Impact of the Missouri Middle Mathematics Project on the Preparation of Prospective Middle School Teachers

TEACHER EDUCATION AROUND THE WORLD

IMPACT OF THE MISSOURI MIDDLE MATHEMATICS PROJECTON THE PREPARATION OF PROSPECTIVE MIDDLE SCHOOL

TEACHERS

IRA J. PAPICK, JOHN K. BEEM, BARBARA J. REYS and ROBERT E. REYS

In the previous issue ofJMTE, Reys, Reys, Beem and Papick (1999)described the Missouri Middle Mathematics (M3) Project1 (1995–1999).The goal of the project was to improve the teaching and learning ofmiddle school mathematics through collaborative Standards-based mathe-matics curriculum investigations. The project not only contributed to theimprovement of teaching mathematics in the participants’ classrooms, butit also significantly affected the program for prospective middle schoolmathematics teachers at the University of Missouri-Columbia. This teachereducation program is described in this article.

An essential ingredient in the successful transition to Standards-basedpractice at the middle school level is the development of teacher educationprograms that reflect the fundamental principles of the NCTMStand-ards (1989). In particular, the mathematical preparation of prospectivemiddle grade teachers, which traditionally had been integrated into theprograms for elementary teachers, needs careful consideration. The Mathe-matical Association of America, inA Call for Change(MAA, 1991),outlined recommendations for the mathematical preparation of middlegrade teachers. These recommendations differ significantly from recom-mendations for the preparation of elementary teachers and provide guid-ance to those developing new programs for middle grade mathematicsteachers.

Currently, as in the case of the M3 Project, much attention is beingfocused on the improvement of the knowledge and instructional skillsof inservice teachers. This is important in order to stimulate imme-diate and substantive change. However, it is imperative that preserviceeducation be simultaneously improved, so that new teachers entering thefield are knowledgeable and can collaborate with their more experiencedcolleagues in transforming the classrooms in which middle grade studentsstudy mathematics. In response to this urgency, college and universityfaculty throughout the nation are examining and restructuring their teacherpreparation courses and programs. These academic activities have created

Journal of Mathematics Teacher Education2: 301–310, 1999.© 1999Kluwer Academic Publishers. Printed in the Netherlands.

302 IRA J. PAPICK ET AL.

a strong demand for resources and materials, and a desire to share ideasand successes.

At the University of Missouri-Columbia, faculty from the Departmentof Mathematics (within the College of Arts and Sciences) and the Depart-ment of Curriculum and Instruction (within the College of Education) havedesigned a comprehensive middle school mathematics teacher preparationprogram that implements Standards-based curricular materials and instruc-tional strategies. In this paper, we highlight some of the distinctive courseswithin this program that evolved from our work with inservice teachers.

BACKGROUND

The M3 Project employs collaborative curriculum investigations as avehicle for teacher enhancement and systemic reform (Reys, Reys, Barnes,Beem & Papick, 1997). For the past three years, we worked withteams of middle school mathematics teachers and administrators from23 Missouri school districts. Our collaboration involved extensive reviewand exploration of NSF-sponsored Standards-based middle school mathe-matics curricula and helped create and support a foundation necessary formaking informed decisions about middle school mathematics programs(Reys, Reys, Barnes, Beem & Papick, 1997; Reys, Reys, Beem & Papick,in press).

Although the M3 Project was an inservice teacher enhancementproject, the long-term and ongoing dialogue with practicing middle schoolteachers, as well as the involvement of university faculty in extensivecurriculum review and regular visits to middle school classrooms, influ-enced our thoughts about preservice teacher education. In fact, we foundthe curricula reviewed by the inservice teachers in the M3 Project (Mathe-matics in Context, Connected Mathematics Project, Math Thematics, andMathScape) rich in mathematics and pedagogical prompts. Consequently,these materials were often taken into the preservice classroom and usedto initiate and build important mathematical and pedagogical ideas. It isimportant to note that, true to the spirit of reform, the Standards-basedcurricula not only present mathematics differently, but they also intro-duce many important topics which have traditionally been reserved forthe secondary level. In particular, the new curricular materials containsignificant amounts of algebra, geometry, probability, and statistics. Ourexperiences with the M3 Project have made it clear that teachers need toknow quite a bit more mathematics than was required just a few years ago.These experiences convinced us of the real and immediate need to modifyboth content and pedagogy courses for preservice teachers.

