G-TEAMS

Fellow Profile: Chantel Blackburn

Chantel Blackburn
  • G-TEAMS Cohort: 2009-10
  • Graduate Program: Mathematics
  • Teacher Partner: Janet Liston
  • School: Cholla High Magnet School
  • Grade level: 10-12
  • Topics: Honors Intermediate Algebra, International Baccalaureate Standard Level, International Baccalaureate Studies Level

"I want to help cultivate mathematical thinking in students because when you learn to think carefully and logically in life you can anticipate problems and solutions."

Research Interests

Chantel completed her master’s thesis in the area of algebra (more specifically, modular group theory) in the spring of 2009. For her work she wrote a program using the programming language GAP (Groups, Algorithms, Programming) to determine the simple representation modules of a large number of finite simple groups. To do this work she utilized the character information for finite simple groups available in the Atlas of Group Representation. Her other research interests in mathematics include mathematical modeling in biology and the Hausdorff Metric Geometry.

Chantel is currently working toward her PhD in mathematics with an emphasis on mathematics education for her dissertation. Her mathematics education research interests include development and training in reasoning and problem solving, relationships between arithmetic skills and algebraic manipulation, and collaborations between mathematicians and mathematics educators. She is also interested in how the structure of the mass education system in the United States influences the ways in which mathematics is taught.

Classroom Activities

Chantel has been working with Janet Liston at Cholla High Magnet School. Janet’s classes this year are Honors Intermediate Algebra, junior and senior IB Studies and junior IB Standard level mathematics.

Chantel spends her time in the classroom:

Lessons Learned

One of the big lessons Chantel has learned in the process of bringing her research in algebra into the classroom is a new perspective on mathematical modeling. Typically, mathematical modeling is done using techniques from analysis and involves applications in physics, chemistry, and now more commonly, biology. Physics sometimes utilizes group structures in modeling but more commonly a major part of algebra, linear algebra, is used as a tool in mathematical modeling. However, over the course of the year Chantel’s perspective has changed to realize that algebraic structures (and their properties) are not as abstract as they first appear – they are actually models too. For example, the commutative group structure of the integers is a model of our everyday experience with quantity. Now she can see how even fields that are typically considered more abstract, like algebra or geometry, can be viewed in terms of how we use that field to model our experiences in the world.

When teaching mathematics and/or applications, it is never a good idea to assume that anything is obvious. What is obvious to the teacher may not be obvious to the students and vice versa. You must always be prepared to explain your reasoning or be willing to say “I don’t know” and have the desire to find out. Helping students realize this can help them with communicating mathematics verbally and in writing.

Teaching mathematics for conceptual understanding involves a careful balance between explicitly teaching a concept, following procedures, and revisiting conceptual ideas. Sometimes an idea can be overwhelming and the only way to get through the work is to memorize a scary formula. Once a student is more comfortably with the intimidating formulas, making sure to revisit the conceptual ideas can help the student make a more solid conceptual connection. For example, once students are comfortable with the formula for calculating the distance between two points in the plane, it is easier for students to grasp the formula conceptually when you revisit its relationship to the Pythagorean Theorem.

Teaching Materials