In today's world, middle school teachers may find it challenging to teach mathematics if their education resulted in a K-8 teaching certificate.

- How can those who teach or aspire to teach middle school attain the knowledge of mathematics content that they will need to prepare students?

- How can we satisfy either the Mathematical Education of Teachers (MET) or No Child Left Behind (NCLB) mathematics requirements for prospective teachers?

**Question from**

Los Angeles

Where does pedagogy fit in the MET recommendation that middle school teachers should 1) develop a deep understanding of the mathematics that they teach and 2) broaden their understanding of mathematics connections between one educational level and the next? How do we ensure that teachers attain the math content knowledge, as well as gain a deeper understanding for how to best teach this mathematics to students?

**Johnny Lott**

Good questions! Remember that this document was created by a mathematics organization. Also know that mathematics is necessary but not sufficient for good teachers. Good teachers have to have knowledge of pedagogy, how students learn, and different strategies to reach students with different learning styles. There is no one model that fits all when it comes to teaching.

As another part of your questions, people like Deborah Ball and others have been working to learn how to reach that deeper understanding. Examples come from being able to answer classroom questions, to realize when students may have super mathematical ideas that may not be the norm in answering questions. To use a take-off on an older book, perhaps what we are considering at the middle school teacher preparation level is An Advanced Understanding of Simple Mathematical Ideas. Simply having more content studied may give some of the breadth needed, but it might not give the depth sought.

**Question from**

West Palm Beach, Florida

What is NCTM's position on the propriety of requiring all 8th graders to take algebra? Our school district will implement this policy next school year, without waiting to see the results of a pilot study underway in the district with several schools teaching algebra to all 8th graders. Will you at least specify the pros and cons of such a policy? I really appreciate NCTM's guidance and sharing of ideas!

**Johnny Lott**

NCTM does not have an official position on "the propriety of requiring all 8th graders to take algebra." Having said that, I am on record as encouraging all school districts considering this approach to have a very carefully thought out plan for how students are prepared before they get to this "algebra class" and a very well thought out plan for what happens to students in their final years of high school if they take algebra in the 8th grade. If there is no plan in place, there is a potential disaster in the making. I believe that this has been done in several places. One possibility to check is the San Diego schools; I believe that it was implemented there.

NCTM is on record in encouraging that algebraic thinking be taught from the early grades. This is very different from a specific course in a specific grade.

**Question from**

Houston, Texas

If Algebra I and/or Geometry is offered at the middle school level, teachers of the same should receive training in both NCTM and state standards. What is the NCTM recommended sequence of secondary courses? Is it different for ESL or ESOL students? Our district faces tremendous challenges with non-English speaking students. Can you provide direction?

**Johnny Lott**

I sincerely hope that if traditional Algebra I and/or Geometry is offered at the middle school level that the school system has a plan for (1) how to prepare students for those courses before they have to take them; (2) what types of courses are available to all students in the final years of high school if Algebra I and/or Geometry are taught in middle school; (3) evidence that the courses are not being used as gatekeepers so as not to allow ESL, ESOL, or ELL students into future mathematics courses. It is difficult to provide direction without knowing what planning is in existence before the courses as described are taught. This challenge is so related to your school system that I hope direction is being provided with those close to the system.

**Question from**

Los Angeles

To best prepare mathematics educators, you mentioned the need for development of coursework that is appropriate for middle school teachers. Do you have examples of universities and/or teacher preparation institutions that are leading the way to this charge?

**Johnny Lott**

There are several schools that are doing this. I hesitate to list a school without first asking its permission. You might want to check out the Mathematics Education of Teachers document that I referenced from the Mathematics Association of America (MAA) for some ideas. I believe that a Californian is the current chair of the Committee on the Mathematics Education of Teachers of the MAA right now.

**Question from**

Indianapolis, Indiana

How do you make pre-algebra interesting to inner urban students who don't care about anything?

