GAMES!!! ... and math of course!

I love playing games and what makes one game superior to another, in my mind, is the quality of construction. This 'quality' stems from the balance of elements, one element being strategy. A game that has a discernible optimal strategy is not completely governed by chance (War would be an example of a game that is completely chance, it takes no 'skill' to play because there is no such strategy to help you win [without cheating of course]). However, games with optimal strategies can be 'mastered' or become impossible to succeed without both the time and cognitive ability to dedicate to the game (chess is the perfect example of this type of game). Thus a game that combines both strategy and probability is my kind of perfect game. Well this brought me to love the game of Magic many years ago, this collectible card game [ccg] has been immensely successful in the genre and understandably; it blends the fun elements of a card game with the strategical skill of chess and the element of chance like poker. Here are some links to better inform you of this classic adventure in fun and mathematics (don't worry you might not even see the math at first). The first link describes in more detail the links to the realm of mathematics within the game, the second will introduce you to the game itself and the last to another great blog that details mathematics and gaming.

The Mathematics of Magic: The Gathering

Learning about Magic: The Gathering

A Math/Gaming Blog: Giant Battling Robots

Matrix Operations: Addition and Subtraction

This video was created as an instructional tool to help teach Algebra II students about matrices, and matrix addition and subtraction. I'm very happy with the outcome of the movie and I would like to expand it to include matrix multiplication as well. I hope to continue making videos to supplement my lessons. To better enhance this video I would have liked to include more examples of matrices and perhaps some animation, but what could have been most helpful is some better equipment in taking the video of the pool table. High quality in lighting and audio/video recording would encourage me to continue the exact same format for demonstrating matrices and perhaps expand into other subject areas. However, I'm still going to continue to use what I have and make the best of it, just like a good teacher does!

Matrix Operations Interactive Worksheet

I have created an interactive worksheet on a spreadsheet document. The worksheet continues with my unit on matrix operations and makes use of the formula function to demonstrate matrix addition, subtraction, and multiplication. However, instead of having the students simply repeat the formulas or solve the equation A #B=C where # is one of the three operations and have them simply solve C, I instead had C reflect the answer of the given A#B where B is a constant and A is to be inputed by the students. Additionally there is a key so the students know what C is supposed to be. This requires them to remember the formula and apply it in a different way, this diversity in application helps students comprehend the procedure more thoroughly thus acquiring greater conceptual knowledge as well. I hope to expand on this worksheet in the future, I don't believe it needs any other resources but I would really like to expand beyond 2x2 matrices given more time. Let me know what you think of the worksheet, I'll link a copy of the file below.
Here's the worksheet, however this is not interactive when posted as a web page.
http://tinyurl.com/matrixworksheetpage

But here is a link to it as a shared google doc, feel free to use it yourself.
http://tinyurl.com/matrixworksheet

But there are some quality more traditional worksheets available. This one by EdHelp.com has a little interaction as well.
http://edhelper.com/Matrices7.htm

WebQuest - Matrix Operations and Applications

In my WebQuest on matrix operations and applications I send students on a journey to find resources to learn about matrices on their own and additionally how matrices are used in the 'real world.' This activity allows students to dig into the subject matter for a great conceptual understanding of matrix operations, but also, this activity encourages students to teach themselves.

This WebQuest was designed so that the subject matter (in this case Matrix Operations) could easily be substituted for almost any mathematical topic found in the classroom. Feel free to adapt such a format to your own needs. I would have loved to add my own suggestions on where to look for information, but this would have taken away such discovery from the students and thus undermined one of my goals. (However I did manage to sneak in a Yaymath.org video, I'm a big fan)

Here are a few sites I would hope the students discovered along the way:
http://library.thinkquest.org/20991/alg2/matrices.html - not elaborate, but effective
http://www.youtube.com/watch?v=EFApWAl3NJw&feature=related - Good video for matrix addition/subtraction
http://www.youtube.com/watch?v=sYlOjyPyX3g&feature=related - same person doing multiplication
http://www.youtube.com/watch?v=aKhhYguY0DQ&feature=related - because videos are more interesting
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_matrices_AddSubtract.xml - simple but effective interactive instruction

These links could be some of the better sites to connect students with the procedural knowledge involved and thus may have helped achieve my objective, but like I mentioned above, one of my goals was to teach students how to research this kind of information for themselves.

Have more ideas for the WebQuest or for more info on teaching matrix operations, please leave a comment, they are appreciated.

Interactive Inspiration Worksheet

Strength comes with diversity and when addressing the issue of instructional media, diversity provides strength in optimizing student interest and involvement. Traditional lectures have a well-deserved important place in the classroom, however, providing alternative modes of instruction and classroom interaction. Non-traditional or alternate modes of instruction can meet many different INTASC standards such as 4, 5, and 6. Here are a list of those standards and how they may apply to the Inspiration interactive worksheet I developed and posted above.
STANDARD 4: MULTIPLE INSTRUCTIONAL STRATEGIES
The teacher understands and uses a variety of instructional strategies to encourage student development of critical thinking, problem solving, and performance skills.

Obviously alternative instructional media, such as Inspiration worksheets relate to 'a variety of instructional strategies to encourage student development.' The challenge that lies within is addressing 'critical thinking, problem solving, and performance skills.' My worksheet combines interactive technology along with problem solving skills while requiring subject knowledge.

STANDARD 5: MOTIVATION AND MANAGEMENT
The teacher uses an understanding of individual and group motivation and behavior to create a learning environment that encourages positive social interaction, active engagement in learning, and self-motivation.

Interactive worksheets create motivation strictly from the process of its own interaction, however the quality of that interactivity is key to promoting quality motivation. The degree of diversity can increase the effectiveness of individual instruction as well.

STANDARD 6: COMMUNICATION AND TECHNOLOGY
The teacher uses knowledge of effective verbal, nonverbal, and media communication techniques to foster active inquiry, collaboration, and supportive interaction in the classroom.

Communication's effectiveness is also strengthened through diversity. The worksheet above allows students to visualize a previous lesson on matrix operations and connect ideas with an interactive interface. Using technology in the classroom not only provides a diverse instructional medium, increase motivation but also helps teach skills needed beyond the classroom.


These standards are also illustrated here in Robert Ahdoot's webcasts of his classroom instruction. By introducing webcasts, Robert adds excitement to an already energetic lesson and also allows students a very practical mode of reviewing instruction.

Jump Start

This is my blog that I am using during the Summer of 2009 at the University of Northern Iowa. Hope you enjoy the rest of my postings.