WPP: Part A

I am having a problem.  The problem is that my students are not making lasting connections with the hierarchy of numbers.  Lets tart from the beginning.

The Hierarchy of numbers is a way of classifying numbers.  When you are very young you learn about some very simple numbers like 1, 2 3, 4, 100, and so on.  Even though there a lot of these types of numbers (infintly many), they are very easy to understand.  You can see one car, you can touch two apples, you can even hear 1,000 football fans all cheering for their favorite team.  These number are called the Natural numbers.  That makes sense because these are the number that come most naturally to us. 

Then, Things start to get more complex.  The all mighty zero is added to the mix.  This is a very hard concept to understand because it is not easy to see, touch, or hear zero.  It takes time to let that concept sink in.  If you think about all of your natural numbers AND you also include zero then you have the set of numbers that are known as the Whole numbers.  Some people think they should actually be called the "hole" number instead but that's just a bad math joke (get it?).

Then another big step takes place when negative numbers are introduced.  These are another challenging concept because once again, it is harder to show people what a negative number looks like.  When these negative numbers are added to the Whole number (The Natural numbers and zero) you have a collection that is known as the Integers.  And the process continues as you add in fractions, decimals, and even stranger types of numbers. 

Students seem to do well with the first few tiers of the hierarchy but as things become bigger and more numbers are added to the mix they lose their connection to the material.  One of the problems is the one that I have already mentioned.  It becomes harder and harder to see and touch the different kinds of number.  Its not possible to show the square root of two apples.  The other problem is the way the number sets are defined.  As the sets get bigger and include more numbers they tend to stop being defined by what they are and start being defined by what they aren't.  Its kind of like trying to explain what it means to be alive.  "Alive" and "living" are very general terms that apply to a lot of different things.  You can't say that all living things have bones, or hearts, or leaves.  You will miss a larger portion of life by using these terms so it is sometimes easier to define "living" by stating what it means to NOT live.

All of this means that students don't particularly care about the hierarchy of numbers and even when they do learn it the information doesn't stick with them for very long.  I have tried to teach this topic a number of different ways in my classroom but I still struggle.  It is as if there just aren't enough examples in the world.  My students don't leave my classroom seeing the same things I see.

I have tried using diagrams and they work well but they are far from perfect.  They require a lot of examples.  I feel like I have to come up with hundreds of different examples of numbers that fit into each tier and that is impossible.  I can;t write all of the numbers that I need to write.

I have also tried interactive lessons like the one described HERE.  In the lesson the kinds have to put number they have been assigned into certain locations.  This is good but it lacks the concept that some sets of numbers exist within other sets.

I want to remedy this issue that I am having and the only way I can think to do it is to differentiate my instruction in a lot of different ways so that at least one method clicks with each individual in the class. 

My proposed technique.

I would like to start the first day with what I am comfortable with and that is the diagrams. I fully know that the diagrams are flawed but they still hold some value for some students so I would still like to use them.  I would also like to create a video version of this diagram so that it stops being a static item and becomes dynamic.  I would like to have students create short videos of themselves finding the different kinds of numbers in the world.  Natural numbers will be very easy and irrational numbers will be much harder but I believe it is possible.

To continue with the diagram, I would like student to create their own "trick" to help them remember the the hierarchy.  My initially thought for my "trick" would be that my finger tips would represent natural numbers.  Then if you touch your thumb to your index that creates a "0" so my hand would be Whole numbers.  Then my elbow would be integers because it can swing back and fourth representing positive and negative numbers. And so on.  another great idea would be a song or rap.

I would also like to work on the interconnected nature of the different tiers by having students create a collection of yes/no questions that could be answered to determine where a number belongs.   we could then turn the questions into an online quiz or a program (graphing calculator or C++).  I think this would be very beneficial for student because it would really force them to understand exactly how each of the number sets were interconnected.

I have definitly identified a problem in my class and come up with a number of different techniques to help but I won't know if it works until much later down the road.  As stated earlier, students usually retain information about the hierarchy long enough to do well on a chapter assessment but they lose it after that. My indicator for success would occur at exam review time or even at standardized testing.  I am trying to create activities that will help my students hold onto what they have learned for more than just a couple of weeks.  I want to see student recall this knowledge months later when they really need it.

Have you ever taught the number hierarchy or number systems?  What have you tired that I am not thinking about?

