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Embracing Accountability

chat archive

Moderator
Good afternoon and welcome to this month’s online chat with NCTM President Cathy Seeley. The topic of today’s chat is Cathy’s President’s Message on “Embracing Accountability” from the July/August NCTM News Bulletin.

Here is our first question:

Question from:
Wilburton, Oklahoma

I have no problems with accountability. But I do have a problem if the teacher is the only one being held accountable. In Oklahoma we currently test the 3rd, 5th, and 8th grades in Mathematics and have an End-of-Instruction (EOI) exam for Algebra I. At this time the only person held accountable for these scores is the teacher! I believe there needs to be some accountability on the student and their parents. I know I may be in a minority in this particular chat. But I have overheard students say, “Why try hard, it doesn’t mean anything.” My school has tried several incentives to change this attitude but none have worked. I am open to suggestions.

Cathy Seeley:
You are correct that we all have a responsibility in helping students learn mathematics—the teacher, the student and the family. How this is implemented seems to be a bit different in each state and even within states. Some states require a certain score on a test in order to be promoted or to graduate. But this type of consequence can have either a positive or a negative influence on student learning and student test scores. Perhaps others participating in the chat can share methods that have worked for them.

Question from
Unknown City and State

I am a high school math teacher and have taught students of all levels of academic ability. I have some concerns about teacher accountability for low-level students that I would like to address and I hope that someone at NCTM will be able to respond:

I believe in teacher accountability when students are placed in courses that prepare them for the world that they will likely encounter. I do not believe in teacher accountability when students are not given appropriate choices in the math curriculum. Even though I see the necessity to teach calculus to advanced students I wonder whether it is necessary for the below-average student to learn the intricacies of trigonometry or even algebra in some cases.

I have taught AP Calculus courses with much success, but the success is not mine, it is merely that my students were taking a course that was appropriate for them! On the other hand, I have had low-level classes in which students worked as hard as they could and yet did not succeed. Is it possible that the course was not right for these students?

We are not being realistic or fair to these low-level students when we force them to take “college prep” math courses and withhold from them the real everyday, practical mathematics that they will eventually need. (The applications in most textbooks seldom
seem relevant to these students.)

In years past, we offered courses for students who were not planning to go to college. Many of these students were excited about the math they were learning because it seemed worthwhile, and teachers felt the importance of what they were teaching. There was a greater chance of both the student and the teacher being successful!

Technology has changed the way we teach mathematics but not the mathematics itself! It seems that we now expect all students to be able to perform algebraic tasks even though for many it is meaningless. We have somehow forgotten that many jobs available to our graduates have no bearing on pure mathematics. And lest we forget, the ability to be a good mathematical thinker may not involve the use of sophisticated mathematical symbols at all!

When I am confronted with the common question “When will I ever need this?” I tell my low-level students that the mathematics they are learning will teach them to be better logical thinkers, that they are exercising their brains, and that any new knowledge will enable them to understand the world around them a little better, (and of course, they will be able to solve more complicated problems etc.) But they know, as well as I do, that they learn better when they are presented with new mathematical knowledge that they think is relevant!

Is this truly the direction that we have taken in the teaching of mathematics? Would we rather have these students graduate with a poor understanding of college math than a working knowledge of the essential mathematics that they will need to function
successfully as adults?

Is it the teacher or the system that should be accountable when these students do not achieve?

Cathy Seeley:
Thanks for your thoughtful discussion of these important issues. I think it is both the teacher and the system that should be accountable for student learning, as well as students themselves. You raise several points that I think deserve discussion.

First, if the kind of algebra we are teaching is focused primarily on abstract use of symbols without relevant applications, then I agree that this is not a course we want for all students. However, if we make the shifts in algebra (and secondary mathematics) called for in Principles and Standards for School Mathematics, we should be teaching an algebra course that is based in the real world, focused on understanding and useful in a wide range of relevant applications. Lynn Steen, a mathematician, has written eloquently on the subject of Algebra for All. Two particular references are given below:

Steen, Lynn Arthur. “Does Everybody Need to Study Algebra?” Mathematics Teacher, 85:4 (April 1992) 258-260. Also appeared in Basic Education, 37 (January 1992) 9-13.

Steen, Lynn A. “Algebra for All: Dumbing Down or Summing Up?” in The Algebra Initiative Colloquium, Carol LaCampagne, et al., Editors. U.S. Department of Education, 1995, pp. 121-140.

You mention the difficulty of “low-level” students taking higher-level mathematics courses. One of the greatest challenges we face today is to find ways to provide opportunities for more students to study challenging mathematics. The problem we have seen for many years (including when I started teaching over 30 years ago) is that we simply don’t know which students might want to or be able to attend college. We used to think that some students were college-bound and some were not. However, it turns out that we were often wrong. Some young adults decide after working a year or two that they need more education to get ahead. If the only mathematics a person has studied is remedial or low-level, they will have to spend a year or two paying for developmental courses at a community college before they can even begin their studies for credit. Many students in high school do not realize that they might one day want to (or be able to) pursue a college education.

Furthermore, we know we have a problem with access to educational opportunities if the demographics of our low-level mathematics courses are different from the demographics of our most advanced classes. For example, do our advanced calculus classes reflect approximately the same racial and socio-economic balance as our lower-level classes? Too often, we find students coming from poverty situations disproportionately represented in lower-level classes, thus destining them for a limited future. This situation of a significant achievement gap between groups of students is one of the driving forces behind improvement efforts in our schools, as it should be. Students who come from diverse backgrounds and who bring different levels of success in previous mathematics classes might not necessarily have less ability to succeed. When we actively engage students in meaningful mathematics tasks, we often discover different stars who have bright futures. It may be true that not all jobs require advanced algebra or calculus procedures. However, is it the job of the teacher to decide who gets access to which types of jobs? If we arm students with more high-quality (and high-level) mathematics, they can have more options for their future.

Finally, it is surely more challenging to teach students who have not been successful in the past. However, there may be many reasons why students have not succeeded. Increasingly we are finding examples of bright students who may be able to go far in mathematics when we engage them in meaningful, useful mathematics, including algebra and complex problem solving. They certainly need to know functional mathematics, but in today’s world, they need much more.

Question From
Cedar Rapids, Iowa

How do we best get parents to understand accountability?

