Math: Not a spectator sport

To assess the students that fed into the middle school from the elementary school, Ellin Rossberg went to each fifth grade classroom and wrote on the chalkboard in her meticulous handwriting a Shakespearean sonnet with all the Old English spellings, capitalizations and punctuation and asked the students to copy it exactly as it had been written.

From you have I been absent in the spring,
When proud-pied April dress’d in all his trim
Hath put a spirit of youth in every thing,
That heavy Saturn laugh’d and leap’d with him.
Yet nor the lays of birds nor the sweet smell
Of different flowers in odour and in hue
Could make me any summer’s story tell,
Or from their proud lap pluck them where they grew;
Nor did I wonder at the lily’s white,
Nor praise the deep vermilion in the rose;
They were but sweet, but figures of delight,
Drawn after you, you pattern of all those.
Yet seem’d it winter still, and, you away,
As with your shadow I with these did play.

                                                      – William Shakespeare

Teachers collected the copies, reviewed them and sorted students based on the number of errors they made when copying the sonnet. Students with zero or one error went to the “high” group in sixth grade, students with two to three errors went to the “middle” group and students with more than three errors to the “low” group.

Relying on elementary schools for recommendations on group placement was 80 to 85 percent accurate, while Ellin’s placement rate based on this simple test was 95 percent accurate. Initially, I didn’t believe her but she convinced me with data on student transfers that resulted – or didn’t result – from her initial placements.

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When it was introduced, the much vilified English language arts (ELA) Common Core exam administered to students in grades three through eight in New York State was an ordeal taking four-and-a-half hours spread out over three school days. (In 2016, New York State began to rein in test times. )

I saw students vomit over fears about the Common Core tests. The tests take months to grade and the results sort students into four skill groups: excel or well above proficient; proficient; partially proficient; and well below proficient with 98 percent reliability.
Ellin’s test sorted students into three groups instead of four and took little time to produce. She gave students 15 minutes to copy the sonnet and each teacher spent an hour reviewing and scoring an entire class assessment.

And Ellin’s test had 95 percent reliability. So to gain 3 percentage points we spent billions of dollars nationally and invested enormous amounts of teacher and student time. This is part of the reason why the public and especially parents have become increasingly unsupportive of the new testing expectations, opting out and using other tactics to demonstrate their displeasure.

And these new English language arts exams have none of Jim McMahon’s play’s enthusiasm, “soft skill” development and memorability.

I am certain if we could identify one of the key English language arts (ELA) test designers from the international corporation Pearson, which receives (or received) most of the millions of dollars spent nationally on newly required testing, and compel her/him to provide us with a one-hour, one-day ELA test that sorted grade three through eight students into four performance groups based on their ELA skills s/he could do it, reluctantly, but s/he could do it.

The cost and time savings would be enormous. Pearson wouldn’t like it but we need to remember: We pay them and they work for us. We design the tasks and they complete them as we expect.

Wouldn’t test reliability suffer? Yes, reliability would drop from the present 98 percent to between 96 and 97 percent, and we can all live with that. Pearson and a few other companies have controlled the test design process across the country with little competition and (surprise!) they have designed a high-priced, over-engineered monster that makes them millions in profits. As a profit-making enterprise that is their goal. We should not be surprised.

Test secrecy begets fear

The roll-out of the Common Core in New York failed for multiple reasons. Besides over complicating the process, the teachers were unable to review sample tests, which produced fear among teachers, parents and students.

What exactly are they asking the students to do? How will the questions be worded? How can I make certain my students will be ready when I can’t see the test? Such secrecy also prevents teachers from uncovering the errors that always creep into even the best standardized tests.

The reason teachers can’t see the tests is not just for exam security; it’s because of cost. If the tests become public after they’re given, then Pearson and test companies like them have to design completely new tests every year and that costs more money for an already expensive enterprise.

Another reason for the secrecy: Pearson uses the actual tests as a way to integrate potential future test questions that don’t count in student scores (field testing them on the students). Making the tests public is incompatible with test security.

Why not keep the field test questions secret and reveal the questions that count in student scores? We’d save enough with a switch to a one-hour-long test from a four-and-a-half hour test, and then we could release the tests to everyone. It’s a move that would calm a lot of fears.

Releasing the tests would also facilitate work going on in many school districts right now to gear up for the new Common Core standards and test expectations. The smartest districts, principals and teachers are already well on their way to adjusting the curricula, and the huge drop in student proficiency rates seen in the first two years of Common Core test implementation in New York State and other early implementation states will largely be made up in the next 10 years. We could make this process much more efficient and cut the transition time to five years by releasing the tests.

Instructional strategies that make the Common Core work

Anthony Tompkins, a sixth grade teacher in the Common Core training group I attended with Candle Central School District educators, was a tall, slender, 28-year-old African American math teacher. He had been teaching math for seven years and during our three-day-long training session offered some excellent tips on how he’d produced outstanding results on the new Common Core sixth-grade math test – a test students statewide found impossibly difficult.

One of the teachers in our training voiced concern over her students’ weak math fact and computational skills and the time she had to invest to help these students improve these key skills while the students who knew these skills sat on their hands.

“This is one of the few areas where technology can really help,” Anthony told her.
He explained how all of his students use five computers set up in a corner of his classroom in rotating groups during five-minute sessions throughout the class period. During the brief sessions students complete quick math fact and computational challenges at the appropriate level based on their previous performance on the program.

The software program Anthony recommended works on leftover computers found in closets in most schools, and gives the teacher diagnostic information on each student. With that diagnostic information, Anthony zeros in on student weakness and with one or two minutes of focused one-on-one tutoring, while the other students are working on other math activities, moves them past their mini math roadblock. Anthony likened this work on the computer to athletes working out in the weight room every day to gain strength.