Multi-Genre Project: Wilderness Survival

In the novel "The Hunger Games", the main character, Katniss, is a wilderness survival expert.  She knows a lot about nature, plants, animals, hunting, foraging, and surviving.  The interesteing thing about Katniss is that she is so good at these skills that so many people are unaware of and yet she truely struggles with her own emotions.  While she is in the Hunger Games, Katniss will often times use these skills to occupy her while she is dealing with all of the other things that are happening between her and her family, friends, coach, and the capital.

I created a prezi that is a list of some of the bigger Do's and Don'ts that people should follow when they find themselves stranded in the woods.

Multi-Genre Project: Learning to Shoot a Bow and Arrow.

In the novel "The Hunger Games", the main character, Katniss, is lethal with a bow and arrow.  One of the only times that Katniss is ever happy in the story is when she is out in the woods hunting game with her trusty weapon.  The bow reminds her of her father that she misses deeply and it comforts her while she deals with all of the turmoil that surrounds her.  It is as if the bow is an emotional compass for Katniss.

I thought I would give it a try so I went to the Bass Pro shop and got a lesson.  I ended up shooting a 55 lbs all wood recurve bow.  It was a lot of fun and I found out I was far from lethal.

Here is a video I made of the event

Multi-Genre Project: The Reaping Poster

In the story "The Hunger Games" Everything starts to really go down the tubes for the main character, Katniss, when her little sister is chosen in the Reaping.  Katniss loves her little sister Prim with all of her heart and when Prim gets chosen to for the Hunger Games is breaks Katnisse's heart.  She has two choices, she can either sit back and watch as her innocent little sister marches off towards certain death or she can take her sisters place and most likely end up dead herself.  This causes a lot of emotional distress for Katniss and she reflects on her decision and her feelings often throughout the book.  I created a fictitious poster that may have been displayed around District 12 by the Capital to inform the citizens about the upcoming event.  I'm certain that if Katniss had seen this poster before the Reaping she would have been filled with rage and would have probably ripped it right off the wall.

Multi-Genre Project: The Hunger Games Quiz Gale vs. Peeta

There are two very strong male characters in the novel "The Hunger Games" and the main female character, Katniss, is caught is a love triangle with them.  Katniss is constantly thinking about the two young men in her life and this creates a lot of confusing emotions for her.  He doesn't know if she is feeling love, lust or hatred most of the time.  This type of situation always causes readers to choose sides.  I created a quiz to help people decide if they would rather be with Gale or Peeta.  Which team are you on?

TAKE THE QUIZ!

Multi-Genre Project: The Hunger Games Soundtrack

I have read the novel "The Hunger Games" By Suzanne Collins.  As I read the gripping tale of Katniss I would find myself feeling the same ways that Katniss was feeling.  If Katniss was depressed then so was I and if Katniss was feeling mushy and in love then so was I.  One of the major ways that I express my emotions is through the kinds of music that I listen to.  AS I read the book my emotional link to Katniss created a soundtrack.  I decided to create a podcast that highlighted some of the songs that I was listening to as I read and connected emotionally with Katniss.



OR you can download the mp3 HERE.
Please comment and let me know what songs were playing in your head when you read the book.

Online Learning

Online learning is the future.  Or so I have been told.  I fully agree that the world is changing, the way we access information is changing, and the things students need are changing.  I see that education must change in order to serve the masses and online learning seems to be the answer to the question.  The problem that I see is in the quality of the education that can be gained in an online environment.  Online courses today don’t have the kind of robust depth or interaction that I would look for in an educational experience.  That being said, I think they could.  I think online learning could be extremely wonderful and fantastic but I feel it needs to grow out of its infancy.

While reading through the Michigan Merritt Guidelines on online learning I noticed right away that there was an emphasis on “substantive conversation”.  The guidelines require that online learning have some from of interpersonal interaction happening so that students and teachers can learn from one another.  As of right now, that usually means that students have to create post on blogs, forums, or discussion board.  Then, other students need to reply to those posts.  The problem is that most online students are not  going to take the time to reply to something unless they absolutely have to.  This causes instructors to require replies and then something terrible happens.  People interact with one another because they have to.  Its almost like virtual small talk.  As an educator, I feel like this type of interaction is the worst type of interaction that can take place in a learning environment.  I would almost prefer that students not interact at all if they are only doing it on a superficial level because they are being required to.

I would like to create a way to make substantive conversation an authentic experience like it is in a brick and mortar classroom.  There are ways that we can get online students to interact in more authentic ways than post and replies to blogs.  I think products like Voice Thread are creating a great way to interact.  I would like to implement that kind of interaction in my classroom because I think it is much better than simple text on a screen.  I would also bet that a product such as voice thread will intrigue most students enough that they would want to respond and interact.