Cathy Seeley:
It is critical to involve families in students’ mathematics learning. Frequent communication with parents can offer opportunities to show various types of authentic assessment of their student’s progress. Samples of student work, performance on different types of assessment measures, results of interviews, and simply discussion between the teacher and the parent can all be helpful for parents and families to get a sense of what their student knows. When we involve families throughout the process, we can help develop an understanding that the large-scale tests administered by districts and states are one indicator of student learning. Parents and families can see the relationship of this one measure to the actual progress of student learning.

Question from
Bismarck, North Dakota

I am the testing coordinator for two rural school districts in North Dakota. Identifying the weak areas with our assessment results is relatively easy. It is the curriculum changes that will provide the increase in student achievement that is difficult. This is particularly challenging in light of some students who don’t care or cannot learn for a variety of reasons.

Cathy Seeley:
You are correct that making curriculum decisions to address areas of weakness is challenging. I would suggest that motivating more students to learn can be accomplished by energizing the curriculum in directions described in Principles and Standards for School Mathematics. In particular, I think that shifting our teaching techniques away from a reliance on lecture toward more active student engagement can ensure that more students achieve success in mathematics, even those who may appear to have difficulty learning or being motivated to learn.

Question from
Cape Girardeau, Missouri

In your opinion, what is the ONE MOST IMPORTANT thing that schools can do to improve scores on state and national assessments?

Cathy Seeley:
This is a great question. I have one thing, but it's a big one: Teach mathematics the way we know how to teach it best without being sidetracked by an overemphasis on any test. I honestly believe that when we focus on teaching a well-balanced mathematics curriculum and get students actively engaged in rich and appropriate tasks, that our students will learn mathematics. When they have learned it well, they will do fine on any test, even a low-level one, even a multiple-choice one, even a narrowly focused one. The biggest challenge in doing this is to withstand the pressure to spend too much time doing "test-prep" techniques or practice tests. A little of this type of thing is probably adequate to alert students to what to expect. The big thing needs to be the teaching, and therefore the learning, not the testing.

Question from
Blanco, Texas

How are we, as teachers, supposed to improve accountability on state tests, like our TAKS, when many students refuse to accept their own responsibility for learning? These 15 to 20 percent of the students cause our school to be judged at a lower level because of their refusal to take these tests seriously.

Cathy Seeley:
You are correct that students should share in responsibility for their learning. In order to have this happen, we need to shift our teaching techniques so that students assume this responsibility on a daily basis, not just on the state test.

For example, when students approach engaging tasks in small groups, and when we expect them to justify their approaches and participate in actively discussing mathematics, they are more likely to learn mathematics and perhaps more likely to participate fully in your state testing program. I know that this is not a simple task, but I think we need to look at how to shift our teaching in ways that involve students doing more of the talking (and learning) and the teacher doing less talking. I am not suggesting open, unstructured classrooms. On the contrary, to structure classrooms with active student engagement, where students are guided in making connections between the activities they do and the mathematics that goes with them, requires a lot of teacher planning and work. But over and over again, I see examples of where this type of shift pays off big in terms of student learning.

Question from
Brooklyn, New York

I teach elementary, junior-high math at an inner city school in Brooklyn, New York. I've been teaching for 20 or so years, and over that period of time it has become evident to me that there are a significant number of students that couldn't care less if they passed or failed, or if they were left back or not. How can you hold a teacher accountable and take this into consideration?

Cathy Seeley:
I think there needs to be a shared responsibility for student learning among teachers, students, and families. However, it is indeed challenging to help students develop this responsibility. I have come to believe that the key to developing this student responsibility lies in engaging students in an active way in their day-to-day learning. The best examples of this that I have seen are when a teacher sets up a learning situation and has students work in small groups toward a solution. The teacher becomes more a facilitator, helping students pull together what they have learned with the mathematics they have used, rather than telling students what they are to memorize. When the teacher holds the students accountable for what each member in the group learns, students eventually come to rely on themselves more and more. This is not simple, and it does not solve all the problems. But we do have a responsibility to structure the classroom so that students come to be more active participants in the learning process.

There is some fascinating research being done by researchers at Stanford, headed by Jo Boaler, with urban schools. This research will be highlighted at the NCTM Annual Conference in Anaheim in April.

Question from
San Antonio, Texas

I develop test items that are used in statewide mathematics assessments. I believe not all teachers understand how much input goes into the creation of a good test item, and that the state’s teachers are a necessary part of that effort. Teachers who have participated in the process frequently remark that they had no idea so much went into a test item. They also express increased confidence in the way the tests are used.

Cathy Seeley:
I have seen this process up close when I was Director of Mathematics at the Texas Education Agency, and you are absolutely correct. This is why I advocated in my President’s Message that educators should take advantage of every opportunity to work within the system to influence it. By volunteering to serve on committees, review test items, and even testify before committees or the State Board of Education, more educators can become familiar with and a part of the various aspects of the accountability system. Many states go through a comprehensive development process like the one you describe in Texas. Thanks for alerting teachers to this dimension of testing.

Question From
Dayton, Ohio

I see that one of the issues relevant to accountability is one of professional development opportunities. Many of our teachers may have the best intentions, but they have had little or no access to professional development that would introduce them to the new strategies and curriculum for teaching math in ways that are more engaging for students and make understanding more accessible. They continue to have weak content understanding themselves, and continue to teach using outdated strategies, not because they don't care but because they don't have opportunities that would facilitate change.

Cathy Seeley:
You are right on target. If we are going to hold teachers accountable for student learning, we must arm them with the knowledge and expertise to facilitate that learning. I see professional development as a responsibility of every district and state, in terms of what is offered and in terms of continued funding for high-quality experiences for all teachers as part of their work responsibilities. I also see a commitment to career-long professional development as one of the most important elements of choosing to be a mathematics teacher today.

Professional development is a strategic priority of NCTM. Our Professional Development Services Committee is in the process of completing a comprehensive plan for how we can continue to ramp up and coordinate our professional development offerings to meet the needs of teachers at every stage of their careers.

Question from
Dunkirk, Indiana

I have created a two-page list of our state standards. I enter each student’s progress on that standard by quarters and send a copy to parents with grade cards each quarter.

