Good afternoon and welcome to today’s chat with NCTM President Johnny Lott. Here’s the first question:
What exactly does this statement mean? What are the stalkers of math education?
In the President’s Message in the January-February NCTM News Bulletin, I identified types of stalkers of mathematics education. I identified no type without evidence of the type. I would be very surprised if there are not examples within your state of people, or groups, who are attacking change in mathematics at the pre-collegiate level, and possibly at the collegiate level, using primarily anecdotal evidence and attempting to change policies and testing based on this “evidence.” In some states, I have been told of threats, personal and professional, of individuals who have promoted change in mathematics education. This type of behavior should not be tolerated. One person suggested that the reason that participants in www.mathematicallysane.org were anonymous initially was because of professional threats.
New Haven, Connecticut
You speak of a critic who uses their stature to denigrate an opinion that disagrees with their own and actually threatens to smear the journal if this opinion is not altered. How was this specific difference of opinion addressed? Was there an open forum that examined both opinions?
Differences of opinion have been expressed both in writing and verbally. One aspect of the NCTM journals is Readers Dialogues for expressing differences of opinion. NCTM has always presented that forum for differences of opinion.
Binghamton, New York
Your message was very thought provoking (as always). I personally would like to see more parents visit classrooms to see what learning math is like from an adult perspective. Every time I read a letter to the editor in my local paper in which the writer puts down teachers, I wish they could come and see what we really do every day. They might be surprised to see what they could learn in some of our classrooms, and it might give them a more accurate picture of what’s going on than what they hear from either their children or other parents (or the “stalkers”). Do you know of any effective ways or existing programs to get parents into high school classrooms? Thank you.
I agree that we are far better off when parents visit the classrooms and see what is going on there. However, we as mathematics educators have to make them feel that they are welcome to visit the classrooms. Simply having a parents’ night once a semester or year is not sufficient to accomplish this. It is a start, but it is only a start. If you can find ways to integrate families into the classrooms in a meaningful way, these would be best. Successful methods have included family tutoring in the library, families donating time in the school for different components of the school day, and having a parent come-to-school day in the way that many businesses have bring-your-child-to-work day. In different situations, each could be problematic, but much depends on the school, the school’s attitudes toward families, and on a teacher’s time to work on these ideas. None are trivial.
New York City
In your article you say, “continuing research shows that such curricula do in fact work when used by knowledgeable teachers.” Would you acknowledge that teachers who are not knowledgeable in their content area staff many urban schools? Has any research been done to show the effect on students when uncertified, untrained, or inexperienced teachers use reform mathematics curricula?
I think that the answer to your basic question is not as simplistic as “teachers who are not knowledgeable in their content area staff many urban schools.” According to the recently released NAEP Trial Urban District Assessment, for students who are eligible for free/reduced-price lunches, at the fourth grade the percentages for large central city (public) is 69 percent while the nation is at 44 percent. At the eighth grade the percentages are 38 percent for the nation and 60 percent for the large central city (public) districts. While “non-knowledgeable teachers” might be a part of the issue here, it is far from the complete picture. Poverty in many urban schools is a more fundamental problem.
You asked about the effect on students when uncertified, untrained, or inexperienced teachers use reform mathematics curricula. I seriously doubt (though I have little evidence) that the results would be very different from having uncertified, untrained, or inexperienced teachers using so-called “traditional” curriculum. Neither is a great situation.
Nevada City, California
Jack Price, from the podium at the San Diego meeting a few years ago, suggested that folks that question the vision of the 1989 Standards might just be worried that minority kids would be doing as well as their own. Does that count as stalking, or innuendo? Dr. Price, as a past president, claimed later that the movers behind Mathematically Correct were the ones afraid that minority kids would do as well as their own (and Jack didn't retract the statement when confronted with it on a public e-mail list). Do you think that counts as innuendo, or is that just slander?
