New CLAS Test Cloaks Math Problems in Words

Designed to relate mathematical concepts to the real world, the state’s new standardized test disguises arithmetic, geometry and algebra in word problems that are mostly about children’s lives.

According to copies of the closely guarded 1994 California Learning Assessment System test obtained by The Times, fourth-graders must make a schedule for an afternoon at an amusement park, eighth-graders are asked to design a soft-drink survey for a snack-bar owner, and 10th-graders must select the best long-distance telephone service for their family.

The math test contains three types of questions:

* Open-ended, which encourages graphs, charts, diagrams and essays to explain answers.

* Multiple-choice, which differs from old standardized tests because most problems include several steps.

* Constructed response/short answer, in which students must solve problems and show their work.

In hundreds of math problems reviewed by The Times, CLAS takes pains to employ multicultural children’s names in work, play, school and family situations.

“Four children in a family were given cookies,” begins an open-ended item on the fourth-grade assessment. According to the problem, Jeff received seven cookies, Lydia 12, Stanley nine and Tamika 10. The instructions are to “show how the four children can share the cookies fairly.”

Eighth-grade students had two separate math booklets, with a total of two open-ended questions, eight multiple-choice questions and eight short answer items.

Some of the open-ended queries, like those that follow, are straightforward: using one-centimeter cubes, draw all possible figures with 12-centimeter perimeters; enlarge a rectangle in proportion; or find the patterns in a triangle formed by rows of numbers.

Others employ real-life situations, asking students to determine how long it would take to replant a forest destroyed by fire, design a movie-theater schedule or plan surveys for a jean-maker, snack-bar owner or paper recycler.

One of the open-ended questions on the eighth-grade exam also appears on a 10th-grade exam.

“My job is the same as the one that Grandpa had when he started working in 1934,” the question begins. Using then-and-now wage information and prices for round steak and potatoes, students must explain whether food prices are relatively higher now than they were 60 years ago.

Like the eighth-grade test, the 10th-grade assessment includes two open-ended questions, but it has only three constructed responses and four multiple choice.

Open-ended items on these tests range from plotting students’ trips home from school to determining discounts on new bicycle accessories to labeling fish in a pet store.