Cathy Seeley:
It sounds like you have worked to keep students and parents informed about Indiana’s accountability standards and their role in student learning. Communication can be very helpful, and I am guessing that parents are appreciative of your efforts along these lines. I hope you also give students opportunities to see how these potentially isolated items become part of a connected, cohesive curriculum that leads to flexible and powerful mathematics learning. Thanks for sharing this tip.

Question from
Somerset, New Jersey

How can we encourage teachers in other disciplines to teach math and to help prepare students for statewide assessments?

Cathy Seeley:
As we increase the emphasis on student test scores, especially in reading and mathematics, more and more schools are calling on all teachers to assume some role in student learning in these areas. The first step has been for many schools to recognize that fifth-grade student scores, for example, do not reflect just what students learn in Grade 5, but reflect the cumulative knowledge of students up through that time. Recognizing this aspect leads to looking beyond mathematics to other disciplines. I believe that there are ways to use students' strengths in how they approach problems in one discipline to how they can approach problems in another. So a strong mathematical problem solver may be able to use this tool in solving other problems as well. Conversely, if a student is a creative problem solver in the social sciences, we should be able to tap into the successful approaches the student uses in how the student approaches mathematical problems.

Strong school leadership, especially from the principal, is necessary to call on all teachers for how they can contribute to student success. So the starting point is often working with the principal. The related challenge, however, is that once we have this kind of commitment from teachers in other disciplines, we must be ready to work with these teachers on how they can incorporate mathematical thinking and problem solving, and not just use more numbers in their activities. This requires real collaboration and articulation among the faculty, so instructional leaders should be prepared to offer opportunities for this kind of collaborative work to occur.

Question from
Baltimore, Maryland

Accountability in our school district means that we administer standardized tests for each chapter of an algebra text, which is not well, if at all, aligned with goals of state assessment tests. (The geometry text is better aligned with the state assessment for that content area).

The unit tests are problematic because they must be kept secure (students have limited access to the tests and are not allowed to take them home), and yet the overall “security” of the tests is dubious.

Everyone must administer the tests on a set timetable. Teachers spend a lot of time tabulating (by hand) itemized results of these tests to forward to the county offices. Teachers have been able to experience all the negatives involved with accountability of students’ learning and test performance. We have yet to see what happens when students themselves become accountable—when they must pass the state exit exam in order to graduate from high school.

In addition, there are problems with the state assessments—questions with no right answer listed and questions that indicate a poor grasp of mathematics on the part of the test designer.

The assessment materials are quite poor on these state tests. Compare them to the “Balanced Assessment in Mathematics” materials that were developed at Harvard, now archived somewhere else (Concordia??). Here are some assessment tasks and methods that would really engage teachers with their students in a meaningful way.

Cathy Seeley:
Unfortunately, there are many instances of school systems putting a disproportionate emphasis on administering and scoring tests and on reporting test results. I worry that sometimes we may spend so much time dealing with tests and preparing for tests that we take away from time that could be spent on student learning. When tests are not well aligned with the curriculum we are teaching, there can be damaging results. In cases like this, it is surely our responsibility to participate in trying to shape the system, or in raising our voices as professional mathematics educators to redirect our focus to student learning. There’s an old saying (from Australia, I think) that weighing the hen more often doesn’t make it heavier. I hope you are successful in sharing your examples of high-quality assessment approaches with people in your school district responsible for making these decisions.

Question from
Boerne, Texas

While I am not opposed to accountability, we spend so many days pre-test, practice TAKS testing, and Competency Testing for our district that many days I wonder when I am supposed to teach the students what they are going to be tested on. Because for every day we test, students need to have another day to go over the test. The district also wants teachers to analyze the data, and come up with new and creative ways to present the material to the students using real-world situations. I am putting in 20 hours days and still not getting it all done. Now in Texas we also have to contend with not using food, so the fun activities using M&Ms are out. The rules at either state or requirements at district level keep tying our hands to do what we know the students really need. Districts are reducing class time and increasing class size, so that movement of students in hands-on group activities is almost impossible. I personally feel we are getting mixed messages from NCTM and our administration.

Cathy Seeley:
The “too-much-time-on-testing” phenomenon is a huge problem. (See the response to the previous question.)

In terms of the limitations on using food, it does seem that there are continually new stresses on teachers that tend to limit your innovation and your ability to implement the kind of teaching that you would like to do. Unfortunately, the mixed messages you are receiving involve NCTM putting forth recommendations regarding best practice, and policymakers often make decisions based on many other factors. My experience over the years tells me that policymakers need to hear when trends like reducing class time and increasing class size are interfering with student learning. This may mean communicating concerns (individually or collectively) with administrators and policymakers at the school, district, state, and federal level. We cannot quietly accept reduced resources at a time when we are doing everything possible to help more students reach higher levels of achievement.

Question from
Brooklyn, New York

What is your opinion of self-contained classrooms? How high do you think self-containment should go?

Cathy Seeley:
The issue to me is not whether or not to structure learning in self-contained classrooms, but whether the teacher is willing, able and well prepared to teach mathematics deeply at a particular grade level. There are pros and cons to self-containment, but the real issue becomes how thinly we may stretch teachers to be highly qualified in every field they teach. Teaching mathematics, even at an early elementary level, involves some sophisticated knowledge of how numbers relate, what operations represent, how objects can be manipulated in space, and how working with patterns and making generalizations can lead to algebraic thinking. And these are just a few examples of what an elementary mathematics teacher needs to know. So the issue becomes one of professional development and commitment to knowledgeable teachers structuring and facilitating mathematics learning based on their own deep understanding of mathematics and how to teach it.

Question from
Santa Rosa, California

I'll be starting my fifth year of teaching next week. I agree with the comment about professional development opportunities. One thing I've noticed -- it seems that being textbook dependent, as we are, makes it a LOT harder for new teachers even to teach the kinds of lessons that we know we should. We are often "under pressure" to be "on the same page" as other teachers of the same class at our site. Being a new teacher, it's often difficult to find your own way. Any suggestions, especially for breaking away from the textbook?

