ETHETE, Wyo. — On one of the last days of school at Wyoming Indian Elementary School in the spring, Cheryl Williams is playing a game of “8-plus” with Atsa, a first grader with a round, reflective face under a fuzzy thatch of black hair. These sessions are often playtime for Atsa, but they are always serious for Williams, a teacher who works one-on-one with young children to jump-start their stalled mathematical thinking.
The game is simple. Atsa throws a die with the numerals 4 through 9 on its six faces.
“Seven,” he says.
Next Atsa must add 7 to 8. Adding 8 + 7 might seem simple, but Williams watches to see how he addresses the problem. It’s his strategy, not his answer that will tell her what kind of progress he’s making.
Before he started working with Williams, Atsa would have approached the 8 + 7 problem by looking around for objects to count. If he didn’t have enough fingers, he might have counted objects lying on the table. He did this because he lacked what the Common Core standards call “number sense,” the notion that 8 is composed of smaller numbers like 4+4 or 5+3. Without the ability to “compose” and “decompose” numbers, Williams says, children are unable to deal with large quantities and fall behind on the path to understanding division, decimals, fractions and percentages.
Atsa and Williams have grown close after spending a half hour together every day for a semester. They lean in over the small table like collaborators, if not quite playmates. He looks at her for approval. She snakes her arm around the back of his chair as she watches him work out the problem on a wooden bead rack.
The rack holds two rows of 10 beads, five red and five white on each row. It looks a bit like an abacus and is designed to help children understand that numbers from 11 to 19 are made up of tens and ones — a crucial concept in the development of number sense, as laid out in the Common Core first grade standards.
Atsa counts out eight of the 10 beads on the upper rod. He slides them to one side. Then he moves seven beads into place on the lower rod. Next, Williams asks him to take the crucial step toward forming numbers from tens and ones.
“Can you swap the beads?” Williams asks.
Atsa looks at the row with eight beads on one side and two on the other. He slides the two beads over to the group of eight beads to make 10. Then he takes two beads away from the cluster of seven, leaving five.
“How many is eight and seven?” Williams asks.
Atsa considers the bead rack. He began with a row of eight beads and a row of seven, but transformed them into a row of 10 beads and another row of five.
“Fifteen,” he answers.
Dozens of exercises like this one, used in one-on-one sessions and in classrooms at schools like Wyoming Indian, seem as though they were designed to teach to the new Common Core standards rolled out in 40 states and the District of Columbia.
But they weren’t. This teaching approach, called Strength in Number, was developed in 1999, ten years before work started on Common Core. First People’s Center for Education, a small non-profit organization based in Sheridan, Wyoming, trains teachers at poor, mostly Native American schools throughout the West, like this one on Wyoming’s vast Wind River Indian Reservation. And although the sample size is small — Wyoming Indian Elementary enrolls about 350 students including pre-K — the program’s results have been a near miracle.
Before 2006, when First People’s first came to Wyoming Indian Elementary, less than a quarter of the students rated as proficient or advanced in third grade on Wyoming’s statewide standardized math tests. Since then, more than 60 percent have achieved this benchmark every year until 2013-14, when scores dipped sharply after Wyoming made the state test more rigorous. At a time when the long-term benefits of Common Core are being debated across the country, a handful of isolated, Indian schools may provide an indication that — and how — a Common Core approach can work.
Diagnosis is personal
Atsa did not come to Williams because he failed a quiz or a standardized test. He was selected for this “math intervention” based on teacher recommendations and a diagnostic interview midway through first grade. Because Williams must spend so much time with each student, she must choose her candidates carefully. Only one in 10 first-graders gets an intervention, but school officials say that many more would benefit if they had the money to hire and train more teachers for this role. When Williams interviewed Atsa, she asked him to solve problems with some of her math toys. She identified two “number sense” issues in particular that were holding him back.
“He was a one [on a scale of one to five] in arithmetical strategies,” said Williams. “Also, he was a one in number structure. He only knew how to make up and tear apart five. He had nothing on board with ten stuff.” These are Strength in Number terms. But they align closely to the Common Core standards. Atsa was not on course to meet the first-grade standards.
Williams made video recordings of every moment of every exercise with Atsa, as she does with every child. She spends hours each week replaying the lessons, looking for clues about how a child is thinking, what his problem-solving strategy is.
