Khamis, 27 September 2012

Excellence for All

October 2008 | Volume 66 | Number 2
Expecting Excellence Pages 14-19

Excellence for All

Robert J. Sternberg
There's more to excellence than reading, writing, and arithmetic.
What does it mean for a school to be “excellent”? Is it excellent if no one fails but no one does terrifically well either? Is it excellent if the best, but only the best, do superbly? This question is important because the way we define excellence dictates the way we achieve it.

Common Models of Excellence

Let's look at four models of excellence that operate in our schools today. The following portraits are based on real schools that I have observed, although the names are pseudonyms.

Looking Only at the Bottom

Administrators at Shadyside School know which side their bread is buttered on. The district's rewards go to the schools that best meet the mandates of No Child Left Behind (NCLB). So Shadyside has put its resources into ensuring that it looks as good as possible under NCLB's definition of excellence.
The school places heavy emphasis on reading and math. Several other subjects get some attention, but less. The school has dropped physical education and minimized music and art. It has discontinued its gifted program, which, the administration believed, always consumed more resources than it was worth for students who need special services the least.
Heavy spending goes into ensuring that students in the bottom half of the class perform well enough to meet minimum-competency standards. Because many of these low-performing students come from one section of town, some Shadyside administrators have been quietly lobbying for a redistricting plan that would reassign that area to a different school, thus raising Shadyside's test scores.
So far, the result of all these efforts has been modest but noticeable success in enhancing compliance with the federal law.
No Child Left Behind was advocated as a national model for achieving excellence in our schools. But this model is problematic because it focuses attention on only the bottom of the distribution. Imagine a hypothetical school in which, indeed, no child is left behind, but all children are achieving barely passing grades—in letter terms, D-. Would anyone call such a school excellent?
Further, No Child Left Behind encourages schools to drop or minimize important programs that are essential to truly excellent education—such as music, arts, and physical education—because these programs do not boost passing rates on particular tests. Even social studies may get short shrift. Do we really want our schools to resemble the test-preparation cram courses given by private tutoring organizations?
The law discourages schools from providing special services for gifted students because they will pass the tests anyway. It has even motivated some schools to stoop to such dubious practices as encouraging weaker students to drop out. Is this any way to achieve excellence?

Looking Only at the Top

Sunnyvale School is in one of the most economically advantaged sections of a wealthy suburb. The school is considered “la crème de la crème” in the district. To be admitted to Sunnyvale's gifted program, students need to have IQs in the top 1 percent of the general population. The school boasts of the number of its graduates who end up going to Ivy League schools and has a Hall of Fame for its most illustrious graduates.
Sunnyvale puts relatively few resources into students at the academic low end. Because few of these students are actually at risk for failing to meet minimum-competency standards, the administration believes it can afford to focus on stronger students who are likely to succeed in gaining admission to the most prestigious colleges.
The administration's general view is that weaker students do not really belong in the school. In many different, often not-so-subtle ways, the school sends the message to these students that they are a drag on its reputation. For example, academically challenged students tend to get the weakest teachers and diluted courses. Although the school is careful to meet its legal obligations to students with special needs, any parents who demand more are told that they always have the option of a private school.
Sunnyvale's model is the opposite of Shadyside's. Sunnyvale lavishes its attention on the top end, and the result is a Matthew effect—the intellectually rich get richer, and the intellectually poor get poorer. Can we really consider a school excellent if it settles for mediocrity for a large portion of its students and gives only the academic superstars the opportunity to flourish?

Looking Only at the Middle

Brookdale School believes that one size fits all. It does not group students by ability or achievement, nor does it recognize or celebrate any kind of diversity within the heterogeneous groups. The teachers are not sure what to do for students with special needs; some teachers wish that such students would just go away. The school has no gifted program, and it provides the minimum service mandated by law, if that, to students with developmental disabilities.
The school reflects its community, which celebrates social and intellectual conformity. Many of the residents have similar belief structures, which they want to pass on to their children. Excellence, they believe, is a well-rounded child who does what he or she is told and does not stick out through exceptionally weak or strong academic performance. Being popular is good, but being intellectually excellent is suspect. People know that “tall poppies” tend to be cut down.
The administrators and parents of children at Brookdale believe they have created an excellent school and a superb environment for learning. Students and faculty are comfortable with one another, having similar ways of thinking, beliefs, and values.
Brookdale defines academic excellence as intellectual conformity. But Brookdale students are being educated for a world that does not exist—a world in which everyone thinks like they do. Some may be afraid to leave the community because they are unprepared to cope. Those who do leave may be bewildered by and perhaps resentful and intolerant of the astonishing diversity of people, values, ideologies, and worldviews they will encounter. This model of education poorly serves its students and their community because it isolates them from a rapidly changing world. We can hardly view Brookdale as providing an excellent education.

Looking Only at the Statistical Average

Every year, the Riverside Observer publishes the average test scores of the five elementary schools in the Riverside School District as well as those of other districts in the state. The newspaper does a detailed analysis comparing the local schools to one another and comparing the district as a whole to other districts. Parents are well aware that real estate prices coincide closely with the test scores, and the board of education has exerted pressure on district administrators to raise the statistical averages. The five schools in the district engage in a not-always-friendly competition to have the highest average scores. In one school, a principal was reprimanded for engaging in shady practices to enhance his school's ranking: Certain students' scores were “overlooked” when the averages were computed.
Currently, there is a national craze in the United States to raise statistical averages. Such averages are reported in the media and play a prominent role in U.S. News and World Report's ranking of colleges and graduate schools.
Riverside's model looks for excellence in high average scores. Individual students become cogs in a machine that operates like a huge calculator. Students are valued only to the extent that they raise the average scores. The model ignores students at both the upper and lower end—and it dehumanizes all students, including those in the middle.

An Alternative: The Three Rs and the Other Three Rs

A better model for defining and achieving excellence is to focus on excellence in education for all students and let the numbers emerge as a result of seeking excellence, rather than the main goal. Actually, this is what many schools once did before testing mania co-opted education.
The criteria for excellence are neither arcane nor complicated. I propose a simple model that focuses on the traditional three Rs plus what I call the other three Rs (Cogan, Sternberg, & Subotnik, 2006; Sternberg, 2006; Sternberg & Subotnik, 2006). You are probably familiar with the first three Rs: reading, 'riting, and 'rithmetic. So let me focus on the other three: reasoning, resilience, and responsibility. These latter three Rs complement and enhance the first three: It's not either/or, but rather, both/and.


Reasoning is a broad term that encompasses the comprehensive set of thinking skills that a person needs to be an engaged, active citizen of the world. These skills include
  • Creative thinking to generate new and powerful ideas.
  • Critical and analytical thinking to ensure that the ideas (your own and those of others) are good ones.
  • Practical thinking to implement the ideas and persuade others of their value.
  • Wise thinking to ensure that the ideas help build a common good.
Schools can teach reasoning in a number of ways, either through the disciplines (Sternberg & Grigorenko, 2007) or through a separate course (Sternberg, Kaufman, & Grigorenko, 2008). Either way, good reasoning complements knowledge by enabling students to use that knowledge well.
For example, presenting stories like the following can introduce students to scientific reasoning:
Professor Flowers believes that his special plant food, Proflower, helps plants grow to their full potential. He wishes to design an experiment to show that Proflower really does help plants grow. He takes five individual plant stems of each of three types of plants—orchids, tulips, and roses—and carefully places them in his special experimental room. He measures the height of each plant. Then, each day, he places in the soil for each plant exactly 15 drops of Proflower. All plants are watered the exact same amount and receive the same amount of sunshine. After 20 days, he compares the height of each plant to its height 20 days before. He finds that all of the plants have grown by at least 10 percent, and some by more than 20 percent. He then prepares a speech in which he argues that he has scientifically proven that Proflower really does help plants grow.
Is Professor Flowers' reasoning correct? Why or why not?
The answer is that Professor Flowers is not correct. The problem is that there is no control group that received equal amounts of water and light—and no Proflower at all. It is possible that all of the plants in the sample would have grown by the same amount (or more!) if they had not been given Proflower. Hence, Professor Flowers' reasoning is flawed.