Cathy Seeley:
It is truly challenging to deal with pressure to cover exactly the same thing as others. It's a positive sign that you recognize how to teach the way you think would help student learning and to see that this may lie outside of your textbook. Sometimes it is possible to teach your lesson the way you want, as long as you are addressing the particular objective being addressed in the textbook. Ideally, you could work with your colleagues to identify what content would be addressed in a given period of time, generally at least several days or a few weeks, not day-by-day. This involves working for opportunities to collaborate and really plan together. My experience is that the more shared professional development experiences a group of teachers have, the more likely this is to happen. So this comes back to school or district leadership and working with the principal or district mathematics supervisor. As a fifth-year teacher, you have some credibility as a professional mathematics educator. Often administrators (and even some colleagues) are open to accepting input from someone with a fresh perspective. Also, working with your local mathematics group (such as the California Mathematics Council or a local group) can bring you together with other teachers who may be able to share ideas on how to accomplish your goals. Good luck, and thanks for your energy and enthusiasm. I hope we will have opportunities to continue this type of discussion over the next 30 years of your career (though I may need help typing answers at that point).

Question from
New York City

What is your opinion of having one set, orchestrated curriculum that allows very little innovation in the classroom?

Cathy Seeley:
This type of prescribed curriculum is becoming more common. A set curriculum that pushes student engagement, problem solving, and mathematical thinking can be a great motivator for teachers to develop their knowledge, expertise, and effectiveness in the classroom.

However, your question makes me think that this is not the type of curriculum you are talking about. I believe there is always room for innovation in the classroom, although sometimes it is more challenging than others. I would suggest working on two levels. First, within the structure you have, I hope you can push the limits of what is possible in terms of teaching quality mathematics the way you believe to be most effective. Second, I think it is our responsibility as professional educators to challenge the system when it may not be serving students well. Raising our voice to shape the system in positive ways is becoming one of our most important roles as mathematics educators, and yet it is the role we are least accustomed to playing. Sometimes this can be done individually, but often it is best done in cooperation with other teachers. This may be the teachers in your grade level or school, or may involve working with teachers from outside your school. Your state and local mathematics organizations can be powerful policy-influencing groups. I hope you are able to connect with colleagues in this way to push for appropriate mathematics programs. I have often seen tremendous results when professional mathematics educators raise their voices in constructive ways to participate in shaping the system.

Moderator:
Thank you all for your participation this afternoon. The questions that were submitted in advance of the chat will be included in the transcript that will be posted on the Web site tomorrow.

The next online chat with NCTM President Cathy Seeley will be at 3:00 p.m. EDT on Friday, September 24 and the topic will be NCTM’s Focus of the Year

Cathy Seeley:
Thanks to everyone for your thoughtful and energetic participation in this chat. Any time we can exchange ideas among colleagues, we all grow.

I look forward to continued opportunities to exchange ideas with you all, either in this format or in person. Keep up the good work toward our common goal of high-quality mathematics education for every student!


The following questions were submitted in advance or during the chat and couldn’t be answered during the hour. Cathy Seeley has provided these written answers.

Question from
Fayetteville, North Carolina

Accountability can be more than just a tool to measure the progress, or lack of progress, of students.   It can also be a useful tool to see if there are patterns or trends in how a teacher is teaching.  When individual teachers as well as administrators start looking at scores as a means to see if teachers are scoring consistently high or consistently low, then staff development opportunities can be planned accordingly to raise the bar in the weak areas.  We can’t expect our students to make quality progress unless teachers also evaluate their own teaching and work to improve weak areas.  Especially in the elementary grades where most teachers have to “teach it all,” we have to become more focused on ways to let teachers teach what they are strongest in and look for ways to improve the other areas that they still sometimes have to teach.

Cathy Seeley:
An accountability system should provide information for improving learning. This must be the purpose of whatever testing and reporting we do. In order to improve learning, taking a close look at teaching is important. If many or all the teachers in a school seem to have difficulty teaching a particular part of the mathematics curriculum, such as measurement, this definitely gives us insight into avenues for professional development. Also, when a teacher implements a program or approach such as those described in Principles and Standards for School Mathematics, and when that teacher consistently has positive test scores, there may be an indication that something positive is happening in the classroom that might be looked at by other teachers. We must be careful, however, not to overgeneralize from short-term test results. There are ways to raise test scores on next week’s test without positively affecting student learning for the long term. As you suggest, we need to look at patterns over time. This means looking at student performance both for teachers during the year in which their students are tested, and in years that follow.

Question From
Pendleton, South Carolina

I feel as if the pressure of accountability should be embraced as a means of examining our practices as educators.  Within our school, we have used the pressure to study why we are teaching certain topics (all the possible ways to factor and two column proofs) especially within our Algebra I and Geometry courses.  Through this examination, we have a strong feeling within the department how all of the courses go together to provide the high school student with a better high school mathematics career.  This study has helped all teachers understand the relevance of each mathematics course within the spectrum of high school mathematics.  As department head, I have enjoyed encouraging others not to view the accountability measures as yet another “flaming hoop” in education but as something to challenge us to further introspection.  

Cathy Seeley:
What a great way to tap into teachers’ own powers of reflection and self improvement. It sounds like you have a real commitment to work together to improve the practice of teaching in your school. Keep it up, and thanks for sharing!

Question From
Logan, Utah

Certainly there are many components to accountability that must be considered.  We so often skew our perspective by looking at achievement measured by limited tests.  We have an obligation to teach all children to know and use mathematics.

I believe we must be accountable for presenting mathematics to our diverse learners in ways that mirror their diverse ways of thinking and knowing.  Certainly, developmentally appropriate practices matching our students’ maturational developmental levels are imperative but I worry that since most teachers are Western and middle-classed, we forget the impact of culture in teaching and learning.

The Native American students with whom I have worked are very bright and clever but benefit from situations and explanations that reflect lived experiences of their families and communities.  As teachers we are obligated to learn who our students are before we can teach them.  I believe that instruction that flows from such insights develops bridges of understanding between the children’s world(s) and the mainstream mathematics of the classroom.  I have seen so often that students have been forced to give up their ways of knowing to memorize procedures they do not “know” to be successful in the classroom.  I ponder the cost of such a trade in terms of how far such “learning” may remove children from who they are culturally.

When students do poorly on tests we must first question what we have done to create contextual instructional linkages children can understand. We must seek additional ways that students do show comprehension and mastery as they apply the mathematical knowledge they have gained.  We must broadcast these successes for all to hear to ensure that competence is reflected in many dimensions.  In these ways we are demonstrating that we are very conscious of teacher and student accountability.

