The New York Times – Room for Debate Blog, October 15, 2009
Only 39 percent of fourth graders and 34 percent of eighth graders scored at or above the proficient level on the nationwide math test given this spring. With little improvement over the past six years, it’s seems unlikely that all children will reach grade-level proficiency by 2014, a central goal of the No Child Left Behind law, which imposed federal testing rules on schools nationwide.
Bruce Fuller, professor of education and public policy
Lance T. Izumi, Pacific Research Institute
Holly Tsakiris Horrigan, parent of public school children
Richard Bisk, math professor
Barry Garelick, U.S. Coalition for World Class Math
End Federal Oversight
![]()
Bruce Fuller
Bruce Fuller, professor of education and public policy at University of California, Berkeley, is author of “Standardized Childhood: The Political and Cultural Struggle Over Early Education.”
This week’s dismal test-score results is bad news for President Obama, just as his education secretary, Arne Duncan, begins to rethink Washington’s role in lifting the schools, searching for a less punitive, more robust blend of policies that energize students and teachers alike.
Mechanical forms of testing are not the right tool to gauge the acquisition of complex forms of learning.
The progress of the nation’s fourth graders in mathematics has hit a plateau, while eighth graders did only slightly better compared with their performances a year earlier, according to the National Assessment of Educational Progress. And gaps between students from poor versus middle-class families grew wider. The only good news is that students attending Catholic schools — ironically the institutions sheltered from Washington’s accountability regime — displayed a robust jump in achievement.
In New York, just two-fifths of the state’s fourth graders were found to be proficient in math. This, despite Mayor Michael Bloomberg’s claims of astonishing progress.
Many governors advanced tough-love policies, starting in the 1980s. This state-led accountability strategy — blending clear curriculum standards, atomizing knowledge to fit standardized tests and punishing lifeless schools — worked well for almost two decades. Racial achievement gaps closed significantly during the 1990s. (The school attainment of African-American mothers, a far stronger driver of children’s development, had climbed as well, thanks to earlier affirmative action.)
After George W. Bush arrived in Washington, he quickly agreed with Senator Ted Kennedy of Massachusetts to centralize how student learning should be monitored and measured under the No Child Left Behind law, placing enormous faith in didactic teaching and fill-in-the-bubble tests. But soon, reading scores flattened out. Now we see earlier gains in math petering out as well, more evidence that the clout of Washington’s top-down accountability strategy has weakened considerably.
These latest tests results say something about the culture of standardized testing. While the unrelenting press on teachers to raise scores can succeed in stoking the basic literacy and math skills of weak students, Washington’s accountability regime can’t take students to the next level. And mechanical forms of testing are not the right tool to gauge the acquisition of complex forms of learning. It’s little wonder that good teachers are leaving the profession when political leaders judge their worth solely by their ability to drill-and-kill material that appears on stultifying tests.
Secretary Duncan’s strategy — so far, oddly pulled from George W. Bush’s playbook — aims to experiment with promising innovations, especially those charter schools that consistently boost achievement, and rewarding strong teachers with cash incentives. But reliance on market remedies will do little to attract new teachers who care deeply about children’s growth, or to enrich the craft of mindful teachers.
The culture of standardized testing — legitimated by Washington policies — has served to de-skill and demoralize our best teachers. Sure, the unions must be challenged to purge terrible, burned-out teachers, but until the daily work of teachers becomes more fulfilling, more professional no one should be surprised by the pallid progress of the nation’s students.
Don’t Shoot the Messenger
![]()
Lance T. Izumi
Lance T. Izumi is the senior director of education studies at the Pacific Research Institute.
Disappointing test scores, like the recent National Assessment of Educational Progress math scores, don’t mean that testing systems need to be abandoned. The key question is what have schools, school districts and states done with those results to improve teaching in the classroom? Often times the answer is not much.
The issue is not testing, but what is going on in classrooms that lead to poor test results.
California, for example, has collected longitudinal student testing data going back to 2002, but has expressly prevented this data from being used to evaluate the classroom effectiveness of individual teachers. Education Secretary Arne Duncan has rightly singled out California for putting up this major roadblock to improving both teacher and student performance. Only in the last few days has Gov. Arnold Schwarzenegger signed legislation that allows testing data to be used to measure the effectiveness of teachers and their teaching. Thus, since the No Child Left Behind law was enacted until now, California had banned itself from making the best use of test results.