David Klein, a co-author of the letter to Secretary of Education Riley, has rebutted your claim that many had requested to remove their signatures. Dr. Klein states that only one person had requested this after the publication, and that it was done promptly. Rather than more innuendo, do you think either a substantiation of your claim or an apology is in order?
I am not sure what Dr. Price referred to in making his statement. He would have to be asked about that one. I would ask that people look at the evidence presented on the ARC Web site from Massachusetts when one considers reform curriculum evidence.
In the case of the letter to Secretary of Education Riley, I am not privy to the information that Dr. Klein has. Though one may choose not to believe me, I was asked specifically not to reveal names of people who signed the letter who did not like the way it was used. I am sorry but I am not at liberty to do that.
Clinton Township, Michigan
I came from a strong mathematics background into a graduate mathematics education program. I love the program, but feel harassed by some mathematicians who feel the program is “weak” or focuses on areas they feel are insignificant and pointless (e.g., the process of solving a problem). While my mathematics background is strong, I am nowhere near their level. How do you defend yourself against such attacks and bullying when they refuse to even listen? It’s almost as if they have turned their backs on mathematics and are now committed only to fighting any change in mathematics education that they perceive as a threat to their “teaching style.” It’s just very frustrating when your philosophy is constantly attacked yet the attacker refuses to listen to your defense. Also, one item to note is that mathematicians are not trained as mathematics educators. So why do so many feel the need to criticize mathematics education to such an extent?
Ironically, what you have expressed is classic from many different settings. Included in those are (1) an insecurity on the part of the non-listener, (2) a defensive posture as a result of insecurity, (3) a lack of understanding and an intolerance of that which is not understood, and (4) a reaction to a threat to comfortable beliefs. Many colleagues from both the mathematics community and the mathematics education community do not understand the other community. Interestingly enough, much of the outside world does not understand that there is a difference in the two communities. All are “mathematicians” in the sight of the outside world. Internal strife among “us” is neither appreciated nor understood.
What can be done? Some colleagues have begun to demonstrate the need for each group to understand the other. Hy Bass’s talk at the recent joint AMS/MAA meeting in Phoenix provided one example. He talked about famous mathematicians who have had an influence on mathematics education. His two initial examples were Felix Klein and his transformational geometry, and Hans Freudenthal, the Dutch mathematician who was a guiding force behind Educational Studies in Mathematics. These two examples do not stand alone.
Examples of methods of starting conversations that are being tried around the country, even in small schools, include having joint seminars and study groups that concentrate on one topic or book in a term and having mathematicians and mathematics educators watch a lesson and then identify the mathematics that is needed to answer student questions and to respond to student ideas.
Kinderhook, New York
While reading parts of the chat on “abuse” and seeing the upcoming theme, I thought about a situation/response setting that I have witnessed hundreds of times if not more and that nauseates me. It occurs when another teacher or administrator has the opportunity to say, in front of the students, that they were no good at math either, and actually SAY IT! I believe that undermines whatever the math teacher is trying to do.
I could not agree with you more. It is past time that statements like these go the way of other slurs against mathematics in the media, in movies, and in other forms of mass communication. Public perception definitely needs to be changed. One NCTM effort to do that was the Figure This! campaign. See it at www.figurethis.org.
New York City
Johnny Lott describes three menaces to mathematics education which I wholeheartedly concur are indeed clear and present menaces.
However, I firmly disagree with what I believe he wishes the reader to infer, that those three menaces reside only in advocacy for mathematics education differing from and critical of that espoused by the NCTM.
For those three menaces have in fact regularly been practiced by NCTM advocates as well, at the local, state, and federal levels.
What steps and policies would lead to the dissolving of the “three menaces,” that would lead to mathematics education reform that is (a) informed by a broad range of expertise, that would include the experiences and values of those most often excluded: parents, senior classroom teachers, and university level mathematics instructors, (b) that allows for open transparent public involvement and oversight, (c) that is not driven by financial incentive or political partisanship, (d) that is driven by the needs and ambitions of our nation’s students first and foremost (e) that is driven by the needs and ambitions of research and development in the various math-based fields, so clearly in the best interest of our nation’s future?