Cathy Seeley:
Thanks for sharing these important insights. It is too easy to overlook particular needs, strengths, and perspectives of certain groups of students. As you have so eloquently observed, we can use the results of our accountability system to point out areas where we need to pay more attention. By disaggregating our test data, we cannot hide behind our overall average achievement. Instead, we come face to face with areas of potential weakness in our program, and we can identify where we have to learn more about teaching mathematics in order to help students learn more mathematics.

Question From
Boston

In our District, accountability is mainly limited to students. If they fail in the standard tests, they are the only ones paying a price by not being promoted. Schools and teachers remain untouched. I find this to be unfair and against the nature educators are supposed to have. By washing their hands and waving the flag of accountability while taking on the weakest link in the educational system, the students, educators put themselves outside the realm of advocacy in which they should live.

Cathy Seeley:
Certainly, students have a role in taking responsibility for their learning. However, as you observe, we cannot separate out the influence of teaching, as well as the influence of the school system and its culture and policies. Learning is absolutely related to teaching, and when the former isn’t happening, we need to look at the latter for a significant part of the solution. Indeed, many of our lowest-performing students have been limited in their opportunities to learn higher-level mathematics by the system itself. In some ways, this can fall into the category of blaming the victim for the crime. We all have a role, especially to advocate in favor of a high-quality mathematics education for every student. This is the underlying mission of the National Council of Teachers of Mathematics.

Question From
Orange Park, Florida

Florida’s achievement test really is a strain for the sophomores that are not in prep or technical education.  Yet the system does not make any allowances for that.  I teach liberal arts math and find it difficult to gauge the potential for student success—yet I am asked to state goals for their progress based on little or no knowledge of their past performances.  Yech!

Cathy Seeley:
It sounds like some disturbing things may be happening here in the name of accountability. This may be an opportunity to speak up as a professional educator (or a group of educators if you have a local mathematics group or professional association). When we let people know that we are not afraid to be held accountable, but that the measures must be relevant to our learning goals, we can get a lot farther than we can by simply complaining about the system. I hope there is a way for you to voice your concerns constructively. I also hope that “liberal arts math” arms students to have options in their future if they decide they want to pursue a college education. We may have to look both at the curriculum and the assessment when there is a mismatch.

Question from
City Unknown

Embrace accountability? After many years of embracing social promotion, where is the accountability from a system that put its head in the sand? It’s nice to mention accountability as a means of curing a problem, but this problem appears to be much larger. Unless you visit the low-functioning schools to see for yourself and experience the conditions as well as the abuse teachers go through, you would not overburden the teachers with accountability.

A teacher accused of a crime is removed from the classroom. After the investigation, the teacher found not guilty is returned to the classroom. A teacher’s lifelong profession (including future income and past expense to achieve permanent certification) rests on the balance (with possible jail term involved) on this investigation. What stress for this teacher. What happens to the student that made the false accusation? A 5-day suspension and things are back to where they were before. One can ask, did the punishment fit the crime? And what has the student learned? It appears that the system needs to address a more stringent punishment to 1) deter future copycats, and 2) show that teachers need to be respected.


I know there are teachers who commit crimes, but there are many who do not. Embrace accountability via math teachers? Yes, agree to strengthen their purpose as a teacher. But to not address other issues that confront teachers is to place a small Band-Aid on a large wound.


Your comments will be appreciated.

Cathy Seeley:
Accountability by itself does not cure a problem. But avoiding accountability only masks problems that may exist. Certainly we must raise our voices against misuses of the system that unfairly treat either teachers or students. However, in too many places we have hidden behind reasons why our students could not learn. There are many examples of schools that have been low performing but have changed every aspect of their system in a coordinated effort to improve. One such school that I visited this past year is Pearce Middle School in Austin, Texas.

As you observe, we must absolutely address many issues confronting teachers and students if we are going to commit to long-term rehabilitation rather than applying a Band-Aid.

Questions/Responses from Chicago

From Cathy Seeley’s President’s Message: Being accountable for students’ learning is indeed our professional responsibility, but accountability involves more than just these limited indicators.

Response from Chicago: RIGHT!  But what are those other indicators?  One major one: Are students taking more mathematics, particularly mathematics beyond what they are required to take?  Another:  Do students appreciate the mathematics they have taken enough to want to use it when they leave the classroom?

From Cathy Seeley’s President’s Message: I suggest that as teachers of mathematics and those who support teachers of mathematics , we should not complain about accountability; rather, we should embrace it.

Response from Chicago: RIGHT AND WRONG!  We should not be afraid to be held accountable if (1) the standards of accountability are appropriate and (2) the reasons for accountability will improve the schooling of our children.  The current move towards accountability does not satisfy either of these criteria.  The standards are mathematically impossible to hold—namely, it is not possible to expect schools to increase each year on every facet of what they do any more than one can expect a baseball player to get more hits, more RBIs, fewer errors, and score more runs each year.  I think it can be argued that the effect of accountability rules being put forth by the federal government has been to change schooling from educating children to wanting to learn because it is important to learn, to wanting to learn because it is going to be on the test.  Successes in learning are not rewarded, but failures in learning are punished.  This is no way for the nation’s education system to operate.  No one would prefer to work under such conditions but we put our children and our nation’s teachers through them.  It is a 19 th-century philosophy in a 21 st-century world, and it will not work in the long run.

Cathy Seeley:
I agree with your observations. The President’s Message this month addressed some of these concerns.

My first belief about accountability is that we should not sidetrack a good mathematics program in the name of any test. Second, we should work within the system whenever we can to ensure that the measures and systems we use support the mathematics learning we believe to be important. Finally, there are times when we must raise our professional voices in moral indignation if we are to serve our students and society.

Question from
New York City

We are a small faculty in an alternative high school with limited time and funds.  All we have been able to do is to ensure that the types of problems being presented on the New York State Math A Regents Exam are covered within the curriculum mandated by the Department of Education. We do embrace accountability, but are constrained from innovation by the enforced use of a programmed curriculum for our students.  I’m looking forward to getting some ideas at your online session.

