Communication with colleagues and discussion on teaching strategies is vital to grow as an instructor.
I believe that good instructional design requires training as well as practice. To design a course, the learning goals need to be planned, the assessments written, and the instruction developed. To make this process easier and the course experience for the students more meaningful, an instructor should be aware of and use available resources, e.g. communicate with colleagues, use official guidelines, or participate in courses on education. One of the biggest challenges in undergraduate mathematics education is the number of students participating in courses like college algebra or calculus. Students have various needs and expectations for such a class, and it is the instructor's responsibilities to address these.
To fulfill this requirement I completed two courses on STEM education. In Summer 2016 I participated in MTH 490, a reading course on teaching college Mathematics. In a small class setting we discussed recent research in the field and improved our own teaching based on the findings. In addition I participated in the MOOC "An Introduction to Evidence-Based Undergraduate STEM Teaching", which gave me a lot of specific ideas to build into my own teaching. Teaching Strategies I encountered include backward design, learning goals, active learning techniques, and inclusive teaching.
Artifacts
In Summer 2016 I participated in MTH 490, Readings in Undergraduate Math Education by Andrew Krause. We learned about various resources on current math education and had weekly discussions. The syllabus can be found here.
In Fall 2016 I completed MOOC "An Introduction to Evidence-Based Undergraduate STEM Education" offered by the CIRTL Network. My completion letter can be found here.
Materials Developed During Courses
MTH 490: Teaching Philosphy Statement.
As a final project we wrote a teaching philosophy statement. That assignment was a great opportunity to reflect on my teaching. I included this version here, to highlight the development I've gone through since then, and to contrast it to my current teaching philosophy, at the end of this portfolio.
MOOC: Peer Graded Assignment: Learning Goals.
Writing learning goals is an essential part of writing a meaningful syllabus. Students should always be aware of the learning goals and how to achieve them. Every class period I try to set the current topic in the broader course context.
MOOC: Peer Graded Assignment: Active Learning Strategy.
Active learning is an integral part of modern college teaching. I incorporated active learning in my own classes, for example when teaching Calculus 1 in a flipped classroom setting. This was meaninful practise for me in designing those activities.
MOOC: Final Peer Graded Assignment: Lesson Plan here.
With a good lesson plan teaching becomes very easy. I learned in this segment especially that the lesson plan depends on the student population. Since this assignment I try to always check my lesson plan for alignment with the objectives.
Reflection
Through MTH 490 and "An Introduction to Evidence-Based Undergraduate STEM Teaching" I realized that there are numerous resources available to improve my teaching in mathematics. I can use the abilities I have as a researcher to become a better teacher. As a graduate teaching assistant I do not have to design my own course, but I already have to lesson plan myself. Being aware of the process of backwards design and reading the learning goals helps me to align my teaching with the course objectives. On top of that it is very likely that I will have to design a course myself in the future. It is great that through the courses I took and through the resources they made me aware of, I feel prepared to do so.
The practice of backward design can be described by the following three stages:
Identification of the desired results.
There are many resources that can help with this step. A good starting point for designing a course in undergraduate mathematics would be the recommendations from the Mathematical Association of America (MAA). In MTH 490 we investigated for example the College Algebra Guidlines of the MAA. Another good resource to get started are other syllabi from other instructors (either at the same, or at a different college). Even though these might differ from the desired course due to a different student population, a different mission statement as a college, or just a different focus in undergraduate education, it is good to investigate other peoples solutions to gather ideas.
One of the big challenges in designing a course in lower level undergraduate mathematics courses is the diversity of the student body. These courses are often a requirement for a big variety of majors (science and non-science). Therefore it is important to stay in conversation with representatives from these departments to determine the course goals. As a starting point, the MAA makes recommendations from partner disciplines for college algebra available . Additionally to partner disciplines, there might be requirements from businesses, that want to employ future graduates.
I practiced writing course goals in "An Introduction to Evidence-Based Undergraduate STEM Teaching". In my first assignment I had to identify the difference between course-level learning goals and topic-level learning objectives. I also learned that it is essential to make students aware of these learning objectives. This can be done by including them in the syllabus, or reminding students during class time of the current topical learning goal, and place the current class in the broader context.
Determine assessment.
After deciding on learning goals, it is design assessments that are in alignment with the goals. The MAA-guidelines can help with deciding on these assessments again. Before writing quizzes or exams for my own classes, I often try to access old quizzes or exams from colleagues that previously instructed this particular course. These can help as a guideline for the new assessment and give ideas. However it should always be checked that these assessments are in alignment with the course goals. In summer 2016 I got the unique opportunity to entirely design the assessment for my course Calculus 1. Being an expert, it is sometimes hard for me to determine, where exactly the students might struggle and how long they might need to solve a particular problem. In "An Introduction to Evidence-Based Undergraduate STEM Teaching" it was emphasized that students should be able to close their feedback loop. This means that students should get meaningful feedback from the instructor during a class. One way I have tried to implement this was in my course Calculus 1 in Summer 2016. During the three-and a half hour class period, there were two assessments. The first one was a group quiz, i.e. the students would work in groups of three or four on challenging problems. In addition to peer feedback, I would walk around the room and give hints if needed. This quiz was worth few points for the students' final grade. Additionally there was a quiz at the end of the class period, that students had to take on their own. This quiz would be fairly similar to the previous group quiz, so that students could apply the previously learned material.
Design teaching activities.
The design of teaching activities is the last step of backwards design. I practices this for example in my second assignment in "An Introduction to Evidence-Based STEM Teaching", and I also needed this ability for my mentored teaching project. Colleagues of mine often say that they do not have time for active learning in their classroom. In my experience, it is more about using my class time more effectively. In Fall 2016 I made the concious decision to turn my class into a hybrid class. This meant that students watched videos at home on the content I would otherwise have to cover in class. Therefore I could spend the precious class time on examples. For me as a teacher it is very helpful to supervise my students while they are working in groups. This way I can identify common misconception and also help students individually. Sometimes I even skipped a topic in class, since my students told me that they understood it well enough from the videos. I would still assess their knowledge in a quiz afterwords and maybe do some review during the next class period if necessary.
My students seemed to appreciate this approach, because it showed them that I was taking their individual needs into consideration.
The whole process of backward-design came together for me in my final peer graded assignment, where I wrote a lesson plan for a calculus class. I understand that students are always going to learn in different ways and at different speeds. As an instructor I make it my priority to make the classroom experience as effective as possible for as many students as possible. Some students do not like group work and some students enjoy it a lot. When starting to teach a class I have to be flexible enough to accomodate the current student population.
Especially Week 6 of the MOOC, which is debating Inclusive Teaching, had a great impact on me. It is easy to discriminate against and discourage students by not realizing the instructor's impact. Being a woman in a predominantely male field, I am sensitized to gender discrimination. The examples they showed made clear, that I can still make other females in class feel uncomfortable, or make unconcious desicions that have a negative impact on some part of the student population. The concrete examples they gave me help me being vigilant when it comes to these issues.
I believe that the classes I took gave me the tools to become a better teacher, to be able to design my own courses, and to converse with my future colleagues about teaching.