TEACHER EDUCATION AROUND THE WORLD 303

The process of curriculum change at the university level is oftencomplicated and rather deliberate, even if there is a demonstrated needfor such change. If separate colleges within a university, such as theCollege of Education and the College of Arts and Science, are involvedin curricular changes, complexity increases. The creation of a core groupof determined faculty from each college, equipped with strong research tosupport change, is a necessary first stage of the procedure. The M3 Projectnot only provided compelling evidence for substantive curricular modi-fications, but also established a strong link that connected mathematicsfaculty and mathematics education faculty. This robust collaboration wascrucial for achieving the desired goals, and as inexplicable as it seems, itis somewhat unique within the academic walls of large U.S. universities.

In 1995, the Missouri Department of Elementary and Secondary Educa-tion announced a new certification area at the middle school level (Grades5–9). Previously, only elementary (Grades 1–6) and secondary (Grades 7–12) certificates had been available. With the addition of the middle schoolcertificate, the secondary certificate was changed to Grades 9–12. For thefirst time, teachers specifically trained for service at the middle school levelwould be certified by the state. This action provided a supporting frame-work for change at the university level. Utilizing insights and experiencesderived from the M3 Project, in conjunction with the new state certifica-tion platform, the core group of mathematics and mathematics educationfaculty began to develop and implement a middle school certificationprogram. This program was built upon the following Standards-basedprinciples:

• Preservice students will be engaged in extensive and supported fieldexperiences so they will gain a deeper understanding of schools,classrooms, and learners.

• Mathematics content preparation will be designed and delivered byestablished mathematicians who are recognized for their teachingexpertise and are knowledgeable of both the NCTMStandards(1989)and the recommendations of the MAA inA Call for Change(1991).

• Mathematics pedagogy preparation will begin in the junior year andwill be linked to the mathematics students study in the final two yearsof their program.

• Middle grades Standards-based curricula and instructional strategieswill be prominent in the mathematics and mathematics educationcoursework and in the field experiences.

• The program will be a four-year undergraduate certification programwith a minimum of 27 credit hours in mathematics and 6 credit hoursin mathematics education.


• Mathematics studied will be based on a foundation of algebra,geometry, and concepts of calculus. Additional courses, speciallycourses for middle school majors, will build on this foundation.

MIDDLE GRADES MATHEMATICS CERTIFICATION:A GENERAL VIEW

Students preparing to become middle school mathematics teacherscomplete the general education requirements of the University, the middleschool professional education requirements, and 21 semester hours ofsocial studies, English, or general science for a second-field teachingcertificate (minor). In addition, nine 3-credit-hour courses in mathematicsare taken along with two 3-credit hour courses in mathematics educa-tion. As part of the mathematics education courses, students participatein two linked field experiences in which they work with middle gradeteachers and students in classrooms throughout the two semesters prior tostudent teaching. The fundamental goal of the mathematics courses is thatthey thoroughly prepare middle school mathematics teachers to effectivelyutilize Standards-based curricula. (Course syllabi are available from theauthors.)