There are certainly problems with No Child Left Behind, but the law’s encouragement of testing is not one of them. Oakland Charter Academy is a hugely successful middle school in one of the toughest inner-city neighborhoods in Oakland, Calif. One hundred percent of the student body is socio-economically disadvantaged. Yet, on the state’s rigorous algebra 1 exam in 2009, 100 percent of the school’s eighth graders scored at or above the proficient level. Oakland Charter Academy’s principal, Jorge Lopez, says that No Child Left Behind’s testing and progress requirements makes it the “best law that ever happened to minority kids.”
The math achievement at Oakland Charter Academy demonstrates that the issue is not testing, but what is going on in classrooms that lead to poor test results in so many other schools. Teaching methods, curriculum, lack of adequate subject matter knowledge among math teachers and lack of real consequences in school accountability systems, rather than tests and standards, could be the real culprits for low scores. For example, in Massachusetts, eighth graders whose teachers majored in math scored significantly higher on the National Assessment of Educational Progress math exam than peers taught by teachers without a math major. Let’s examine these issues first before concluding that low scores are the result of testing.
It’s the Curriculum, Not the Test
Holly Tsakiris Horrigan, an economist, is the mother of three children who attend public school in Massachusetts.
Not meeting a goal is never justification for deeming the goal unworthy. Standardized tests in can and do help students. Data support this. Standardized tests are essential in identifying what we as adults are doing right for our children and where we are falling short.
If we want to improve mathematics education, we should banish nonsensical curricula like Trail Blazers, Everyday Math and Investigations and make sure that our teachers are properly educated and proficient in math content. These curricula substitute writing, drawing and calculator usage for solid math content, leaving children unprepared for more advanced math topics. The precious few children who go on to succeed in higher math after being subjected to one of these programs are those that had the benefit of substantial reteaching outside of the classroom.
In wealthy towns around Massachusetts where these curricula are widely used and state standards are well defined, tutoring shops and independent instructional programs thrive. Parents in my community with extra time and resources make sure their children get what they need to meet or exceed the standards. It is not surprising that children lacking access to these outside resources aren’t succeeding with the content-poor, misguided curricula.
Some families in Massachusetts (including mine) send their children long distances to attend charter schools like the Advanced Math and Science Academy in Marlborough — a school that has content-rich curricula and high expectations. The Massachusetts standardized testing reveals the success of the school’s approach.
Focus on Mastery of Concepts
![]()
Richard Bisk
Richard Bisk is professor and chair of the Mathematics Department at Worcester State College. He was an adviser to the Massachusetts Department of Education in the development of the “Guidelines for the Mathematical Preparation of Elementary Teachers.”
To give students a firm foundation in math, we must start in the elementary grades by providing three things: a substantial improvement in elementary teachers’ knowledge of mathematics; a more focused curriculum that emphasize core concepts and skills; and more challenging textbooks that teach for mastery and not just exposure.
Many math textbooks now use the ’spiral’ approach, where the same topics are repeated year after year.
Many elementary teachers have strong backgrounds in reading and writing, but will readily admit their discomfort with math. Typically they have taken little mathematics in their teacher training programs. Too often the math they studied has no connection to the math they teach in the classroom.
In Massachusetts, we’ve begun to address this issue through new certification requirements. Prospective elementary teachers will have to pass a math test that assesses their understanding of the mathematics that is taught in the elementary grades. Institutions of higher education in Massachusetts are being asked to provide prospective elementary teachers with a sequence of three math courses to develop their math skills and knowledge. Since these changes do not affect teachers who have already been certified, they need professional development to gain the background we now expect of new teachers.
A second issue is that too many states have curriculum frameworks that have been described as “a mile wide and an inch deep.” The Massachusetts Curriculum Frameworks is considered one of best, but it too suffers from this condition. There are 33 math standards listed for grade 3. One of them includes: “Know multiplication facts through 10 x 10 and related division facts, e.g., 9 x 8 = 72 and 72 ÷ 9 = 8.” But our state testing never assesses student knowledge in this area. How likely is the third grade teacher, who is not a math expert, to sufficiently emphasize this critical area when there are 32 other standards?
