Two times two will always be four. But how Kalmiopsis Elementary School students arrive at this answer might be different from the way parents learned.
With Brookings-Harbor School District, along with the rest of Oregon, adopting new Common Core standards, teachers at Kalmiopsis are implementing new methods to teach students the math skills that will be necessary to meet the new national standards.
While the skills taught at different grade levels vary, with kindergartners learning how to count, third graders learning to multiply and fifth graders slogging through long division, how the concepts are being presented to students is similar - and different - than in years past.
"Common Core is asking kids to think deeper about math, to make connections about math," said Ken Olsen, third grade teacher. "Instead of just memorizing facts, they are knowing what those facts mean. We are asking them what multiplication and division mean."
In Olsen's third grade class, students are not just taught the algorithm and sent home with a worksheet of 20 examples. The work looks different, with students constantly being asked to make different connections between addition, subtraction, multiplication and division.
"We are developing habits of how they think about math," Olsen said. "Instead of being discouraged when they make mistakes, those stuck points are when we really learn about math."
Teachers are now using a series of steps to introduce new math concepts. Teachers will present a question to the class and then give students private reasoning time to figure out the problem by themselves. Students then explain their answers to a partner, and the teacher will explore the multiple pathways students take to find the answer. Students must then justify and explain their reasoning, with even kindergartners standing at the front of the class explaining why eight is larger than six.
"In the past, the students counted the numbers by rote, but the numbers and what they meant might not have meant anything to them," said kindergarten teacher Terry Brueckner. "Each child is different and needs to find their own way. We need to give them frequent opportunities to count."
Brueckner said the children need meaningful opportunities to count and, when these are presented to them, they are motivated to count. By emphasizing figuring it out by themselves, allowing for mistakes and making students prove how they arrived at an answer, they develop a better and deeper understanding of concepts.
"Instead of seeing how fast they can memorize this, we are asking them to describe what multiplication and division is," Olsen said.
By having the students work on the concepts in depth, the hope is that students will make more connections and be able to generalize how to approach the topics.
In Nikki Darger's fifth grade class, students tackled long division problems using grids, dividing up portions of the grid in order to show how division works. Darger calls on students randomly by rolling dice to make sure all students have an opportunity to show how they worked on the problems and to limit favoritism or having the same students always answering problems.
Children picked a problem and talked about it with a partner in order to see how the problem could be solved.
"The more students verbalize what they're thinking, the more they're able to understand," said Principal Helena Chirinian. "Just because you're quick and good with the algorithm doesn't mean you understand what the concept means."
After working through 120 divided by 30, students showed their work on the board, with some independently coming up with the idea to check their work by multiplying the product by the divisor. The students figured out the algorithm by themselves, using pieces of grid paper and highlighters, and then applied the problem into practical terms by coming up with story problems.
"The confidence that comes with discovering the algorithm is amazing," Darger said.
Chirinian says the students enjoy math more and, while in the past they may have dreaded it, they are now asking for more.
While the new math may be asking students to understand the concepts more deeply, it has left many parents confused when looking at homework at night.
"The hardest part is having to explain it to the parents," Olsen said.
Olsen said he has had parents sit in on lessons in order to understand the new way of introducing the curriculum.
All of these ideas and concepts will hopefully develop better mathematics skills in students and give them a better depth of understanding and improve student success on tests and in life.
"There are many different ways to get to a particular place," Olsen said. "We are asking them to explore the journey and figure out that math is all connected to each other. We are asking them to justify and defend what they are doing."