Working Group Session # 3 - Ruth Heaton and James Lewis
The Mathematical Education of Teachers recommends that the
mathematical education of teachers be viewed as the responsibility of both
mathematics faculty and mathematics education faculty and further recommends
that there be more collaboration between mathematics faculty and K-12
mathematics teachers. This session reviewed one such partnership at the
University of Nebraska-Lincoln that brings together faculty in Teachers College,
faculty in the Department of Mathematics and Statistics, and Lincoln Public
School elementary teachers.
UNL’s Math Matters is a NSF funded project designed to strengthen the preparation of future elementary school teachers. The centerpiece of the project is an 18-hour block of courses that integrates mathematics instruction with pedagogical instruction and field experiences. Math Matters students take integrated mathematics and methods courses two mornings each week and participate in a field experience two days each week under the supervision of master teachers at Roper Elementary School, a Lincoln Public School. The project also includes the development of several new math courses, designed especially to be relevant and accessible to future elementary teachers.
In this session, Heaton and Lewis discussed their experiences in building a three-way partnership between education faculty, mathematics faculty and mathematics teachers as well as their efforts to deepen their students' understanding of mathematics by connecting the mathematics to the tasks faced by an elementary school teacher. The session overview that follows contains a description of the context in which this partnership takes place, the goals for Math Matters, and some of the barriers Heaton and Lewis have encountered in creating this partnership. It also includes a close look at what Heaton and Lewis are doing inside the 18-hour block of mathematics, pedagogy, and field experiences to prepare elementary mathematics teachers, along with some beginning evidence of the project’s success. The overview also includes a description of several new math courses for elementary teachers being developed and taught by other faculty from Teachers College and the Department of Mathematics and Statistics at UNL working in partnership to improve the mathematical preparation of teachers.
Mathematics education is based in Teachers College on UNL’s campus. There are
no formal designated faculty positions in mathematics education within the
Department of Mathematics and Statistics. There is, however, a long and healthy
history of cooperation between faculty in Teachers College and the faculty in
the Department of Mathematics and Statistics. Lewis, who has served as chair of
the Department of Mathematics and Statistics for the past 14 years, has played a
major leadership role in establishing the partnership between Teachers College
and the Department of Mathematics and Statistics. He is also active in
mathematics education on a national level as evidenced by his role in chairing
the steering committee that produced The Mathematical Education of Teachers
Elementary education majors at UNL have a three-course, 9 credit hour mathematics requirement. The courses include Math 200, Mathematics for Elementary School Teachers, Math 201, Geometry for Elementary School Teachers, and Math 203, Contemporary Mathematics. All three mathematics courses are generally taken prior to CURR 308, the math methods course in the Elementary Teacher Education Program, and students are left on their own to make any connections between the content of the required math classes and what they are learning in math methods and field experiences. Often, the math courses are viewed by students (and occasionally by advisors) as irrelevant experiences to be endured.
The current Elementary Teacher Education Program at UNL has been in place since 1992. The basic structure of the program allows for practicum linked to methods courses with a primary aim to help students build connections between theory and practice. The program includes 23 hours of general teacher education requirements, 23 hours or eight discipline specific methods courses, including math methods, and 23 hours of field experiences including five different practicum experiences and student teaching. All students choose one of six areas of concentration. For mathematics, students take an additional 6 hours of mathematics and an additional math methods course for their concentration.
Math Matters is a NSF-funded adaptation and implementation project. The project, now in its second year, has three main goals. The first is to create a partnership between mathematicians and mathematics educators with the goal of improving the mathematics education of future elementary teachers. The second is to create meaningful links among field experiences, pedagogy, and mathematics instruction. The third goal is to create math classes that are both accessible and useful for future elementary teachers.
In the process of trying to establish their partnership, Heaton and Lewis have encountered a number of barriers to success. Among the challenges they encountered in establishing a partnership that bridged their worlds of mathematics education and mathematics are the following:
|Student evaluations of mathematics faculty teaching courses for future
elementary school teachers tend to be quite critical, even for faculty who are
used to receiving outstanding student evaluations in most courses that they
teach. Students in these math courses do not see relevance in the mathematics
they study to their future work as elementary teachers. Frequently, these
students have had one or two courses directly related to their preparation to
be teachers by the time they take their required mathematics courses.