Getting the right answers on test questions isn’t enough for First People’s. Like many of today’s Common Core practitioners, Strength in Number teachers require students to explain their work. For very young children in reservation schools, this can be a problem. Social workers and teachers on the Wind River Indian Reservation estimate that 5-year-olds in their community arrive at school with a vocabulary of 3,000 words — about 2,000 less than average for that age. Even as first graders, many lack the vocabulary to explain their reasoning.
“That’s when you can go back and watch the video and see if there is any finger stuff going on, any head bobbing stuff, any tapping going on,” Williams said. Those actions are evidence of counting. That’s a sure clue, Williams says, that the child does not yet understand something important — and that the teacher needs to diagnose the problem.
First People’s has been taking its approach to numeracy into Native schools in Wyoming, Montana, Washington and Alaska since 1999. Craig Dougherty, a native of Powell, Wyoming who is now the superintendent of the Sheridan, Wyoming school district, began the organization after spending much of his early teaching career at Native schools in Alaska.
“I could see the low achievement in those schools,” said Dougherty. “And I knew that Indian kids were as smart as any other kids. I concluded that we needed to do something about how they were taught.”
So Dougherty created First People’s to train teachers to teach math in a more natural, orderly way than rote memorization.
By the mid-2000s, First People’s had become a nonprofit and attracted funding from foundations and the federal government. U.S. Senator Mike Enzi, who went to high school in Sheridan, attached individual funding provisions known as “earmarks,” to the federal education budget in order to fund First People’s. Lawmakers often demanded earmarks to pay for programs in their districts in exchange for supporting a colleague’s bill. While this loosened congressional gridlock, critics of the practice said it turned the federal budget into a fund to reward lawmakers’ favored constituents.
In 2008, First People’s earmark funding exceeded $800,000, according to Taxpayers for Common Sense data. As the program expanded, it offered Strength in Number for free to more than two dozen schools across the West, paying travel and accommodation expenses for teachers who came to Sheridan, and covering the expenses of trainers who visited schools as far away as Alaska.
After the House of Representatives banned earmarks in 2011, First People’s stream of federal money dried up. The center began charging schools for services and many schools dropped out. Administrators at the center said only nine schools are still receiving training from the center today, but others continue to use the methods and train their own staff. Many schools no longer have the money to implement Strength in Number as it was designed.
An amendment to the Wyoming state budget that would have appropriated $285,000 in state money for First People’s died in a legislative committee this spring.
“One problem we have now is that many schools cannot afford to train all of the teachers, and they can’t afford a math interventionist,” said Lucinda “Petey” MacCarty, a teacher/ trainer who has been with First People’s from the beginning.
La Vina Witt, a second grade teacher at St. Stephens Indian School, a Bureau of Indian Affairs school about 20 miles from Wyoming Indian Elementary, is one of the math interventionists who landed in the classroom after budget cuts. When she started at St. Stephens in 2009, she took Strength in Number training in Sheridan, an experience that changed everything she had learned about teaching math in a 35-year career.
“It totally flipped my world upside down,” said Witt, who taught middle school math at non-Native schools in South Dakota before moving to Wyoming. “The philosophy is so different.”
The philosophy, Witt later discovered, is very much like the Common Core. When she learned Strength in Number, she adopted an approach to teaching that, she says, aligns very closely to the new standards.
“Probably the biggest change in my teaching [after learning Strength in Number] is allowing the students to do more discovery,” Witt said. “And giving them the time to do that.”
Like Strength in Number, the Common Core emphasizes the role of guided discovery in student learning as well as the notion that students must prove they understand a concept by explaining how they used it. The new standards also require first and second graders to tackle more difficult concepts than those expected of them in the past.
Witt has read complaints about the standard requiring second graders to add and subtract numbers up to 1,000, and to count by hundreds or thousands. Some critics of Common Core believe this material is appropriate to third grade. From Witt’s point of view, if the concepts are presented correctly, much younger children can work with the bigger numbers.
“When I taught math recovery, which was a first grade intervention, we were [using those bigger numbers] with first graders,” she said.
In her classroom today, she uses many of the techniques she learned in one-on-one teaching. In particular, she relies on the kinds of tools and toys that Williams uses and lets students play with them to seek the answers to the problems.
“You still do some drilling. But you give them the time to try to figure it out, and to explain to you how they are doing it.”
Test scores rose at St. Stephens after teachers began using the First People’s system in 2009, much as they had at the Wyoming Indian Elementary three years earlier. The percentage of students who were proficient or advanced hovered around 25 percent in 2009 and climbed to 67 percent in 2013, according to self-reported data by the school. Scores for the past two years were not available.
