Deliver A Lower-Level Curriculum With Appropriate Discipline Specific Skill Sets
The curriculum will provide freshman and sophomore students with opportunities to develop the skills typically required of professionals in the area of study.
Objective
Foundation Areas - Calculus I
Mth142 (Calculus I): Students will demonstrate the following knowledge and skills: differentiation of standard mathematical functions, apply the Fundamental Theorem of Calculus to evaluate integrals, and use calculus techniques to solve optimization problems.
Indicator
Course Assessment - Mth142
All students enrolled in the program are required to complete Mth 142. Students will be administered a final exam developed and approved by the department faculty. The exam will require them to demonstrate the knowledge and skills mentioned in the objective.
Criterion
Optimization Using Calculus Techniques
On the final exam, 70% of the students will use appropriate calculus techniques to solve an optimization problem.
Finding
Optimization Results
The following optimization problem was included on all calculus finals: An open top box is to be made from a 3 ft by 8 ft piece of cardboard by cutting out squares of equal size from the four corners and then bending up the sides. Find the maximum volume that the box can have.
Of the 120 students taking the exam, 54 - 45% came up with the correct solution.
Criterion
Differentiation Of Mathematical Functions
On the final exam, 70% of the students will provide the correct derivative for a given mathematical function.
Finding
Derrivative Results
The following problem was included on all calculus finals:
f(x) = x²sin(e^2x)
Of the 120 students taking the exam, 82 - 68% gave the correct derivative.
Criterion
Fundamental Theorem Of Calculus
On the final exam, 70% of the students will correctly use the Fundamental Theorem of Calculus to evaluate a given integral.
Finding
Integration Results
The following integration problem was included on all calculus finals
Find the definite integral of the function x^2-x^(-1/2) between 1 and 4.
Of the 120 students who took the exam 84 - 70% were able to find the correct value of the definite integral.
Action
Actions For 2011-2012
Last year's percentages were 47%, 78%, and 64% respectively. So the first two items experienced a decrease, while the third item had a modest increase.
Last year, we noted:
It is clear from the data collected that Calculus I students are somewhat adept at symbolic manipulation, but still lack the necessary mathematical insight needed to apply these skills.
The results this year still support that conclusion. Since the problems used weren't exactly the same, it is not really possible to determine if the drop in two of the critera are significant, the nature of the problems themselves, or the random nature of testing.
Last year, we also wrote: In fall of 2010 chair and faculty will discuss and adopt measures designed to improve student learning in Mth 142, such as increasing the amount of classroom attention given to applied skills, implementing earlier testing of applied skills prior to the final exam, providing students with more tutorial help, etc.
These discussions did take place with increased tutorial help being strongly stressed. The fact that there was, essentially, no real change in performance may mean the changes we implemented were not sufficient or, if sufficient, then perhaps their implementation lacked impact.
One possible change that will be discussed is making on-line homework available for students. The tutorial aspect of this may help students.
Goal
Deliver An Upper-Level Curriculum With Appropriate Discipline Specific Knowledge
The curriculum will address the discipline specific knowledge dictated by professional societies and/or professionals in the workforce for upper-level instruction in mathematics.
Objective
Advanced Areas For Majors
Students preparing to graduate will demonstrate advanced mathematics knowledge and skills.
Indicator
Mth363 Project
Students will complete a project on the role of proof and technology in communicating mathematics.
Criterion
Project Assessment
At the end of the semester, 70% of the students submitting their project will receive a grade of 8 or better according to the attached rubric.
Finding
Project Assessment Results
Twelve projects were submitted, 9 of them received an 8 or better based on the given rubric. Of those 9, three received a grade of 10.
Indicator
Mth467 Paper
Students will be administered a final exam in which they will be required to write two essays: one that outlines the ascent of algebra in mathematics, the second required the students to discuss three mathematical crises in mathematical history and their impact on mathematics.
Criterion
Ascent Of Algebra
On the final exam, 70% of the students were expected to identify three specific mathematicians (Diophantus, Descartes, and Galois) as making significant contributions. This equates to a 2 or 3 on the attached rubric.
Finding
Ascent Of Algebra Results
Students were to receive at least a 2 on the Ascent of Algebra, students were expected to identify at least the following three mathematicians: Diophantus, Decartes, and Galois. Seven of the 10 students identified these three as making significant contributions and could briefly describe these contributions.
Criterion
Essay On Historical Crises In Mathematics
On the final exam, 70% of the students will identify at least three crises in mathematics. This equates to a score of 2 or 3 on an essay that describes a historical theme in mathematics according to the rubric provided.
Finding
Historical Crises Results.
To receive at least a 2, students were expected to identify the issue of commeasurability, the question of Euclid's Fifth Postulate, and the issue about the meaning of "function". Only 4 out of 10 students identified all three, and 7 out of 10 identified the first two issues.
Action
Implications For 2011-2012
Students are meeting our minimal standards in Math363 and at least one of the themes in Math467. Perhaps it is time to raise our expectations in those areas. Another idea would be to change the focus. In particular instructors in both courses are exploring the idea of a joint topic that can be used to satisfy partial course assessment in both classes.
We did not meet our standard related to historical crises in mathematics in Math467. Since major developments in mathematics often occurred as the result of crises and questions about the foundation of mathematics, we believe more time needs to be spent on this topic. Moreover, students seemed resistant to the very idea that development of mathematics could even have crises or involve conflicts. More emphasis needs to be placed on this topic so that students understand that mathematics is a human endeavor, always complete.