Knowledge of pedagogy acquired in these courses provides a basis, or at least
a vocabulary, for offering harsh criticisms of the pedagogy of their
mathematics instructors. As a consequence, tenure-track mathematics faculty
resist teaching these courses, and so these courses are frequently taught by
graduate students or part-time lecturers.|
|There are cultural differences in how instruction is delivered and
students are assessed. Math faculty expectations seem to overwhelm students in
the Elementary Teacher Education Program. As a student moves through the
Elementary Teacher Education Program, the evaluation for their work as
students becomes more dependent on projects than on homework and tests. This
means that there is often stark contrast in the kinds of expectations students
encounter in the math courses and their courses directly related to learning
to teach. The math courses and their accompanying expectations are perceived
as being much higher than what is expected of students in their education
courses. Grading is also an issue. On UNL’s campus, Teachers College faculty
give among the highest grades on campus while the mathematics department gives
|Many students are typically advised to take the math content courses prior
to admission to the Elementary Teacher Education Program. This is related to
an attitude held by many students and advisors of just getting through the
math courses as soon as possible. This attitude and reality has made it
difficult to identify large number of students eligible for our project,
designed to teach two of the three required math content courses at the same
time students are taking pedagogy courses. |
|Few students choose mathematics as an area of concentration within the
Elementary Teacher Education Program. Generally, advisors in Teachers College
direct students or students self-select themselves away from additional
mathematics classes because of the perception that the courses are too
|The Elementary Teacher Education Program is designed in a highly sequenced way with methods courses offered in blocks, linked to other methods courses and field experiences. This design makes trying to offer something new, without adding credits or courses, difficult.|
yearlong (Fall-Spring) Math Matters block of courses allows for logistical and
conceptual integration of content, pedagogy, and field experiences for
prospective elementary teachers. Heaton and Lewis teach an 18-hour block of
courses with Heaton having responsibility for 12 hours of pedagogy and field
experience and Lewis having responsibility for 6 hours of mathematical content.
Students meet on Tuesday and Thursday mornings in the same campus classroom for
their mathematics and pedagogy classes. Both semesters, they also spend Mondays
and Wednesdays in a practicum experience at Roper Elementary School. Heaton has
been working on teacher education and mathematics education with the Roper
principal and teachers for the past five years. Thus, Math Matters students
benefit from a yearlong practicum under the guidance of cooperating teachers
with experience as elementary school mathematics teachers and as mentors for
Math Matters students take Math 300 in the fall and Math 301 in the spring. These courses are offered in place of the required courses, Math 200 and Math 201, with the 300 level numbers reflecting the added challenge of these courses. Math 300 focuses on number and number sense and Math 301 on geometry.
At UNL, math methods, CURR 308, is a one-semester course. To facilitate a two-semester pedagogical experience focused on mathematics, Heaton teaches CURR 351 in addition to CURR 308. CURR 351 is typically a generic pedagogy course designed around the topics of classroom management, cooperative learning, and constructivism. When linked to Math Matters, its curriculum is taught by situating it in the context of mathematics. Thus students take a yearlong, integrated math methods/pedagogy course while formally registering for CURR 351 in the fall semester and CURR 308 in the spring.
Heaton and Lewis meet their students in the same classroom back-to-back. To bypass the UNL room-scheduling problem this arrangement poses, they use a resource room whose schedule is controlled by the math department. The courses meet from 8-10:45 on Tuesdays and Thursdays. Usually Lewis teaches first, followed by Heaton. Lewis and Heaton are present for most of both classes.
For the first two years, students have been recruited into Math Matters. Students typically have done well in Math 203, have high GPA’s, are interested in becoming an outstanding mathematics teacher, and are willing to make a commitment to the high expectations and challenges of this project. While this pilot project is aimed at helping a select group of students with special interest and expertise in teaching mathematics become outstanding elementary teachers, the long term goal is to take what is learned from this special project with a small number of students and adapt it to create an integrated math content, pedagogy, and field experience for all students in the elementary teacher education program.