Cathy Seeley:
I know that Math A has been a challenge in your state for a number of years, in terms of trying to meet the needs of students who may not be pursuing advanced mathematics (if I understand it correctly). Sometimes it is difficult to influence a system within a state as large as New York. I encourage you to express your concerns, regardless of how well you think they may be heard. Even a small school can have a voice in influencing policy makers. I know that in my state of Texas, sometimes a single letter to a member of the State Board of Education has influenced a state-level decision (for better or worse). If policymakers do not hear from their most knowledgeable professionals, they will be making decisions blind. It may also be helpful to work through your state mathematics organization, the Association of Mathematics Teachers of New York State or perhaps your state supervisors’ organization, the New York State Association of Mathematics Supervisors. Even small groups of mathematics educators may be able to play a role in expressing recommendations for improving the system.

Question From
Denver

I really like your message of embracing accountability instead of finding ways to avoid it. I really think that the NCLB initiative has made it possible for many of us who have advanced degrees in math to reenter education from the professional world. I think this impact is huge and should not be underestimated in the impact that it makes upon kids and the process of teaching in the sense that we bring with us a vast amount of knowledge and ability. Previously, it was not as possible to come back and teach because so many occupied math teaching jobs where they were not wholly or in part qualified to teach the subject. My students constantly thank me and others like me for being there and being able to fully explain and teach the subject with new ideas and many ideas about how to use it in the world. Further, we are able to quickly utilize technology and show students and other teachers how to integrate this into their classroom.

Cathy Seeley:
Thanks for sharing your thoughts. Mostly, welcome to the profession! Bringing together professionals with different perspectives, both from inside mathematics education and outside, can help us all grow together.

Question from
Philadelphia

As an assistant principal and former secondary math certified middle school teacher I just want to thank you for your efforts.  We indeed need to be held accountable to transfer a love of mathematics to our students, but we cannot be accountable for test scores on tests that many times do not meet the agendas of our students.  Many of our students do not get the supports of practice and teamwork at home that are so vital to mathematical success. Instead teachers try to incorporate these practice skills into classroom time and after-school programs.  The most important and necessary goal is for teachers to transfer a love of math and a feeling that students can be successful with the strategies that they learn.  If they are successful, it will be a self-fulfilling prophecy: Students will want to learn more and strive to achieve.

Thank you for efforts and support of all members of the NCTM.

Cathy Seeley:
Thanks for sharing your ideas. Certainly our major goals must include not only what mathematics students learn, but also an interest in learning more and confidence that students can use what they learn to solve many problems they will encounter after they leave us. I sure do believe in that self-fulfilling prophecy, and I have seen evidence of it in both positive and negative directions, even in my own teaching. Thanks for this important reminder.

Question from
Lake Elsinore, California

It is time for us to set the bar high and support our students in reaching and exceeding our expectations.

Too often, math is a rote learning experience focused on algorithms, rules, and memorized facts having little to do with true understanding. It’s time to help students develop deep understandings of the big ideas associated with math. Students need learning opportunities that meet them at their level. Multiple access points and rich discussions (sometimes called math congresses) enable students to construct meaning for themselves through the discovery process. They then “own” that understanding, and it becomes foundational for an increasingly complex level of understanding as they are exposed to more challenging mathematical ideas. There is no reason to allow students to languish in mathematical illiteracy. Every student can learn. We need to expect that they will, and support them along the way. In such a situation, accountability becomes a celebration of success instead of a dreaded word.

Cathy Seeley:
What a great take on accountability! Thanks for your positive perspective and your commitment to student learning. I absolutely agree with you that every student can learn and that our role is to help them get there. To borrow the slogan of Home Depot: You can do it—We can help!

Question from
Chaplin, Connecticut

In Connecticut we have a set of state-generated standards in mathematics, among other subjects.  NCTM is a leader in setting national standards.  One component of accountability should be to show that each school’s curriculum conforms to each of these sets of standards in both intention and delivery.  A second component would involve demonstrating student success, through grades and presentations of completed work, in learning the curriculum material.

Cathy Seeley:
This is a nice, comprehensive approach to accountability. Using multiple indicators of student learning and of evaluating how and what we teach is a positive step, especially when our indicators are consistent with our goals.

Question From
Erie, Pennsylvania

What is this No Child Left Behind Act going to do to our students? I teach 5th grade.  Besides the four Math and three Language Arts PSSA tests our students take, the state has determined that it will move the writing assessment from 6th grade to 5th grade. The time that we spend in just administering these tests is instructional time we are taking away from the students.  How can we teach the curriculum, if we are spending so much time on testing?  I had a student with Asperger’s Syndrome who spent 4 hours and 45 minutes on just one of the reading assessments. He spent 4 1/2 and 4 hours on the other two.  Isn’t anyone out there listening?   We are robbing from our students their childhood!

Cathy Seeley:
This is one of the most dangerous directions I see as a consequence of the excitement over accountability systems. As you have observed, the problem is significant, and not just for students with special learning problems, but for all students. This is one of those instances that I mentioned in my President’s Message where we must raise our constructive, professional voices in moral indignation. When we embrace accountability, when we say, “Yes, we want to be held accountable,” we must also then say, “There must be reasonable and appropriate ways of demonstrating accountability that support learning, and don’t detract from it.” The bottom line of all accountability efforts must be to improve learning. This requires adequate instructional time, as well as a number of other factors mentioned elsewhere such as professional development and opportunities for collaboration.

Question From
Phoenix, Arizona

A good support group, “MATH-TUTORING,” or extra help in every school. Teachers are accountable, and the learners are responsible. Let’s embrace together! Keep our minds open. Everyone could learn math, simple math.

Cathy Seeley:
Providing extra help is one way to help students meet high goals. We must indeed share responsibility for learning mathematics. Thanks for sharing.

Question from
Charleston, Illinois

Too many bad and lazy teachers are protected by tenure laws and the dreaded union.  We need some professional educators, NCTM, to stand up and make some much-needed changes.  Get rid of those people who consider teaching “a job.”

Cathy Seeley:
It is unfortunate that there may be teachers in the classroom who are not as effective as they might be. A primary goal of NCTM is to help all teachers become the most effective teachers they can be through professional development, personal growth, and networking. Just as all students can learn, I believe all teachers can teach. Not all teachers may be willing to do what it takes to teach effectively, but perhaps that is an indicator for teachers that they may be better off in another profession.