Mathematics Courses for Middle Grade Teachers

Pedagogically speaking, it may be advantageous to have a program inwhich each of the constituent mathematics courses services only educa-tion majors. In most cases, this is not practical, and alternate approachesare necessary. In particular, some of the required mathematics coursesin our program are not teacher preparation specific but are intendedfor more heterogeneous audiences. A useful strategy employed in ourmodel is the creation of a few distinctive mathematics courses that aredesigned specifically for preservice middle grade mathematics teachers.These courses introduce and explore significant mathematical conceptsand directly relate them to middle school mathematics. In fact, specificunits from the NSF-funded middle school curriculum projects serve asfocal points for classroom discussion and analysis. Important feedbackfrom the middle school teachers participating in the M3 project, as well as adetailed inspection of the materials, helped determine the nature of our newcourses. In particular, in-service teachers highlighted areas of mathematicsthat they felt unprepared to address. They also argued for the developmentof mathematical knowledge that would allow them to understand how the


mathematics they were teaching fit and connected to more sophisticatedmathematical ideas.

Algebraic and geometric concepts are central to the new Standards-based middle grade curricular materials, and the middle school teacherpreparation program has been significantly strengthened with the addi-tion of relevant algebra and geometry courses (Algebraic Structures andGeometric Axioms and Structures). These mathematics courses havebeen constructed in the spirit and philosophy of the NCTMStandards(1989, 1991, 1995), MAA’sA Call for Change(1991), and the jointNCTM/NCATE guidelines entitledInitial Programs Preparing Teachersto be 5–8 Mathematics Teachers(NCTM, 1999). They are designed toprepare middle grade teachers to meet the mathematical challenges oftheir future assignments. They primarily serve middle school mathematicsteacher education students but also are open to and attract other majors.

Algebraic structures for middle grade teachers. A few natural questionsserve as a prelude to our discussion:

1. Why should middle grade teachers study modern algebra?2. What modern algebra concepts are essential for middle grade teachers?

In traditional middle school curricula, eighth grade is usually the first timestudents are engaged in a formal course in algebra. The nature of thiscourse is generally abstract and skill driven and often does not connect thesubject matter to the real world or to other mathematics. Moreover, histor-ical and conceptual perspectives are rarely considered, and this contributesto the isolation of the subject. Given these deficits, resourceful teachersexpend a great deal of effort and time searching for meaningful and inter-esting applications. This task, although not elementary, can be achieved. Acarefully constructed and administered modern algebra course can providemiddle grade mathematics teachers with enormous insight and maturityinto algebraic thought. Furthermore, intensive exposure to inductive anddeductive reasoning in the context of selective axiomatic structures helpsprovide the middle grade teacher with important foundational perspectivesand the ability to understand and convey a wide spectrum of algebraicideas.

In contrast to traditional curricula, Standards-based materials introduceand study algebra throughout the entire middle grade program. Algebraoccurs in the context of other mathematics, in real world situations, and isprominent as a tool for modeling various problems. The requisite skills arecontinually reinforced, and necessary practice is appropriately included.If teachers feel more practice is warranted, it is not difficult to find addi-tional sources (e.g., any traditional textbook contains numerous practice


exercises). Consequently, much less time and effort are spent on findingand distributing supplementary materials, and more energy can be devotedto the teaching and learning of algebra.

Our reflections on Question 1 helped set the stage for Question 2, i.e.,the course content. In developing our modern algebra course, we care-fully chose topics that would adequately prepare teachers to effectivelyuse Standards-based curricular materials. For example, a detailed studyof the ring of integers provides an ideal setting for the analysis of suchfundamental topics as: the division algorithm, GCD, Euclid’s Algorithm,GCD Identity, prime numbers, The Fundamental Theorem of Arithmetic,modular arithmetic, and natural generalizations to polynomial rings. Also,a rigorous examination of arithmetic properties in various algebraic struc-tures deepens the understanding of traditional arithmetic and accentuatesthe importance of axiomatic mathematics. These concepts, as well as otherrelated ones, are essential to the middle grades mathematics teacher andare pervasive throughout the Standards-based curricula. It should be notedthat this course is not static and will continue to improve as it evolvesthrough additional iterations.