Heaton and Lewis are trying to create an integrated experience for students. To do so requires reconsidering the content and assignments of individual courses as well as looking for ways to overlap content and assignments. This session offered a closer look at some of the materials Heaton and Lewis have used in teaching future elementary teachers.
|Welcome to Math Matters |
On the first day of class Heaton and Lewis begin by distributing an overview of what they have planned for Math Matters. The purpose of this document is to communicate to the students the instructors’ high expectations for the course and the idea that it is a joint effort. Thus, while students register for specific courses for which Heaton or Lewis is the instructor of record, there are many assignments jointly made by Heaton and Lewis and for which students will be assessed as part of their grades in both their pedagogy and their math class.
Part of the goal for this NSF project is to adapt and implement appropriate NSF-funded curriculum materials. Heaton and Lewis have used materials from two different NSF funded curriculum projects.
Schifter, D., Bastable, V., & Russel, S. J. (1999). Number and operations, part 1: Building a system of tens. Parsippany, NJ: Dale Seymour.
Schifter, D., Bastable, V., & Russel, S. J. (2001). Geometry: Examining features of shape. Parsippany, NJ: Dale Seymour.
Sowder, J. et al. (2000). Number and number sense. San Diego State University.
Sowder, J. et al. (2000). Shapes and measurement. San Diego State University.
The other materials are ones Heaton believes offer students opportunities to learn important ideas about pedagogy.
Reys, R., Lindquist, M., Lambdin, D. V., Smith, N. V., & Suydam, M. N. (2001). Helping children learn mathematics. NY; John Wiley & Sons, Inc.
Charney, R. (1992). Teaching children to care. Greenfield, MA: Northeast Foundation for Children.
Weinstein, C. S., & Mignano, A. J. (1997). Elementary classroom management. NY; McGraw Hill.
Baloche, L. A. (1998). The cooperative classroom. Upper Saddle River, NJ; Prentice-Hall, Inc.
Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
In trying to understand the similarities and differences of their students to other elementary education majors, Heaton and Lewis are collecting information about their students’ mathematical abilities and beliefs. Instruments used early in the course include a Mental Math Quiz and a Mathematical Beliefs Survey. In each case, the instruments are also used with a reasonably comparable population. The Mental Math Quiz is given to all students in Math 200 and the Mathematical Beliefs Survey is given to all students in CURR 308.
Students have 10 minutes to work the Mental Math Quiz reprinted below. They are instructed to avoid any paper and pencil computation, solving all problems mentally and then recording the answer. The quiz was first used in Louisiana as part of LASIP (the Louisiana Systemic Initiative Program). Lewis obtained the quiz from R. D. Anderson, Emeritus Boyd Professor of Mathematics at LSU and past president of the Mathematical Association of America. Future elementary school teachers have more difficulty than one might expect. Math Matters students missed an average of 6.5 questions while the control group missed an average of 8.6 questions.
Math Matters Beliefs Survey Sample Responses
|Sample Reflective Writings|
Heaton uses reflective writings to make connections within and across mathematical, pedagogical, and field experiences through writing. The reflective writings ask students to consider issues related to mathematics education fueled by their own experiences and things they have read. Lewis reads these and includes points from Heaton’s evaluation in his course grades. Here are several sample reflective writing assignments.
Sample 1: Some educators argue that there is real value in teaching children mathematics in diverse, heterogeneous classrooms. Some teachers may counter this position, contending that it is best for children if students are homogeneously grouped for mathematics instruction. Pick a position in this argument and articulate it in writing. State your position and explain why you believe what you do. Your reasons for believing what you do may come from past teaching and learning experiences (your own and others’), and things that you’ve read, or learned in other courses.
Sample 2: What is geometry? If someone understands geometry, what is it that they know and are able to do? How well do you think you understand geometry? Why do you say this? What have your past experiences with geometry as a student been like? Describe what you remember? Are the memories favorable or not and why? Many elementary teachers do not like teaching geometry. Why do you think this is the case? What kinds of things do you hope to learn about geometry this semester?
