The ultimate question is the following: does incorporating technology in the classroom, a limited spiraling pattern, and Interdisciplinary Lively Application Projects, really help students have a deeper understanding of the material, a better appreciation for what math is and what it can be used for, and improve their problem solving ability and self-confidence? To answer these questions, Project Intermath hired an external evaluator who is following approximately 30 students as they proceed through our program.
The first step is to recruit the students and to satisfy human resource requirements this must be done carefully – on a voluntary basis, without the instructors knowing which students are involved in the evaluation process, and actually remaining in contact with these students for a period of 2 years. We recruited students in Calculus 2 by having the PI attend the different sections of Calculus 2 and discussing the project with the students while the instructor was not in the classroom. This eliminated students who decided for whatever reason, not to take Calculus 2. Students were given a form to fill out which gave us demographic data and then asked to either accept or decline participation in the project. These students agreed to be evaluated once a year for two years, and to have their ILAPs collected and copied so that progress could be evaluated.
The first midterm evaluation report includes results from interviews with students who are at the end of Calculus 2 (so that most of them have had two semesters of Calculus at CU-DHSC). Some results from the interviews:
Attitude toward Mathematics
When asked about their present attitude toward math, as compared to when they entered Calculus 1, all 10 students indicated a positive change. Such comments as “I feel more confident now”, “I am more comfortable with it now” and “I can now see the practical value of math” reflected the positives in terms of levels of confidence, comfortableness, and functionality. In terms of the functionality dimension, one student expressed it this way, “Now I can see the actual use (of math) in chemistry, statistics and other applied areas”.
Use of Technology
The students were asked about their level of comfort in using technology now as compared to before participating in Calculus 1 & 2. Eight mentioned that they are now more comfortable with using it. The other 2 respondents indicated no change in comfort level, but both reported being competent in using technology. One of the 8 noted that she felt “more comfortable with it now because my Calc 2 teacher is using it”. Earlier in the interview this student noted that her Calc 1 instructor was against using the technology and, thus, never used it in her class.
ILAP Influence in Non-Math Courses
With the exception of three students who indicated they had “not yet” experienced an ILAP influence in related non-math courses, the remaining 7 participants noted positive influences. Most noted how they can now see math concepts within other courses and now know why they are there. Interestingly, two students mentioned the ILAP process helped them with their report writing skills. As one of students said, “it (ILAP experience) taught me how to better organize and present a report in my other courses”.
ILAP Value in Increasing Math Understanding
When asked about the ILAP role in adding to their understanding of math, the students offered positive responses in three areas. The most common response was “the ILAP has showed me how math applies”. Then a close second was the comment “it helps me build upon what is known”. The third observation, offered by one of these students, was that the ILAP “helped me articulate, in plain English, what is happening”.
Faculty Course Questionnaires (written evaluations of courses by students) have also given us some feedback.
Here are some of the comments from Calculus 1 students:
What is the most beneficial aspect of doing the ILAP in this class?
Applying what we learn to everyday experience.
It integrated most of what we learned throughout the semester into one project.
It helped figuring some problems out.
Getting to apply what we learned to a situation in real life.
It helped me with graphing better.
Group activity.
You get to see a practical example of the course material.
The practical application of the material learned in class.
What do you think could be done to improve your experience with doing ILAP?
Less writing. It’s difficult to write a paper on math subjects.
Start it earlier.
Remove math beyond calc. 1, such as diff. eq. and very abstract equations.
Provide better examples of what needs to be turned in.
Not so long and hard.
Nothing.
Make physics section less difficult.
By Calculus 2, the comments are not so harsh. Here are some of the comments from Calculus 2 students:
E. What is the most beneficial aspect of doing the ILAP in this class?
Seeing an actual application of the math.
The ILAP gives more real life situations as compared to just having equations and solving.
It did have you look further at the material we are learning.
The application to Calculus II such as differential equations.
Gives you a more not necessarily hands on but almost a more hand on use for the math.
It helped me grasp the concept of the differential equations.
Extra treatment of a difficult subject.
Gives and experience to liven up class. Move around and wok on something in a “real” environment.
Using the calc project to apply concepts to real life situations.
Gave a real life purpose to calculus. At least an example of how to use it.