Mathematics Department

The Tempe Preparatory Academy Mathematics Program is a six-year, problem-based curriculum designed to hone student thinking and elicit quantitative reasoning to solve relevant problems, guide decision making, and answer questions of wide concern.

Our program exposes students to varied interrelated experiences, introducing them to connections and relationships between math and related scientific disciplines. We create learning experiences that periodically demonstrate the relationship of the disciplines and real world application.

Students study formal methods, structured protocols, mathematical concepts and patterns of reasoning, but go beyond the memorization of axioms to develop a deep sense of analytical reasoning and justifiable logic. Through a cultivation of mathematical fluency, students learn how to transform and analyze data themselves, and apply estimation methods to problem solving in everyday life.

We do not simply drill students in the techniques of arithmetic, we teach students how to use the discipline’s unique concepts and propositions to examine and solve a central theme, issues, problem, topic or experience, thus heightening the relevancy of mathematics in our daily life.


Coursework is framed around five general goals for all students:

  • Apply abstract concepts in concrete situations
  • Translate problem situations into mathematical models
  • Organize and effectively communicate mathematical questions and results
  • Distinguish between correlation and causation
  • Understand the role of mathematics in society
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Tom Hickernell – Mathematics Department Chair

Keith Thurston – Mathematics Department Co-Chair


Students in Pre-Algebra address mathematical concepts by using numerical analysis. Students master the operations of addition, subtraction, multiplication and division using whole numbers, fractions, decimals and percents. In addition, students learn to use first order equations and inequalities to solver real world problems.

Using complex first and second order equations and inequalities, Algebra I will teach students to expand their understanding of mathematical models to the coordinate plane and begin to understand functions.

In Geometry, students build an axiomatic system of definitions, postulates and theorems in order to write well-developed proofs of geometric ideas. They combine their knowledge of algebra and start to analyze geometric ideas analytically

Students further develop their algebraic skills by analyzing higher order functions. In addition to linear and quadratic functions, students study exponential, logarithmic, polynomial, rational and radical functions. Students begin to use the graphing calculator as a tool to solve real world problems graphically and algebraically.

Students study the use of trigonometric functions, as well as study conic sections to end their pre-calculus study. In the second semester, students begin the study of calculus by examining limits and derivatives.

Calculus application problems become more complex and students learn to use all the tools of mathematics incorporating numerical, algebraic and graphical analysis in their solutions. Students reach the pinnacle of their study as they master mathematical logic and proof.