Sample 3: Read “What do Math Teachers Need to Be?” The author is Herb Clemens, a professor of mathematics at The University of Utah, and the article was published in 1991 in Teaching academic subjects to diverse learners (pp. 84-96). New York: Teachers College Press. M. Kennedy, Editor. In this article, Herb Clemens lists what he thinks teachers of mathematics need to be. After reading his article and his meaning and use of these words, where does your own practice of teaching mathematics stand in relationship to what Clemens says mathematics teachers need to be: unafraid, reverent, humble, opportunistic, versatile, and in control of their math. On p. 92, Clemens lists four fundamental questions about mathematics teaching that matter to him. If he came to your practicum classroom and watched you teach a math lesson tomorrow, how would he answer his own last question about your practice: Can this teacher teach it [math] with conviction, and with some feeling for its essence? Explain.
Sample 4: Read "Teaching While Leading a Whole-Class Discussion," Chapter 7 from Lampert’s book. In this chapter Lampert examines problems of practice that arise while addressing a whole group of students or choosing students to answer questions. As you read the chapter find places in the chapter where you can relate Lampert's writing to your own experiences in the practicum setting while teaching math and maybe even other subjects. Use quotes from the text that connect to your experiences. Explain how and why they relate.
|Examples of Early Mathematics Assignments|
Early each fall, Lewis makes certain assignments as an opportunity to set the expectations for the year. The first problem offers students an opportunity to make connections between mathematical content and pedagogy. Students who focus too much on creating an entertaining story and too little on the mathematical challenge (“help children understand how big the values really are”) are often quite surprised when their work receives a fairly low mark.
Write a children’s story that uses at least five quantities with large values in ways that will help children understand how big the values really are. Include references to places, things, and events that will make sense to them. The story should have between 500 and 1000 words. (#5, page 21, Number and Number Sense)
The next problem follows a class discussion of the number of grains of rice one gets if they start with one grain on the first square of a checkerboard, two on the second, etc., doubling the number for each subsequent square. The homework assignment is basically to gain some understanding of the size of the number, 264-1, and thus estimate the volume of that much rice. The problem is rich in opportunities for students to handle calculators, large numbers, converting from one unit to another, estimating an important but unknown piece of data (e.g., How many grains of rice are there in a cubic meter or in a pound of rice), etc. It also sends a clear message that some assignments are ill posed and will take a serious time commitment to complete. They learn that the expectations of Math Matters are significant and that not everything is nicely packaged, ready for memorization and repeating on a test.
Recall our discussion about the game of chess and how a humble servant for a generous king invented it. The king became fascinated by the game and offered the servant gold or jewels in payment, but the servant replied that he only wanted rice—one grain for the first square of the chess board, two on the second, four on the third, and so on with each square receiving twice as much as the previous square. In class we discussed how the total amount of rice was 264 grains of rice. (To be completely precise, it is this number minus one grain of rice.) Suppose it was your job to pick up the rice. What might you use to collect the rice, a grocery sack, a wheelbarrow, or perhaps a Mac truck? Where might you store the rice? (This assignment builds on #13, page 18 of Number and Number Sense.)
In 1994, Lewis received a letter from four elementary school students at a small school in central Nebraska. The students in Mrs. Thompson’s 1st and 2nd grade class have discovered a large number in one of the magazines their class receives and they wrote Lewis seeking the name of the number. Heaton and Lewis give their students a copy of the letter and challenge them to write a response pointing out that both will grade the assignment in their class. Heaton stresses that when she grades the assignment she will be looking for evidence that the future teachers have successfully used this as a teaching opportunity. Lewis indicates that his interest is in whether students find the mathematics in the letter and respond to the mathematics adequately. The letter was signed by the four students and the teacher. In the bottom right hand corner they had stapled the item they had cut out of Kid City magazine.
The Math Matters students have found this assignment to be quite challenging. Some focus narrowly on the question of what is the name of the number and they search the web for an answer. Several fail to count the number of zeros and notice that the students have miscounted the number. Very few of our students ever question the truth of the basic statement. After all, it appeared in a magazine. Here is the text of the letter from Mrs. Thompson’s class.
Dear Math Professors,
We are 1st and 2nd graders in Wheeler Central Public School in Erickson, Nebraska. We love to work with big numbers and have been doing it all year! Every time we read something with a big number in it we try to write it. Then our teacher explains how to write it. We are getting pretty good at writing millions and billions!
