PHIPPSBURG — For most of us, the beach is a place to bask in the sun and perhaps catch cool ocean waves on a warm summer day — or to stretch our legs and clear our minds.

But for students in Richmond High School teacher Carolyn Arline’s math classes, Popham Beach State Park served as a laboratory on Wednesday. Instead of stretching out in the sand, juniors and seniors in Arline’s precalculus and advanced algebra classes stretched the boundaries of their understanding of math.

“We came out here to measure the waves; measure their amplitude, and we came here to figure out whether the waves are periodic or not,” student Lauren Umberhind said.

“If it keeps going,” it’s periodic, explained classmate Julian Leavitt. “If there’s a pattern to it. Like (Umberhind) said, (we’re) testing wave lengths; checking the time at which they break,” to collect data to make a determination.

With notebook in hand, Alyssa Pearson said, “We’re writing down the height (of the wave).”

Kristina Burch would yell out “peak” indicating when the wave was at its peak, “and then Lauren tells us how high it is so we measure the height of how big the peak of the wave was,” Pearson said.

They measured the waves using yard sticks stuck in the ground and — by squinting — sighted the peak of the waves.

According to Umberhind, students had to subtract whatever distance the yard stick was in the ground from the height, “or else that completely messes up your data.”

Leavitt was measuring the time between the wave peaks with a stopwatch to calculate the frequency of the wave, which was recorded by Dylan Clifford, so they can determine the amplitude.

“After we’re all done, we have to analyze the data and put them into graphs,” Clifford said.

To do so, the students use software called Logger Pro.

As a backup, he said, students captured the waves with a video recorder. It was hazy, which made it difficult for students to measure the waves with their eyes, so with the video clips “we can tell which waves we’re going to look at,” Clifford said.

One student in each group used a tripod and camera to capture video of the waves to assist in their analysis later in the classroom.

None of the students have used Logger Pro before but as Leavitt noted, they were born “in this day and age when technology just comes to us.”

Clifford said he liked the hands-on assignment, which helps some students retain what they study in the classroom.

“It’s on topic for what we had to do for our learning,” Leavitt added.

In lessons on trigonometric functions, Pearson said, “I know that I struggled in the wave category during our quizzes and stuff. I didn’t really understand it, but now being out here, I understand it pretty well.”

Dan Tompkins is the technology integration teacher for Richmond schools. Tompkins said the measuring of waves Wednesday addresses a learning target that is part of Regional School Unit 2’s standardsbased education.

Arline said RSU 2, which includes Richmond, is teaching with standards rather than teaching out of a book. Student performance is graded on standards 1 through 4. All the students at Popham on Wednesday have received a 3, which is “proficient.”

“So we decided, ‘Well, to get a 4, we have to apply what we’ve learned,’” Arline said.

The misty, moist weather wasn’t ideal as students and teacher had hoped for more sun, particularly because students raised funds themselves for the field trip.

Reflecting on the data collection Wednesday, Arline said she doesn’t think students can use some of the data because they needed to measure continuous waves rather than skipping waves in between, “but that’s going to be a classroom experience talking about why we can’t use that data.” That is why the video footage of the waves will be imperative.

“It’s operating at a level that’s beyond the paper and pencil,” Tompkins added.

“They’re excited about learning stuff and excited about talking about it, and I start to hear them using the word ‘periodicity,’” said Arline, a 15-year teaching veteran who is in her first year at Richmond High School. “They’re using math words and it’s kind of fun to see them changing from being fearful” about math topics.

The idea for Wednesday’s project originates from a tutorial created by MLTI Integration Mentor Phil Brookhouse, who joined the students Wednesday at Popham. He taught science and math for 30 years at Lewiston Middle School before moving on to MLTI, where he now does professional development for teachers. He travels all over the state and gives workshops for teachers.

“The idea is: It isn’t about the technology. It’s about the teaching and learning,” Brookhouse said. “That’s what we try to push as much as possible because all the people we have been doing professional development with have been teachers, not technologists.”

“We have our mind set on inquiry, the idea that book learning isn’t enough for the 21st century,” Brookhouse said. “Kids have to be able to ask good questions; they have to be able to think of how they can answer those questions in a meaningful and valid way; and they have to be able to find information and take a look at how valid that information is. And they have to be able to construct arguments from evidence and that’s basically what this class is about: constructing an argument from evidence.”

Asked how often he gets to come out and watch students use such ideas, Brookhouse said, “Not often enough. Working with students is a treasure … Watching the kids work and thinking about what they were doing and why they were doing it, that’s the sort of thing you don’t get in a multiple choice test.”

dmoore@timesrecord.com