You asked what might be done to promote an end to the three menaces as you described.
You asked for an effort that is informed by a broad range of expertise, including parents, senior classroom teachers and university level mathematics instructors. Let me address that first. Your group leaves out some of those with the most expertise about how students learn, and that is mathematics educators. You may not like to admit that group is needed, but it is. You included college and university level mathematics instructors. I agree that they should be there and should be more than willing to share the role with others. In fact, the new publication of the MAA (Mathematical Association of America) by the Committee on the Undergraduate Curriculum in Mathematics makes recommendations very like those in the NCTM standards. On open conversation would be very good.
I’m not sure what you mean by transparent public involvement and oversight. You would have to explain that a bit more. If the public involvement is from the federal level, many in the country want to know what role states have and what role the federal government plays.
To put our students first, we have to realize that public school teachers are faced with all students and not just a small sector of the student population. We need to have a curriculum for those who will be future mathematicians and scientists. We also have a major obligation to have a mathematics education for those with other interests. That is the majority of the student population. In addition, teachers have the responsibility for working to have mathematically literate adults for the future. This is no easy task and one that NCTM has been promoting in all its publications. Help is needed, but let’s make sure that when we have open discussions we do not create a situation in which some students are ignored or when those students who do not now have a mathematics and science interest have enough mathematics to develop those interests at a later time.
The chat on December 11 opened with the comment from Baton Rouge, Louisiana:
“I think use of the word ‘abused’ in this context is completely inappropriate. Of course there are millions of children who are not being mathematically (or linguistically) prepared to function successfully as adults. This is inexcusable, and we should be working tirelessly for change, but it doesn’t fall within common usage of the word abuse. Let’s leave this kind of hyperbole to the tabloids—it diminishes our message.”
My comment is that the same idea is now reflected in the NCTM portraying its opposition as being “stalkers.” Granted, suppressing free exchange of ideas is standard practice in the education industry—being opposed to Whole Language reading is “child abuse,” being for immersion English is “xenophobic,” critics are “right-wing Neanderthals,” etc., but it always diminishes the position of the speaker and often is a porous lid on a cesspool of educational malfeasance. The smell still comes through.
As one of the signers of the letter to Secretary of Education Riley, I resent the implication that people were somehow misinformed or that more than a couple of the other signers had second thoughts about their decision; almost all of us feel exactly as we did then and with even better evidence. Instead of a witch hunt to root out “a lurking menace looking to denigrate these accomplishments” why not actually confront the controversy openly? Are these curricula more successful over time? Do they meet the goals that they were authorized to address? Or do they go belly-up as IMP has done across California and the city of Philadelphia? Do they reflect the response to three years of Core-Plus in Austin, Minnesota, when they dropped it midyear 2000-01? “We gave our students a diagnostic test and they were doing awful.”
Be very careful when you talk about tabloid language. I stand behind everything that I wrote in both essays. That includes the use of the words “abuse” and “stalkers.”
You asked about NCTM being willing to confront controversy openly. I believe that is exactly what the Council has done for a very long time. The Principles and Evaluation Standards were open to the public for three years. Now there is still an Executive Summary available to all on the Web. We have stood for quality mathematics for all students and to have that mathematics taught by well-qualified teachers (those who know both mathematics content and pedagogy) for as long as I have been a member of the organization—since 1965.
One thing that some do not realize is that the organization does not and has not supported commercial products. NCTM does not give a Seal of Approval to curricular materials. We, as a Council, certainly believe and have research to back up what is proposed in the Standards. The Council has written no texts. It has left that to others.
You have identified sites where a curriculum may not have been successful. I believe that there are equally many areas that can be identified where reform curricula have succeeded. Have you considered the results of TIMSS-R in Michigan schools where reform materials were used? What is your response to those results of students who succeeded and the data appeared to cross socio-economic lines?