We have a problem that we need your help with. We were reading amazing ‘Super Mom’ facts in a Kid City magazine. It told how many eggs some animals could lay. We came across a number that we don’t know. It had a 2 and then a 1 followed by 105 zeros!! We wrote the number out and it stretches clear across our classroom! We know about a googol. We looked it up in the dictionary. A googol has 100 zeros. Then what do you call a number if it has more than 100 zeros? Is there a name for it? Another problem is that we learned about using commas in large numbers. In the magazine article they used no commas when writing this large number. That confused us. Also, if you write a ‘googol’ with 100 zeros, how do you put the commas in? It doesn’t divide evenly into groups of 3 zeros. There will be one left over.
We appreciate any help you can give us solving this “big” problem. Thank you for your time.
Mrs. Thompson’s 1st & 2nd graders Apple Of My Eye Megan Kansier
The tiny female apple aphid is a champ
as an egg layer. This insect can lay as
many as 21000000000000
eggs in 10 months.
|Sample Test Items for Math 300|
Lewis’ exams have proven to be stressful for the Math Matters students. As indicated earlier, most of their other courses do not give exams, thus the experience stands out as different. Many students seem to expect the worst, i.e. to assume that test items may be similar to the most difficult homework assignments. Here are a few test items from the Number and Number Sense course.
- Give a rough estimate of how long it would take you to drive across the U. S. averaging 50 mph for 8 hours per day. Explain how you arrive at the estimate.
- Why do the usual algorithms for adding and subtracting decimals require “lining up” the decimal points? Why is it not necessary to line up the decimal points when you multiply?
- Give an example of one number that you are sure is an irrational number. Explain why you know that it is irrational.
- What is the smallest positive integer with exactly 10 factors?
- Let B = 11232. Factor B into a product of prime powers. Then factor B2 into a product of powers of prime numbers.
- Is 250 a factor of 10030? Explain your answer.
The responses to the last question were very interesting. Several students used their calculator to divide 250 into 10030. Some looked at the calculator’s answer (8.881784197 E44) and stared angrily at Lewis. After the test, Lewis explained how to work this problem and then left the room. Several students asked Heaton to comment on the test. Rather than respond, Heaton asked the students to tell her in writing, "Why is this stuff so hard?" Here are several responses.
I believe this test, this class, this subject, are all difficult because they involve thinking in different ways than what we are used to. We have all been conditioned, in our own education, to believe that things are the way they are, and that's all there is to it. We haven't challenged ideas and proofs nearly as much as we should have, to be able to have a thorough understanding of a subject. Asking "Why" to an idea or trying to understand the reasoning behind something is just not something most of us are used to doing. That's why this stuff is hard. It involves, not only thinking more deeply, but also being able to explain these thoughts and processes in words that clearly communicate the explanations and reasoning so that other people will see these points of view.
I don't think that I have a difficult time with abstract ideas. I love it when we work with new concepts that I have not studied in depth before. … You often like to throw in problems that relate to the text but are not found directly in the text. I think it's a great technique to make us think but possibly you could give us a hint. … I just want you to know that I have almost always been able to figure math problems out and I get VERY frustrated when I get stumped. I am very stubborn like that. Please don't take my temper personally. I like to be challenged on tests, but I usually like to have a hint about what direction the challenge will be in!
I didn't think the test was too bad. … I suppose the challenge is a good thing. The fact that there were abstract items on the test made it more difficult. I have been taught for years and years to prove what l am saying through examples. So it is difficult for me to prove an abstract idea without examples.
The major problem that I had on the test was my reasoning for the factoring problem. I started off on the right track, thinking that I should try dividing 2^50 into 100^30, but the large numbers were daunting, so I panicked and tried using my graphing calculator. The answer it gave me did not look pretty, which I think is what triggered my fall down a road of insanity (see my test for more details on that one). Bad, bad calculators....once you started to explain the problem on the board, I wanted to smack myself in the head for being so silly about the whole thing. I had just been going over some trig with my boyfriend last night and was helping him simplify a nasty looking equation, and I was telling him how much I like simplifying problems like that...then I go and screw it up on my own test!
