## Redesign Results

### Course Redesign Impact on Teaching and Learning

I first began implementing projects within my Pre-Calculus course five years ago and I have been able to collect data and improve the course during this period. Over this 5 year period I collected samples from various levels of student performance, significant data, and also located topics for projects which were extremely difficult to find, and combined these with a strong desire to continue doing research with undergraduates. When I began working on my redesigned course for Fall 2017, I developed topics for projects, rubrics for grading, sample projects, instructions on how to complete each topic, videos, and additionally posted a letter to students about my course and my spotlight, etc. All of this information was posted on Canvas prior to the semester starting as well as a very descriptive calendar for when every task should be completed. I also implemented the use of a Learning Assistant (TA). The TA who was one of my formal students who provided fantastic help to my students when they were not able to attend my office hours.

In Fall 2017 I continued to work with undergraduate research, however, I made some significant changes. One major change that I made concerned strategy for exam preparation. Prior to the redesign, even when I implemented projects into my course, I had never used Zoom meetings. My study group sessions with students were usually set up in my office or in the conference room or the library, and we had many attendees. In Fall 2017, I used Zoom meetings for two hours a day before each exam. I had a very positive success with attendees. Every session there were between 40 – 60 students online, among three courses, out of 110 students in total. I used a touch screen computer to write solutions on the white board. Students constantly asked questions through a chat or by speaking up. I recorded all slides and posted them later on Canvas, so other students who were not able to attend the meeting will be able to use them. I noticed that students were very comfortable asking questions and they corrected each other if they noticed any mistakes, and they also tried to help each other as well.

Another change that I made involved utilizing Canvas by creating pages with a significant amount of description toward how projects should be completed. Each topic had a sample project, supporting videos, articles, and a plan to follow as well. Also, groups were built regarding students’ interest toward a particular topic. There were pages about lessons that we covered and links to Khan academy and educational Youtube videos as well as my own videos.

This is the example of my video.

Also, I added more group work time during lectures. I built groups using Canvas. This helped to assign students randomly in a different group and gave them some exercise to move from their sitting spot in a classroom to another one. Also, it helped students to know each other better.

With the help of the CRT grant I was able to buy TI-84 graphing calculators and accommodate my students during lectures when the topic that we covered required the usage of a calculator. Since I did not have a class set of calculators and there was no lock box at the classroom, I was carrying them from my office to the classroom consistently. It would be very beneficial if we would be able to distribute calculators at the beginning of the semester for students with a required return at the end. Hopefully, this will change in a future. I used Desmos and TI-84 for graph visualization and I also let students use graphing calculators during their exams with the requirement of showing their work as well.

As the semester progressed, I noticed significant growth in students’ relation to the project. At the beginning of the semester many students were lost, and they were not sure what they needed to do. However, at the end of the semester, students were more focused, they followed deadlines and tried to accomplished their goals according to graded criteria. Rubrics for each task they were required to accomplish were posted on Canvas.

Following my incremental changes, I began to receive submissions with higher quality projects, however then a very unfortunate event happened in my area. The Thomas Fire hit our community with its full devastation of acres of land and houses. On the day that projects were due for presentation, the university was closed and for an extended period of time. Many students with their families did not have access to their computers or the internet. Due to heavy smoke in my area, schools were closed for a week and more. This was the time when the CRT team sent an email to my students asking them to do a survey regarding the redesigned course. I am not sure how well this went. The university was open for the final exam, and my focus was to at least do a review for the final exam, however the work with the research had been completed. The grade for the project was given to students without a class presentation. Below are two links to the rubrics for the main part of the research work and presentation.

Rubric for the Undergraduate Research Project

Rubric for the Oral Presentation

This is a sample of student’s poster.

#### Assessment Findings

Results for the redesigned course were much better compared to the non-redesigned course. Following my implementation of projects in 2012, I already knew that I will have a higher success rate compared to the traditional lecture course. In Fall 2017 I redesigned three sections of the Pre-Calculus course. Below are results only from one section; however, all three sections showed an increase toward successfully passing the course.

In the bar graph above, you can see there are more A, B, and C grades in the redesigned course compared to a non-redesigned course. There is also a shift within the non-passing grades. This mostly happened to students who gave up on the course at the beginning of the semester and then subsequently missed the deadline to withdraw from the course.

In the redesigned course there were 74% of students who passed compared to 54% in the pre-redesigned course. Additionally, there were 26% of students who failed the redesigned course compared to 46% in the pre-redesigned course.

### Student Feedback

#### Challenges my Students Encountered

The survey with this question “Please explain, using 3 to 5 sentences, the most challenging part that you experienced with the project” was posted on Canvas. Below are samples of students’ responses. Since I implemented the project in three sections, I had many repetitive responses.