Question from
Vashon, Washington

Accountability is an essential element of schooling, but it is extremely complex given large numbers of students, a tremendous range in aptitude and achievement level, and different learning styles.  My thought is to share accountability with parents and students. Teachers need to communicate on a regular basis with parents and students, regarding goals, specific objectives, and assessment.  Teachers must be accountable, but this is best achieved when students share responsibility for their own learning.  I feel I have been successful in this respect, although there is always much to do in the way of improvements.

Cathy Seeley:
This is absolutely correct. We all share responsibility for student learning—the teacher, the student and the family. We can help students develop responsibility for learning by restructuring our mathematics classroom so that they have opportunities to make decisions, solve problems, and justify their thinking. We can help families take responsibility for their part in the learning process by keeping them informed and involved in what we do in school.

Question from
Ames, Iowa

What are some specific ideas on meeting accountability in mathematics learning yet still teach a balanced program?

Cathy Seeley:
I honestly believe that if we teach a balanced, comprehensive program that combines facts, procedures, conceptual understanding, applications, and the development of problem solving and other processes as described in Principles and Standards for School Mathematics, students will do fine on just about any test they encounter.

Question From
Phoenix, Arizona

While it is true that teachers need to find ways to pique the interest of their students, I find that the majority of students who do poorly in math are not being encouraged enough at home and that the parents need to make sure that their child puts their school work ahead of TV, video games, and playing with others.

My son does well in all his classes because my wife and I insist that he do his homework, and during the summer we have him spend an hour a day (weekdays) doing math and reading.  This keeps him from forgetting a lot during the long summer break.

Cathy Seeley:
Thanks for reminding us about the critical role families play. Where students have this kind of support at home, they will surely learn more and retain what they learn better. I know that my father missed no opportunity to give my sisters and me mathematics word problems when we were in the car. We always groaned, but I know that we did better in school as a result. I worry a lot when families may not be in a position to play the kind of role you describe because of work responsibilities or other challenges in the home situation. In the long run, our students will surely benefit when we support their learning as a team.

Question From
Glastonbury, Connecticut

Accountability demands a teacher to preassess and postassess. How else can we really know that the child has made progress?

To be effective for all we must disaggregate the data.

Cathy Seeley:
Knowing where students start and end is clearly important. This can be done through formal assessments or through informal techniques. We must also be careful, however, not to spend too much time in this process, especially at the beginning of the year. I have too often seen students who enter school in August or September not remembering everything they have learned. Sometimes we need to assess what they know in the context of getting them engaged with mathematics that also extends what they know.

In terms of disaggregating data, I couldn’t agree with you more. In Texas, we have done this for many years, and No Child Left Behind has now made this necessary in all schools. When we disaggregate our data, we can no longer hide behind averages. An overall satisfactory average is not acceptable if certain groups of students consistently fall behind. When the category a student falls into based on his or her birth is related to the student’s level of achievement, there is a systemic problem to be addressed. We know from too many examples that there is no reason to think that certain racial, language, or socio-economic groups should perform at lower levels than other groups of students. So when we see performance of some groups falling below that of other groups, we must ask ourselves what educational opportunities we have been denying to these groups of students. Too often, a traditional lecture-and-listen approach to teaching has left out significant numbers of students who may be bored or feel disengaged from the learning process. We know now that to help all students succeed, we must engage students in their own learning. This means we must ask the question, “Who’s doing the talking?” in our classrooms. If the teacher does most of the talking, the likelihood is that many students are not engaged. If the teacher shifts her or his role to facilitate learning where students discuss, write, and do mathematics in active ways, we can reach many more students, including those who were successful in a lecture situation as well as those who were not.

Question From
DeKalb, Illinois

In Illinois, the writing portions of the state test in both language arts and mathematics are going to be dropped to save money on the huge cost of grading.  Having the writing in mathematics being tested really helped to motivate teachers to include problem solving in their classrooms.  Students had to tell what they did and why they did it.  I think this is very valuable, and I fear that in the race to get test scores up, that not enough time will now be spent in this important area.  What are your thoughts about this?

Cathy Seeley:
What a shame to lose such a powerful positive motivator. Unfortunately, this is becoming all too common. I think that the main reason we have large-scale tests that do not reflect the most innovative assessment practices is because of the logistical and financial considerations that states and districts must consider. If it’s any consolation (and I think it is not), most states have never made the commitment to such open-ended assessments. Perhaps the fact that educators and the public have now seen this in Illinois can be used as a tool to advocate its return. This may be an opportunity for organizing your professional mathematics colleagues (and probably your language arts colleagues as well) across your state to work with state policymakers, generally the legislature and the State Board of Education, on the importance of this type of assessment for improving student learning (and those all-important test scores). Investing in this type of assessment program is truly an investment in our children and the future of society.

Question from
Boone, North Carolina

As professionals, we are teaching and hopefully watching children grow and develop each day. We need to watch for and incorporate new goals within our daily duties. Sometimes we need more support as to the exact meaning and extent of developing those state goals and objectives. As a former question writer and long-time teacher I know that the exact interpretation or intent of objectives varies in different settings. Without verbal dialogue, sometimes the best intent is lost or misleading. I don’t believe accountability is a question, but true understanding of what we are accountable for is sometimes open (unintentionally) for discussion.

Cathy Seeley:
I absolutely agree with you. Dialogue and discussion among colleagues is critical as we plan on how to implement state standards, goals, and objectives. Articulation across the grades is one of the most powerful tools available to us. In doing so, each grade level/teacher can be clear about the priorities of the grade level and about where the major focus of various topics should lie.

Question from
Greenwood, Arkansas

I feel Lisa Carter was correct when she said to keep children motivated we must keep them right on the edge of their chairs.  If students are too relaxed they do not learn well, and if they are too stressed they do not learn well.  As teachers I feel we are the same way—we need a little push.

The benchmark scores are enough of a push to make our teachers feel ownership. Our administration tries to help our teachers to ease the stress, but again it puts our teachers right on the edge, which makes them do a better job. 

Cathy Seeley:
It sounds like you may be working in a positive environment with leaders who recognize how we can balance accountability and achievement. In studying about mathematics anxiety several years ago, I learned that a small amount of anxiety can be healthy and motivating. It’s a delicate balance to find where to draw the line, but I think you are right on target that we need a bit of pressure (not excessive) in order to do our best.