A highlight of the Fall semester is the Curriculum Project assigned jointly by Heaton and Lewis and counting for about 10% of the total points in each of their courses. Students are challenged to compare certain NCTM standards with material found in one elementary curriculum project and material typically taught at the college level to future elementary teachers. A sub theme is that teachers will need to continue learning mathematics after they become teachers if they are to stay abreast of the material they will need to teach. Here is the essence of the curriculum project in Fall 2000.
|Teaching a Math Lesson|
As part of their practicum experience at Roper Elementary School, Math Matters students are given many opportunities to learn to teach under the guidance of the master teachers who supervise their practicum experiences. Math Matters students teach math at least once a week both semesters and they are frequently asked to teach other subjects as well to individual students, groups of students or the whole class. Four times each semester they have a formal assignment to teach a lesson and prepare a report to Heaton on their teaching experience. Below find a example of one of these “formal lessons” from Fall 2000. It has been edited slightly for space considerations.
|Geometer’s Sketchpad Assignment|
Each spring we introduce our students to The Geometer’s Sketchpad. A colleague, Dr. David Fowler, gives a presentation to the Math Matters students offering a brief tutorial in using Sketchpad. Fowler has created several worksheets that allow individual students to learn to use the various Sketchpad commands and even more assistance is available on his web site. A follow-up class is held in a computer laboratory with each student working at a different machine. Fowler, Heaton and Lewis wander from student to student providing hints when a student gets stuck on a particular part of the tutorial. After two class periods, Fowler assigns a set of problems that the students are to work using The Geometer’s Sketchpad. The problems are chosen so as to practice various commands and (hopefully) use the dynamic nature of The Geometer’s Sketchpad to gain a valuable geometric insight. Below are two problems from the assignment given in Spring 2001.
For the Spring semester the mathematical topic shifts to geometry using primarily the Shapes and Measurement materials developed by Judy Sowder et. al. at San Diego State University. In addition to the material contained in that book, Lewis likes to discuss Polya’s problem solving advice and to regularly give students problems that they can first seek to “solve” and then make the effort to give a “proof” of what they have discovered. Here are a few examples of the geometry problems Lewis has assigned to the Math Matters students.
|Shapes from Four Triangles|
Lewis’ first exam in the geometry course, Math 301, included a bonus problem that he found among the supplementary materials for Shapes and Measurement. The problem asks how many shapes can be made using four congruent isosceles right triangles. Students could respond in class or work on the problem over night but they were told that work done outside of class would be held to a higher standard. The results were modest at best, with few of the students providing a correct solution and none of the students accepting the challenge of explaining why they had found a complete set of shapes.
Heaton and Lewis decided to use the problem as the basis for a spring project that would involve solving a mathematics problem that had once been viewed as difficult, and then teaching the same material to an elementary school student. Working in pairs, the Math Matters students were “sent off into battle” without the benefit of any validation from Heaton or Lewis that they had a correct solution to the problem. As part of their report, they were to solve the mathematics problem and to use the problem as an opportunity to teach geometry to a single student. Finally, they were asked to reflect on their student’s understandings and on their own role in teaching geometry to elementary school children.
Below find a copy of the Shapes from Four Triangle assignment.
As a part of the Math Matters project, UNL faculty are
designing new courses that are both accessible and relevant to elementary math
teachers. One course, Experimentation, Conjecture, and Reasoning: Problem
Solving Strategies in Mathematics, is being taught for the first time in Fall
2001. It is a joint effort of Patience Fisher, Teachers College, and Gordon
Woodward, Department of Mathematics and Statistics. The focus of the course is
on investigating interesting problems and questions in mathematics with the
overarching goal of learning how an understanding of these topics will make
mathematics more enjoyable and relevant for future elementary students. Fisher
and Woodward are using The Heart of Mathematics by Ed Berger and Mike Starbird
as a text for the course. Topics covered this year include, numbers and logic,
patterns in nature, the meaning of infinity, Pythagorean Theorem, contortions in
space, geometry and knot theory, probability, and statistics.