Students’ Answers (in their words):

- The most challenging part of the project was getting everyone to work together at the same pace. Everyone had different schedules or different due dates that they set for themselves. It would have been way easier if everyone would have met up more.
- The most challenging part of the project was figuring out where to start. Once we did that it was also difficult to do research on our own. However, I think that it’s important for me to learn how to do research as a freshman.
- The most challenging part I experienced with this project was finding the equations to create a spirograph. After finding the correct equations it was really hard to calculate them because I wasn’t really sure how to do it. I also experienced trouble when trying to tie math spirographs and art, but eventually was able to find a few things after extensive research. Aside from that, I was also faced with the challenge of doing most of the group work on my own since my partner(s) were not doing much of their part.
- The most challenging part of this project was figuring out exactly what to model and how to model it. When my group and I decided to do the ocean’s tides, it took us quite a while to figure out exactly how we were going to do it. But once we understood what we were doing, it was pretty simple.
- The project is a good concept for an assignment. It integrates math and research together and shows us the poster template we will use throughout college. I feel the project would better fit in an upper division math class because most students in precalculus are first and second year students and the project is an unnecessary assignment that we could spend the time working on it on learning more math
- Doing the math was very hard because we have to analyze what it means and how it relates to the topic and how it connects to math. Understanding the formulas for photography was hard but at the end I was able to do the math.
- The most challenging part of this project was working with others that had conflicting schedules and didn’t live on campus. Setting times and meeting up with one another was very hard and rarely happened, when we did meet up the meetings did not last long and it was a struggle to get work done with the amount of time we had left. The most difficult part outside of that was that we had to rely on an outside source to get our work done and most of the time this person was unavailable to help my group work and complete the project.
- The most challenging part that I experienced with the project was figuring out how I would complete my section of the financial damages caused by hurricanes. After looking through several websites I saw the different types of category hurricanes with specific wind speeds among other details. I was then finally able to get a hold of a list with tons of different damage costs from various hurricanes and narrowed it down to our projects specific time frame
- With the project, a lot of information was very confusing and some of it i did not even know about such as deadlines. I figured it out as we went on. Meeting as a group was also difficult because of schedule conflicts.
- The most challenging part that I have experienced with this project was hoe to incorporate math with music. It did get easier once me and my partner did a lot of research. Once I got into the flow of the project it was easier to complete it.
- Mostly picking a topic to do the project on was hard because I did not know how I was going to relate it to math. Until now that it is due, I still have not fully understand what my topic is about but I do have a better idea. Also working in groups of 2 could have been easier maybe because it is easier to work faster and not have to worry about people doing work.
- I was in the math and photography group for the project and I think the most challenging part was creating the stereographic projection. The 3D printer on our campus doesn’t print holes very well, so it was extremely difficult to create a sphere that created a real stereographic projection. The 3D printer also prints very small, so that was another thing my group struggled with.

Another question that I posed to students was: “Write at least one suggestion for the redesigned math course with technology that will be beneficial for students. You may use the same aspects that were incorporated into your course such as the project, zoom meetings, TA help, graphing calculators, online homework and videos or add something else.” The following are some students’ responses in their words:

- I think this course was probably the best designed course I’ve ever taken, in mathematics!
- Zoom meetings are extremely helpful I was able to study for my test during the meetings because the professor solve the problems i could not do and also the times were very accessible.
- Having a graphing calculator will really help with classwork, homework, and tests. Without a calculator it will be very tough to pass the class.
- The project was the most helpful part of this course and it allowed for outside information to make its way into the math class. Math in Climate Change is part of my major, so it was really interesting to work on this project.
- Continued access to graphing calculators. What we are learning today we will be using in 4+ years and technology is expanding. We need to make sure we use technology now so we can better use it later in our studies. This also applies to formulas – in the future I will simply look them up when I need them, not recall the exact formula from that time I memorized it in calculus. This is also true of the Unit Circle. Most of us will forget it before the second semester even starts… So we’ll look it up again when we need it.
- I feel like the online homework was very helpful throughout the course. especially for the exams
- The zoom meetings, TA, graphing calculators, and online homework were all very helpful. I benefitted most from those but I personally struggle with math and even with this it is hard for me to keep up with the class. The project was my least beneficial aspect in the class. I just felt very lost on the project and would stress out often, since I would worry I would do the project wrong and have my class grade go down.
- More videos would help.
- I think having a TA for the class was very helpful. As well as having graphing calculators and being able to do online homework.
- I think for the XYZ Homework maybe include a video or examples on what is expected when completing the problems and what is expected when importing the answer. Another thing, for the project give a guideline for the project. Show videos that can help illustrate a better understanding of the project and what is expected when needed to submit drafts or final submission. What will effect your grade if you make a mistake or do the project wrong.
- I feel that if the redesigned math course with technology will be beneficial for students if it continues to provide zoom meetings, graphing calculators, online videos, and TA help. I feel like these aspects of the course are the most beneficial and helpful for the students.
- The videos were extremely helpful for me, so if more videos were made I think it would be very beneficial for the class
- I think that the project was good and should stay in the course.