Resilience refers to persistence in achieving goals despite the obstacles life places in our way. Some children grow up with many obstacles strewn across their paths; others have relatively smooth roads to travel. Either way, everyone encounters roadblocks sooner or later; the question is how you surmount them. Resilience involves
  • Willingness to defy the crowd in your thinking and actions—to take the road less traveled.
  • Willingness to surmount obstacles in trying to achieve your goals.
  • Passion in your pursuits—going for your goals with drive, motivation, and personal involvement.
  • Self-efficacy—belief in your ability to achieve your goals.
Schools can build students' resilience by modeling it; by implementing programs designed to develop it (see Patrikakou, Weissberg, Redding, Walberg, & Anderson, 2005); and by creating challenging experiences for students that require resilience to see them through.
One way of developing resilience is to tell students about a challenging experience you have had in your own life, preferably when you were about the students' age, and how you got through the challenge. You can then encourage students to share their own challenges and how they have coped with them. The class can discuss what constitutes better and worse coping mechanisms, and how people can decide to employ better ones. (In my own case, when I talk to elementary school students I often tell them of how I used to do poorly on standardized intelligence tests as a child, and nevertheless, when I was 22, I was graduated with highest honors from Yale. Resilience pays off!)
Resilience is an important component of academic excellence. For example, Dweck (1999) found that students who have an incremental view of intelligence—who believe they can modify their intelligence—perform better when faced with challenging courses than do students who believe that intelligence is a stable, fixed entity.


Responsibility covers the ethical and moral dimension of development. Four components are particularly important:
  • Ethics—distinguishing right from wrong.
  • Wisdom—forging or following a path that represents a common good and balances your own interests with those of others.
  • Care—genuine understanding of and empathy for others' well-being that goes beyond an intellectual sense that you should care.
  • Right action—not only knowing the right thing to do, but doing it.
Schools can teach responsibility by modeling it, by providing case studies, and by challenging students with situations that require them to develop their own unique and personal sense of responsibility.
One way to learn about personal responsibility is by reading biographies of people who have shown wisdom and positive ethical values in their own lives. Examples might be Martin Luther King Jr. and Nelson Mandela, both of whom made many personal sacrifices to help others. Mandela spent much of his life in prison before becoming the first president of South Africa in an election with broad participation from South Africans. King led civil rights marches at great personal risk to his life, which he eventually forfeited in the cause of justice for all.
Students can contemplate their own lives and how they have taken opportunities either to work for a common good or to be selfish and look out only for their self-interest. The great leaders of society, and of communities and families, are inevitably those who care about and for others and not just about and for themselves.

Changing Direction

Our society is moving in the wrong direction. If we continue to turn our schools into test-preparation centers, we are neglecting the important three Rs of reasoning, resilience, and responsibility. What's more, test prep is not even an adequate way of teaching the first three R's.
We need to educate students, not merely prepare them for tests. We need to immerse them in the full range of curriculum, including music, the arts, and physical education. We also need special programs that meet the needs of gifted students and those with developmental disabilities.
If we return to education rather than test preparation, we may find that students improve in both the first three Rs and the other three Rs. We must not just concentrate on the top, bottom, middle, or statistical average of the distribution. We must concentrate on all students and teach them how to be active, productive citizens in a rapidly changing world.

How to Teach for the Other 3 Rs

  1. Emphasize excellence for all—not just those at the top, bottom, or middle of the distribution—and recognize diverse forms of excellence.
  2. Provide students with opportunities to learn through multiple modalities.
  3. Value subject matter not only as important in its own right but also as a vehicle for teaching students to think critically.
  4. Value creative thinking applied to a knowledge base, recognizing that knowledge forms the backbone for creativity.
  5. Teach students to apply their learning to practical, real-world problems.
  6. Promote students' dialogical thinking—the ability to understand things from multiple viewpoints and to appreciate diversity.
  7. Promote students' dialectical thinking—the understanding that what is “true” now may not be true in the future and may not have been true in the past.
  8. Teach students to take personal responsibility for mistakes and learn from them.
  9. Teach students to care about people other than themselves and to think about the effects of their actions on others and on institutions, both in the present and in the future.
  10. Teach students to use their knowledge ethically, promoting universal values like sincerity, integrity, honesty, reciprocity, and compassion.


Cogan, J. C., Sternberg, R. J., & Subotnik, R. F. (2006). Integrating the other three Rs into the curriculum. In R. J. Sternberg & R. F. Subotnik (Eds.), Optimizing student success in schools with the other three R's: Reasoning, resilience, and responsibility (pp. 227–238). Greenwich, CT: Information Age.
Dweck, C. S. (1999). Self-theories: Their role in motivation, personality, and development. Philadelphia: Psychology Press.
Patrikakou, E. N., Weissberg, R. P., Redding, S., Walberg, H. J., & Anderson, A. R. (Eds.). (2005). School-family partnerships for children's success. New York: Teachers College Press.
Sternberg, R. J. (2006). Reasoning, resilience, and responsibility from the standpoint of the WICS theory of higher mental processes. In R. J. Sternberg, & R. F. Subotnik (Eds.), Optimizing student success in schools with the other three R's: Reasoning, resilience, and responsibility (pp. 17–37). Greenwich, CT: Information Age.
Sternberg, R. J., & Grigorenko, E. L. (2007). Teaching for successful intelligence (2nd ed.). Thousand Oaks, CA: Corwin Press.
Sternberg, R. J., Jarvin, L., & Grigorenko, E. L. (in press). Teaching for intelligence, creativity, and wisdom. Thousand Oaks, CA: Corwin Press.
Sternberg, R. J., Kaufman, J. C., & Grigorenko, E. L. (2008). Applied intelligence. New York: Cambridge University Press.
Sternberg, R. J., & Subotnik, R. F. (Eds.). (2006). Optimizing student success in schools with the other three R's: Reasoning, resilience, and responsibility. Greenwich, CT: Information Age.
Robert J. Sternberg is Dean of the School of Arts and Sciences, Tufts University, Medford, Massachusetts;
Copyright © 2008 by Association for Supervision and Curriculum Development

Knowing Your Learning Target

March 2011 | Volume 68 | Number 6
What Students Need to Learn Pages 66-69

Knowing Your Learning Target

Connie M. Moss, Susan M. Brookhart and Beverly A. Long
The first thing students need to learn is what they're supposed to be learning.
One of Toni Taladay's students walked into Lenape Elementary School wearing a colorful tie-dyed shirt with a tiny bull's-eye shape in the lower front corner. That small design caught the eye of his classmate, who exclaimed, "Look, Joey, you're wearing a learning target!" In the Armstrong School District in southwestern Pennsylvania, learning targets are everywhere: in lesson plans, on bulletin boards, in hallways—and as this story illustrates—firmly on students' minds.

What Is a Shared Learning Target?

If you own a global positioning system (GPS), you probably can't imagine taking a trip without it. Unlike a printed map, a GPS provides up-to-the-minute information about where you are, the distance to your destination, how long until you get there, and exactly what to do when you make a wrong turn. But a GPS can't do any of that without a precise description of where you want to go.
Think of shared learning targets in the same way. They convey to students the destination for the lesson—what to learn, how deeply to learn it, and exactly how to demonstrate their new learning. In our estimation (Moss & Brookhart, 2009) and that of others (Seidle, Rimmele, & Prenzel, 2005; Stiggins, Arter, Chappuis, & Chappuis, 2009), the intention for the lesson is one of the most important things students should learn. Without a precise description of where they are headed, too many students are "flying blind."

The Dangers of Flying Blind

No matter what we decide students need to learn, not much will happen until students understand what they are supposed to learn during a lesson and set their sights on learning it. Regardless of how important the content, how engaging the activity, how formative the assessment, or how differentiated the instruction, unless all students see, recognize, and understand the learning target from the very beginning of the lesson, one factor will remain constant: The teacher will always be the only one providing the direction, focusing on getting students to meet the instructional objectives. The students, on the other hand, will focus on doing what the teacher says, rather than on learning. This flies in the face of what we know about nurturing motivated, self-regulated, and intentional learners (Zimmerman, 2001).
Students who don't know the intention of a lesson expend precious time and energy trying to figure out what their teachers expect them to learn. And many students, exhausted by the process, wonder why they should even care.
Consider the following high school lesson on Jane Eyre. The teacher begins by saying,
Today, as you read the next chapter, carefully complete your study guide. Pay close attention to the questions about Bertha— Mr. Rochester's first wife. Questions 16 through 35 deal with lunacy and the five categories of mental illness. The next 15 questions focus on facts about Charlotte Brontë's own isolated childhood. The last 10 items ask you to define terms in the novel that we seldom use today—your dictionaries will help you define those words. All questions on Friday's test will come directly from the study guide.
What is important for students to learn in this lesson? Is it how to carefully complete a study guide, the five types of mental illness, facts about Brontë's childhood, meanings of seldom-used words, or facts about Mr. Rochester's first wife? Your guess is as good as ours.

