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Fellow Profile: Angelica Gonzalez

Research Interests

Angelica Gonzalez is a second year graduate student in the Mathematics program at the University of Arizona. Her current research interests lie in the area of probability. She is currently studying self-avoiding walks.

Classroom Activities

Angelica spent her fall semester working with Ms. Nina Miller at Peter Howell Elementary School. Her main goal was to help students see the beauty of mathematics. In doing so, she hoped to develop their mathematical maturity, problem solving skills, and conceptual understanding. She helps with teaching, assists in small group activities, works with students individually, and introduces new projects. Some of the projects she has introduced into Ms. Miller's classroom are the following:

• Finding the factors of X day of School: This is a daily activity to help students analyze the properties of an integer. This also complements Ms. Miller's morning worksheet of finding the fraction of X/100 days of school.
• Challenge Problems: Challenging problems that will complement their classroom objectives or future projects.
• President's Choices: Teach students some basic concepts in Combinatorics while introducing the social science concept of taxing.
• Secret Messages: Introduce students to cryptography with the goal to have them understand RSA encryption. Students learned basic modular arithmetic. This lesson also motivates questions in pure mathematics. For example the difficulty of factoring and the importance of prime numbers.
• Fractions are all around us: Students will make their own videos to explain how fractions are used in engineering, chemistry, sports, and everyday activities.

Lessons Learned

I am learning about the importance of conceptual knowledge in elementary school. The Investigations curriculum prioritizes conceptual knowledge rather than efficiency. Although some of the students are not using efficient algorithms, they are usually using the right ideas. This helps when learning new math, because they are building their knowledge and intuition as opposed to memorizing and never bringing the subject together. After a lot of practice, they do realize the importance of efficiency. They begin to make better choices about which strategies they will use to solve a problem. This approach requires more time, patience, and dedication but it is worthwhile. The students are able to apply their learning and solve challenging problems. This approach also helps expand the students' mathematical creativity and maturity.

I am also learning how to better communicate mathematics. Ms. Miller does a good job at communicating important mathematical concepts without confusing the students. I am learning how to do this for myself. To do this effectively, I have to be concise and precise while catering my response to the student's knowledge. The latter has required a lot of practice and awareness.

Teaching Materials

• Introductory Presentation


• Class Notes and Lectures
  • RSA Encryption: lesson plan for our RSA encryption project (PDF).
• Days at Peter Howell
  
  
  

• Angelica Gonzalez
• Research Interests
• Classroom Activities
• Lessons Learned
• Teaching Materials

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