For Spring 2002, Fisher and Woodward will pilot a second math course that will focus on using mathematics to model solutions for realistic problems. One goal of the course is to counter the view of mathematics as a set of formulas to be applied to a list of problems that can be solved by following the examples in the chapter. In Math Modeling, it will not always be apparent in advance what mathematics to apply. The mathematics used to model solutions in the course will be a mix of algebra, geometry, and logic. Mathematical terminology, concepts and principles will be introduced as needed, often emerging from class discussions of solutions. Graphing calculators and computers will be used as tools to help focus on important concepts and ideas and to make the mathematics more accessible. The explorations of interesting topics in mathematics will include discussions of how to use this new mathematical knowledge in teaching mathematics to children.
A third new course will be a number theory course for future elementary and middle school teachers. The course will be designed and taught by Judy Walker, a faculty member in the Department of Mathematics and Statistics. Walker has taught a version of this course as a freshman honors seminar, having obtained both the idea for the course and a significant amount of curriculum materials from Ron Rosier who had created a course called “The Joy of Numbers” at Georgetown University.
In this course, students will experience the beauty and power of mathematics by exploring the properties of the integers and some of their modern applications. Students will learn about the history of some long-standing unsolved problems in number theory---problems which can be stated in such a way that elementary and middle level students will understand the question, but which have not been solved yet even though mathematicians have been working on them for hundreds of years. One special focus of this course will be to study prime numbers. Using an inquiry based approach; students will discover key facts about primes that are needed for many of the modern applications of number theory. They will then learn how these facts are used in everything from card shuffling to shopping on the Internet.
A fourth new course will be a quantitative literacy course built on ideas from Elementary Quantitative Literacy materials developed by the American Statistical Association. It will be designed and taught by Linda Young, a faculty member in UNL’s Department of Biometry. In this course, students will learn that because data influences every part of their lives, the ability to critically evaluate data is an important life skill. Learning how to design studies, collect and analyze data, and interpret results will be the focus of this course. In addition to studying the statistical concepts needed for intelligent data analysis, the modern pedagogy of teaching these concepts, especially in grades K-8, will be demonstrated and discussed in the classroom.
Math Matters is in its second year of NSF funding and there are some signs of
success. For example, Heaton and Lewis are receiving good administrative support
at the department and college level within Teachers College to consider making
an integrated math content, pedagogy, and field experience the experience of all
students within the elementary teacher education program at UNL, thereby making
a transition from Math Matters as a pilot project funded by NSF to Math Matters
as an experience for all students in the Elementary Teacher Education Program
supported by UNL.
Eight undergraduates from the first cohort of Math Matters students are now involved in undergraduate research projects related to mathematics education in the year following their Math Matters experience. Three are doing undergraduate theses. The topics of their research include algebra in the elementary curriculum, Japanese lesson study and its applicability to professional development in the US, and mathematical practices that highlight mathematical knowledge use teaching. Five other students have continued to work with Heaton on a child study project based on the Shapes from Four Triangles problem.
Math Matters was recognized as an exemplary practice in teacher education by the American Association of Universities in Fall 2001. Heaton, Fisher, Phyllis Burchfield (Roper Elementary School Second Grade Teacher), and Jeanette Norman (undergraduate from the first cohort of Math Matters students) gave a presentation on Math Matters at the National Academy of Arts and Science, Cambridge, MA, October 2001.
Anecdotal evidence indicates that Math Matters students are better prepared to be teachers than other students in the Elementary Teacher Education Program. Beginning in Spring 2002, Heaton will lead data collection intended to follow the progress of Math Matters students after their involvement in the yearlong project and acquire the perspectives of faculty outside of Math Matters on the quality and progress of Math Matters students in the process of learning to teach.
Math Matters will continue to develop and offer math classes for elementary
teachers that are alternatives to the traditional offerings. Work toward
institutionalizing the Math Matters’ vision of integrated mathematical content,
pedagogy, and field experiences to be a part of the regular elementary teacher
education program has begun. Heaton and Lewis plan to analyze and publish
findings from the data collected in the context of this project. They also plan
to continue to follow, support, and study Math Matters students as they continue
to grow in their roles as elementary teachers beyond their experiences in the
Elementary Teacher Education Program.