Constructing a Learning Target

A shared learning target unpacks a "lesson-sized" amount of learning—the precise "chunk" of the particular content students are to master (Leahy, Lyon, Thompson, & Wiliam, 2005). It describes exactly how well we expect them to learn it and how we will ask them to demonstrate that learning. And although teachers derive them from instructional objectives, learning targets differ from instructional objectives in both design and function.
Instructional objectives are about instruction, derived from content standards, written in teacher language, and used to guide teaching during a lesson or across a series of lessons. They are not designed for students but for the teacher. A shared learning target, on the other hand, frames the lesson from the students' point of view. A shared learning target helps students grasp the lesson's purpose—why it is crucial to learn this chunk of information, on this day, and in this way.
Students can't see, recognize, and understand what they need to learn until we translate the learning intention into developmentally appropriate, student-friendly, and culturally respectful language. One way to do that is to answer the following three questions from the student's point of view:
  1. What will I be able to do when I've finished this lesson?
  2. What idea, topic, or subject is important for me to learn and understand so that I can do this?
  3. How will I show that I can do this, and how well will I have to do it?
The online-only figure at illustrates this process with examples for younger and older students. Carefully tailor your descriptions to your students' unique developmental levels, cultures, and experiences. A learning target should convey to your students what today's lesson should mean for them.

Beginning to Share

When teachers in the Armstrong School District began sharing learning targets with their students, their early efforts were tentative and in consistent. Not all teachers tried it, and some who tried did not share targets for every lesson. Some simply paraphrased instructional objectives, wrote the target statements on the board, or told students what they were going to learn at the beginning of a lesson. Yet, even their exploratory attempts became game changers. When teachers consistently shared learning targets in meaningful ways, students quickly became more capable decision makers who knew where they were headed and who shared responsibility for getting there.
At Lenape Elementary School, for example, teachers and administrators marveled at the immediate effect of shared targets and how quickly those effects multiplied. Principal Tom Dinga recalls a visit to a 1st grade classroom during the first week of sharing learning targets. The teacher, Brian Kovalovsky, led the class in discussing the learning target for the math lesson that day—to describe basic shapes and compare them to one another. When he asked his students how they would know when they hit that target, one 6-year-old replied, "I'll be able to explain the difference between a square and a rectangle."
Invigorated by the changes they were witnessing, teachers and administrators used e-mail, peer coaching, peer observations, focused walk-throughs, and professional conversations to share what was working in their classrooms and buildings and supported these claims with evidence that their students were learning more and learning smarter.
Students are now more actively engaged in their lessons as full-fledged learning partners. Because they understand exactly what they are supposed to learn, students take a more strategic approach to their work. Students have the information they need to keep track of how well a strategy is working, and they can decide when and if to use that strategy again. In other words, students not only know where they are on the way to mastery, but also are aware of what it will take to get there.

The Power of Meaningful Sharing

Learning targets have no inherent power. They enhance student learning and achievement only when educators commit to consistently and intentionally sharing them with students. Meaningful sharing requires that teachers use the learning targets with their students and students use them with one another. This level of sharing starts when teachers use student-friendly language—and sometimes model or demonstrate what they expect—to explain the learning target from the beginning of the lesson, and when they continue to share it throughout the lesson. Here are two powerful ways to do that.

Designing a Strong Performance of Understanding

The single best way to share a learning target is to create a strong performance of understanding—a learning experience that embodies the learning target. When students complete the actions that are part of a strong performance of understanding, they and their teachers will know that they have reached the target.
When introducing the lesson, the teacher should explicitly share the learning target for the day and explain how each of the tasks that are part of the lesson will lead students toward that target. Remember the lesson on Jane Eyre? Consider this lesson introduction:
Today we will learn more about how Brontë uses her characters to explore the theme of being unwanted. Remember, a theme is an underlying meaning of the story. Yesterday, we examined Jane Eyre's life experiences as they relate to the theme of being unwanted. Today we will do the same for Adele, Mr. Rochester's ward. As you read, find examples of Adele being unwanted, unloved, uncared for, or forgotten. Then, in your learning groups, discuss your examples and your reasons for choosing them. At the end of class, use your notes to draft a short paragraph that answers the question, How does the character of Adele deepen Brontë's theme of being unwanted in the novel Jane Eyre?
Note how the teacher explains what students will learn that day and how each task explicitly connects to that target. If students perform all of these actions, they will better understand how Brontë uses her characters to explore the theme of being unwanted. The tasks clearly lead students to the target, and the students can see how each task leads them to their goal. A strong performance of understanding helps students understand what is important to learn, provides experiences that will help them learn it, and gives them a chance to observe their growing competence along the way.

Explaining the Criteria for Success

Success criteria are developmentally appropriate descriptions and concrete examples of what success in a lesson looks like. They are not the grades students should earn, the number of problems they must get right, or the number of times they should include something in a performance or product (for example, how many descriptive adjectives they should include in a paragraph).
"I can" statements, like those pictured on p. 67, are a great way to explain success. Another useful strategy is to ask students to examine work samples that represent various levels of quality and discuss what makes some samples better than others. Teachers can also use rubrics to define the elements of a successful performance or product and describe various performance levels for each element. An especially powerful way to do this is to have students apply a rubric's organized criteria to work samples with various levels of quality. Then ask students to explain their decisions using the language in the rubric. When students know the success criteria, they can be mindful of what success looks like as they use the rubric to guide their learning.

Empowering Every Student

Armstrong teachers began embedding learning targets into their lessons in October 2009. Now, almost a year and one-half later, shared learning targets guide lesson planning, formative assessment, and classroom walk-throughs. But the most impressive transformation is that of students into full learning partners. Now that students know where they are going, they are more motivated to do the work to get there.
It's just this simple. Do we want classrooms full of empowered, self-regulated, highly motivated, and intentional learners? If we do, then it is time to own up to the obstacles that educators create by withholding the very information that would empower learners. Students cannot regulate learning, use thoughtful reasoning processes, set meaningful goals, or assess the quality of their own work unless they understand what success looks like in today's lesson.


Leahy, S., Lyon, C., Thompson, M., & Wiliam, D. (2005). Classroom assessment: Minute by minute, and day by day.Educational Leadership, 63(3), 18–24.
Moss, C. M., & Brookhart, S. M. (2009). Advancing formative assessment in every classroom: A guide for the instructional leader. Alexandria, VA: ASCD.
Seidle, T., Rimmele, R., & Prenzel, M. (2005). Clarity and coherence of lesson goals as a scaffold for student learning. Learning and Instruction, 15, 539–556.
Stiggins, R. J., Arter, J. A., Chappuis, J., & Chappuis, S. (2009). Classroom assessment FOR learning: Doing it right—using it well. Columbus, OH: Allyn and Bacon.
Zimmerman, B. J. (2001). Theories of self-regulated learning and academic achievement: An overview and analysis. In B. J. Zimmerman & D. H. Schunk (Eds.), Self-regulated learning and academic achievement: Theoretical perspectives (pp. 1–65). Mahwah, NJ: Erlbaum.
Connie M. Moss is director of the Center for Advancing the Study of Teaching and Learning (CASTL) in the School of Education at Duquesne University in Pittsburgh, Pennsylvania; Susan M. Brookhart is an independent educational consultant based in Helena, Montana, and a senior research associate in the School of Education at Duquesne University; Beverly A. Long is coordinator of P–12 Curriculum, Instruction, and Assessment and Accountability for the Armstrong School District in Ford City, Pennsylvania;
Copyright © 2011 by ASCD

How Classroom Assessments Improve Learning

February 2003 | Volume 60 | Number 5
Using Data to Improve Student Achievement Pages 6-11