Finally, many math textbooks in this country use the “spiral” approach, in which topics are not taught for mastery. Instead they are repeated year after year. I strongly agree with the report of the National Mathematics Advisory Panel, which said, “in elementary school textbooks in the United States, easier arithmetic problems are presented far more frequently than harder problems. The opposite is the case in countries with higher mathematics achievement, such as Singapore.”
Content Over Process
![]()
Barry Garelick
Barry Garelick, an analyst, is the co-founder of the U.S. Coalition for World Class Math, a parent advocacy group.
The recently released national math test scores for 2009 are part of a growing body of lackluster results nationwide since the inception of the No Child Left Behind law. The exam, which has been deemed the “gold standard” of testing is hardly what one would call challenging with respect to math, and yet even so, the scores are barely indicative of a pulse.
Students don’t need skills-free math and “real world” problems, they need to learn the skills and concepts necessary to solve challenging problems.
With the prospect that all students may not achieve proficiency by 2014, finger pointing naturally ensues. Some will contend that we need to go to “authentic testing” that measures how well students use prior knowledge in new situations. This would take the form of open-ended, generally ill-posed problems that allow students to gain points just for attempting to guess an answer. With process trumping content, students would surely show gains, but in the end we still have to ask whether the intents of No Child Left Behind will have been realized. And the answer would most likely be a resounding “no,” though everyone would feel good about the test scores.
What is needed is not another test, but sound mathematics instruction that stresses content over process. The education establishment needs to understand that even process is based on skills and exercises, and a logical sequence of topics whose mastery builds upon itself. We need solid math curricula and textbooks that are based on the premise that procedural fluency leads to conceptual understanding. Problem solving does not exist independently of exercises. The belief that content-based math teaches only definitions and procedures needs to be abandoned.
Students don’t need skills-free math and “real world” problems that are nothing more than data mongering and statistical approaches. Students need to learn the skills and concepts necessary to solve challenging problems.
Do the poor results suggest that testing requirements under “No Child Left Behind” have been ineffective and should be abandoned? What’s lacking in math education that makes progress so hard to achieve?
Disappointing test scores, like the recent National Assessment of Educational Progress math scores, don’t mean that testing systems need to be abandoned. The key question is what have schools, school districts and states done with those results to improve teaching in the classroom? Often times the answer is not much.
California, for example, has collected longitudinal student testing data going back to 2002, but has expressly prevented this data from being used to evaluate the classroom effectiveness of individual teachers. Education Secretary Arne Duncan has rightly singled out California for putting up this major roadblock to improving both teacher and student performance. Only in the last few days has Gov. Arnold Schwarzenegger signed legislation that allows testing data to be used to measure the effectiveness of teachers and their teaching. Thus, since the No Child Left Behind law was enacted until now, California had banned itself from making the best use of test results.
There are certainly problems with No Child Left Behind, but the law’s encouragement of testing is not one of them. Oakland Charter Academy is a hugely successful middle school in one of the toughest inner-city neighborhoods in Oakland, Calif. One hundred percent of the student body is socio-economically disadvantaged. Yet, on the state’s rigorous algebra 1 exam in 2009, 100 percent of the school’s eighth graders scored at or above the proficient level. Oakland Charter Academy’s principal, Jorge Lopez, says that No Child Left Behind’s testing and progress requirements makes it the “best law that ever happened to minority kids.”
The math achievement at Oakland Charter Academy demonstrates that the issue is not testing, but what is going on in classrooms that lead to poor test results in so many other schools. Teaching methods, curriculum, lack of adequate subject matter knowledge among math teachers and lack of real consequences in school accountability systems, rather than tests and standards, could be the real culprits for low scores. For example, in Massachusetts, eighth graders whose teachers majored in math scored significantly higher on the National Assessment of Educational Progress math exam than peers taught by teachers without a math major. Let’s examine these issues first before concluding that low scores are the result of testing.
