Program Report for the Preparation of Secondary Mathematics Teachers

National Council of Teachers of Mathematics (NCTM)

NATIONAL COUNCIL FOR ACCREDITATION OF TEACHER EDUCATION

COVER SHEET

1. Institution NameMillikin University

2. StateIllinois

3. Date submitted

MM DD YYYY

09 / 15 / 2008

4. Report Preparer's Information:

Name of Preparer:

Paula R. Stickles

Phone: Ext.

( ) -217 420 6735

E-mail:

pstickles@millikin.edu

Name of Preparer:

Joe A. Stickles, Jr.

Phone: Ext.

( ) -217 424 6290

E-mail:

jstickles@millikin.edu

5. NCATE Coordinator's Information:

Name:

Nancy Gaylen

Phone: Ext.

( ) -217 424 3790

Assessment 2 - Grades of Student Teaching

Candidates in required Mathematics Courses

Assessment 2, Part 1. Description of the Assessment

All secondary mathematics teacher candidates take at least twelve courses in mathematics, ten core mathematics courses and two mathematics electives from a list of six. Since not all mathematics teacher candidates take the same mathematics electives, grades in only the ten core courses are used in the assessment. As listed in Assessment 2, Part 2, these ten courses cover most NCTM process standard indicators. In order to earn passing a grade in a course, mathematics teacher candidates must demonstrate knowledge of the various indicators addressed by that course.

The ten mathematics courses required of all mathematics teacher candidates were specifically chosen to ensure that these candidates would be exposed to almost all of the NCTM/NCATE standards. The two calculus courses not only address knowledge of calculus, but they also integrate graphing calculator technology and introduce mathematical communication, connections to other area of mathematics, and real-world applications of calculus via coursework and projects. By their very nature, discrete mathematics, probability, and statistics require students to connect mathematical ideas and apply them to other disciplines. Further, our probability and statistics courses require students to use technology and communicate mathematics with assigned projects. The geometry and algebra courses require students to investigate problems with technology and to be able to write and understand formal proofs. The content of the history of mathematics course was specifically aligned to the history portions of the Illinois Content Exam, which align with the NCTM/NCATE indicators. The methods course is the primary course in our mathematics curriculum where the candidates learn to integrate their content knowledge, communication skills, and technology background into their future classrooms. The course numbers, titles, and descriptions below are taken from Millikin University Bulletin, 2007-2008, pp. 63-64.

MA 140 - Calculus I - 4 Credits - Differential and integral calculus from the symbolic, graphical and numerical perspectives. Topics covered include: concepts of limit, continuity, derivative and integral; applications of the derivative as rate of change, slope and solving max-min problems.

MA 208 - Discrete Mathematics - 3 Credits - Introduces basic techniques and modes of reasoning of combinatorial problem solving. Introduces rigorous theoretical frameworks within which ideas about computer science can be expressed. Topics include graphs, trees, logic, networks, coding, and combinatorics.

MA 220 - Statistical Methods - 3 Credits - Introduction to major methods of applied statistics. Topics may include simple and multiple regression, analysis of variance and co-variance, model specification and residual analysis, nonparametric inference, experimental design, and, multivariate analysis.

MA 240 - Calculus II - 4 Credits - Applications of definite integral and Fundamental Theorem of Calculus, methods of integration, power series, Taylor series, Fourier series, use of differential equations to model real-life applications.

MA 301 - College Geometry - 3 Credits - Elements of plane and solid geometry treated from a problem-solving approach, historical development of geometry, parallelism and symmetry, area and volume, and non-Euclidean geometry.

MA 302 - Algebraic Structures - 3 Credits - An introduction to abstract algebra. Includes basic ideas and theorems about groups, rings, integral domains, and fields

MA 303 - Linear Algebra - 3 Credits - Matrices, linear systems, finite dimensional vector spaces, vector geometry, linear transformations, quadratic forms.

MA 304 - Probability and Mathematical Statistics - 3 Credits - Combinatorial analysis, probability axioms, random variables and their distributions including binomial, normal, Students t and f, estimation and sampling, hypothesis testing, linear and multivariate regression.

MA 320 - History of Mathematics - 3 Credits - A study of major developments in the history of mathematics and in the mathematical contributions of non-Western cultures using original sources, sources in translation, and commentaries. The interplay between mathematics and culture is emphasized.

