Algebra Starts Early
The word "Algebra" makes most adults cringe while they relive their horrible experiences from high school in which algebra was too abstract and never made any sense, like some foreign language derived from alphabet soup with x and y as the main characters.
The New Mexico Mathematics Content Standards, aligned with the National Council for Teachers of Mathematics (NCTM) standards, require algebra to be taught as early as kindergarten! Of course, Kindergarteners are not expected to solve x2 + x + 10 = y. But the activities they do at their level build the foundation for algebraic thinking in the upper grades. Algebra needs to make sense. Algebra needs to be "hands-on." Algebra is about looking at patterns and analyzing changes and figuring out rules. And algebra can be FUN!
At Isleta Elementary School, Te Tsu Geh Oweenge Day School, and Sky City Community School, teachers in grades 3 - 6 help students develop algebraic thinking skills. A Chinese Folktale, Two of Everything, by Lily Toy Hong, provides an introduction. In the story, an elderly couple finds a brass pot that magically doubles everything they put into it. When they put in 5 gold coins, out come 10 gold coins! When they put in 1 hairpin, out come 2! They even double themselves! After reading the story with the children, the "t-table" method of organizing data is introduced, with the left side labeled "IN" and the right side "OUT." Students fill in what went in and what came out. "5 went in and 10 came out, so we put the 5 on the left and 10 on the right. We can also use symbols for IN (*) and OUT (D). The children discover that we can figure out "rules" for the pot (which is "IN + IN = OUT" or symbolically "* + * = D" or "2* = D") and use these rules to find out what the pot will do with any amount that is put into it (e.g., If I put in 1000 coins, how many will come out?).
In another lesson, we imagine that "One day the pot is doing something different. When 1coin goes in, out come 3 coins. When 2 sweet cakes go into the pot, out come 6." We create a new t-table with the IN and OUT information, and the students figure out what the pot is doing now. Some of the rules become rather complex for the 3rd and 4th graders (e.g., IN + IN +1 = OUT), but students work collaboratively to figure out each rule. Students are challenged to create their own secret rules for the pot and have the rest of the class solve the "mystery." The lessons in this unit connect the "brass pot rules" with tables, graphs, and equations. Students can see the number patterns on the tables, analyze the linear relationships after they graph the data, and create equations that help them solve for huge, or ever unknown, amounts.
Although Two of Everything is obviously not "real life," students enjoy imagining life with their own brass pot that could double everything. Stories that have a math theme are excellent ways for children to express their thoughts in language that comes naturally to them. Using stories to which the students can relate makes math more understandable and a lot more fun!
