Knowing Their Numbers New State Math Tests Will Make Fourth-Graders Show Their Understanding Of Problems, Not Just Right Answer

Tracy Wheeler’s second-graders pried away, question by question, at the contents of the mystery bag.

“Do they make crumbs?” Yes, replied Wheeler.

“Do they have corners?”

No corners. Are they vegetable? Yes. Hard? No. Can you eat them with salad? No. Can you eat them with dip? Yes.

As it became clearer and clearer what the mystery bag contained, the kids grew triumphant.

“Yes!! Potato chips!” they cheered, waving fists.

What does this have to do with math?

“It’s a way of sorting and classifying. Finding attributes,” said Wheeler, 29. “So much of math is attributes. And by knowing attributes, you can sort and classify.”

Thus starts a math lesson by a teacher who is working with the new state essential learnings in mind.

Over the next few weeks, fourth-graders in the Valley’s public schools will take new state tests on math, reading and writing. The math tests, in particular, will be different from anything these students’ parents ever took in their grade school days.

Most math problems on the test will include space for students to explain in words and/or pictures how they arrived at their answer. Test scores will reflect not only if they got the right answer, but whether they show logical reasoning. Effective reasoning, with a mistake in computation, will earn a student partial credit.

“We haven’t had (state) standards like this before,” said Geoff Praeger, Central Valley assessment coordinator. “Under the old law, each district had student learning objectives. They looked different everywhere you went. Some districts had just a few; others had literally hundreds.”

The new state goals are broader. And, Praeger says, harder.

“Because the standards are so much higher than in the past, we fully expect that many, many, many students will not reach those standards on the first assessment. And some people will probably be shocked. But if that doesn’t happen, then we probably haven’t raised the new standards at all.”

Wheeler’s students at Freeman Elementary School won’t take the fourth-grade tests for another two years. But she’s heading in that direction now, so her students will realize there’s more than one right way to the right answer. And so they’ll know what their own strongest strategies are for solving problems.

“I try to help them tune in to where their problem-solving strength is,” Wheeler said. “If they’re only taught one way, and that’s not their strength - then they’re in deep trouble.”

Wheeler has taught three years in Freeman, but she came from California, where public schools were already emphasizing the concepts now in the spotlight in Washington.

One of the “essential learnings” - core state requirements - in math is that they can communicate mathematical ideas in both everyday language and mathematical language.

That includes mathematical terms like numerator and denominator.

A new student in Wheeler’s class means that fractions involving numbers of students have a new denominator.

How many kids ate hot lunch? Nineteen out of 23. How many ate cold lunch? Four out of 23. How many are present? Twenty-three out of 23.

Filling in the calendar with dates for Saturday, Sunday and that day in class - Monday, the 15th of April - gave Wheeler still more material.

“Let’s talk about the number 13. How can you make the number 13 with multiplication?”

Each date lent itself to a different concept. Thirteen is a prime number; 14 is an even number; 15, like all numbers ending in five, is divisible by five. Wheeler led her class through prime numbers, factors, ascending order - with a quick diversion for a lesson in social studies. “What’s special about today? That’s right it’s Tax Day.”

But through out the morning she asked questions: “Who’s got another strategy?” “How did you know it’s divisible by two?” “How did you figure that out? What was your strategy?”

Fourth-graders in some Valley schools have worked on sample questions from the state tests in recent weeks.

At McDonald Elementary School, Allan Myers challenged his fourth-graders with a sample problem that involved naming an overall top athlete. The problem started with individual scores for several fitness contests. Students were expected to write out not just their answer, but their reasoning.

“Read all the directions first. Then see if you can find the question,” Myers said.

A few kids weren’t sure where to start.

“Remember to use pictures, words, numbers - anything to help you solve the problem,” Myers encouraged.

Some of Myers’ fourth-graders plunged right in.

“Easy,” pronounced one dark-haired boy, after finishing up.

, DataTimes ILLUSTRATION: 2 photos (1 color)

MEMO: This sidebar appeared with the story: FOURTH-GRADE BENCHMARKS Here are samples of some of the specific skills and knowledge the new state assessment for fourth graders will measure: Know how to add, subtract, multiply and divide whole numbers. Know appropriate tools for measuring time, money, length, area, volume, mass and temperature. Use estimation to predict results. Express ideas using mathematical language and notations (models, tables, carts, graphs, open sentences). Test conjectures by finding examples to support or contradict them. Identify examples of uses of mathematics in daily life.