**Johnny Lott**

I can guarantee you that your students do care about some things. According to many surveys, malling and shopping are two of those things. What pre-algebra mathematics is there that can use those interests? Ask them how they use money at the mall. What is the mathematics involved? This is only a start, but first try to determine what their interests are. Those interests may not be yours, but mathematics will be in most.

**Question from**

California State University, Stanislaus

Here in California, under the new NCLB (No Child Left Behind) guidelines for "highly qualified teachers" teaching in departmentalized middle schools, those teachers will need to know abstract and linear algebra. My colleague and I are writing a PMET minigrant to develop such courses that would be appropriate for such students—as opposed to the corresponding courses for math majors. Is California an exception or are other states making these types of requirements as well?

**Johnny Lott**

I don't know enough about California's interpretation of the NCLB guidelines for "highly qualified teachers" that are being put in place. If the question is about requiring a mathematics major for middle school teachers in the future, then it is very appropriate that traditional courses such as abstract algebra and linear algebra be modified or adapted to meet the needs of those prospective teachers. More power to you to doing this type of work. When you are finished, will you share it with others?

To answer your real question, it seems that there are as many different variations on requirements as there are states that are trying to comply with the law. Just remember, we do want qualified teachers of mathematics for the students. The students deserve them. We also know that content is necessary but not sufficient for highly qualified teachers.

**Question from**

Trumbull, Connecticut

I was wondering what you think of using Smart Boards to motivate students to become actively engaged in learning.

**Johnny Lott**

Smart Boards are tools for teaching that certainly have some potential for classrooms. To use them effectively will require some training and practice for users—both teachers and students. Like any other tool, they should be used appropriately and when the mathematics can be more effectively learned with their use.

**Question from**

Northampton, Massachusetts

We hear much about "content" training for non-math major teachers of upper elementary and middle school math. How would you describe quality content professional development for these teachers? How would you relate this to preservice preparation for these teachers?

**Johnny Lott**

One realization for preparing teachers and continuing teachers is that the curriculum they will teach or do teach must continue to change. AND all teachers must continue their mathematics education as long as they teach. A static curriculum at any level is a dying curriculum.

Non-math major teachers of upper elementary and middle school math have a tremendous responsibility. Every year for a student is important, but the mathematics content is developing into more generalization and abstraction in middle school. For those who were not prepared in mathematics, there is a burden of learning more and more mathematics that they may not have had. This should have been the case before NCLB but certainly is the case now. These teachers likely will not have had some math topics that are in current textbooks and are becoming more important to all.

**Question from**

Center Harbor, New Hampshire

How do I motivate my seventh grade students to love learning about mathematics and its importance to their future?

**Johnny Lott**

Think about assigning problems that involve using mathematics in local newspapers. If not local, then consider *USA Today*. Importance may be as simple as seeing it used in an adult world. It is no guarantee, but it is a start.

Also let them see your excitement and love for the subject. What interesting math have you read in a non-text lately?

**Question from**

Muscatine, Iowa

What is the NCTM recommended sequence of secondary courses?

**Johnny Lott**

NCTM does not have a recommended sequence of courses for secondary school. There are many avenues for getting the appropriate content to students. You could have a traditional sequence; you could have integrated mathematics courses. *Principles and Standards for School Mathematics* does recommend using connections throughout the mathematics coursework. However you choose to sequence courses, remember the cross connections among mathematics concepts; there is probably no course that should stand alone.

**Question from**

Minneapolis

What is the vision for the preparation of middle grades mathematics teachers: content only OR content and pedagogy for the middle grades?

**Johnny Lott**

There is no doubt that it is the latter. I don't really see how they can be separated in an effective classroom.

**Question from**

Minneapolis

What can be done to support the needs for mathematics and pedagogy for middle grades teachers at the master's degree level?

**Johnny Lott**

Some colleges and universities are designing interdisciplinary masters that encourage the combination of mathematics and pedagogy. Other non-interdisciplinary masters demand courses from each area mentioned. Maybe different degrees need to be thought about seriously.

**Question from**

Minneapolis

What is the data (separately or in the aggregate) of how states are "lumping" middle grades teachers to meet the requirements of NCLB (with elementary or secondary teachers)?

**Johnny Lott**

It is too early to have a clear picture. States are beginning to complete the requirements, but it is still hard to make generalizations about "lumping." You might continue to check the NCLB Web sites to see what different states are planning. Sometimes you may have to go to individual state sites to find out what is being done.

**Question from**

Minneapolis

What are the primary references that should be used to develop a master's program for middle grades mathematics teachers to meet their needs without advising them to take a master's degree in "pure" mathematics?

**Johnny Lott**

There are many, but I will mention only three that you might consider as background work. None of the three specifically has designs for master's programs. They are:

- "One Field, Many Paths: U. S. Doctoral Programs in Mathematics Education," by Reys, Kilpatrick (eds);

- "Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop," published by the National Research Council;

- "Adding It Up: Helping Children Learn Mathematics," published by the National Research Council.

And a very good thin source book is "Improving Mathematics Education: Resources for Decision Making," published by the National Research Council. (This is not necessarily a primary reference but it has good annotations about some primary references.)

**Question from**

Minneapolis

How can "distance learning" or "online" education for middle grades teachers support their acquisition of the required knowledge base and pedagogy skills?

**Johnny Lott**

In today's world whether one likes it or not, distance learning and online education may be the only way to reach some teachers. What certainly has to happen to use this mode of education is a commitment to learn how to do it and how to do it well. We are rapidly reaching the time when onsite education for professional development works only for some and is not an answer for all. NCTM is considering online professional development.

**Question from**

Kalispell, Montana

I agree 100 percent with the idea of a middle school endorsement. So, what do we do now?

**Johnny Lott**

Achieving a middle school endorsement in mathematics in a state where none is recognized means a definite public relations effort with the state school board or governing body, and probably the administrators association and state superintendent or chief state school officer.

**Question from**

Bettendorf, Iowa

One of the recommendations that is listed for improving middle school math instruction is "Provide professional development for teachers who are now in the classroom and do not meet the current expectations required for middle school teachers." In more specific terms, what are some of the critical topics in which current math faculty should be trained?

**Johnny Lott**

Middle school teachers need the deep understanding of algebraic thinking, geometry, measurement, data analysis and probability, and number and operations. Those are the primary standards from *Principles and Standards for School Mathematics*. Specifically, they also need to know the mathematics that students have had before they reach middle school, and they need to have a good feeling for the mathematics that students will need in the high school curriculum. Being in the "middle" demands a wide breadth of knowledge from elementary and secondary; the depth is also needed.

Another piece of the picture is to know connections among math concepts, how to deal with reasoning and proof and problem solving. Also let's not forget how to use technology to teach mathematics.

**Question from**

East Lansing, Michigan

Are there ways to become "highly qualified" without going back to take enough mathematics classes to change our minors to a major?

**Johnny Lott**

The National Science Foundation is sponsoring Centers for Learning and Teaching. At least some are focusing on delivery of content and pedagogy online. You might want to start by seeing what is available in your area.

**Question from**

Bucktown, Pennsylvania

How do we properly place incoming middle school students into their proper homogeneously grouped sections?

**Johnny Lott**

Placement of students is never easy. Of more concern with this question than the placement particularly is whether or not students should be grouped as described. At the opening summit for No Child Left Behind in Washington, Dr. Russ Whitehurst (Director of the Institute of Education Sciences) made some interesting remarks about tracking. If we are grouping, or tracking, to keep some students out of future mathematics, then we should question what and why it is being done.

**Question from**

Reading, Massachusetts

Thanks for beginning this. As I think about middle school mathematics in the "math world" it often feels as though we are not regarded as true mathematicians. Often I feel as though we are only expected to "get students ready for high school" rather than teach them important mathematics. Middle school is a time to expose kids to the math they use for a lifetime—percents, ratio and proportion, area and perimeter. All of this at a difficult time in students' lives. How can we strike a balance between preparing our students for their next experiences with math and make our time with them enriching?

**Johnny Lott**

How can students be with us and not enjoy their experiences with math and have an enriching time? Middle school is when students have the most energy and drive (in many different directions and often at the same time). Teaching at that level has been very rewarding for me personally. They are open to ideas and new mathematics—they are sponges in some sense. Yes, this is a time of preparation for other times in their lives, but what level of learning mathematics is not? Some of us experienced citizens could still be described as you did middle school students.

**Question from**:

Chatham, New Jersey

Why are you holding a chat during school hours when most members will be unavailable to participate?

**Johnny Lott**

Excellent question! The first pilot was just that and a time was picked out of the air but at a time that some teachers might be at lunch and could participate. The second was based on the first. We will think more about what time we choose for future online chats, but know that NCTM has members from far eastern Canada to Hawaii. So there is no perfect time when everyone is out of school and up to participate.

**Question from**

Spring, Texas

Middle grade students would benefit from using spreadsheets (AppleWorks or Excel) in math and science classes. What a great way for them to see how data generates graphs. It is also easy for them to see how changing data affects the graph. Using spreadsheets helps students better understand equations, formulas, and functions.

What is the NCTM leadership doing to help state leaders (especially in Texas) recognize that there is more to technology than TI calculators?

**Johnny Lott**

NCTM has a technology position paper that is certainly not specific about the variety of technology. *Principles and Standards* addresses technology in general. You mentioned spreadsheets. They are probably the second most used type of technology in today's world. We can't afford not to teach mathematics using them.

**Question from**

Washington, New Jersey

We are a regional MS/HS, and students come from elementary sending districts, with an inconsistent K-6 curriculum. What does research show to be the best way to raise test scores? We don't have thousands of dollars for new curriculum. We do lots of problem solving, partner work, and opener problems on review topics. Our teachers are diligent and hard working. But we have to work smarter. Any suggestions for where we should focus our time and energy?

**Johnny Lott**

One vital thing to do is to have all teachers have a general understanding of how what each is doing fits into the mathematical picture for all students. This is a fairly simple statement, but accomplishing it demands that teachers talk and work in groups to know what the mathematics is, how it is taught, where it coming from, and where it is going. This type of discussion might help make the K-6 curriculum more consistent and also help those schools being "fed" as well as informing the higher-level curriculum.

**Question from**

Dayton, Ohio

The number of college mathematics courses needed to teach middle school has been hotly debated in Ohio. The MSEB (Mathematical Sciences Education Board) recommends a minimum of 24 semester hours of mathematics coursework. What is your NCTM position? Which courses would you recommend?

**Johnny Lott**

It is clear that "my NCTM position" in this regard is not an official position because NCTM has no official position paper on this topic. *Principles and Standards for School Mathematics* clearly points to a knowledge of algebraic thinking, geometry, measurement, data analysis and probability, and number and operations. Then we have to mention problem solving, teaching with technology, reasoning and proof . . .

All are important.

**Question from**

Strunk, Kentucky

I have heard and read articles indicating middle school math teachers should have more than a 1-8 degree. What are your feelings on this topic? What evidence is there to document these thoughts?

**Johnny Lott**

There is pretty good evidence that teachers certified K-8 have studied less formal mathematics that those certified in middle or high school. What do you think is the mode number of math courses teachers of K-8 have had? Think of a small whole number. There is also evidence that teachers who have had more mathematics tend to have students who score higher on math tests.

**Question from**

Hohenfels, Germany

What guidelines and criteria do NCTM recommend teachers use in recommending middle school students for Algebra I, a high school course. Is there a particular test that is a good indicator? I need a reliable and accurate process.

**Johnny Lott**

NCTM does not recommend any particular test. I suspect that a mix of teacher recommendations, test results, conversations with parents about expectations of students might all be worthy factors to consider.

**Question from**

Harbor City, California

With the continued emphasis on language arts and mathematics, should these two disciplines have 2-hour blocks in the middle school—especially for remedial situations?

**Johnny Lott**

That's a tough question with no background for me to answer it. As with most remedial coursework, I would want to know if it works, how well it works, and if students can re-enter the mainstream after this work. What are the goals of the schools, parents, teachers and students in these programs? Does participation in these programs guarantee that students cannot ever take higher-level courses in these or other disciplines? If so, I would re-think.

**Question from**

Alexandria, Virginia

Why are many schools/districts/universities still focused on the requirement for a written lesson plan? The future of teaching math is directed toward use of Web-based modules and lessons or teacher-generated CDs containing the lessons for the week or other math activities that will be projected. The need is for development of new methodologies and techniques for using the new technology, rather that insist on stepping back to written documentation.

**Johnny Lott**

If I had to submit a written lesson plan, it would be done electronically. Whether or not Web-based modules or teacher-generated CDs are used depends to a great extent on what is available in a school. Yes, we need to use technology as a tool to teach mathematics BECAUSE some topics are better taught that way, but I don't think that is your question.

**Question from**

Windsor, Canada

Is there communication between your feeder middle school and high school math teachers? How does this occur, and what benefits have there been for students?

**Johnny Lott**

To answer the first question, in any school system or connected set of schools, if there is not, there should be. It is probably far easier to give you examples of disasters where there was no communication. One was the potential use of the same textbook for some students for FOUR years.

**Question from**

Manhattan, Kansas

How should the preparation of middle school teachers differ from that of high school teachers? In other words, what do middle school teachers need to know that is different or additional to what high school teachers need to know?

**Johnny Lott**

Middle school teachers need a knowledge of and understanding of the mathematics that is taught to students before they arrive in middle school classes. You need to know about elementary school mathematics and about some of the secondary school mathematics. It is also important that high school teachers know what math is expected of students in middle school and in post secondary study. I'm not sure how specific to be. If I'm not careful, I might be answering more than you asked.

**Question from**

Cheboygan, Michigan

I am in the process of developing professional development for my teachers. Can you recommend a program that as a staff we could work through together that would also help the teachers meet the requirements of NCLB?

**Johnny Lott**

I am not sure that there is one model that fits all for professional development. Think about what the school needs are, what the system needs are, and what mathematics is appropriate. Also, the requirements of NCLB are being interpreted in many states. What does yours require?

**Question from**

Salt Lake City, Utah

I have two questions about the current accountability system for teachers. 1. Do you believe that standardized (state) testing is good for students and schools? and 2. What do you think that the standardized (state) tests scores show?

**Johnny Lott**

1. There is nothing wrong with standardized (state) testing. There are misuses of results, however, which should be avoided. In the Assessment Standards (NCTM 1995) there is an excellent chart showing how schools and teachers might use different types of tests. Let's try to use tests for purposes for which they were designed.

(2) It is hard to answer your second question without a specific test and some context. In general, standardized tests show a comparison of a student with some group with which the test was normed. Those administering the test should determine whether or not the comparisons are worthwhile.

**Question from**

Bloomington, Illinois

Why are these chats scheduled for a time when teachers will not be able to participate? That's 1 p.m. here, and 11 a.m. in California. I want to be present, but I am, after all, a teacher with a contract!

**Johnny Lott**

We will rethink the time before we do the next chat next month. However, to help, we will leave a transcript of the chat on the NCTM Web site for a month. You may link to it from the NCTM homepage.

**Moderator**

Thank you all for your participation today and thanks to those who submitted questions in advance. Good afternoon.

**Johnny Lott**

Thank you all for participating today in this chat. The questions were excellent. I look forward to doing this again with you on October 20. Thanks again.

Johnny

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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