technology. Even so, we have much more today. Maybe the price difference is that substantial that we do spend less, but I don't think this should be an indictment on schools for not spending, but a nod to the people who produce the technology for making it cheaper and more efficient. 


In general, I agree with most of what Dr. McLeod has to say. With many more comments from the summit to analyze, what do you agree or disagree with? Are there any I left out that should be included and discussed? 

Credit given to ASBIndia1 through flickr.com/creativecommons

Challenges Before Technology: Three Uphill Battles that Preservice Teachers Face

Being in a class with many potential educators is a wonderful experience. I am out of date as to what is being focused on in the preservice ranks. I am entrenched in my seventh year of teaching, and as I think back to the challenges that I faced early in my career, it is interesting to think how technology fits with other educational pitfalls.

I do not see myself as being negative, but real. Technology was being pushed even when I started, so I can imagine the transition from college to having a job is not that much different. Implementing technology is a great idea, and when used correctly can allow students to create and invent for themselves. The following is a list of three items that are important to have under control before going all in with technology:

1. Classroom Management

This may be the number one problem that faces any teacher coming out of college. Some students are not mentally prepared for dealing with students even with all the training provided. Until you have your own classroom, you cannot get a clear model of the experience. Surprisingly, classroom management was not a big focus when I was an undergrad. I do not remember many instances where this was addressed, and I went to UNI. When I started my first year of teaching, my time was consumed with putting out fires and not on learning. After year two, I had things figured out and I continue to improve every year. I tried to always integrate technology, but my management was so poor that it always backfired. Even my rich technology tasks that were oozing with motivation did not work as well as they should. Have this aspect of your class settled before relying too heavily on technology.

2. Testing

I am a firm believer that test scores will take care of themselves with quality instruction that does not have to be simply memorizing facts. While this is my personal opinion, I causation that relying strictly on projects that integrate technology may backfire in regards to various assessments. Here is a great example. How could any parent argue with you using technology to provide a quality, real-world experience? Sounds impossible, right? Many districts run into this problem when referring to ACT scores, and even ITBS. Our districts ITBS scores are fine (that was not always the case for my class, but my students are 90%+ proficient currently), but our ACT scores have dropped. This could be for a lot of reasons, but many parents see the problem as being the move from old school teaching. They may be wrong, but when they make up a large chunk of your audience and community, a problem emerges. Until our society goes away from testing like the ACT, this will always be an issue. Just make sure your projects and experiences using technology can also translate to base-level knowledge needed to succeed in these testing situations.

3. Time

What I would not give to be back to my old college schedule. I do not think I was lazy, but I did have a lot of free time during those years. These days I have much less time to do anything I want to do besides school. I wake up at 3 and get to school by 5 just to plan and be ready for a normal day. Finding time to prepare for the use of technology takes time. If you want to do something right, it has to be planned and tested, rethought and revamped. You cannot use the same idea year after year because you have different students at various levels with varying interests. Teaching is a time consuming profession. Trying to put together something last minute is never a good idea. Please allow for large amounts of planning time and do not try to do everything all at once. Time can also come into play when accessing technology. If your district does not have a wealth of technology, plan on spending a lot of time on the grant writing process. We have a lot of technology and I still write 4 or 5 grants each year. Each of those takes weeks to put together.

I hope that this post did not come off as negative. I put a lot of time and effort into my job. I do, however, wish I would have known some of these points before diving in head first. I am a great teacher (my opinion) because of these trials I have faced, but I want everyone's transition to be as smooth as possible. What are other obstacles you see as preservice teachers in regards to technology?

Credit given to Peter Huys through flickr.com/creativecommons

Credit given to kewcreative through flickr.com/creativecommons

Changing the World: Three Other Examples of Disruption

I enjoyed the Disrupting Class book for many reasons, but I specifically liked the examples of disruption happening around us. The thought of a new idea not competing, but finding a place in society only to take over for an old idea is intriguing (p 44). The example from the text that stood out to me was the shift from the Digital Equipment Corporation's super computer to the original Apple (p. 50). I cringe to think what technology in education may look like today had Apple not lead the way. As I thought about this process, I came up with a few more examples of disruption.