How to Improve National Math Scores
Pacific Research Institute
The New York Times – Room for Debate Blog, October 15, 2009
Only 39 percent of fourth graders and 34 percent of eighth graders scored at or above the proficient level on the nationwide math test given this spring. With little improvement over the past six years, it’s seems unlikely that all children will reach grade-level proficiency by 2014, a central goal of the No Child Left Behind law, which imposed federal testing rules on schools nationwide.
Bruce Fuller, professor of education and public policy
Lance T. Izumi, Pacific Research Institute
Holly Tsakiris Horrigan, parent of public school children
Richard Bisk, math professor
Barry Garelick, U.S. Coalition for World Class Math
End Federal Oversight
Bruce Fuller
Bruce Fuller, professor of education and public policy at University of California, Berkeley, is author of “Standardized Childhood: The Political and Cultural Struggle Over Early Education.”
This week’s dismal test-score results is bad news for President Obama, just as his education secretary, Arne Duncan, begins to rethink Washington’s role in lifting the schools, searching for a less punitive, more robust blend of policies that energize students and teachers alike.
Mechanical forms of testing are not the right tool to gauge the acquisition of complex forms of learning.
The progress of the nation’s fourth graders in mathematics has hit a plateau, while eighth graders did only slightly better compared with their performances a year earlier, according to the National Assessment of Educational Progress. And gaps between students from poor versus middle-class families grew wider. The only good news is that students attending Catholic schools — ironically the institutions sheltered from Washington’s accountability regime — displayed a robust jump in achievement.
In New York, just two-fifths of the state’s fourth graders were found to be proficient in math. This, despite Mayor Michael Bloomberg’s claims of astonishing progress.
Many governors advanced tough-love policies, starting in the 1980s. This state-led accountability strategy — blending clear curriculum standards, atomizing knowledge to fit standardized tests and punishing lifeless schools — worked well for almost two decades. Racial achievement gaps closed significantly during the 1990s. (The school attainment of African-American mothers, a far stronger driver of children’s development, had climbed as well, thanks to earlier affirmative action.)
After George W. Bush arrived in Washington, he quickly agreed with Senator Ted Kennedy of Massachusetts to centralize how student learning should be monitored and measured under the No Child Left Behind law, placing enormous faith in didactic teaching and fill-in-the-bubble tests. But soon, reading scores flattened out. Now we see earlier gains in math petering out as well, more evidence that the clout of Washington’s top-down accountability strategy has weakened considerably.
These latest tests results say something about the culture of standardized testing. While the unrelenting press on teachers to raise scores can succeed in stoking the basic literacy and math skills of weak students, Washington’s accountability regime can’t take students to the next level. And mechanical forms of testing are not the right tool to gauge the acquisition of complex forms of learning. It’s little wonder that good teachers are leaving the profession when political leaders judge their worth solely by their ability to drill-and-kill material that appears on stultifying tests.
Secretary Duncan’s strategy — so far, oddly pulled from George W. Bush’s playbook — aims to experiment with promising innovations, especially those charter schools that consistently boost achievement, and rewarding strong teachers with cash incentives. But reliance on market remedies will do little to attract new teachers who care deeply about children’s growth, or to enrich the craft of mindful teachers.
The culture of standardized testing — legitimated by Washington policies — has served to de-skill and demoralize our best teachers. Sure, the unions must be challenged to purge terrible, burned-out teachers, but until the daily work of teachers becomes more fulfilling, more professional no one should be surprised by the pallid progress of the nation’s students.
Don’t Shoot the Messenger
Lance T. Izumi
Lance T. Izumi is the senior director of education studies at the Pacific Research Institute.
Disappointing test scores, like the recent National Assessment of Educational Progress math scores, don’t mean that testing systems need to be abandoned. The key question is what have schools, school districts and states done with those results to improve teaching in the classroom? Often times the answer is not much.
The issue is not testing, but what is going on in classrooms that lead to poor test results.
California, for example, has collected longitudinal student testing data going back to 2002, but has expressly prevented this data from being used to evaluate the classroom effectiveness of individual teachers. Education Secretary Arne Duncan has rightly singled out California for putting up this major roadblock to improving both teacher and student performance. Only in the last few days has Gov. Arnold Schwarzenegger signed legislation that allows testing data to be used to measure the effectiveness of teachers and their teaching. Thus, since the No Child Left Behind law was enacted until now, California had banned itself from making the best use of test results.