How Classroom Assessments Improve Learning

Thomas R. Guskey
Teachers who develop useful assessments, provide corrective instruction, and give students second chances to demonstrate success can improve their instruction and help students learn.
Large-scale assessments, like all assessments, are designed for a specific purpose. Those used in most states today are designed to rank-order schools and students for the purposes of accountability—and some do so fairly well. But assessments designed for ranking are generally not good instruments for helping teachers improve their instruction or modify their approach to individual students. First, students take them at the end of the school year, when most instructional activities are near completion. Second, teachers don't receive the results until two or three months later, by which time their students have usually moved on to other teachers. And third, the results that teachers receive usually lack the level of detail needed to target specific improvements (Barton, 2002; Kifer, 2001).
The assessments best suited to guide improvements in student learning are the quizzes, tests, writing assignments, and other assessments that teachers administer on a regular basis in their classrooms. Teachers trust the results from these assessments because of their direct relation to classroom instructional goals. Plus, results are immediate and easy to analyze at the individual student level. To use classroom assessments to make improvements, however, teachers must change both their view of assessments and their interpretation of results. Specifically, they need to see their assessments as an integral part of the instruction process and as crucial for helping students learn.
Despite the importance of assessments in education today, few teachers receive much formal training in assessment design or analysis. A recent survey showed, for example, that fewer than half the states require competence in assessment for licensure as a teacher (Stiggins, 1999). Lacking specific training, teachers rely heavily on the assessments offered by the publisher of their textbooks or instructional materials. When no suitable assessments are available, teachers construct their own in a haphazard fashion, with questions and essay prompts similar to the ones that their teachers used. They treat assessments as evaluation devices to administer when instructional activities are completed and to use primarily for assigning students' grades.
To use assessments to improve instruction and student learning, teachers need to change their approach to assessments in three important ways.

Make Assessments Useful

For Students

Nearly every student has suffered the experience of spending hours preparing for a major assessment, only to discover that the material that he or she had studied was different from what the teacher chose to emphasize on the assessment. This experience teaches students two un-fortunate lessons. First, students realize that hard work and effort don't pay off in school because the time and effort that they spent studying had little or no influence on the results. And second, they learn that they cannot trust their teachers (Guskey, 2000a). These are hardly the lessons that responsible teachers want their students to learn.
Nonetheless, this experience is common because many teachers still mistakenly believe that they must keep their assessments secret. As a result, students come to regard assessments as guessing games, especially from the middle grades on. They view success as depending on how well they can guess what their teachers will ask on quizzes, tests, and other assessments. Some teachers even take pride in their ability to out-guess students. They ask questions about isolated concepts or obscure understandings just to see whether students are reading carefully. Generally, these teachers don't include such “gotcha” questions maliciously, but rather—often unconsciously—because such questions were asked of them when they were students.
Classroom assessments that serve as meaningful sources of information don't surprise students. Instead, these assessments reflect the concepts and skills that the teacher emphasized in class, along with the teacher's clear criteria for judging students' performance. These concepts, skills, and criteria align with the teacher's instructional activities and, ideally, with state or district standards. Students see these assessments as fair measures of important learning goals. Teachers facilitate learning by providing students with important feedback on their learning progress and by helping them identify learning problems (Bloom, Madaus, & Hastings, 1981; Stiggins, 2002).
Critics sometimes contend that this approach means “teaching to the test.” But the crucial issue is, What determines the content and methods of teaching? If the test is the primary determinant of what teachers teach and how they teach it, then we are indeed “teaching to the test.” But if desired learning goals are the foundation of students' instructional experiences, then assessments of student learning are simply extensions of those same goals. Instead of “teaching to the test,” teachers are more accurately “testing what they teach.” If a concept or skill is important enough to assess, then it should be important enough to teach. And if it is not important enough to teach, then there's little justification for assessing it.

For Teachers

The best classroom assessments also serve as meaningful sources of information for teachers, helping them identify what they taught well and what they need to work on. Gathering this vital information does not require a sophisticated statistical analysis of assessment results. Teachers need only make a simple tally of how many students missed each assessment item or failed to meet a specific criterion. State assessments sometimes provide similar item-by-item information, but concerns about item security and the cost of developing new items each year usually make assessment developers reluctant to offer such detailed information. Once teachers have made specific tallies, they can pay special attention to the trouble spots—those items or criteria missed by large numbers of students in the class.
In reviewing these results, the teacher must first consider the quality of the item or criterion. Perhaps the question is ambiguously worded or the criterion is unclear. Perhaps students mis-interpreted the question. Whatever the case, teachers must determine whether these items adequately address the knowledge, understanding, or skill that they were intended to measure.
If teachers find no obvious problems with the item or criterion, then they must turn their attention to their teaching. When as many as half the students in a class answer a clear question incorrectly or fail to meet a particular criterion, it's not a student learning problem—it's a teaching problem. Whatever teaching strategy was used, whatever examples were employed, or whatever explanation was offered, it simply didn't work.
Analyzing assessment results in this way means setting aside some powerful ego issues. Many teachers may initially say, “I taught them. They just didn't learn it!” But on reflection, most recognize that their effectiveness is not defined on the basis of what they do as teachers but rather on what their students are able to do. Can effective teaching take place in the absence of learning? Certainly not.
Some argue that such a perspective puts too much responsibility on teachers and not enough on students. Occasionally, teachers respond, “Don't students have responsibilities in this process? Shouldn't students display initiative and personal accountability?”
Indeed, teachers and students share responsibility for learning. Even with valiant teaching efforts, we cannot guarantee that all students will learn everything excellently. Only rarely do teachers find items or assessment criteria that every student answers correctly. A few students are never willing to put forth the necessary effort, but these students tend to be the exception, not the rule. If a teacher is reaching fewer than half of the students in the class, the teacher's method of instruction needs to improve. And teachers need this kind of evidence to help target their instructional improvement efforts.

Follow Assessments with Corrective Instruction

If assessments provide information for both students and teachers, then they cannot mark the end of learning. Instead, assessments must be followed by high-quality, corrective instruction designed to remedy whatever learning errors the assessment identified (see Guskey, 1997). To charge ahead knowing that students have not learned certain concepts or skills well would be foolish. Teachers must therefore follow their assessments with instructional alternatives that present those concepts in new ways and engage students in different and more appropriate learning experiences.
High-quality, corrective instruction is not the same as reteaching, which often consists simply of restating the original explanations louder and more slowly. Instead, the teacher must use approaches that accommodate differences in students' learning styles and intelligences (Sternberg, 1994). Although teachers generally try to incorporate different teaching approaches when they initially plan their lessons, corrective instruction involves extending and strengthening that work. In addition, those students who have few or no learning errors to correct should receive enrichment activities to help broaden and expand their learning. Materials designed for gifted and talented students provide an excellent resource for such activities.
Developing ideas for corrective instruction and enrichment activities can be difficult, especially if teachers believe that they must do it alone, but structured professional development opportunities can help teachers share strategies and collaborate on teaching techniques (Guskey, 1998, 2000b). Faculty meetings devoted to examining classroom assessment results and developing alternative strategies can be highly effective. District-level personnel and collaborative partnerships with local colleges and universities offer wonderful resources for ideas and practical advice.
Occasionally, teachers express concern that if they take time to offer corrective instruction, they will sacrifice curriculum coverage. Because corrective work is initially best done during class and under the teacher's direction, early instructional units will typically involve an extra class period or two. Teachers who ask students to complete corrective work independently, outside of class, generally find that those students who most need to spend time on corrective work are the least likely to do so.
As students become accustomed to this corrective process and realize the personal benefits it offers, however, the teacher can drastically reduce the amount of class time allocated to such work and accomplish much of it through homework assignments or in special study sessions before or after school. And by not allowing minor errors to become major learning problems, teachers better prepare students for subsequent learning tasks, eventually need less time for corrective work (Whiting, Van Burgh, & Render, 1995), and can proceed at a more rapid pace in later learning units. By pacing their instructional units more flexibly, most teachers find that they need not sacrifice curriculum coverage to offer students the benefits of corrective instruction.

