Facing Reality as We Embrace the Challenge of Overhauling K-12 Education, Part Five

Part Four: The University of Minnesota’s School of Mathematics Center for Educational Programs (MathCEP) as a Model for Developing the Teaching Talent That Our K-12 Students Deserve

“As I finished my undergraduate degree,” reflected Carraig Hegi, “I wanted to pursue a career in education, but I also wanted to build my math skills. To my delight, I found that the University of MInnesota had a program that would do precisely that: the M. S. in Mathematics with an Emphasis in Education."

So Mr. Hegi is quoted as saying on the website of the School of Mathematics at the University of Minnesota that pertains to the School of Mathematics Center for Educational Programs (MathCEP).

Mathematics instruction at the University of Minnesota is expansive enough that mathematics professors offer courses in what is designated a “school,” rather than a “department,” of mathematics.

For prospective teachers living in the Twin Cities area who are serious about the study of mathematics as an academic discipline, the options for in-depth training at the graduate level are limited. If they want to take courses somewhere in the Metro area, in fact, the option is one: The master’s in mathematics offered by the University of Minnesota (Twin Cities).

And to be sure, there is a great difference in a master’s degree in mathematics education and a master’s degree in mathematics as an academic discipline.

The Essential Difference Between a Degree in Mathematics Education and a Degree in Mathematics as an Academic Discipline

Typically, the college or university student who aspires to be a math teacher gets a bachelor’s degree in mathematics, in combination with courses taken in a school, college, or department of education. This combination earns the prospective teacher certification to teach math in Minnesota. Several universities in the area offer graduate training for math teachers, but the resulting master’s degree is in education, not math.

The only academic institution at which the serious student of mathematics can take rigorous courses at the graduate level is the University of Minnesota, in the School of Mathematics located in Vincent Hall, on the quad running southward from Northrop Auditorium.

The University of Minnesota (Twin Cities) School of Mathematics actually offers four different master’s degrees (all of them M. S.). One of these degrees, the Master’s Degree in Mathematics, offers Plan A and Plan B options. These plans entail the same level of mathematic rigor; in Plan A, the student specializes in a given area of mathematics and writes a thesis; in Plan B, the student studies a greater array of subfields of mathematics and does not write a thesis. Both of these plans require 30 academic credits, about half of them in each case coming in math courses, the other half coming in related fields necessitating the use of mathematics: disciplines such as physics, chemistry, economics, and some areas of business.

Both plans of the Master’s Degree in Mathematics most typically lead to the Ph. D., but the student gets an M. S. and may stop at that point if she or he decides to do so. The student who does stop at this point, therefore, has opted for a rigorous academic route to what is known as a “terminal degree.” Up to the point at which the master’s degree is conferred, the course of study mirrors in difficulty the curriculum of the aspiring Ph. D. candidate.

The three other degrees offered by the mathematics department at this campus of the University of Minnesota follow the Plan B type. The options include the M. S. Degree in Mathematics with Emphasis in Industrial and Applied Mathematics, the M. S. Degree in Mathematics with an Emphasis in Actuarial Science, and the M. S. Degree in Mathematics with an Emphasis in Mathematics Education. Courses are all at the upper (5000 and 8000) level and include offerings such as Theoretical Neuroscience, Dynamical Systems and Chaos, Stochastic Processes, Manifolds and Topology, and Calculus of Variations and Minimal Surfaces. This M. S. Degree with an Emphasis in Mathematics Education is the option for Twin Cities Metro area teachers with a serious interest in graduate level mathematics.

The website quotes Professor Harvey Keynes, who established this program in 1995, as saying,

“Students aren’t accepted into the program unless they are qualified for a T. A. position in the School of Math.”

This means that they must have been highly successful undergraduate math students and have a primary focus on mathematics. Students have a strong interest in teaching, but since the courses that they take are the same as those taken by Ph. D. aspirants, these scholars have impressive credentials as mathematicians and great professional flexibility. Most do in fact take positions in high school, as professional mathematicians who love teaching.

The mathematic rigor of the curriculum leading to this M. S. math degree for prospective teachers means that recipients are fully qualified to continue on to the Ph. D.

Says program graduate John Hall,

“After receiving an M. S. in Mathematics and high school teaching licensure, I decided to return to school to pursue the Ph. D. in Mathematics. The department was very supportive in helping me make the transition, and I feel that the two years I spent in the M. S. program was invaluable. I believe that I am much better equipped to handle the rigors of the Ph. D. program now than I was when I had just completed my undergraduate degree.”

Students considering applying for acceptance into the program administered by the math department are cautioned,

“Please be aware that the Mathematics Education program is, first and foremost, a Mathematics Master’s Program. It would provide significantly more than the background needed to be certified to teach. Students who do not meet admission requirements for this program might wish to consider, instead, a program in Curriculum and Instruction [Department of the College of Education and Human Development].”

The master’s program for math teachers administered by this college of education requires no courses at the level of mathematical rigor pertinent to courses taken in the programs administered by the School of Mathematics.

For this autumn of 2013, the complete education school course offerings in mathematics education are the following: Learning Theory and Classical Research in STEM [Science, Technology, Engineering, and Math] Education, Algebraic Structures in School Mathematics, Teaching and Learning Mathematics, Mathematics for Diverse Learners, Directed Studies in Mathematics Education, and Problems: Mathematics Education.