A most important tenet of Standards-based curricula is that content andpedagogy share equal importance. How students understand and employthe power and utility of mathematics is strongly dependent upon how thesubject is taught. New roles for teacher and student, including coach andco-investigator, are an essential part of the reform classroom, and multipleforms of assessment provide greater versatility in the measurement ofstudent achievement. In order to support and sustain the substantivechanges in the middle school mathematics classroom, it is quintessen-tial that professional development and teacher education jointly respondto the appropriate alterations needed for inservice and preservice teachertraining.

Modern algebra not only is a foundational imperative for mathe-matics teachers, but provides a natural setting for exploration, conjecture,modeling, problem solving, and the analysis and construction of rigorousarguments. Exposure to such mathematical endeavors contributes to theteachers’ content base, and, concomitantly, equally reinforces criticalStandards-based teaching strategies. In our modern algebra course, wehave structured the classroom environment to parallel the Standards-basedclassroom. Group learning combined with traditional lecture help guidethe way through the course topics. Consequently, individual and collectivepresentations, as well as written assignments, constitute the regular dailyactivities. Other forms of assessment include: take-home and in-classexams, historical assignments, critical analyses of Standards-based and


traditional curricula, and term papers. Student feedback has been quitepositive.

Geometry for middle grade teachers.The need for teaching more geometryin the middle grades is very clear. Teachers in the M3 Project found thegeometry content of the Standards-based curricula to be significantly moreintegrated and sophisticated than in traditional materials they had previ-ously used. They argued for more attention to the connection betweengeometric and algebraic concepts, and they desired to study more deeplythe ideas presented in middle school curricula.

We focus primarily on Euclidean geometry. However, we also covertaxicab geometry and non-Euclidean geometries in order to providecontrast. The introduction of alternative geometries serves to deepen theunderstanding of Euclidean geometry because one must see what non-Euclidean is about in order to better understand the special nature ofEuclidean geometry. Proof and rigor are emphasized to some degree, butintuition is also highlighted. Geometry is equally well suited for buildingintuition and for bringing home the need for precise definitions and state-ments. It is an excellent place to illustrate the power of logic and proof. Inaddition, geometry has a concreteness that people invariably see as relevantto the real world.

Standards-based mathematics curricula introduce more geometry tostudents at much earlier ages and investigate geometry through discoverytechniques, problem solving, and modeling strategies. We have used activ-ities from the middle school mathematics curriculum projects with thepreservice teachers. These activities are vivid reminders for the preser-vice teachers that middle school students are doing this mathematics.The preservice teachers are motivated to engage in the exploration ofthese activities and, in the process, become aware of the rich mathematicsavailable in these middle school curricula.

We find that dynamic software programs, such as the Geometer’sSketchpad, enable future teachers to see firsthand the power of technologyas an investigative tool. We also utilize a range of organizational strategies,including cooperative learning and group presentations of content. Thesepresentations provide evidence of the preservice teachers’ growing know-ledge as well as their understanding of how to present mathematicalcontent and how to engage learners (in this case, their peers).

Mathematics Education Courses for Middle Grade Teachers

The two 3-credit-hour pedagogy courses for middle grade mathematicsmajors are taken at the beginning of the junior year and concurrently


with the advanced mathematics courses (e.g., Algebraic Structures andGeometry courses described above) and with related field-based experi-ences. The first course immerses students into teaching mathematics byengaging them in the study of middle grades curricula, instructional tech-niques, assessment strategies, and resource materials. These in-class fociare supported and enriched by weekly visits to middle grade classrooms.Students also work one-on-one with individual middle grade students ina supervised after-school tutoring environment. This course is meant tostimulate their thinking about appropriate and effective teaching strategiesand challenge their beliefs about appropriate content for middle gradestudents. The second course builds on the first and provides supportedopportunities for developing lesson plans, teaching small groups ofstudents, and engaging in more in-depth study of particular units of studyor big ideas at the middle school level (e.g., proportional reasoning).Preservice teachers also explore ways to integrate content with othersubjects and complete several projects with preservice teachers who pursuea different major (e.g., middle school literacy). These activities are aimedat helping them develop collaborative working partnerships with teachersin other discipline areas.