Give Second Chances to Demonstrate Success

To become an integral part of the instructional process, assessments cannot be a one-shot, do-or-die experience for students. Instead, assessments must be part of an ongoing effort to help students learn. And if teachers follow assessments with helpful corrective instruction, then students should have a second chance to demonstrate their new level of competence and understanding. This second chance helps determine the effectiveness of the corrective instruction and offers students another opportunity to experience success in learning.
Writing teachers have long recognized the many benefits of a second chance. They know that students rarely write well on an initial attempt. Teachers build into the writing process several opportunities for students to gain feedback on early drafts and then to use that feedback to revise and improve their writing. Teachers of other subjects frequently balk at the idea, however—mostly because it differs from their personal learning experiences.
Some teachers express concern that giving students a second chance might be unfair and that “life isn't like that.” They point out that that a surgeon doesn't get a second chance to perform an operation successfully and a pilot doesn't get a second chance to land a jumbo jet safely. Because of the very high stakes involved, each must get it right the first time.
But how did these highly skilled professionals learn their craft? The first operation performed by that surgeon was on a cadaver—a situation that allows a lot of latitude for mistakes. Similarly, the pilot spent many hours in a flight simulator before ever attempting a landing from the cockpit. Such experiences allowed them to learn from their mistakes and to improve their performance. Similar instructional techniques are used in nearly every professional endeavor. Only in schools do student face the prospect of one-shot, do-or-die assessments, with no chance to demonstrate what they learned from previous mistakes.
All educators strive to have their students become lifelong learners and develop learning-to-learn skills. What better learning-to-learn skill is there than learning from one's mistakes? A mistake can be the beginning of learning. Some assessment experts argue, in fact, that students learn nothing from a successful performance. Rather, students learn best when their initial performance is less than successful, for then they can gain direction on how to improve (Wiggins, 1998).
Other teachers suggest that it's unfair to offer the same privileges and high grades to students who require a second chance that we offer to those students who demonstrate a high level of learning on the initial assessment. After all, these students may simply have failed to prepare appropriately. Certainly, we should recognize students who do well on the initial assessment and provide opportunities for them to extend their learning through enrichment activities. But those students who do well on a second assessment have also learned well. More important, their poor performance on the first assessment may not have been their fault. Maybe the teaching strategies used during the initial instruction were inappropriate for these students, but the corrective instruction proved more effective. If we determine grades on the basis of performance and these students have performed at a high level, then they certainly deserve the same grades as those who scored well on their first try.
A comparable example is the driver's license examination. Many individuals do not pass their driver's test on the first attempt. On the second or third try, however, they may reach the same high level of performance as others did on their first. Should these drivers be restricted, for instance, to driving in fair weather only? In inclement weather, should they be required to pull their cars over and park until the weather clears? Of course not. Because they eventually met the same high performance standards as those who passed on their initial attempt, they receive the same privileges. The same should hold true for students who show that they, too, have learned well.

Similar Situations

Using assessments as sources of information, following assessments with corrective instruction, and giving students a second chance are steps in a process that all teachers use naturally when they tutor individual students. If the student makes a mistake, the teacher stops and points out the mistake. The teacher then explains that concept in a different way. Finally, the teacher asks another question or poses a similar problem to ensure the student's understanding before going on. The challenge for teachers is to use their classroom assessments in similar ways to provide all students with this sort of individualized assistance.
Successful coaches use the same process. Immediately following a gymnast's performance on the balance beam, for example, the coach explains to her what she did correctly and what could be improved. The coach then offers specific strategies for improvement and encourages her to try again. As the athlete repeats her performance, the coach watches carefully to ensure that she has corrected the problem.
Successful students typically know how to take corrective action on their own. They save their assessments and review the items or criteria that they missed. They rework problems, look up answers in their textbooks or other resource materials, and ask the teacher about ideas or concepts that they don't understand. Less successful students rarely take such initiative. After looking at their grades, they typically crumple up their assessments and deposit them in the trash can as they leave the classroom. Teachers who use classroom assessments as part of the instructional process help all of their students do what the most successful students have learned to do for themselves.

The Benefits of Assessment

Using classroom assessment to improve student learning is not a new idea. More than 30 years ago, Benjamin Bloom showed how to conduct this process in practical and highly effective ways when he described the practice of mastery learning (Bloom, 1968, 1971). But since that time, the emphasis on assessments as tools for accountability has diverted attention from this more important and fundamental purpose.
Assessments can be a vital component in our efforts to improve education. But as long as we use them only as a means to rank schools and students, we will miss their most powerful benefits. We must focus instead on helping teachers change the way they use assessment results, improve the quality of their classroom assessments, and align their assessments with valued learning goals and state or district standards. When teachers' classroom assessments become an integral part of the instructional process and a central ingredient in their efforts to help students learn, the benefits of assessment for both students and teachers will be boundless.


Barton, P. E. (2002). Staying on course in education reform. Princeton, NJ: Statistics & Research Division, Policy Information Center, Educational Testing Service.
Bloom, B. S. (1968). Learning for mastery. Evaluation Comment (UCLA-CSEIP), 1(2), 1–12.
Bloom, B. S. (1971). Mastery learning. In J. H. Block (Ed.), Mastery learning: Theory and practice. New York: Holt, Rinehart & Winston.
Bloom, B. S., Madaus, G. F., & Hastings, J. T. (1981). Evaluation to improve learning. New York: McGraw-Hill.
Guskey, T. R. (1997). Implementing mastery learning (2nd ed.). Belmont, CA: Wadsworth.
Guskey, T. R. (1998). Making time to train your staff. The School Administrator, 55(7), 35–37.
Guskey, T. R. (2000a). Twenty questions? Twenty tools for better teaching. Principal Leadership, 1(3), 5–7.
Guskey, T. R. (2000b). Evaluating professional development. Thousand Oaks, CA: Corwin Press.
Kifer, E. (2001). Large-scale assessment: Dimensions, dilemmas, and policies. Thousand Oaks, CA: Corwin Press.
Sternberg, R. J. (1994). Allowing for thinking styles. Educational Leadership, 52(3), 36–40.
Stiggins, R. J. (1999). Evaluating classroom assessment training in teacher education programs. Educational Measurement: Issues and Practice, 18(1), 23–27.
Stiggins, R. J. (2002). Assessment crisis: The absence of assessment for learning. Phi Delta Kappan, 83(10), 758–765.
Whiting, B., Van Burgh, J. W., & Render, G. F. (1995). Mastery learning in the classroom. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
Wiggins, G. (1998). Educative assessment. San Francisco: Jossey-Bass.
Thomas R. Guskey is Professor of Education Policy Studies and Evaluation, College of Education, University of Kentucky, Taylor Education Bldg., Lexington, KY 40506;
Copyright © 2003 by Thomas R. Guskey

Nine Ways to Catch Kids Up

Summer 2008 | Volume 65
Best of Educational Leadership 2007–2008 Pages 16-21

Nine Ways to Catch Kids Up

Marilyn Burns
How do we help floundering students who lack basic math concepts?
Paul, a 4th grader, was struggling to learn multiplication. Paul's teacher was concerned that he typically worked very slowly in math and “didn't get much done.” I agreed to see whether I could figure out the nature of Paul's difficulty. Here's how our conversation began:
Marilyn: Can you tell me something you know about multiplication?
Paul: [Thinks, then responds] 6 × 8 is 48.
Marilyn: Do you know how much 6 × 9 is?
Paul: I don't know that one. I didn't learn it yet.
Marilyn: Can you figure it out some way?
Paul: [Sits silently for a moment and then shakes his head.]
Marilyn: How did you learn 6 × 8?
Paul: [Brightens and grins] It's easy—goin' fishing, got no bait, 6 × 8 is 48.
As I talked with Paul, I found out that multiplication was a mystery to him. Because of his weak foundation of understanding, he was falling behind his classmates, who were multiplying problems like 683 × 4. Before he could begin to tackle such problems, Paul needed to understand the concept of multiplication and how it connects to addition.
Paul wasn't the only student in this class who was floundering. Through talking with teachers and drawing on my own teaching experience, I've realized that in every class a handful of students are at serious risk of failure in mathematics and aren't being adequately served by the instruction offered. What should we do for such students?