There are certainly problems with No Child Left Behind, but the law’s encouragement of testing is not one of them. Oakland Charter Academy is a hugely successful middle school in one of the toughest inner-city neighborhoods in Oakland, Calif. One hundred percent of the student body is socio-economically disadvantaged. Yet, on the state’s rigorous algebra 1 exam in 2009, 100 percent of the school’s eighth graders scored at or above the proficient level. Oakland Charter Academy’s principal, Jorge Lopez, says that No Child Left Behind’s testing and progress requirements makes it the “best law that ever happened to minority kids.”
The math achievement at Oakland Charter Academy demonstrates that the issue is not testing, but what is going on in classrooms that lead to poor test results in so many other schools. Teaching methods, curriculum, lack of adequate subject matter knowledge among math teachers and lack of real consequences in school accountability systems, rather than tests and standards, could be the real culprits for low scores. For example, in Massachusetts, eighth graders whose teachers majored in math scored significantly higher on the National Assessment of Educational Progress math exam than peers taught by teachers without a math major. Let’s examine these issues first before concluding that low scores are the result of testing.
It’s the Curriculum, Not the Test
Holly Tsakiris Horrigan, an economist, is the mother of three children who attend public school in Massachusetts.
Not meeting a goal is never justification for deeming the goal unworthy. Standardized tests in can and do help students. Data support this. Standardized tests are essential in identifying what we as adults are doing right for our children and where we are falling short.
If we want to improve mathematics education, we should banish nonsensical curricula like Trail Blazers, Everyday Math and Investigations and make sure that our teachers are properly educated and proficient in math content. These curricula substitute writing, drawing and calculator usage for solid math content, leaving children unprepared for more advanced math topics. The precious few children who go on to succeed in higher math after being subjected to one of these programs are those that had the benefit of substantial reteaching outside of the classroom.
In wealthy towns around Massachusetts where these curricula are widely used and state standards are well defined, tutoring shops and independent instructional programs thrive. Parents in my community with extra time and resources make sure their children get what they need to meet or exceed the standards. It is not surprising that children lacking access to these outside resources aren’t succeeding with the content-poor, misguided curricula.
Some families in Massachusetts (including mine) send their children long distances to attend charter schools like the Advanced Math and Science Academy in Marlborough — a school that has content-rich curricula and high expectations. The Massachusetts standardized testing reveals the success of the school’s approach.
Focus on Mastery of Concepts
Richard Bisk
Richard Bisk is professor and chair of the Mathematics Department at Worcester State College. He was an adviser to the Massachusetts Department of Education in the development of the “Guidelines for the Mathematical Preparation of Elementary Teachers.”
To give students a firm foundation in math, we must start in the elementary grades by providing three things: a substantial improvement in elementary teachers’ knowledge of mathematics; a more focused curriculum that emphasize core concepts and skills; and more challenging textbooks that teach for mastery and not just exposure.
Many math textbooks now use the ’spiral’ approach, where the same topics are repeated year after year.
Many elementary teachers have strong backgrounds in reading and writing, but will readily admit their discomfort with math. Typically they have taken little mathematics in their teacher training programs. Too often the math they studied has no connection to the math they teach in the classroom.
In Massachusetts, we’ve begun to address this issue through new certification requirements. Prospective elementary teachers will have to pass a math test that assesses their understanding of the mathematics that is taught in the elementary grades. Institutions of higher education in Massachusetts are being asked to provide prospective elementary teachers with a sequence of three math courses to develop their math skills and knowledge. Since these changes do not affect teachers who have already been certified, they need professional development to gain the background we now expect of new teachers.
A second issue is that too many states have curriculum frameworks that have been described as “a mile wide and an inch deep.” The Massachusetts Curriculum Frameworks is considered one of best, but it too suffers from this condition. There are 33 math standards listed for grade 3. One of them includes: “Know multiplication facts through 10 x 10 and related division facts, e.g., 9 x 8 = 72 and 72 ÷ 9 = 8.” But our state testing never assesses student knowledge in this area. How likely is the third grade teacher, who is not a math expert, to sufficiently emphasize this critical area when there are 32 other standards?