1. Downloading/Steaming Music, Movies, and Video Games

Disks and cartridges were the norm for these types of technologies. While they still exist, I could potentially see a strictly digital format for all three. I download all of my music and stream most of my movies in various capacities. I have yet to move to only downloading video games, as that disruption seems to be a little further behind. Most of the top sellers come on disks for the PS3, XBOX 360, and Wii, but each has an online network where they could stream everything in the future. World of Warcraft and Minecraft are two games that are largely popular and available without the need of a disk.

2. Television

I do not know how far off this disruption is from taking full force, but in the Dangerously Irrelevant blog, the Shift Happens video says that people under 25 watch almost 30% of their television online. I am too busy to actually ever sit down and watch television, but I still watch many of my favorites online. I can even watch all my Buccaneers games online as well. The physical television may not go away soon, but stranger things have happened.

3. Cell Phone

Back in the day when only Zack Morris had access to a cell phone, the uses were few and far between. I had an old bag phone in high school and the niche was that I only used it in an emergency. These days, cell phones have numerous uses and I would be lost without mine for sure. The specific disruption in question here is the home phone line. I do not see the original purpose of a cell phone to ever take over for the home phone, but it effectively has. As of a year ago, about 25% of homes in the United States used a cell phone exclusively. This is trending upward, and I could see a time not too far down the line that the cell phone could take over completely for the home phone.

Disruption has worked well in society producing cutting edge technology and fascinating ideas for the future. Hopefully education can follow suit. What are your examples of disruption?

Credit given to hannah_wilson through flickr.com/creativecommons

Creating Educational Change: An Alternate Route

The book, The Disrupting Class: How Disruptive Innovation Will Change the Way the World Learns, deals with the need to pave a new path in education rather than try to renovate what is already present (Christensen, Horn, & Johnson, 2011). When looking for educational change, schools typically attempt to make a fancier version of what they already have through the use of technology. While technology has an endless amount of uses in education, the norm is usually not that innovative.

This is an idea that I have thought about for awhile. What exactly would it take for change to occur? An increased amount of technology is nice, but that has not shown revolutionary change. I feel that for technology to be valued for something more than just an bell or a whistle, change needs to come from the top...at the state and federal level. This can come in the form of fewer restriction like No Child Left Behind, and an emphasis on assessing for quality and innovation rather than the ease of tabulating for statistical reasons. The blog, Two Cents Worth, agrees and thinks our bubble test society is hurting creativity and teaching our students to think unilaterally (in a bad way).

Let's be realistic, I see standardized tests and mandates being around for the foreseeable future. That leaves teachers and their own classrooms. Teachers must be the innovators with technology. This is of course easier said than done. In a posting by Scott McLeod, he refutes comments from an article that look negatively on education and technology, and addresses why teachers are behind the eight-ball. The biggest hurdles I see from his comments are training and support, as well as the old-school mindset from the public. Even with these pitfalls, teachers need to rise up and make a difference.

In a posting on the iLearn Technology blog, the following quote discusses how technology SHOULD be used...

***The tools have to be used as essential tools, not supplementary.  Supplementing with technology doesn’t move the needle.  Essential means that technology is in hand 24/7 students have complete access to the tool.  Essential means that students are actively engaged in doing and creating.***


The comment about moving the needle fits in well with our theme of altering the route of technology in education. No one can be counted on to do this besides the classroom teacher. 


Teachers have a big responsibility to today's students. One might say that the future of our country is predicated on teachers and the ability to shake things up in regards to technology. Instead of taking the safe road around the mountain that includes updating notes by putting them on Powerpoint, climb up one side of the mountain and down the other by having students engaging in something different than note taking through technology. Let students be creative. 


In closing, support of these ideas in often difficult based on the standardized educational world we live in. All three blogs I mentioned are great examples of how to break down the technology wall to get to the other side. The blogs support teachers and give ideas on how to use technology to help improve the futures' of students. The blogs are not without criticism and harsh words about what has been done in the past. One cannot take offense to this, but see the challenge that lies ahead. Do not take the safe route. Take the alternate route to improving education.

Credit given to Team PLTW through flickr.com/creativecommons

Credit given to Team PLTW through flickr.com/creativecommons