Grappling with Interventions

My exchange with Paul reminded me of three issues that are essential to teaching mathematics:
  • It's important to help students make connections among mathematical ideas so they do not see these ideas as disconnected facts. (Paul saw each multiplication fact as a separate piece of information to memorize.)
  • It's important to build students' new understandings on the foundation of their prior learning. (Paul did not make use of what he knew about addition to figure products.)
  • It's important to remember that students' correct answers, without accompanying explanations of how they reason, are not sufficient for judging mathematical understanding. (Paul's initial correct answer about the product of 6 × 8 masked his lack of deeper understanding.)
For many years, my professional focus has been on finding ways to more effectively teach arithmetic, the cornerstone of elementary mathematics. Along with teaching students basic numerical concepts and skills, instruction in number and operations prepares them for algebra. I've developed lessons that help students make sense of number and operations with attention to three important elements—computation, number sense, and problem solving. My intent has been to avoid the “yours is not to question why, just invert and multiply” approach and to create lessons that are accessible to all students and that teach skills in the context of deeper understanding. Of course, even well-planned lessons will require differentiated instruction, and much of the differentiation needed can happen within regular classroom instruction.
But students like Paul present a greater challenge. Many are already at least a year behind and lack the foundation of mathematical understanding on which to build new learning. They may have multiple misconceptions that hamper progress. They have experienced failure and lack confidence.
Such students not only demand more time and attention, but they also need supplemental instruction that differs from the regular program and is designed specifically for their success. I've recently shifted my professional focus to thinking about the kind of instruction we need to serve students like Paul. My colleagues and I have developed lessons that provide effective interventions for teaching number and operations to those far behind. We've grappled with how to provide instruction that is engaging, offers scaffolded instruction in bite-sized learning experiences, is paced for students' success, provides the practice students need to cement fragile understanding and skills, and bolsters students' mathematical foundations along with their confidence.
In developing intervention instruction, I have reaffirmed my longtime commitment to helping students learn facts and skills—the basics of arithmetic. But I've also reaffirmed that “the basics” of number and operations for all students, including those who struggle, must address all three aspects of numerical proficiency—computation, number sense, and problem solving. Only when the basics include understanding as well as skill proficiency will all students learn what they need for their continued success.

Essential Strategies

I have found the following nine strategies to be essential to successful intervention instruction for struggling math learners. Most of these strategies will need to be applied in a supplementary setting, but teachers can use some of them in large-group instruction.

1. Determine and Scaffold the Essential Mathematics Content

Determining the essential mathematics content is like peeling an onion—we must identify those concepts and skills we want students to learn and discard what is extraneous. Only then can teachers scaffold this content, organizing it into manageable chunks and sequencing these chunks for learning.
For Paul to multiply 683 × 4, for example, he needs a collection of certain skills. He must know the basic multiplication facts. He needs an understanding of place value that allows him to think about 683 as 600 + 80 + 3. He needs to be able to apply the distributive property to figure and then combine partial products. For this particular problem, he needs to be able to multiply 4 by 3 (one of the basic facts); 4 by 80 (or 8 × 10, a multiple of 10); 4 and by 600 (or 6 × 100, a multiple of a power of 10). To master multidigit multiplication, Paul must be able to combine these skills with ease. Thus, lesson planning must ensure that each skill is explicitly taught and practiced.

2. Pace Lessons Carefully

We've all seen the look in students' eyes when they get lost in math class. When it appears, ideally teachers should stop, deal with the confusion, and move on only when all students are ready. Yet curriculum demands keep teachers pressing forward, even when some students lag behind. Students who struggle typically need more time to grapple with new ideas and practice new skills in order to internalize them. Many of these students need to unlearn before they relearn.

3. Build in a Routine of Support

Students are quick to reveal when a lesson hasn't been scaffolded sufficiently or paced slowly enough: As soon as you give an assignment, hands shoot up for help. Avoid this scenario by building in a routine of support to reinforce concepts and skills before students are expected to complete independent work. I have found a four-stage process helpful for supporting students.
In the first stage, the teacher models what students are expected to learn and records the appropriate mathematical representation on the board. For example, to simultaneously give students practice multiplying and experience applying the associative and commutative properties, we present them with problems that involve multiplying three one-digit factors. An appropriate first problem is 2 × 3 × 4. The teacher thinks aloud to demonstrate three ways of working this problem. He or she might say,
I could start by multiplying 2 × 3 to get 6, and then multiply 6 × 4 to get 24. Or I could first multiply 2 × 4, and then multiply 8 × 3, which gives 24 again. Or I could do 3 × 4, and then 12 × 2. All three ways produce the same product of 24.
As the teacher describes these operations, he or she could write on the board:

It's important to point out that solving a problem in more than one way is a good strategy for checking your answer.
In the second stage, the teacher models again with a similar problem—such as 2 × 4 × 5—but this time elicits responses from students. For example, the teacher might ask, “Which two factors might you multiply first? What is the product of those two factors? What should we multiply next? What is another way to start?” Asking such questions allows the teacher to reinforce correct mathematical vocabulary. As students respond, the teacher again records different ways to solve the problem on the board.
During the third stage, the teacher presents a similar problem—for example, 2 × 3 × 5. After taking a moment to think on their own, students work in pairs to solve the problem in three different ways, recording their work. As students report back to the class, the teacher writes on the board and discusses their problem-solving choices with the group.
In the fourth stage, students work independently, referring to the work recorded on the board if needed. This routine both sets an expectation for student involvement and gives learners the direction and support they need to be successful.

4. Foster Student Interaction

We know something best once we've taught it. Teaching entails communicating ideas coherently, which requires the one teaching to formulate, reflect on, and clarify those ideas—all processes that support learning. Giving students opportunities to voice their ideas and explain them to others helps extend and cement their learning.
Thus, to strengthen the math understandings of students who lag behind, make student interaction an integral part of instruction. You might implement the think-pair-share strategy, also called turn and talk. Students are first asked to collect their thoughts on their own, and then talk with a partner; finally, students share their ideas with the whole group. Maximizing students' opportunities to express their math knowledge verbally is particularly valuable for students who are developing English language skills.

5. Make Connections Explicit

Students who need intervention instruction typically fail to look for relationships or make connections among mathematical ideas on their own. They need help building new learning on what they already know. For example, Paul needed explicit instruction to understand how thinking about 6 × 8 could give him access to the solution for 6 × 9. He needed to connect the meaning of multiplication to what he already knew about addition (that 6 × 8 can be thought of as combining 6 groups of 8). He needed time and practice to cement this understanding for all multiplication problems. He would benefit from investigating six groups of other numbers—6 × 2, 6 × 3, and so on—and looking at the numerical pattern of these products. Teachers need to provide many experiences like these, carefully sequenced and paced, to prepare students like Paul to grasp ideas like how 6 × 9 connects to 6 × 8.

6. Encourage Mental Calculations

Calculating mentally builds students' ability to reason and fosters their number sense. Once students have a foundational understanding of multiplication, it's key for them to learn the basic multiplication facts—but their experience with multiplying mentally should expand beyond these basics. For example, students should investigate patterns that help them mentally multiply any number by a power of 10. I am concerned when I see a student multiply 18 × 10, for example, by reaching for a pencil and writing:

Revisiting students' prior work with multiplying three factors can help develop their skills with multiplying mentally. Helping students judge which way is most efficient to multiply three factors, depending on the numbers at hand, deepens their understanding. For example, to multiply 2 × 9 × 5, students have the following options:

Guiding students to check for factors that produce a product of 10 helps build the tools they need to reason mathematically.
When students calculate mentally, they can estimate before they solve problems so that they can judge whether the answer they arrive at makes sense. For example, to estimate the product of 683 × 4, students could figure out the answer to 700 × 4. You can help students multiply 700 × 4 mentally by building on their prior experience changing three-factor problems to two-factor problems: Now they can change a two-factor problem—700 × 4—into a three-factor problem that includes a power of 10—7 × 100 × 4. Encourage students to multiply by the power of 10 last for easiest computing.

7. Help Students Use Written Calculations to Track Thinking

Students should be able to multiply 700 × 4 in their heads, but they'll need pencil and paper to multiply 683 × 4. As students learn and practice procedures for calculating, their calculating with paper and pencil should be clearly rooted in an understanding of math concepts. Help students see paper and pencil as a tool for keeping track of how they think. For example, to multiply 14 × 6 in their heads, students can first multiply 10 × 6 to get 60, then 4 × 6 to get 24, and then combine the two partial products, 60 and 24. To keep track of the partial products, they might write:
14 × 6
10 × 6 = 60
4 × 6 = 24
60 + 24 = 84
They can also reason and calculate this way for problems that involve multiplying by three-digit numbers, like 683 × 4.

8. Provide Practice

Struggling math students typically need a great deal of practice. It's essential that practice be directly connected to students' immediate learning experiences. Choose practice problems that support the elements of your scaffolded instruction, always promoting understanding as well as skills. I recommend giving assignments through the four-stage support routine, allowing for a gradual release to independent work.
Games can be another effective way to stimulate student practice. For example, a game like Pathways (see Figure 1 for a sample game board and instructions) gives students practice with multiplication. Students hone multiplication skills by marking boxes on the board that share a common side and that each contain a product of two designated factors.