Question From
Susanville, California

I agree with an earlier comment about the problem with only the teacher being held accountable. Here are two ideas:

For Students: One thing a few teachers are trying this year is telling students that if they score in the Proficient or Advanced category of the CA STAR test (where NCLB says that all students will be by 2013–2014) that they will go back and raise their letter grade for the course. This may motivate our high school students to try harder and help with the apparent lack of interest on their part.

For Parents: I have an idea that may help keep parents accountable, especially at the high school level, where many parents seem to reduce involvement in their child’s academics: have the federal child tax credit be tied to their child’s performance on these tests, either by showing improvement or by reaching the Proficient or Advanced levels.

Cathy Seeley:
Thanks for sharing these thoughts. There may be a range of options to encourage this shared responsibility. Your suggestions are indeed provocative.

Question From
Dallas, Texas

I was glad to read about this chat.  Two weeks ago a union representative of a union that I don’t belong to tried to tell me that I may want to switch because my union voted for accountability.  I informed him that I was glad to hear it because in my opinion, good teachers don’t mind being held accountable.  He asked what if I get a “bad class.”  I told him that there is no such thing.  I have taught for going on 27 years and for 22 of those years I taught at a school that has the reputation of having some of the worst-behaved students in the district.  In my class they treated me with respect because I treated them with respect.  They knew that I genuinely cared about their education.  I was the Southern Region recipient of the Excellence in Teaching Award in 2000 because of the gains and programs I put in place at that school.  There are no “bad classes.”  What is bad is how we react to them.

Cathy Seeley:
Thanks for this great perspective! I have come to believe that in my own teaching, every time I have made an assumption about a student or a group that might not be able to learn as much as another, there is someone out there who could prove me wrong. I am thankful for the times I figured it out for myself in time to help a student reach a level I didn’t at first think the student could reach.

Question from
The Woodlands, Texas

Are you hinting at math specialists for all grades, even early elementary?

Cathy Seeley:
No hinting about it… Every student deserves to be taught mathematics by a teacher who knows mathematics deeply and who knows a variety of ways to teach it. If this can be done in self-contained classrooms, that’s great. Most often, it calls for someone who has specialized in the teaching of mathematics. Schools that have made this kind of investment have seen the positive results (as in Alief, on the other side of Houston, as well as in other districts).

Question from
Houston, Texas

What are the implications of assessment for English as a Second Language and Bilingual students?

Cathy Seeley:
These students provide us with some of our greatest challenges. Eugene Garcia, in a recent speech, observed that we can never know what mathematics a student really knows if we are assessing him in a second (or third) language. In my opinion, we have challenges on two levels. We must find the best ways we can to assess what students know if their first language is not English. Of perhaps even more importance, we must be careful not to make inappropriate judgments based on limited test results for these students. Too often, students are far more sophisticated in their understanding of mathematics than they can adequately communicate on our limited measures. Of course, we also have to work on how we can help students develop this sophisticated understanding in the classroom when they may not have the reading, writing, or comprehension skills necessary to deal with the mathematics in either of their languages. This is an area of critical attention if we are to close the achievement gap among groups of students and, more important, if we are to help every student achieve high levels of mathematics.

Question from
Cedar Rapids, Iowa

Some of the encouragement for development has to fall on the district’s leaders.  If the leaders see no need to change, it is hard for individual teachers to paddle upstream.

Cathy Seeley:
Instructional leaders at the school and district level play a critical role in enabling and encouraging teachers to teach in ways that best serve all students. This is why I see working with administrators as one of the most important elements of professional development. Not long ago, I participated in a day of professional development at a school district where all the administrators, including the superintendent, were part of the mathematics activities for at least part of the day. I think the likelihood of success in this district is considerably greater than where this kind of commitment is not present.

Question From
Brooklyn, New York

Do you believe the New York City policy of holding students back because they fail one test, even given a complicated appeal process, has any merit?

Cathy Seeley:
Promoting or retaining students is far more complicated than it first appears. I have worked with systems (both state-level and local) where students have been overretained or overpromoted. The challenge lies in recognizing that what we have done the first time has not worked for this student. So we must do something different. If we promote the student, we need to implement some kind of support structure that will enable the student to succeed where he or she has not succeeded in the past. This may mean a special summer school program with something different from what the student experienced during the year. It may mean some kind of after-school support throughout the year or some kind of mentor or buddy process. We must be open to looking for ways to help students succeed if they have not succeeded in the past.

On the other hand, we have very good evidence that most students who are retained, especially more than once, have a high likelihood of not completing school. So we must be very careful in retaining students, especially based on limited measures. This is too often not a good solution for most students. If we retain a student, we must ensure that the next time the student goes through the grade level or course, something different happens from what happened the first time. And if the student has made satisfactory progress in one or more disciplines, we must be sure the student can advance that progress even if held back for a different discipline.

Question From
Dixon, Illinois

Although this isn’t rocket science, I believe that our math department has made great strides in administering and analyzing common final exams.

Cathy Seeley:
Common exams can be helpful if they reflect current best practice and appropriate learning goals. Identifying what these learning goals are is an important collaborative activity that needs to take place as part of a move to make teaching and learning more consistent within a school or district. Often the goals, and our ways of reaching them, are not the same as they were a few years past, so we must be careful not to fall into patterns of entrenching old ideas.

Question from
Manhattan, Kansas

What is your advice on how to involve institutes of higher learning in the whole accountability process? Too often, recent graduates are entering our schools with little knowledge of accountability, national standards and what it means to be a standards-based teacher. Do you have any suggestions on how we as teachers can encourage this?

Cathy Seeley:
Thanks for this reminder about an important aspect to accountability. The role of teacher education institutions is extremely important in this arena. Teachers need high-quality professional development about standards, assessment, accountability, and policy issues. Ideally this is done at both the undergraduate and the inservice/graduate level.

This type of additional focus to teacher preparation programs can be one of the outcomes of the many collaborative efforts beginning to appear in cooperative projects around the country. It is also a topic that may benefit from the efforts of local and state mathematics organizations. Proficiency in this area should be a top priority of professional development programs, beginning with preservice teachers and continuing throughout the career.

Your feedback is important! Comments or concerns regarding the content of this page may be sent to nctm@nctm.org. Thank you.