Getting from four to six

Mike Swanson

Kindergartners at Perry Elementary School spent 15 minutes Tuesday

learning how to add four and two while being guided rather than

instructed by their teachers.

While 5-year-old Taigen Hegberg came up with the answer off the

top of his head, most students needed number lines or blocks to see

how four and two became six.

“You need to show me your answer,” teacher Socorro Alvarez told

Taigen. “You can’t just say six.”

The school teaches math to kindergartners using a method called

cognitively guided instruction, which focuses on showing children how

to solve problems using visual aids instead of memorization.

“The teacher just facilitates the lesson without telling them what

the answer is,” said Alvarez, who was trained in cognitively guided

instruction two years ago. “We’re getting them to visualize math

instead of just teaching them what four plus five equals.”

Alvarez’ kindergartners last year were able to understand

multiplication by June after a full year immersed in the cognitively

guided process, Alvarez said, and she expects a similar outcome this

year.

“It’s still early, so we only spend about 15 minutes at a time on

math,” Alvarez said. “We gradually pick up the pace to where we’re

solving three problems at a time, spending 30 minutes on a lesson. At

this point of the year, it would get ugly if we spent that much time

on it.”

The 10 children in Alvarez’ class were joined by 11 from Melanie

Kos’ class next door for the lesson, all gathering on the carpet

Indian-style with their hands folded, waiting patiently to be

prompted. Children let out “oohs” and “ahs” at everything Alvarez set

on the overhead, from pencils to number lines.

Alvarez first read the problem: “Ms. Rebecca has four pencils.

Taigen gives her two more. How many pencils does Ms. Rebecca have

now?”

After about five minutes of brainstorming, 5-year-old Chandler

Ooms approached the overhead and explained to the rest of the

children how it could be done using colored markers and a number

line.

“I put four there because she started with four, then I put two

more on because he gave her those much,” Chandler said. “Now there’s

six.”

When it came time to move to their desks and come up with six on

their own, children used different methods to do so. Connor Batte, 5,

stacked four blocks next to two blocks first, then squeezed them

together and counted. Alvarez asked Connor if he wanted to set the

two on top of the other four so he could count them easier, but

Connor declined.

“They’ll fall down if I do that,” Connor said.

Taigen, meanwhile, put six markers on his number line so quickly

that he allowed himself enough time to focus on a seventh marker,

making it hop around the uncovered numbers for a few seconds before

apparently losing interest.

“Am I done yet? Now what do I do?” Taigen said.

After the short lesson, the students were allowed to celebrate

with language arts. They stood in a line looking up the alphabet on

the wall, mimicking the animals that represented each letter with

their bodies while making the sounds each letter makes. They handled

everything but the “Q” with ease.