### Lessons Learned & Redesign Tips

#### Teaching Tips

- Pre-Calculus course is usually attended by freshmen and many of them are taking this course because it is required by the GE. For many of them mathematics is one of the most challenging subjects. They are afraid of math, and they are taking this course because they have too. Try to make your course super cool! I developed projects with students that helped them to see the beauty of mathematics and make a connection with real life.
- The best way to get the highest attendance for study groups for exams is online meetings through Zoom or any other video messenger.
- Students prefer to follow deadlines when the reminder is sent to them electronically through email or any other messenger.
- If you are going to implement group projects then you need to control each group and have at least three meetings with each group per semester. Meetings can be done in person or online.
- The best way to work on the projects is to save them in Google Slides. This will help students to access files at any time since students have a difficulty to meet as a group.

#### Course Redesign Obstacles

- Many students do not know how need to work in teams. They either will try to rely on other students in group or do all the work by themselves. It is very important to have a meeting with all members in each group to discuss responsibilities of each student, constantly encourage students to follow deadlines, and accomplish each task on time. Projects that I implemented had many stages, and each stage is supposed to be published on Canvas by each student. This helped me to track students who fall behind and at the same time to not decrease the grade for students who accomplished their work on time. As the semester progressed students showed a significant improvement in time management.
- Another obstacle that I experienced was keeping up with the schedule and covering all necessary topics in my course. Since a part of the many projects that my Pre-Calculus students were developing was a statistical analysis of their research, I needed to cover extra material on some statistical topics. This was managed by holding extra office hours, study groups, posting reading material on Canvas and developing video lectures.
- Course redesign took a lot of my personal time in preparing videos, worksheets, meetings with students, etc.

#### Strategies I used to Increase Engagement

- Weekly small graded activities that were done in groups helped students to understand mathematical topics that we covered in class. I used Canvas to create new groups all the time, and since it was mandatory to upload a photo of each user into their Canvas account it helped students to get familiar with each other quickly.
- Online Zoom meetings as well as regular office hours helped students to be better prepared for exams.
- Homework that was done online helped students to receive immediate feedback. Students had an opportunity to use late passes for their homework as well as three attempts with a different variation of a problem.
- Many students attended office hours that were held by Learning Assistant (TA). The responsibilities of TA were not only to explain a certain mathematical topic and help students with their homework but also guide them through the project.

### Instructor Reflection

I have been involving students in research projects in Pre-Calculus courses since 2012. My records show that from 2012 through 2016 academic years, the passing rate for the courses with project-based modules was 62%, as compared to 57% of students who passed these courses without doing projects. The graphs below compare student performance in both types of courses. Gaps indicated that there were no projects done in a particular term. Note that in the Fall 2016 all students had individual Signature Assignments. These projects were done individually, and their impact was not significant as compared to other semesters when students accomplished projects in teams. Hence students perform better when projects are done in teams. That is the reason for the redesign, as we need to engage students and improve their perseverance.

The above bar graphs show there were higher success rates for passing the course if students were engaged into a team project compared to sections where students had a traditional class. My work for Fall 2017 semester showed that there was a significant improvement in a student’s success if the instructor will implement this technology. This is a new way of teaching and learning. The feedback that I received from students showed that not all freshmen are ready for team work and a project. Many of them still did not understand the purpose of the project. They were regularly looking at the course as though it should be taught as a traditional math course with the implementation of Zoom meetings and graphing calculators. They struggled with deadlines and team work. The most beneficial aspects of the new course in the students’ opinions were: Zoom meetings (39%), followed by the online homework (35%), next was the usage of graphing calculators (23%) and only 7% of students mentioned that the research project helped them to understand mathematics better. I was not surprised to see these results. This simply tells me that it is very important to show students a connection between mathematics and real life.

On a very positive note, during spring 2018, one of my students presented his research at MAA conference in San Diego and won the award in his category. A few other students presented their projects in SAGE conference for undergraduates at CSUCI at a different time. Some students decided to change their undecided major and become a STEM student.

In Spring 2018 semester I continued to use Zoom meetings, online homework component, graphing calculators and the TA. I did not do projects with students in the same way as they were done in the Fall. However, there were small assignments that were given to students that required their reading outside of the textbook.

Due to a significant change in Fall 2018 semester with all developmental math courses, I will continue to incorporate this technology since the study showed this is the best way to help students to learn, examine the benefits of emphasizing student-centered learning activities and how such facilitation of the mathematics classroom helps students in STEM disciplines stay in the pipeline. Also, I will work on my new grant Project PROMESAS 2018 which also will involve Pre-Calculus course.

The development of an ePortfolio helped me to narrow my research in Pre-Calculus course. It made me feel that the work that I do is important for students and the community. It is also very important to collaborate with colleagues in person or through webinars and exchange ideas, follow leaders and become a leader on your own. I am looking forward for continuity of this research and dissemination of my results in educational magazines as well as a continuity of work as a course coordinator of Pre-Calculus course at Channel Islands university.