Figure 1. Pathways Multiplication Game

9. Build In Vocabulary Instruction

The meanings of words in math—for example, even, odd, product, and factor—often differ from their use in common language. Many students needing math intervention have weak mathematical vocabularies. It's key that students develop a firm understanding of mathematical concepts before learning new vocabulary, so that they can anchor terminology in their understanding. We should explicitly teach vocabulary in the context of a learning activity and then use it consistently. A math vocabulary chart can help keep both teacher and students focused on the importance of accurately using math terms.

When Should We Offer Intervention?

There is no one answer to when teachers should provide intervention instruction on a topic a particular student is struggling with. Three different timing scenarios suggest themselves, each with pluses and caveats.

While the Class Is Studying the Topic

Extra help for struggling learners must be more than additional practice on the topic the class is working on. We must also provide comprehensive instruction geared to repairing the student's shaky foundation of understanding.
  • The plus: Intervening at this time may give students the support they need to keep up with the class.
  • The caveat: Students may have a serious lack of background that requires reaching back to mathematical concepts taught in previous years. The focus should be on the underlying math, not on class assignments. For example, while others are learning multidigit multiplication, floundering students may need experiences to help them learn basic underlying concepts, such as that 5 × 9 can be interpreted as five groups of nine.

Before the Class Studies the Topic

Suppose the class is studying multiplication but will begin a unit on fractions within a month, first by cutting out individual fraction kits. It would be extremely effective for at-risk students to have the fraction kit experience before the others, and then to experience it again with the class.
  • The plus: We prepare students so they can learn with their classmates.
  • The caveat: With this approach, struggling students are studying two different and unrelated mathematics topics at the same time.

After the Class Has Studied the Topic.

This approach offers learners a repeat experience, such as during summer school, with a math area that initially challenged them.
  • The plus: Students get a fresh start in a new situation.
  • The caveat: Waiting until after the rest of the class has studied a topic to intervene can compound a student's confusion and failure during regular class instruction.

How My Teaching Has Changed

Developing intervention lessons for at-risk students has not only been an all-consuming professional focus for me in recent years, but has also reinforced my belief that instruction—for all students and especially for at-risk students—must emphasize understanding, sense making, and skills.
Thinking about how to serve students like Paul has contributed to changing my instructional practice. I am now much more intentional about creating and teaching lessons that help intervention students catch up and keep up, particularly scaffolding the mathematical content to introduce concepts and skills through a routine of support. Such careful scaffolding may not be necessary for students who learn mathematics easily, who know to look for connections, and who have mathematical intuition. But it is crucial for students at risk of failure who can't repair their math foundations on their own.

My “Aha!” Moment

Mary M. Lindquist, Professor of Mathematics Education, Columbus College, Georgia. Winner of the National Council of Teachers of Mathematics Lifetime Achievement Award.
My “aha” moment came long after I had finished a masters in mathematics, taught mathematics in secondary school and college, and completed a doctorate in mathematics education. Although I enjoyed the rigor of learning and applying rules, mathematics was more like a puzzle than an elegant body of knowledge.
Many years of work on a mathematics program for elementary schools led to that moment. I realized that mathematics was more than rules—even the beginnings of mathematics were interesting. Working with elementary students and teachers, I saw that students could make sense of basic mathematical concepts and procedures, and teachers could help them do so. The teachers also posed problems to move students forward, gently let them struggle, and valued their approaches. What a contrast to how I had taught and learned mathematics!
With vivid memories of a number-theory course in which I memorized the proofs to 40 theorems for the final exam, I cautiously began teaching a number-theory course for prospective middle school teachers. My aha moment with these students was a semester long. We investigated number-theory ideas, I made sense of what I had memorized, and my students learned along with me. My teaching was changed forever.

Marilyn Burns is Founder of Math Solutions Professional Development, Sausalito, California; 800-868-9092;
Copyright © by Marilyn Burns

The Flexible Teacher

December 2010/January 2011 | Volume 68 | Number 4 
The Effective Educator Pages 46-50

The Flexible Teacher

Leila Christenbury
Good teaching comes not from following a recipe, but from consistently putting student needs first.
After almost 35 years in secondary and university classrooms, I know something about effective teaching. I have certainly seen inspiring examples from other teachers; I have written and reflected extensively on the topic; and occasionally in my own practice I exemplify effective teaching myself.
I also have a modest reputation in my part of the academic world for exploringineffective teaching— and the source of my most telling examples is still, embarrassingly, myself. In articles and books throughout my career, I have felt compelled to detail my recurring instructional struggles and failures (Christenbury, 1996, 2005, 2007) to serve as a cautionary tale.
This article stems directly from my years of experience and reflection and from my stubborn and consistent aspiration to be a better teacher. I am not yet where I want to be, but as T. S. Eliot (1952) reminds us,
For us there is only the trying. The rest is not our business. (p. 128)
For those of us who are still trying to become the most effective teachers possible, it may be useful to consider a bit of history and a recent real-world example.

Scapegoats and Superstars

Although it might seem self-evident that effective teaching is at the heart of student learning, teaching has not always been a central part of the public discussion on education reform. Changing the patterns of school days and school years, establishing a common core curriculum, linking assessments to that curriculum, holding schools accountable for student test scores, altering administrators' preparation and responsibilities, incorporating new technologies into instruction, empowering community groups and school boards—these have all been and continue to be topics on the education reform discussion board. The teacher, an individual who is crucial to the success of any reform effort, has often been sidestepped, minimized, or even ignored.
Only recently has it occurred to a number of otherwise bright people that effective teaching is central to education success. Yet rather than being a wholly heartening development, as many of us initially hoped, this belated recognition of the importance of effective teachers has had unintended and even pernicious consequences. Both at the height of No Child Left Behind and in its current twilight era, the significance of the teacher's role has often been hijacked and distorted.
Some have claimed that because individual teachers are so important, they should be able to overcome any and all instructional, contextual, and societal issues and consistently raise student test scores every year. Some have argued that teachers are so vital that they must be strictly regulated; they must follow scripted curriculums and be tracked, rewarded, or punished for the performance of their students (again, as measured by test scores).
Further, because teachers are so central, some pundits and policymakers now propose that the best way to improve schools is to strip teachers of tenure and seniority protections so that newer and supposedly brighter and better teachers can quickly take the place of "underperforming" veterans. Certainly in the past year, the wholesale firing of an entire Rhode Island high school's teaching staff and the dismissal of hundreds of teachers from the District of Columbia schools were premised on the idea that teachers are all-important.
The public discussion no longer ignores teachers and their centrality; now it lays most of the onus of blame for student failure on the individual teacher. And it must be reiterated that in these days of high-stakes testing, student success is mostly determined by only one measure: test scores.
Can the individual teacher bear this responsibility alone? Carter (2009) critiques the image of the "teacher-as-saint" (p. 86). The public, he contends, expects teachers to work miracles and blames them when the miracles somehow do not materialize. In an online forum on teacher effectiveness, Kate Walsh (2010) points out that these "superstar" teachers are relatively rare. And although good teaching is integral to student success, it cannot by itself supersede the many other factors that contribute to educational success or failure.

What Is Effective Teaching?