MA 425 - Methods of Teaching Mathematics, Grades 6-12 - 3 Credits - Microteaching and structured classroom participation required. The course focuses on teaching standards based mathematics content with the inclusion of appropriate technologies. Required for both middle school and high school Illinois Mathematics Teacher Certification.

All mathematics teacher candidates passed all core courses they took. In fact, according to Millikin Universitys definition of grades (see part 3), all ten candidates earned at least satisfactory grades in these courses. Further, the major GPAs of all mathematics teacher candidates are well above the requirement of 2.2 they must meet before being allowed to student teach (see part 3). Since higher grades and higher GPAs would suggest a higher level of understanding of this content, these data indicate that these candidates have gained knowledge of the indicators covered by these core courses. Further evidence for this statement is the fact that all mathematics teacher candidates passed the Illinois Certification Testing System Mathematics Content Exam (see Assessment 1) on their first attempt. The content exam also addresses most of the NCTM/NCATE indicators, so all the mathematics teacher candidates must have retained the content from their coursework in order to complete the content exam successfully.

Please note that grade data are missing for MA 220 and MA 302. These two courses were instituted as requirements for all mathematics teacher candidates in the 2005-2006 Millikin University Bulletin and are still in practice. The candidates for whom the data are provided were not required to take these two courses, and only MA 302 was allowed as an elective that would count toward the major. However, we analyzed candidates Illinois Context Exam scores prior to 2005, and we determined that, even though our students were passing the exam, their subscores in algebra and statistics were lower than we liked. Therefore, we changed the requirements to include MA 220 and MA 302.

Some items for future consideration are:

Effectiveness of adding MA 220 and MA 302 as requirements. No candidates took MA 220, and only two took MA 302. As more candidates matriculate through our program, we will be able to assess the effectiveness of this change.

Requiring a minimal passing grade. There are many redundancies built into our current system that alleviate issues that may arise if a student earns a D in a required course. Different courses address many of the same indicators, the various GPA requirements would not allow students to earn many Ds and still meet those standards, and a student still must pass the Illinois Certification Testing System Mathematics Content Exam before student teaching.

GPA of 2.2 in all mathematics courses. None of the candidates GPAs approached this minimum number, and all candidates passed the Illinois Certification Testing System Mathematics Content Exam on their first attempt. Once more data have been gathered, this issue can be reevaluated, and any necessary adjustments can be made at that time.

Assessment 2, Part 2. Alignment with NCTM Standards

The following table contains the alignment of the NCTM indicators with the required ten core courses used for this assessment. The third column identifies how the course meets the cited indicators if it is not clear from the course title.

Required Course

NCTM/NCATE Indicators Addressed

How Course Meets Cited Standards

(If Course Title Is Not Clear)

MA140 Calculus I

4.1-4.3, 5.1-5.3, 6.1, 9.2-9.4, 10.1, 10.4, 10.5, 12.1-12.4

-Applications and projects address 4.1-4.3, 5.1-5.3, and 10.4

-Graphing calculator integrated; addresses 6.1 and 10.5

MA240 Calculus II

4.1-4.3, 5.1-5.3, 6.1, 9.2-9.4, 10.1, 10.4, 10.5, 12.1-12.4

-Applications and projects address 4.1-4.3, 5.1-5.3, and 10.4

-Graphing calculator integrated; addresses 6.1 and 10.5

MA208 Discrete Mathematics

4.1-4.3, 5.1, 9.5, 9.6, 13.1-13.3

-Elementary number theory is included; addresses 9.5 and 9.6

MA220 Statistical Methods

3.1-3.4, 4.1-4.3, 5.1-5.3, 6.1, 9.1-9.5, 10.1, 10.4, 10.5, 14.1-14.7, 15.3

-Written projects assigned; address 3.1-3.4, 4.1-4.3, 5.1-5.3

-Statistical software integrated; addresses 6.1, 10.5 and 14.3

MA301 College Geometry

3.1-3.4, 6.1, 11.1-11.7, 15.1, 15.2

-Reading and writing proofs required; addresses 3.1-3.4

-Geometry software integrated; addresses 6.1

MA302 Algebraic Structures

2.1-2.4, 3.1-3.4, 4.1, 4.3, 5.2, 5.3, 9.1, 9.5, 9.7, 9.8, 10.3, 10.5, 11.