Several teachers in the training mentioned not having enough time to cover all the material expected by the new curriculum and the difficult challenge level of the math concepts.

Anthony shook his head: “Man, you guys are stressing way too much and letting these students off too easy,” he said.

For each unit Anthony told them he covered only the topics in the curriculum. And that meant weeding out extraneous topics in the math textbook and in his old lesson plans that were not in the new curriculum, which amounted to about 50 percent of what he had previously taught his students prior to the Common Core standards.

Anthony also said he limited the days he spent on each required topic to the number of days suggested on the state education department’s online curriculum map. For example: Ratios and unit rates, 35 days.

Some teachers objected and said this amounted to spending all their time teaching to the test. Anthony responded that his textbook included every conceivable topic any sixth grade math teacher in the country might address and no one could do justice to all of that curriculum material. Trying to cover the whole textbook was a guaranteed way to ensure the curriculum was a mile wide and an inch deep.

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“By focusing solely on the topics in the curriculum and on the tests, I do a much better job of ensuring students master the critical and more intellectually challenging skills,” Anthony said. And, he said, this approach leaves the teaching of other critical skills to teachers at other grade levels where they belong.

When teachers argued that 35 days for this unit was insufficient, he told them his sixth graders finished the test for the ratios and unit rates on day 28. The trainer, who knew Anthony personally and had planned to use him as a plant to improve the training all along, smiled and asked Anthony to explain how he did this. Anthony described an elaborate and very scientific approach to his work in the classroom.

During the first 20 days of instruction on a unit, each week included three days of what teachers would normally call “instruction.”

Each 40-minute math class began with a two-minute math challenge on the front board based on the previous day’s or week’s lesson. This warm-up activity was collected and graded by Anthony before the next day’s class.

He followed with an eight to 12 minute lecture on the new content and skills he wanted students to understand and use for the rest of that class period. The eight to 12 minutes of lecture included one or two minutes of preview to tie what he was saying into previous lessons and one or two minutes of wrap-up and summary.

“Talk less and teach more” was Anthony’s motto.

What Anthony meant by “teach more” became apparent as he described his methods and what happened in his classroom on a typical day in greater detail. Following his initial mini lecture on the ratio and unit rates unit, he divided his students into groups of four or five, grouping them based on ability and personality type.

These groups then solved math problems related to Anthony’s mini lectures, but with a few problems mixed in from mini lectures from previous days, weeks and months.
Every five minutes, Anthony’s phone alarm sounded and one or two students from each group of four or five would head to the computers to practice math computational and math fact skills for five minutes. When they returned to the group, one of their peers in the group helped them get up to speed on what the group had done during their absence. With five minutes to go in the period Anthony announced he would collect the group’s work in two minutes. When the time came, all of the students handed in their work to
Anthony in a group packet.

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Anthony reviewed student work every day, returned it to students the next day with feedback and gave bonus points on major tests to each group based on the number of correct answers given by the entire group.

If the weaker students performed poorly, their performance negatively impacted the group’s bonus opportunities so the better performing students had an incentive to help their weaker peers. But because the students were working for bonus points on the test, no one was penalized if her/his group did not do well on the tests. Anthony used the errors he saw students making in this group work and on their daily start-up challenges and adjusted the next day’s mini lecture accordingly.

“I figured out early on when I was talking at the front of the room my students weren’t really doing the math; I was doing the math,” Anthony said. “They’re the ones who need to do it with me there to monitor and help them if they’re going to learn.”

This process – a kick-off activity followed by group work – went on each day for the first three days of the week. On day four students completed a 20-minute review activity in groups and took a 20-minute independent test covering the content and skills taught in the three lessons from days one, two and three of the week (with a few review questions from previous units thrown in).

Anthony collected the tests and graded them that night and used the results to break the students into three bigger groups of six to nine students.

The next day in class (the fifth and last day of the week or mini unit) the group of six to nine students with the highest scores on the mini unit test were assigned “challenge” activities requiring them to go beyond what had been taught in class that week with the possibility of earning bonus points for correct solutions to the challenge activities. Some of the students worked on these tasks individually and others worked in groups. They all turned in their completed work at the end of class to be graded.

The six to nine mid-level scorers on the mini unit test were given “extension” activities that reinforced the content and skills at the same level of difficulty demonstrated on the mini unit test.

This same group also worked in small groups of two and three students or singly as they chose and their work was collected at the end of class and graded. Correctly completed “extension” activities could be used to replace incorrect answers on mini unit tests for grading purposes.

Anthony took the remaining six to nine weakest mini unit test performers to the side of the classroom and retaught some of the key concepts they missed on the exam using a different approach. After 12 to 15 minutes of working with the “re-teach group,” Anthony circulated in the room to check on student progress for the other groups while the re-teach group completed tasks he would collect and grade to determine whether or not his re-teach efforts were successful.

Again, corrected work on the re-teach activities was used to replace incorrect answers on the mini unit exam for grade book purposes.

Math: Not a spectator sport

I had the same experience as Anthony when I was a math teacher in the 1970s. After a long day of teaching at the blackboard and overhead projector, I turned around and realized my math students were just sitting back and watching and listening while I did all the work in the front of the classroom.

Their test scores on unit after unit showed that my hard work was not resulting in their understanding and being able to apply what I had taught. It was discouraging to say the least. I remember one day in frustration blurting out to one of my classes: “Math is not a spectator sport. You can’t just sit there and watch me do it.”

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