Integrate Math & Computer Science
Math Lessons That Introduce Computer Science to K-8 Students.
Mar 25, 2008
With all of the requirements placed on classroom teachers already, who has time to add yet one more? And, of all things, computer science? Through math games and lessons K-8 teachers already include many of the topics suggested by the Association for Computing Machinery. Here are some examples:
Number Theory
Counting if fun! Once children master counting by 1’s and 10’s have them try 2’s. Two’s, also known as binary, are the counting base for computers. Most games that involve counting can be modified to count by a different number. Do you already do that to prepare them for multiplying? Then you are already teaching them a basic concept of computer science.
Once students are ready for exponents, look for opportunities to expose them to the number 2 as a base. Also, changing bases using 2, 8, 10 and 16 exposes them exposes them to how a computer manipulates numbers.
Graph Theory
A foundation for graph theory is built when concept maps are used to organize thoughts. The circles represent the idea (or vertex) and the lines (arcs or paths) link them together and create a simple graph. Add arrows to the lines and you have a directed graph.
The four color theorem adds a fun element. Take a map of a continent and four colors. Color each country or state so that no two touching regions are the same color.
A popular math puzzle is the three cottage problem. Suppose you have three cottages and three utilities (gas, water and electric) on a plane or sphere. Can you connect each cottage to all three utilities without crossing any lines, going through another cottage or utility, or using a third dimension?
A set of Instant Insanity cubes can demonstrate how to use graph theory. The faces of the four cubes are each one of four colors. The object is to arrange the cubes in a line so that only one of each color is visible as you turn the cubes as a set. Draw a graph with four vertices, one for each color, and then draw the arcs for each cube. Then, draw a line to show how each color is connected for each cube. Decipher the graph, and you have solved the puzzle.
Algorithms
Algorithms are a step-by-step problem solving technique and a major part of all areas of computing. Perhaps one of the most famous is PEMDAS, the mnemonic for the order in which to solve a computation problem. Please Excuse My Dear Aunt Sally or Parenthesis Exponents Multiplication Division Addition Subtraction is a common tool for by the time they reach high school, but it is not the only way to teach an algorithm.
A fun, multi-discipline activity is to describe how to make a peanut butter and jelly sandwich. Without being told the objectives or how specific to be, students write down the steps (algorithm) to create the sandwich. The teacher then demonstrates one – which tends to be really funny since the steps are rarely specific. Students are then informed that the steps need to be specific and easy to understand. They then rewrite their original steps and then can swap with a partner and try to make each other’s sandwich by following the directions.
For young children, patterns are a way to introduce the idea of following or creating steps. Whether it is to fill in the missing number or the next picture children need to determine what the pattern is to successfully figure out what is missing.
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