SUMMARY

Our experiences with in-service teachers in the M3 Project prompted usto make considerable changes in the preservice middle grades teacherpreparation program. It also informed the changes through the ongoingand intense conversations between in-service middle grade teachers anduniversity faculty. In fact, it became clear that the changes in content andinstructional emphasis advocated by the M3 Project staff were also neededin our own university course experiences.

The first graduates of our new mathematics middle school certificationprogram graduate this year, so they are untested by traditional standards.Nevertheless, they have had a mathematics preparation uniquely focusedon middle school, along with extensive experiences in middle schoolclassrooms. Conversations with these students as they complete their 16-week student teaching internship, and with their cooperating teachersand administrators, confirm that they feel confident and well prepared toinitiate their careers.

An important goal of our program is to help graduates realize that theirundergraduate program prepares them for a good start, but that continuedgrowth and professional development must become an integral part of


their careers as middle school mathematics teachers. In that spirit, we willcontinue to monitor their development and transition to full-time teachers.

Our program is not offered as a utopian model. However, our approachillustrates how the experience and knowledge gained from workingwith inservice teachers as they investigate Standards-based mathematicscurriculum materials can help produce significant change in the under-graduate preparation of future teachers. It is described here in the hopethat it may be helpful to other faculty facing similar challenges in programdevelopment. The institutional collaboration of faculty in MathematicsEducation and the Department of Mathematics has been critical in estab-lishing this program. Although this collaboration has been instrumental,it has also been incremental. We succeeded in this initial effort basedon the close collaboration of two mathematicians and three mathematicseducators. For us, the challenge is to sustain the program by expanding thecadre of mathematicians and teacher educators committed to improvingteacher preparation.

NOTES

1 The Missouri Middle Mathematics Project had been supported by a grant from theNational Science Foundation (#ESI 9453932).

REFERENCES

Mathematical Association of America (1991).A call for change: Recommendations for themathematical preparation of teachers of mathematics. Committee on the MathematicalEducation of Teachers, Mathematical Association of America.

National Council of Teachers of Mathematics (1989).Curriculum and evaluation stand-ards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (1991).Professional standards for teachingmathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (1995).Assessment standards for schoolmathematics. Reston, VA: Author.

National Council of Teachers of Mathematics (1999).NCATE-approved curriculumoutcomes: Initial programs preparing teachers to be 5–8 mathematics teachers. Reston,VA: Author.

Reys, B. J., Reys, R. E., Barnes, D., Beem, J. K., & Papick, I. J. (1997). Collaborativecurriculum review as a vehicle for teacher enhancement and mathematics curriculumreform.School Science and Mathematics, 97(5), 253–259.

Reys, B. J., Reys, R. E., Beem, J. K., & Papick, I. J. (in press). The Missouri MiddleMathematics (M3) project: Stimulating standards-based reform.Journal of MathematicsTeacher Education.


Reys, B. J., Reys, R. E., Barnes, D., Beem, J. K., & Papick, I. J., National Science Founda-tion Teacher Enhancement Grant (ESI 9453932) (1995–1998).Reshaping mathematicsin the middle grades in Missouri: A model to improve mathematics curriculum, teaching,and learning(M3 Project).

Department of Mathematics Ira J. PapickUniversity of MissouriColumbia, Missouri [email protected]

Curriculum and Instruction Barbara J. ReysUniversity of MissouriColumbia, Missouri [email protected]

Department of Mathematics John K. BeemUniversity of MissouriColumbia, Missouri [email protected]

Curriculum and Instruction Robert E. ReysUniversity of MissouriColumbia, Missouri [email protected]

Documents

Impact of the Missouri Middle Mathematics Project on the Preparation of Prospective Middle School Teachers