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Reflection on Instructional Change:

Introduction: Based on the following learning outcome: "Develop and interpret graphic representations of curves, vector fields and functions of multiple variables." of my Calculus 3 course, I implemented the following in-and-out-of-class time activity. The purpose of this activity is to emphasize the visualization of certain concepts that we have been studying and to encourage students to learn how to use online graphing calculators, which can be a very powerful tool for them during this course and in the future.

Activity description:

In class: Lecture on the interpretation of the graphs of a variety of two variable functions and guide students through a few introductory practice questions.

Out of class: Students work on homework questions where they are asked to 1) Match different graphs with their corresponding functions and 2) Sketch the graph of different functions.

In class: Students work in groups on a worksheet consisting of similar graphing questions: Matching graphs and functions and sketching graphs.

Out of class: Students are asked to complete and rework their worksheet solutions by using the Geogebra online graphing calculator introduced during our lectures.

I also implemented a similar strategy in the Advanced Math for Science and Engineering course that I am teaching this Fall semester, but focusing on the interpretation of phase portraits of differential equations, and incorporating the use of python programming instead of Geogebra.

Feedback: I am happy with this type of assignment as it emphasizes certain non-symbolic aspects of the concepts discussed in the course that I believe are important for the students to grasp. A number of students enjoy working through these questions together, as they seem to generate good points of discussion between them. Students have also expressed appreciation for the incorporation of technology in these assignments, some of them even told methat they have used some of the python tools we studied in their other classes.

Observe and Analyze Session: I observed Yajenny Pacheco's Math 107A: Fundamental Math Concepts class. The class involved a lot of discussion among the students and group work, the environment was very energetic and students engaged meaningfully with the questions assigned. Yajenny discussed the the fundamentals of addition and subtraction with special attention to the distinction between what they mean for positive and negative numbers, focusing on the meaning of these concepts and how one may explain them to very young students. Yajenny showed that she clearly put a lot of thought on how her students are internalizing these concepts, and pointed out many subtleties in the material that I could personally not have foreseen. It was a great learning experience to see how she interacted with the students and kept them engaged with their work. I am looking forward to teaching this course one day and I hope I can lead these discussions as graciously and expertly as Yajenny does.

I was also observed by Yajenny Pacheco, as I taught one of my Math 105A: Advanced Math for Science and Engineering classes. In that class we were solving a number of linear systems and analyzing the dimension of their solution spaces. At the end of the class the students worked in groups through a worksheet. It was interesting to debrief with Yajenny after that class. She noted that many students nodded quite often during the lecturing time, which is something hard for me to notice sometimes. That is a very quiet class, so I appreciated hearing Yajenny mention that the students were paying close attention to me as I introduced the different questions. We also had a long conversation about guiding a productive group activity and what are possible points of improvements.

**Evidence of Instructional Change**
Math 105A notes discussing the dynamics of elliptic equilibrium points.	In Math 105A students draw phase portraits by hand and also generate them in Python.	ACUE Badge

Changes in Course Syllabus and Schedules:

Pre FLC - Syllabus and Schedule

Post FLC - Syllabus and Schedule

**Faculty Bio**
	I am an Assistant Professor in the Mathematics and Statistics Department at Sacramento State. I am from Rio de Janeiro and I graduated with a bachelor's and masters degree in Applied Mathematics from the Universidade Federal do Rio de Janeiro. I then moved to Santa Cruz and obtained my PhD in Mathematics from UC Santa Cruz. After that I spent one year at UC Berkeley as a teaching postdoc before joining Sacramento State. My research interests include mathematical physics, differential geometry, dynamical systems and scientific computing. My hobbies include playing the guitar, reading books and manga, hiking, traveling and many other fun things.

**Program Sponsors**
	This work was supported by: National Science Foundation Hispanic Serving Institution Project STEM Zone DUE 1832335 US Department of Education Hispanic Serving Institution Project Degree with a Purpose P031S210061 US Department of Education Hispanic Serving Institution Project STEM4Equity P031C210012 *Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or the US Department of Education.