I teach preservice teachers at the university level, and one of the hardest messages I try to impart to them is that there is no definitive recipe, no immutable formula, no simple list of do's and don'ts to ensure effective teaching. As they stand on the brink of entering their own classrooms, many of my students find this news frustrating. Some would prefer the deceptive comfort of Chester E. Finn Jr.'s (2010) reductionist definition, "An effective teacher is one whose pupils learn what they should while under his/her tutelage."
Only when preservice teachers have gained some experience with a range of students and some sense of themselves as teachers do they understand that the individual, idiosyncratic, and contextual aspects of effective teaching are what make it both enormously rewarding and enormously challenging. Students will always learn more, less, or differently than "what they should." Good teachers understand this. Most people outside the classroom, especially those who want to regularize and routinize teaching and learning, do not.
But although there is no precise recipe, we can recognize effective teaching by a number of characteristics.
Effective teaching is variable. Effective teachers use a variety of strategies and a range of methods, and they change and refine these over time. They do not teach the same way and use the same instructional repertoire year after year. Effective teachers also differ from one another; both teachers who use traditional methods and those who employ the most up-to-date pedagogy can be successful.
Effective teaching is contextual. It responds to individual students, school and classroom communities, and societal needs. Effective teachers alter, adjust, and change their instruction depending on who is in the classroom and the extent to which those students are achieving. Effective teachers are not so devoted to their practice that they ignore the students in front of them.
Effective teaching is premised on students' intellectual curiosity. Effective teachers begin with the belief that students are smart and can be enticed to learn. Despite their own skill, knowledge, and experience, effective teachers neither patronize nor condescend to students of any age.
Effective teaching must be somewhat autonomous. Reflective and accomplished teachers do not need to be controlled, managed, or strictly monitored. Such teachers are close to their students in intellectual as well as psychological ways, and they must be empowered to use their judgment to make classroom decisions.
Ultimately, effective teaching is fearless. Because the goal is learning, effective teachers must adjust curriculum, methods, and pacing to meet the needs of the students. Effective teachers put a priority on student needs rather than on the strictly interpreted demands of the school district curriculum guide or the year-end test. Again, to do this, teachers must have a great deal of independence.

Walking the Walk

In spring 2010, I had a teaching experience that illustrates some of the decisions and issues that confront all teachers in all classrooms as we strive for effective teaching.
Because of a scenario that has become common during these recession-plagued days, my university instituted a new round of budget cuts, and I found myself unexpectedly teaching an undergraduate writing course that is cross-listed in English and in education. I had created the course, Teaching Writing Skills, 20 years ago. But my responsibilities had evolved and I had not taught it for a while; it had recently been handled by experienced and talented adjuncts. Now it was mine to teach again.
At first, I welcomed this last-minute change in my schedule, confident that I was in touch with the course focus and the kinds of students who traditionally elected to enroll. In recent years, I had taught almost exclusively graduate students, and returning to teach this favorite undergraduate course would, I thought, be interesting.

New Challenges in an Old Course

Interesting it was indeed. Frankly, a number of issues caught me by surprise. Many of the issues were familiar to me from high school teaching, but I did not expect to find them at my university.
First, it quickly became clear that my 18 students were not prepared for the requirements of the course as I had designed it. On a purely academic level, many students struggled from the outset with the readings, the length and topics of journal assignments, the etiquette of large-group discussions, and the pacing and workload of the course itself. After some awkward class sessions during the first weeks of the semester, I checked student records and discovered that a number of those enrolled in this 300-level course had current grade point averages of 2.5 or lower.
Second, although this course was geared to the teaching of writing in secondary school, few of the course participants planned to go into teaching. (From my experience, this was not the usual course audience, and I wondered whether recent enrollment pressures in the English department had made this course attractive to English majors who needed the upper-level credits.) Not surprisingly, then, early discussions and assignments that addressed teaching scenarios were not successful. When I previously taught the course, the students were relatively able academically and most of them were taking the course as part of their preparation to teach.
As a third issue, some students appeared unaccustomed to norms of academic conduct, a problem I had rarely encountered at my university or even when teaching at the high school level. About half a dozen students had real difficulty with basic expectations: They did not come to class on time; return promptly from the break; or bring the necessary materials, books, and writing journals. When I gave them directions or asked them a question in discussions, some students routinely needed the question repeated; their minds were clearly wandering.
One student was obviously frustrated with the class and dealt with the situation by repeatedly coughing so loudly and persistently in a number of class meetings that class conversations and work had to stop. A least three students, early in the semester, routinely missed assignment deadlines despite an explicit syllabus and reminders.
In short, these students were not an optimal group. The 2010 Teaching Writing Skills course promised to be one hot mess.

Effective Teaching in a New Context

In this context, what did effective teaching look like?
First, it was variable. I ramped up the classroom intensity to the level I usually reserve for one- or two-day inservice workshops in which I need to instruct—and motivate—busy and often tired practicing teachers. As in those contexts, I worked hard with these Teaching Writing Skills students, being more personable and direct than I had been in any classroom in years to keep them awake, aware, and engaged. I used humor with the cougher and with those who needed repeated questioning. I also moved to more direct instruction, which I rarely used in my graduate-level courses.
My teaching in this course was also contextual. Clearly, what I had done before in this course was not going to work with these students. One strategy was to address the elephant in the room; I talked to the students explicitly about what I perceived was going on in the class, and I proposed solutions. I asked for their advice and feedback and gave them time to deliver it both face-to-face and anonymously. Students told me that they wanted more time with assignments, more direction regarding the content of journal entries, and more feedback from me on drafts. All of this I provided. To make the course more appropriate for the students, I broadened the content of discussions and assignments so that the focus was not just on teaching writing but on issues in the students' own writing.
And I found that the students were smart—perhaps not smart in the way I had assumed they would be, but in terms of their own interests. As I made writing assignments more relevant to those interests, students often revealed the kind of intellectual curiosity that I knew was there. One student's traditional argument paper defended the originality of Lady Gaga; another student, in the course of a paper focused on the day he was born, did an extensive—and sophisticated—analysis of affordable Brooklyn apartments that had been available to his young, immigrant parents.
I became more interventionist than I can ever recall in a college setting—or even during my time teaching high school. Specifically, I insisted that students who were struggling meet with me outside of class. I initiated one-on-one conferences, and during the class break I praised students for making progress with behavior and attention. I individually tutored two students whose literacy skills were below par. I used multiple e-mail messages to remind students about deadlines. At students' request, I expanded class time for discussions that were of greatest interest to the students. I also limited large-group discussions—which often veered out of control when students were not able to present comments or ideas civilly—and substituted small groups or pairs.
Most substantially, I concluded that few of these students would pass the course as currently constructed. Therefore I jettisoned some long-standing components of the course—in particular, the culminating assignment, which was a favorite of mine. This assignment had given each student the opportunity to assume the roles of both writing teacher and writing student. Students designed original writing tasks, exchanged and completed them, and then evaluated the final products. However successful this assignment had been in the past, I knew that it would most likely be a failure with these students because their interest in the teaching of writing was not central, and the detailed nature of the work relied heavily on a pedagogical focus.
I also deleted a quarter of the journal entry assignments, doubled the time allotted to writing-group revision, and initiated rewards for completion of minor assignments. I truncated some readings from the two textbooks and skipped other parts of the books entirely. At the end of the course, for the first time in my university teaching career (although I did this regularly as a high school teacher), I provided a two-page, detailed study guide for the exam.
Some of these changes may appear to have weakened the rigor of the original course; from my perspective, however, not making these changes ensured that most students who had signed up for Teaching Writing Skills would falter in the assignments if not fail the course itself. Compromise seemed the better path and gave students a chance to succeed.
How did students react, and how well did they do in Teaching Writing Skills? Over the course of the semester, nine final draft papers were unacceptable; these students were given an R grade (revise) and the opportunity to rewrite and resubmit without penalty, and every student took advantage of that opportunity. For the final exam, the study guide must have been helpful: 14 of the 18 students received As or Bs; there were only one C, one D, and two Fs. End-of-class anonymous student comments were generally positive ("encourages passionate discussions," "willing to help anyone who needed it," "establishes great working environment among all her students") as were instructor and course rankings (on a scale of 1 to 5, high 4s in almost every category). Regarding final course grades, of the 18 students, 12 earned either an A or a B; 4 received a C; and 2 students—who, despite all my efforts, continued to experience difficulties with attendance and deadlines—received Ds.

Giving Teachers the Freedom to Put Students First

All of the adjustments I made in response to the context and the needs of students in this course depended on the autonomy I enjoyed in my university teaching position (a level of autonomy that current reform efforts are unfortunately making less, not more, common among elementary and secondary teachers). I think it would be overstating the case to call these adjustments fearless. But I was pleased that by focusing on effective teaching, I could recognize the need for change, respond to the challenges, and make significant pedagogical and content changes to meet student needs.
The spring 2010 Teaching Writing Skills course looked very different from the course I had taught years before. But the point was not to adhere to some preconceived, ideal course that was no longer appropriate for these students; the point was that effective teaching must be in service of student learning. Once we more fully integrate our efforts to improve teaching with school context and student need, we can look more confidently to a future in which all students experience success.


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Leila Christenbury is Commonwealth Professor of English Education at Virginia Commonwealth University, Richmond, Virginia; a former high school English teacher; and past president of the National Council of Teachers of English; 804-828-1306;
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