Teachers undergo a common experience

For a couple days this week, Laguna Beach Unified School District math teachers reversed roles and became students again.

Beginning Tuesday, about 15 middle- and high-school teachers sat at desks grouped together inside a Thurston Middle School classroom and plugged away at problems that tested their ability to estimate and reason.

The exercises were part of a two-day training course geared toward a new curriculum taking shape in district schools that coincides with the transition to the Common Core state tests, known as the California Assessment of Student Performance and Progress.

Since 2010, some 45 states, including California, have adopted the standards in English and math, according to the state Department of Education.

The tests, to be given next spring statewide, will place a greater emphasis on critical thinking, interpretation and writing — even in math.

Laguna Beach Unified teachers tested their critical thinking with this question: How many descendants of a woman who was a teenager in 1900 would be expected to attend a family reunion 100 years later?

Consultant Patrick Callahan, who led the group, provided additional information to help teachers develop their answers. He noted that at the beginning of the 20th century, the average American family had 3.5 children, and by the century’s end, the number had decreased to 1.7.

Laguna Beach High School instructor Steve Sogo assumed the family line would grow five generations in 100 years, with each household having two children who would subsequently reproduce. Sogo expressed his thought process by writing exponents on a white board, accounting for deaths too.

Gary Shapiro, who teaches Advanced Placement calculus and honors pre-calculus/trigonometry, estimated that 300 people would attend the reunion. He based his assumption on families in the early 1900s having more children than subsequent generations.

“You had to assume how long a generation is,” Callahan said.

In the 20th century, life expectancy doubled while the birth rate was halved, he added. Callahan, co-director of the California Mathematics Project, mentioned the devastating influenza outbreak of 1918 as another factor to consider.

Shapiro was encouraged by the exercise, also called modeling.

“This is a nice way to find out how a particular student thinks and organizes,” he said. “They have to know about history and generations. I want to prepare my students to make realistic assumptions.”

Katie Meyers, who teaches eighth-grade algebra, said she may ask students to estimate how many chickpeas could fit inside her classroom.

“It’s not about one answer but how you get there,” Meyers told the group. “Different teams could present their arguments, and a class discussion could go from there.”

Callahan said these types of exercises translate to real life, citing their use in arriving at estimations for population growth and demographic shifts.

Callahan gave an example of a caterer who must decide how much food to prepare for a certain crowd, such as attendees at a reunion.

“Are there going to be 50 or 300 people?” Callahan asked rhetorically. “If I’m a caterer, my whole livelihood is based on modeling.”

Common Core presents a change in what it means for students to be proficient in math, Callahan said.

Change doesn’t come without critics. Callahan said he’s heard people call the style a form of fuzzy math where students could write down any answer and receive credit if they present a strong argument.

“Some parents feel like they did well in math when they went to school so why change things,” Callahan said. “One of the most valuable parts is being able to quantify a situation and test reasonableness.”

Students return to school Tuesday.