game bucket: game taxonomy project

instead of geometric patterns students make tables and plot the graphs of growing patterns,students look at graphs of distance traveled away from a starting point with the steps being intervals of time. They learn about rates of change.
+they have to make graphs of growing patterns
+contextual representation of functions : i.e. selling hot dogs and the resulting profit middle school, context that makes sense to a students-real life situation
+explore proportional situations that involve rates or proportions.
+within the class the idea of pause and reflect over problem solving is very important
+the idea of graphical representation: graph between sales and profits is linear, and increasing: a clear pattern to the six values
+equations to represent functions: suppose you pick up a letter for each hot dog sold, his income is 1.25 x H dollars etc : emphasis at the order of operations (what would be in game design :levels?)
+illustrate the five representations of function, each of these representations illustrate the same relationship- that the most important thing to see.
+use technology to explore all kind of numbers
+ overall goal: by middle grade, students should be able to understand the relationship among tables, graphs and symbols and to judge the advantages and disadvantages of each way of representing relationships for practical purposes. As they work with multiple representations of function they will develop a more comprehensive understanding of functions. (p 38)

Here are two mind maps based on the visual thesaurus project we saw last friday. Basically some sample scenarios of how a teacher might use this information thus making us better informed of what information we need to gather in relation to each game (questions) and the standards they connect to.

Mind map 1

Mind map 2

Next steps –
Revise questions for games
New set of questions for level editors

In this first post we will introduce some first ideas around pattern recognition and analysis in mathematics.
Patterns are a key concept throughout all grades, and we will start by exploring how we can pull games out of pattern concepts.

Here are some quotes from the book elementary and middle school mathematics, teaching developmentally, authored by John A. Van De Walle

‘the most basic idea in mathematics is that mathematics make sense!’

‘consider the study of Algebra.One can learn to graph the equations of a parabola by simply following rules and plotting points…But understanding why certain forms of equations always produce parabolic graphs involves a search for patterns in the way numbers behave…Pattern is in everything around us, in nature, art,buildings,science, medicine,biology and sociology’ page 13

‘Children develop understanding in maths through:
1)assimilation :refering to the use of existing schemas to give meaning to experiences.
2)accomodation is the process of altering existing things or ideas that contradict or do not fot into existing schemas.’ page 23

To understand the above better we will give an example:
In this exercise children have to ‘make a list of numbers that begin with a ‘start number’ and increase by a fixed amount we will call the jump number. First try 3 as the start number and 5 as the jump number. Your task is to examine this list and find as many patterns as possible’

A game that could be pulled out of the above pattern problem is sudoku. After playing sudoku children could analyze the patterns that they made to solve the puzzle.

A list of more exercises is found below:
exercise two: two machines, one job p.15 this could be similar to tetris
exercise three: one up one down this could be similar to one of the brain age games

We will keep researching pattern exercises, to view more classic problems in Math, please visit : http://mathforum.org/dr.math/faq/faq.classic.problems.html

Also a  visualization of models/patterns that illustrate mathematics concepts can be found below: