Traditionally, nonspecialists at the elementary school level have taught the fundamental ideas that form the foundation of children's mathematics education. NCTM believes that elementary school teachers must reach beyond fundamental mathematics to teach with conceptual understanding.

- Are elementary school teachers qualified to teach mathematics with understanding?

- What do elementary school teachers need to become qualified mathematics specialists?

**Question from**

Portland, Oregon

I totally agree that elementary teachers need the amount and kind of math courses you described in your President's Message (*NCTM News Bulletin,* July/August 2003). But how are we going to get colleges to buy into that?

**Johnny Lott**

One reason that the math departments in colleges may pick up on this is the release by the Mathematics Association of America of the Mathematics Education of Teachers document in 2001. It strongly recommends more mathematics for elementary teachers.

**Question from**

Chander, Ariz.

There still is a controversy about the use of calculators at all levels here in Arizona. Teachers, parents, and administrators still view the use of calculators as "cheating" rather than as a tool to help students explore and assist them in learning basic skills. How can this view be changed? What successes have you had in doing so? What role should the calculator play not only in K-5, but 6-8 and 9-12?

**Johnny Lott**

Though there may still be controversy, the research tells us that there are advantages. See Hembree and Dessart in 1986 and 1992 for a meta-analysis of the results. More recently for high schools, see the report by Burrill and others titled "Handheld Graphing Technology in Secondary Mathematics."

**Question from**

Norman, Okla.

While I agree that there is a need for specialists, I think that we have to be cautious about seeing this as the answer to all problems. If you consider the situation of many reading specialists, it may or may not make a difference in the achievement and learning for students.

**Johnny Lott**

Though there may or may not be a difference in achievement and learning in reading, we do know that students typically have better test results when taught by teachers who have more mathematics knowledge. The specialist notion may not be the sole answer, but it should help with the problem of having teachers who are afraid of mathematics or unsure in their knowledge of mathematics.

**Question from**

Metamora, Ill.

With your call for Pre-K to 5 Math Specialists, you seem to be implicitly saying we need to move away from a "core teacher" for early grades. Do you think the gains from a math specialist outweigh the gains of a singular core teacher for students?

**Johnny Lott**

There has long been the wish to have young children with the same core teacher at the early grades. The move to a math specialist could change that. At some point, we need to weigh the advantages and disadvantages of having a single core teacher versus the mathematics knowledge needed to educate children. With the emphasis currently in test scores and the ways that these may impact students' futures, it is time that we begin to reconsider the earlier notion. Pairs of teachers or teams of teachers even for young children are possibilities, with one person being a math specialist.

**Question from**

Kings Mills, Ohio

This is a story, not so much a question. A colleague has a son who is a young elementary teacher. When he was doing his observations as an undergrad he witnessed the following: The elementary teacher was working with fractions with her students. Someone asked how she would add the two fractions they were working with. She said, "Just add the top numbers together and add the bottom numbers together." I definitely think a math specialist in the classroom would have been better for those kids!!

**Johnny Lott**

It is unfortunate if the anecdote is trueâ€”especially for the students in the class. The anecdote would definitely lend a bit of credence to the need for a math specialist. There are many indicators that may tell us that specialists are needed. Not very long ago, the mode number of mathematics courses required for an elementary teaching certificate was 0. Now it may be 1. Few believe that this gives prospective elementary teachers the knowledge of mathematics needed for teaching. What happens if this continues is that it may force school systems to have strong professional development programs in mathematics for even beginning teachers.

**Question from**

Georgetown, Tex.

I agree that elementary certification needs to include more math hours; however, the university instructors need some help also! I do not think it is enough to know the how and when to use certain algorithms, without an understanding of how children naturally learn mathematics. I find this lacking in higher-ed instruction for preservice teachers.

**Johnny Lott**

I agree that help is needed in higher education for instruction for mathematics education courses. That is one of the reasons that NCTM is participating to support Project NeXT, a program of the Mathematics Association of America, to work with young faculty members in colleges and universities with an interest in mathematics education. There are other potential solutions, including using teachers in schools to plan and help teach the mathematics courses in colleges. There have been very successful programs across the country in doing this, though on a very limited basis.

**Question from**

Missoula, Mont.

Why should I consider a specialist for math when I don't have one for science?

**Johnny Lott**

The call for a specialist in mathematics does not preclude the need for a specialist in science. This call addresses a severe, dire need in mathematics. The call for the specialist in mathematics is on a par with the specialist in reading, music, and physical education found in many elementary schools.

**Question from**

Peoria, Ill.

It seems that the math these teachers need to understand is really not captured in courses taught through the traditional college and university math courses, but is critical for this group. Do you see this as a problem, and is it something that can be solved with math departments or would be better attacked outside math departments? Why?

**Johnny Lott**

This may or may not be a problem, depending not only on the department but also on the teachers involved. If there were to be a specialist in mathematics, having special courses for these specialists would be strongly recommended. To get at the deeper understanding of many mathematics topics, one needs to understand potential errors that students may make and how they may make them. This does take much thought in many cases. In the best of all worlds, a team-taught set of classes with mathematicians and mathematics educators or education professors might be the best. That may be problematic in many universities, but it could help prospective teachers.

**Question from**

Fairfax, Va.

What would the elementary specialists actually do? Would they teach differently? And is this in some way the same as a lead teacher?

**Johnny Lott**

Just what an elementary specialist might do would of course depend on a school system. In some systems, the specialist could be the mathematics teacher and teach that almost exclusively as is done in higher grades. In other smaller schools, duties would have to be defined. In some rural schools where there are only two teachers (and those schools exist), then in the best of all worlds, the math specialist would be one of the teachers. Elementary specialists might teach differently because of different duties, might teach differently because of the knowledge base, or might teach differently because of the use of different mathematics teaching strategies to help different student learners.

Lead teachers have such different duties in different parts of the country that I'm not sure how to answer that part of the question. It might have to be specific to Fairfax, Virginia.

**Question from**

Ames, Iowa

You use words like "deep understanding" and "quality of mathematics preparation" in your article. How do we assess deep understanding of teachers? How can we assess development programs for teachers to ensure this? Are there good examples?

However, we do need to improve mathematics education in the elementary schools, so I am in favor of mathematics specialists. But I doubt just one in each school would be sufficient.

**Johnny Lott**

How to assess deep understanding of teachers is not something that can be answered in a quick response like this one. It is not something that will automatically show up on a teacher exam. To assess it requires that the professors and collegiate personnel have to work on individual classroom assessments to see if prospective teachers or specialists really know why they do the things that they do in mathematics, or why they use the algorithm or approach that they use for an individual problem. And can they understand why and how students are making errors or correct statements in a given setting that are not expected.

There are good examples that exist. One example at the high school level was seen this summer in a video of a lesson study being used with young teachers in a high school in the Chicago area. It is a single example, but the use of peers working together helped individuals to reach a deeper understanding of what they were teaching.

**Question from**

Walla Walla, Washington

We see a range of different curricula for elementary grades. Some more traditional, others more progressive. Should teacher-training programs be geared to specific types of programs to create a better match between teacher and teaching philosophy?

**Johnny Lott**

What you ask about gearing teacher training to specific types of programs is problematic. What colleges and universities have to do is the best job that they can with the time that they have in preparing prospective teachers for a long career. If we gear the current program in college to the specific curricula of today, it may be a mistake, no matter which curricula you use in the process.

A better thought might be to incorporate a variety of school curricular materials into the teacher preparation programs so that the prospective teachers see a wide spectrum of materials. This in fact is practiced in many other countries around the world. In some, it appears to be done very well. It is a practice that we might want to emulate not only for specialists but for all prospective elementary teachers.

**Question from**

Springfield, Va.

In my work with preservice teachers, it seems to me that many of them who are interested in and appropriate for elementary education (i.e., have the personality and desire to be with a group of children of that age) are not necessarily those with a great grasp of mathematics. It's also true that those who are more mathematically inclined or competent are interested in the mathematical challenge of high school and are not "wired" to be with younger students all day, as elementary teachers are.

However, we do need to improve mathematics education in the elementary schools, so I am in favor of mathematics specialists. But I doubt just one in each school would be sufficient.

**Johnny Lott**

Your words are interesting. It seems to me that some of the more challenging mathematics that is taught is found in elementary school. This is the time when the basis for all of mathematics is being established. Though my background in teaching was at the high school level, I have to admit that some of the most challenging and rewarding times have been in the middle school and earlier grades classrooms.

Let me give you one example from a third grade class I was in last fall. I was working for an extended period of time with the class on "big" numbers. One of the first days I was there I asked the students what big numbers that they knew. The responses began as expected: 9; 99; 999; a million, a billion, a trillion; a gazillion, and then one child said "infinity." As I paused, another child said and I quote, "I heard that you can compare infinities. Is that true?"

This question from an average class of students almost blew me away. This was a question I never considered until graduate school. The mathematics buried in that question was far beyond the 9-year old mind. The answer from me had to be very careful and truthful and yet not way beyond the student. The challenge was there.

Don't think that because the children are young the mathematics may not be sophisticated.

In Japan, some universities are now requiring prospective secondary teachers to do internships in elementary schools. We might want to consider it. Some of our secondary teachers might change their minds.

**Question from**

Columbia, South Carolina

This is a bit tangential, but would you support an extended focus on math and language arts for elementary grades, and hold off on other subjects until upper elementary or middle school? That way teachers at these grades would also be more focused in their preparation and students more focused in their learning.

**Johnny Lott**

I would have to think about this one for a while. Math may be better learned in context, and if we do a strict focus on only two areas some of the contexts may be lost.

**Question from**

Hammond, La.

I agree with the idea, but where will the professional development funds come from to help elementary teachers develop their own deep, conceptual understanding of the mathematics and how to foster the same in their students?

**Johnny Lott**

Professional development funding is always an issue. However, most states and school systems require professional development of their teachers. A good question for schools and systems is how are the funds that are currently available are being used.

If funds are not available, then networks and groups of interested teachers can come together to discuss issues in mathematics. This can be as simple as meeting once a week to discuss a specific problem or a specific lesson one teacher is doing. The idea of lesson study or a modified lesson study is one way to implement small study groups. For example, earlier one writer wrote about adding fractions by adding numerators and adding denominators. A good question to investigate is if that is ever possible. If not, why not? If so, when? When could something comparable to this be used in a mathematical setting?

To develop a deep understanding requires many small steps. Big professional development programs are good; the NCTM academies are good examples. Small steps may be needed in some places. Another example is to take parts of the NCTM *Principles and Standards for School Mathematics* and examine parts at different grade levels to see what your school or system is doing there, and use texts and materials in the examination. Discussion and communication are keys here on a small scale.

**Moderator**

Thank you all for your participation this afternoon. See future President's Messages in the *NCTM News Bulletin* for other chat topics. Future online chats will be announced on the NCTM.org home page.

Good afternoon.

**Johnny Lott**

Thank you all for participating today. This is a challenge for me but I think that it is one way that we can keep communication lines open and try to answer some questions. I look forward to doing this again. Have a great Labor Day weekend.

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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