Special Focus: Pint-Sized Algebra
Dressing up like scarecrows in the fall and donning leprechaun hats and jackets in March is all the rage in some kindergarten classes in Indiana. It's hard to tell these students are learning the beginnings of complex math, but it's easy to see they are having fun doing it.
While the pint-sized children giggle with delight in their costumes at Fox Hill Elementary School in Indianapolis, they are learning the core basics of algebraic thinking.
With two scarecrows, they figure out how many hats the two scarecrows would wear. And with five
leprechauns, they estimate the total number of buttons that would decorate the leprechauns' jackets.
"We incorporate algebraic thinking to get children to problem solve ... using manipulatives to solve problems and we have them think about the missing number," says kindergarten teacher Barbara King. "And they're doing some proportional reasoning" using snowmen, scarecrows or leprechauns as fun, visual clues.
In this age of mandatory annual tests for students and accountability rigors for educators, this algebraic thinking for all is a concept that a growing number of districts has adopted to make higher math, like algebra, easier to learn or even master.
Algebraic thinking should start early, even as young as kindergarten, says Johnny Lott, the executive director of the National Council of Teachers of Mathematics.
Getting students to think like this is particularly important because there has been a high failure rate in ninth-grade algebra, he says. "When they start doing it early, it's not a shock to the system when they see it as an official course," Lott says.
Educators in the Washington Township School District in Indianapolis, which is where Fox Hill School is located, understand the importance of such thinking. During the past several years they've been using this idea and implemented Project SEED, a non-profit national mathematics program that uses a Socratic group discovery teaching methodology to teach advanced concepts.
Project SEED started in the district at Crooked Creek Elementary School five years ago, but this is the first year the district has included students from throughout the district. It is a 15-week program that involves 78 fifth-graders, about 8 percent of the total fifth-grade class, and 28 seventh graders, about 2 percent of the seventh-grade class. "We want the kids to be able to take algebra in grade 8, then geometry in grade 9," says Michael Pomerenke, the district's coordinator of math and science. "Then you can take so many more courses in high school. You can take calculus as a senior. ... And colleges look at student transcripts." he says.
Five years ago, math scores on the Indiana State Testing Educational Placement revealed that the district was third or fourth from the bottom of 10 districts in Marion County. "Now, we're at the top, based on the fact that we're teaching algebra in fourth and fifth grade and it's aligned to the state standards," Pomerenke says. "Teachers are teaching to the standards."
The county is "very diverse," with African-Americans comprising 42 percent of the student population and Hispanics comprising 5 percent, he says.
As for the algebraic thinking that starts in kindergarten, grant coordinator Judy Fraps says Washington Township has been using the idea for maybe eight years, but it never had a name. "Our earliest use of algebra has students finding the unknown and having kids make relationships, sorting and seeing patterns so they understand critical thinking," she says. "And we're always asking kids to do things in more than one way."
Fraps is the coordinator for the Lilly Endowment grant that pays the $65,000 for Project SEED.
The SEED students at Allisonville Elementary School work on powers, exponents, and even a little bit of integers, says fifth-grade teacher Sandra Brown. "I've seen growth as far as their ability to solve problems. I've seen a better understanding of numbers sense and algebraic equations."
Angela Pascopella is features editor.