Pine Knot, Kentucky
Why do we as teachers go into math education? It is, or should be, for the students, right? Have we let those “stalkers” change the reason we went into teaching in the first place? What suggestions do you have for teachers in the mathematics classrooms so we may stand fast when there seems to be so much against us?
Interesting question. I’m not sure that I went into teaching for the “right reasons,” that is, students, but they are certainly the reason that I stayed there. If you are in a pre-collegiate setting, my strongest suggestion is to try and build a student family support system behind you and your work. The strongest supporters of schools are those families who recognize the importance of teachers and the work that they do. To build this support, families have to know what we are doing. Ways to let them know include inviting them to the classroom, and making sure that every reporter and legislator personally knows a mathematics teacher in their area. Become the local math expert for your school or community.
Oundle School, United Kingdom
I think the U.S.A. and U.K. share many problems in mathematics in schools: shortage of suitably qualified teachers, and pupils losing interest in the subject.
I firmly believe that the use of dynamic images in the classroom can make the teaching more effective and more efficient, and definitely more fun. But how do we get this across to the teachers, who hardly have time to draw breath?
I fear that the United States and the United Kingdom are not alone when we talk of the shortage of qualified teachers and pupils losing interest in the subject. Other countries have comparable problems—many of them for very different reasons.
There is growing evidence for the use of technology improving student learning, but the research is still pretty limited. The problem is not always getting the message across to teachers; it also involves school funding and accessibility to the technology beyond the classroom. Interestingly, as the use of cell phones has increased, the availability of different types of technology is becoming more and more common. Now can we put the mathematics technology that we want students to have on cell phones? That has the potential to make differences beyond our beliefs in the future. Many have calculators now. This technology is becoming available in countries that still have issues with electrical lines and power transmission. Do you have ideas for creating this type of math technology?
Charleston, South Carolina
During the recent election mania the subject of No Child Left Behind has surfaced—in a condensed form—and it has been said that President Bush did not have in place everything that was necessary for its success. Indeed, it was said that the entire process is failing or falling apart. What does this mean for teachers whose jobs are being threatened because they were certified under the old rules/laws, etc.? With all the daily pressures that teachers face (especially in at-risk schools) what do we tell them will be realistic as we approach 2006—the deadline! Needing reassurance in South Carolina!
Most states have now submitted their individual plans for what it means to be a highly qualified teacher. To my knowledge, many of those plans have not been approved as I write this. From personal knowledge, many of the plans are vastly different, from the status quo in a state to very different plans for certification models. A first step is to determine what your state submitted. See how you are affected. Then you can make plans.
Regardless of what South Carolina submitted, I believe that teachers of mathematics should continue to study mathematics to stay current in the field. It is always changing and must continue to do so if we want the discipline to survive. No one’s education stops when they receive a diploma. Teachers in particular must stay current. What I studied in school would be wholly inadequate now. What I knew and taught as a first-year teacher in 1965 would be wholly inadequate now.
I’m not sure that any of this will reassure you. Right now, one needs a crystal ball to see what changes in implementation of NCLB will occur. We do know that some change needed to be made in schools so that all students have access to mathematics taught by well-qualified teachers, those who are knowledgeable in both content and pedagogy. NCLB is the law; and we have no choice but to plan for it; just how implementation will occur when state budgets are not available to support schools making changes is an issue.
What is your opinion of the NCTM Standards vs. the California Standards, and which are more important? Why isn’t there just one set for all the states? Are one state’s more important than the others?
I am a strong believer in local control of education, and that includes the selection of texts and to some extent the writing of standards. Beyond the local control is the recognition that we are a very mobile society and that students now rarely complete school where they started. The mobility more than anything else may be an issue that demands some overriding set of standards for the nation. If there were such a set of overriding standards, I personally would opt for a wider view than any given state typically has.