The offerings for spring are similar, with additional courses in Geometric Structures in School Mathematics, Rational Number Concepts and Proportionality, Technology-Assisted Mathematics Instruction, Student Teaching in Mathematics, and Seminar: Mathematics Education.

All math students at the University of Minnesota who aspire to teach must get a master’s degree. Students in the college of education typically do their coursework during the summer and fall terms; they student teach in the spring, also taking two education courses online.

Students in the math department, by contrast, take a full load of strictly mathematics courses during one year and spend another year taking education courses and doing their student teaching. The time commitment for the two programs is therefore another difference: The route to the master’s in education takes just three semesters; the path to the master’s in mathematics requires four semesters.

One can observe the lack of rigor in mathematics education programs at other institutions of the Twin Cities, also contrasting with the strong academic training offered in the School of Mathematics at the University of Minnesota.

In the manner of the program at the College of Education and Human Development, math education programs offered at other major teacher preparation centers in the Twin Cities have a pedagogical, rather than mathematical, emphasis. The universities of Hamline, St. Catherine, and St. Thomas offer programs for prospective middle and high school teachers that require a bachelor’s in math, accompanied on the transcript by education courses and a semester of student teaching. Certification is granted along with the bachelor’s degree.

Those three institutions each offer a master’s in mathematics education but no master’s in mathematics. Augsburg College has a limited number of options for teachers seeking master’s degrees, but does not offer a master’s program explicitly for math teachers, even in mathematics education.

The Genuine Interest in K-12 Education Witnessed in the University of Minnesota’s School of Mathematics

Thus, the University of Minnesota Department of Mathematics is unique for having professors interested in training true scholars of mathematics who also aspire to teach in K-12 schools. This interest in K-12 education is demonstrated in other ways than offering the Master’s in Mathematics with Emphasis in Mathematics Education.

Each year an average of five hundred fifty middle school and high school students are enrolled in the University of Minnesota Talented Youth Mathematics Program (UMTYMP) administered by the School of Mathematics Center for Educational Programs (MathCEP). This program offers an opportunity for highly motivated, talented students in grades 5-12 to attend a two-hour session each week after school.

Students congregate with similarly motivated peers to pursue a highly accelerated math course of study designed both to advance their mathematic knowledge far beyond the typical for their ages and to stimulate their interest in mathematics. Students enroll for a five-year sequence that takes them up through high school level and into courses normally taught at the college level.

“So what does this mean for a student who enrolls at Grade 5?” I asked a math professor at the University of Minnesota in late summer 2013. “At what grades are they taking high school and college courses?”

“A student who enters in the fifth grade would typically have mastered high school math--- algebra, geometry, and precalculus--- by the eighth grade year,” he replied.

“So, then, for their final two years in the five-year sequence, they will be taking college level math, meaning that they will be doing this at Grade 9 and Grade 10?”

“That’s right,” he said.

“And that would typically include what courses?” I asked.

“They would of course take the calculus sequence, then differential equations, linear algebra, number theory, multivariable and vector calculus, and topology.”

“Wow,” I began in admiration. “That’s quite an advancement over the typical K-12 experience. What kind of reaction do you get from personnel at high schools? “

“Mostly, we have excellent relationships with our contact people at high schools. Occasionally, we get the complaint that we are taking their best students, because they do not take regular math courses at their schools once they have enrolled in our program. They get their math credits through us. But this is just a matter of keeping the communication lines open. Usually the complaints fade away when middle school and math teachers realize the benefits that their students are getting through their enrollment in UMTYMP.” …………………………………………………………………………………………………………………………………

The Powerful Potential Recognized and Developed in Grade 5 through Grade 12 Student Participants in the University of Minnesota Talented Youth Mathematics Program (UMTYMP)

A major advantage for a math teacher in pursuing the master’s degree through the University of Minnesota Department of Mathematics is the opportunity to work with these students. It speaks volumes about the ability of the students at grades 5-12 who enter UMTYMP that they are often working at a level beyond the capability of most people teaching at the high school level. Even for graduate students who have themselves committed to the master’s in mathematics program, the challenges are great and the intellectual stretch is notable.

The challenge and the stretch may also be in evidence for those master’s candidates who assist in the residential summer enrichment institutes, also sponsored by MathCEP. Students at these institutes advance their mathematics skills and interest by conducting experiments that apply mathematics to problems posed in science and engineering. Mathematics faculty and graduate students work with undergraduate mentors to help the young people, also drawn from grades five through twelve, to gain a sense of what it would be like to be a member of the professional science, engineering, and mathematics community.

The Need for More Mathematics Teachers Who Can Recognize and Develop the Talents of K-12 Students

The quality of math teacher required to work with highly motivated and talented students recalls the level of talent observed in alternative programs such as Teach for America (TFA) and the American Board of Certification of Teaching Excellence (ABCTE). Teachers in the latter programs typically produce better results on objective measures of student math performance than do those teachers who have matriculated in traditional teacher preparation programs.

One suspects that, given the opportunity to train under mathematics teachers who are themselves highly accomplished mathematicians, many more students would rise to a level associated with gifted and advanced students such as those who are served in the MathCEP programs.

The success of the TFA, ABCTE, and MathCEP programs strongly suggests that our K-12 students in Minnesota are best served by teachers who are highly trained in their subject areas, and that quality master’s degrees in departments pertinent to specific academic disciplines are preferable to master’s degrees pursued through schools, colleges, and departments of education.