While teachers and administrators at both schools are happy to see the higher scores, the state tests have little to do with teachers’ day-to-day assessment of progress in the classroom. Witt and her colleagues have a different measure of mastery.
“If they are applying what they learn to a totally different kind of problem than what you are doing in class, and can carry that over and be able to explain what they are doing, then you know they’ve got it,” Witt said.
What test scores don’t measure
If applying the concepts to a new problem is the standard, then some students who have passed state tests fail to demonstrate mastery of crucial mathematical concepts. Kurt Kinsey, one of the longtime trainers at First People’s, likes to show a video of his interview with an eighth grader from a middle school in Sheridan, one of the highest scoring school district in the state. The student, who passed the state’s standardized PAWS (Proficiency Assessments for Wyoming Students) test in fractions, could find the lowest common denominator in order to add fractions, “invert and multiply” to divide them, and reduce a fraction to choose the right multiple-choice answer. But she could not explain a simple diagram that showed a circle divided into three parts: a half, a third and a sixth. Even after prompting and leading questions, she guessed that the sixth was a third.
“She could use the formal procedures for computations with fractions,” Kinsey said. “But she did so without mastering any fractional thinking. She did not understand what fractions are.”
At both Wyoming Indian and St. Stephens, a significant number of students fall short of proficiency on the PAWS test in the best of years. But according to Witt and many of her colleagues, some of the students miss questions like the one the Sheridan student in Kinsey’s example got right, but understand the concepts she failed to grasp.
“PAWS doesn’t ask you to explain,” Witt said. “If they would give kids credit for being able to explain a strategy and recognize that it’s the most efficient strategy, instead of just [giving credit for] a right answer, the scores would look different. They would say, ‘Yeah, these kids do understand math.’”
Ironically, third grade math scores at Wyoming Indian Elementary dropped sharply after the state aligned its test to the Common Core standards. In 2013-14, only 14 percent of third graders scored at proficient or better. In 2014-15, that number dropped to 7 percent. Scores dropped all around the state during as schools adjusted to the new, more rigorous exam. But the drop was sharper at Wyoming Indian.
“A lot of the math test is really a reading test,” said Owen St. Clair, principal of Wyoming Indian Elementary until he was appointed superintendent of the district in July.
“The wording of the problems is difficult. If our kids aren’t reading at a high level, it’s hard for them to take that test.” St. Clair is quick to say that he is not offering the reading issue as an excuse. “We’re making strides in math. I think we’ve hit the low point and are on the way back.”
Limits of success
At poor reservation schools like Wyoming Indian and St. Stephens, some students who do not score well on the exams — and probably do not understand the mathematical concepts — have problems that go beyond reading and number sense. It is not clear that any change in teaching philosophy will reach them. Craig Ferris is the staff member charged with tracking absences at Wyoming Indian, visiting families, and luring truant students back to school.
“There are about a dozen families that just don’t seem to value education,” Ferris says. “They don’t bring their kids to school, or they bring them one day and then keep them out for a week or more. It’s hard to succeed if you are not in school.”
Wyoming Indian and St. Stephens serve breakfast and lunch to every student, whether or not they technically qualify for a free lunch. In a community with higher than average poverty and crime rates, many students not only come to school hungry, they experience so much stress outside of school that they just cannot concentrate.
“I have had students who were in class but had so much on their mind, they just couldn’t apply themselves to the work,” said Williams, the math interventionist at Wyoming Indian Elementary. “Sometimes, you just have to let them have some time to work things out. We’ll be here when they are able to do the work.”
Most of the time, incorrect answers in class help Witt and Williams see what their students need to work on next. Near the end of her session with Atsa, Williams challenged him to think “in fives” about a new situation. The exercise culminated in the test that Witt says proves mastery: Can the student apply a concept to a new situation and explain what he did?
After a short practice session in counting forward and backward by fives, Williams asked Atsa to create a rectangle of tiles by building rows of five. When he reached three rows of five tiles, Atsa was able to look at the array and see that it contained 15 tiles.
After he created six rows of five tiles, Williams asked Atsa how many tiles were in a row, and how many rows he had. Atsa arrived at those answers: five and six. But when he was asked how many tiles he had altogether, he started to count by twos, instead of fives. He understood the strategy, but he could not apply it to the new situation.
The result is not failure, according to Williams. It is simply a clear diagnosis of the limits of Atsa’s ability to apply a particular concept, counting by fives, to a new problem at this stage of his development.
“We try to look at what he knows and build from there,” Williams said. “This is how we find out what he needs to work on next.”
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