Finally, many math textbooks in this country use the “spiral” approach, in which topics are not taught for mastery. Instead they are repeated year after year. I strongly agree with the report of the National Mathematics Advisory Panel, which said, “in elementary school textbooks in the United States, easier arithmetic problems are presented far more frequently than harder problems. The opposite is the case in countries with higher mathematics achievement, such as Singapore.”
Content Over Process
Barry Garelick
Barry Garelick, an analyst, is the co-founder of the U.S. Coalition for World Class Math, a parent advocacy group.
The recently released national math test scores for 2009 are part of a growing body of lackluster results nationwide since the inception of the No Child Left Behind law. The exam, which has been deemed the “gold standard” of testing is hardly what one would call challenging with respect to math, and yet even so, the scores are barely indicative of a pulse.
Students don’t need skills-free math and “real world” problems, they need to learn the skills and concepts necessary to solve challenging problems.
With the prospect that all students may not achieve proficiency by 2014, finger pointing naturally ensues. Some will contend that we need to go to “authentic testing” that measures how well students use prior knowledge in new situations. This would take the form of open-ended, generally ill-posed problems that allow students to gain points just for attempting to guess an answer. With process trumping content, students would surely show gains, but in the end we still have to ask whether the intents of No Child Left Behind will have been realized. And the answer would most likely be a resounding “no,” though everyone would feel good about the test scores.
What is needed is not another test, but sound mathematics instruction that stresses content over process. The education establishment needs to understand that even process is based on skills and exercises, and a logical sequence of topics whose mastery builds upon itself. We need solid math curricula and textbooks that are based on the premise that procedural fluency leads to conceptual understanding. Problem solving does not exist independently of exercises. The belief that content-based math teaches only definitions and procedures needs to be abandoned.
Students don’t need skills-free math and “real world” problems that are nothing more than data mongering and statistical approaches. Students need to learn the skills and concepts necessary to solve challenging problems.
Do the poor results suggest that testing requirements under “No Child Left Behind” have been ineffective and should be abandoned? What’s lacking in math education that makes progress so hard to achieve?
Disappointing test scores, like the recent National Assessment of Educational Progress math scores, don’t mean that testing systems need to be abandoned. The key question is what have schools, school districts and states done with those results to improve teaching in the classroom? Often times the answer is not much.
California, for example, has collected longitudinal student testing data going back to 2002, but has expressly prevented this data from being used to evaluate the classroom effectiveness of individual teachers. Education Secretary Arne Duncan has rightly singled out California for putting up this major roadblock to improving both teacher and student performance. Only in the last few days has Gov. Arnold Schwarzenegger signed legislation that allows testing data to be used to measure the effectiveness of teachers and their teaching. Thus, since the No Child Left Behind law was enacted until now, California had banned itself from making the best use of test results.
There are certainly problems with No Child Left Behind, but the law’s encouragement of testing is not one of them. Oakland Charter Academy is a hugely successful middle school in one of the toughest inner-city neighborhoods in Oakland, Calif. One hundred percent of the student body is socio-economically disadvantaged. Yet, on the state’s rigorous algebra 1 exam in 2009, 100 percent of the school’s eighth graders scored at or above the proficient level. Oakland Charter Academy’s principal, Jorge Lopez, says that No Child Left Behind’s testing and progress requirements makes it the “best law that ever happened to minority kids.”
The math achievement at Oakland Charter Academy demonstrates that the issue is not testing, but what is going on in classrooms that lead to poor test results in so many other schools. Teaching methods, curriculum, lack of adequate subject matter knowledge among math teachers and lack of real consequences in school accountability systems, rather than tests and standards, could be the real culprits for low scores. For example, in Massachusetts, eighth graders whose teachers majored in math scored significantly higher on the National Assessment of Educational Progress math exam than peers taught by teachers without a math major. Let’s examine these issues first before concluding that low scores are the result of testing.
Nothing contained in this blog is to be construed as necessarily reflecting the views of the Pacific Research Institute or as an attempt to thwart or aid the passage of any legislation.