M428/M242: Assessment Report

Fall M 428 Mathematical Modeling for Teachers

Assessment Coordinator: not listed

According to the below description of Mathematics Teaching Program Learning Outcomes and Assessment, 8 students were assessed for Outcomes 5 and 6 in M 428.

Outcome 5

Model, analyze, and interpret situations using data analysis, statistics, and probability.

Outcome 6

Develop, apply and validate mathematical models using current and emerging technologies.

Evaluation

Address the following standard: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. Students complete a project in which they simulate the choice (from a population of all cars on that highway) of 10 at random (assuming normal distribution of mean 51 and SD 15). Create a histogram, summarize variability, and develop a margin of error. Include a discussion of the use of simulation..

Results

Three students displayed a substantial range of appropriate modeling strategies in the statistical content focus that would enable success in the teaching profession. Their use of technology for simulation and explanation was sufficient to indicate their ability to apply and validate mathematical models, and they were deemed “proficient.” Five students displayed an adequate range of modeling strategies and technology use and were deemed “adequate.” The distinction between the “proficient” and the “adequate” students was in the depth of explanation of variability and margin of error as a concept that can be defined through a simulation process rather than through a “rule of thumb.”

The program meets the threshold, since 100% of students were at the acceptable or higher level. 

Recommendations

The course should continue to emphasize simulation as a foundational tool for the teaching of statistical modeling. More in-depth attention to the use of simulation should be included in future offerings of the course. 

Spring M 242 Methods of Proof

Assessment Coordinator: not listed

According to the below description of Mathematics Teaching Program Learning Outcomes and Assessment, 27 students were assessed for Outcome 1 in M 242.

Outcome 1

Reason with and about mathematical statements and construct and validate mathematical arguments. 

Evaluation

The final exam contained (among other problems) 1. A proof by contradiction 2. A proof by contraposition 3. A proof by induction 4. A direct proof. 

Results

25 of the 27 students were successful at the direct proof of a result from number theory. The two who were unsuccessful had partial but incomplete understanding of the proof content and technique. 26 of the 27 students were successful at the proof by induction. The one who was unsuccessful made an error common of unsophisticated proof attempts in assuming the statement to be proved. 25 of 27 students were successful at the proof by contrapositive. The two who were unsuccessful did not properly construct the contrapositive statement.

4 of the 27 students were successful at the proof by contradiction. A further 18 students were able to correctly begin the proof, but had difficulty using the definition of an irrational number to complete the proof. Only 5 students were unable to begin the proof. It is our assessment that the difficulty was not with the proof technique, but arose because most proofs in the course focused on definitions and theorems about integers, but the question on the signature assignment used a question that relied on knowledge of rational and irrational numbers. In that
regard, the signature assignment question could be improved to align more with the content of the course.

Every student reached an acceptable level of reasoning on at least one proof type. 15 students’ overall work was judged to be proficient. 11 students’ work was judged to be acceptable. 1 students’ work was judged unacceptable.

This assessment is of all students in M 242; not all students are enrolled in the mathematics teaching program. The student whose work was unacceptable is not in the mathematics teaching program. The program meets the threshold, since 100% of mathematics teaching program students are at the acceptable level and 50% of students were at the proficient level. 

Recommendations

In further offerings of the course, more emphasis should be placed on writing proofs that come from topics in the real numbers. The course provides sufficient attention to topics in number theory. 

Program Learning Outcomes

Curriculum Map and Assessment Schedule

Rubric

The selection of the assignment that will serve as the signature assignment is left up to the discretion of the course instructor for that semester.

Threshold

For the students completing the program in mathematics teaching, our goal is that 100% of students will be at an acceptable level or better, and 50% will be at a proficient level, for each of the learning outcomes. 

PDF of M428 and M242 Assessment Report