Has anyone really looked at the curriculum for math? I teach 6th grade math now, but have been teaching for 23 years. I am now teaching my 6th graders what used to be new in 8th grade! In Texas (which follows NCTM guidelines) 6th grade math consists of 72 percent NEW material. We do not have time for students to truly MASTER the material and they are NOT ready to handle many of the concepts. We also do not have time for the many fun learning games & activities that help cement concepts & make math enjoyable. With 1-hour classes I feel like a drill sergeant: “We have to get through this today.” The people “in charge” need to really rethink what topics need to be done at each grade level.
You have given a fairly persuasive argument that mathematics is changing in schools. In my mind, that is as it should be. Mathematics curriculum must change as the needs of the world are changing. I do not believe that curriculum can ever be static, or it will die. Ironically, because of the many different state standards and publishing companies “needing” to satisfy the needs of the different states, textbooks have grown significantly over the years. Also ironically, one of the biggest issues for the 1989 standards was the set of increased emphasis and decreased emphasis lists for curriculum. We cannot continue to change curriculum while demanding that all of the “traditional” topics remain in place.
How do we handle the mismatch between funding of programs and expectations? There is a real disconnect!
There is a growing mismatch between the funding of programs and expectations in schools. It behooves all of us to contact local, state, and national legislators to make them very aware of the mismatch. This mismatch must be addressed at all levels. Few states or districts can afford unfunded mandates.
What more can we do to get the textbook publishers on board with us in our quest toward more meaningful mathematics education?
Publishers market what schools are willing to buy. In this one, we may be our own worst enemies. It is a given that if schools were not buying materials from publishers, the publishers would not exist.
Freehold, New Jersey
What are some NEW INTERESTING projects that we can use to connect real-world problems to middle school students? How do I deal with different types of students at this age level? Some feel they are being babied while others are having a great time in class.
The National Science Foundation spent many dollars in allowing people to develop innovative materials for mathematics for middle schools (as well as elementary and secondary schools). Those materials can be mined for mathematical gems. Beyond that, the NCTM journals and Student Math Notes continually contain material appropriate for schools. In addition, not all materials have to be new to be interesting. Sometimes the approach may make a huge difference in interest.
I am concerned that our school is using a particular set of tests to measure students’ progress in mathematics, reading, and language arts. Our principal has requested that we compute the “increase in student concept scores” from the first test in August to the second test in early December. The breakdown of the “concepts” is not consistent—the items tested on the first test are not the same as the items on the second test. This is true for most concepts.
These are my questions:
1. How can I tell if a test is valid? Who has assessed and endorsed this assessment? Who wrote it, and do they really know what they are doing?
2. I do not teach in a multiple-choice environment. How, then can this be valid testing?
3. How can we put a stop to this testing agenda? I am overwhelmed with five, and possibly six, standardized tests this academic year alone: Test A three times, Test B twice, and Test C in the Spring.
Help!! Frustrated in Alabama
As a teacher, you have raised some legitimate questions that go beyond your school. The system should be able to answer questions about the validity and reliability of any test being used in the school, district, or state. In addition, there should be available to anyone who asks the following: (1) a description of the specifications for writing the test questions, (2) a description (generically) of the qualifications of the test writers, (3) a description of the test piloting situation, the types of schools used, a description of the student population used to determine whether or not the population matches the school population where the test is being used, (4) a detailed description of how and why tests are being used and how groups of students are affected by the use, (5) and an explanation to parents of why tests are given with the frequency that they are. I’m sure that these are not all the questions, but answers to these should be readily available. If a testing company cannot provide its part of the information, then one should question the use of the tests. If a school or state cannot provide its part of requested information, then one should question the use of the tests, and so on.
Finally, as a teacher, you might have to adapt to some of the realities in today’s world, and that may include the use of multiple-choice tests. There are some projects in the country that are specifically looking at multiple choice testing and how it can be used effectively. Check out the National Science Foundation and the U.S. Department of Education Web sites to see if information about specific projects can be found to help.
