Add it up: Better critical-thinking skills will improve math test scores

His objective is to use the different-sized shapes to make one larger shape, called a tangram.

The 11-year-old boy twists and moves the plastic shapes around his desk until he has used 13 of them to make the tangram.

"See if you can do it in less," challenges his teacher, Lori Sorber.

Two of Zach's classmates in the fourth grade math class at Northwest's Hunlock Township Elementary School had completed the tangram with just nine pieces.

Zach mixes up his plastic pieces and after a few minutes completes his tangram with just 10 of the plastic shapes.

"Good job," Mrs. Sorber says, as she walks around the classroom.

The class moves on to a more complex tangram that requires the students to first solve mathematical equations and cut different shapes out of paper.

"This is neat," says 10-year-old Katie Gregory, as she finished calculating the answers to some division problems and began to cut out her shapes.

It is the start of geometry for the fourth graders, as well as a lesson in critical thinking. It will help the students prepare for taking the mandatory Pennsylvania System of School Assessment test in math next year, says Mrs. Sorber, who has taught in the district for 20 years.

"We're trying to teach them to think about how they solved the problem, not just memorizing facts," she explains.

About 60 miles northeast from the Luzerne County school, fourth graders in Mary Jo Falbo's math class at Carbondale Elementary School are getting a similar type of lesson on critical thinking.

In front of her classroom, 10-year-old Molly Fox holds half of an orange in her hand. Two other students stand next to her, also holding orange halves in each hand.

"How many parts are there?" Mrs. Falbo asks the class. "Count the orange halves."

The class chimes the correct answer -- "5."

Mrs. Falbo asks the students with two orange halves to put the halves together.

"Now how many do we have?" asks Mrs. Falbo, who has taught in the district for 29 years.

The class shouts -- "2."

"Very good," she says, as she heads to the chalkboard. "Now class, this is something new. You never saw this before. Eyes up here."

She explains to the students that 5/2 and 2 are the same thing -- equivalent.

After showing the students other examples of equivalent fractions and reviewing numerators and denominators, Mrs. Falbo passes out construction paper that has four circles drawn on each sheet.

The students make fractions out of the circles and work on adding the fractions. Then they split up into small groups and use plastic shapes, similar to the ones the Northwest fourth graders use, to work on more fraction problems.

As Mrs. Falbo explains to the students how to use the plastic shapes, she tells them they should think about the reasoning behind what they are doing.

"Remember," she tells the class, "when you take the test (fifth grade state assessment math test) next year to write out what you are doing. They want to see the thinking behind what you are doing."

The math lesson plans for both fourth grade classes are similar. Students are taught fractions and decimals, as well as a little geometry. There is also heavy emphasis on review to make sure the students have grasped the basics.

Both Mrs. Falbo and Mrs. Sorber's teaching methods are also similar: Both use visual aids and a hands-on approach to teach math.

"I do a lot of visual math," Mrs. Sorber says. "I go to math conferences and always give things a try. I want it to be hands-on for them."

Mrs. Falbo uses Bingo and board games during some of her math lessons. Anytime she can use something visual to show her students a mathematical concept, she will.

"It's better to show them," she says.

Both teachers also try to incorporate tips about taking the test in their math classes without allowing their lessons to revolve around it.

However, fourth graders at Northwest have an edge over Carbondale students because they use a software program specifically designed to prepare for the standardized test.

"It's very good," says Mrs. Sorber. "It's on our computers in the computer lab. It has a lot of story problems and critical thinking problems."

The program allows Mrs. Sorber to see areas in math where her students need additional help. The program also gauges the students' progress.

Mrs. Sorber has also switched to a new math book. The book's practice sections are better suited to prepare students for the test. Different types of math problems are included in each practice section -- similar to the test.

"Rarely do you see more than one of the same type of problem," she says.

The software program, called COMPASS, will be available to the Carbondale students next year, says elementary school principal Dominick Famularo.

The students will also be getting new math workbooks next year, he says.

"It's better geared for the state assessment test," he says.