Freehold, New Jersey
This is my first year teaching. I know I am less than 10 years older than most of my students. I try to connect with them as much as possible but other teachers think I am too personal and I need to keep my distance. How do I deal with these kinds of situations? I love my job and I love how I handle it!
I’m certainly not sure that there is an easy or generic answer to this one. I do believe that in order to be an effective teacher, you have to reach students. However, there are many ways to “reach” students, not the least of which is by making lessons interesting, using contexts to present material, and by showing simply an enthusiasm for the subject. At this stage of my career, I think I can reach students, but my interests are certainly nowhere close to students’ interests. Mathematically, there continues to be an opportunity for presentation of topics and the development of topics that are challenging to both my students and me. Don’t forget that as you mature in teaching (and age), the students will typically be the same age that they are now. You will need to develop a variety of skills to deal with the students if you continue to love your job.
Thank you all for your participation today. The next online chat will be announced on the NCTM home page, and a full transcript of this chat will be posted within the next two days.
Thank you for participating in this open forum with me. This avenue is one more way that NCTM is trying to respond both to members and the public in an open way. I do appreciate the questions.
I invite all of you to come to the NCTM Annual Meeting in Philadelphia on April 21-24. There we will talk about a political action platform that NCTM has proposed for mathematics education. We invite all to participate with us in promoting that platform at all levels.
Have a good day.
Note: Because the following two questions were submitted after the conclusion of the online chat, Johnny Lott answered them later.
After a year of careful study and extensive piloting, we selected Investigations in Number, Data, and Space for our K-5 mathematics program. E-mails began circulating recently stating that the chair of the mathematics department at Harvard University had dealt with this program and was well aware of its weaknesses. We spent a great deal of time correlating this program with our new state content standards and found Investigations to match these standards very well. We think we adopted a solid standards-based program, yet some of our parents are being told that mathematicians disapprove of this program. How did mathematics teaching become so politicized?
Though a clear traceable route is not always easy to find, it appears that the beginning movement started when a small number of people felt that their voices weren’t being heard. What ensued eventually became the “math wars.” There are several lessons that can be learned from that experience.
1. A small number of people can force change. This has both good and bad points, and much may depend on your personal philosophy of what and how students learn mathematics.
2. Any group can be threatened if another group tries to change the status quo. Examples may include parents worried that the mathematics their children are studying is unlike what the parents studied; university people worried that the influx of students into the set of traditional first-year courses are not as “good” as they have been in the past; administrators worried that their schools will be disrupted if there is a community uproar over curriculum; and in general, a fear of the unknown—in this case—reform curricula.
A bigger issue is what we do to overcome the conflict. This is harder because it takes two groups being willing to talk and listen, and the emphasis is on listen. This is only my opinion, but we should all be after what is best for the mathematics learning of students. There may be places where we agree to disagree and then let teachers and students get back to what is really important—learning.
A few mathematicians have designated themselves “experts” on fixing the problems of K–12 mathematics education. Why are they given the platform to speak out and act like they represent the entire mathematics community? What is the position of their professional organizations, such as the MAA?
To my knowledge, there is no official position of the MAA on the “representation” you mention. As with NCTM, there a very few people who officially represent the Council, though there are many strong members who either are or have been closely associated with NCTM who are perceived to “represent” the Council. I imagine that organizations like MAA and NCTM are very careful to make clear when positions are official and strongly encourage others to point out very carefully that their personal positions may not officially represent the organization. I believe that this may not have occurred as it should have in many situations in the recent past. Much has to do with public perception of the speaker(s) and how the perception is interpreted in the media. Broad brushes are in many instances not appropriate when statements are being made.
Editor's Note: NCTM moderators retain editorial control over online discussions and choose the most relevant questions for guests and hosts. The moderator and host may decline to answer questions
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