This pilot ascertains to what extent secondary school students articulate basic conceptions that define constancy and change in specific mathematical systems, and develop corresponding habits of mind. Covered systems belong to the following mathematical domains:

Algebra:

• Powers & Radicals- Absolute value
• Sets & Set operations
• Equations & Inequalities

Equations and inequalities of the first degree- Equations and Inequalities of the first degree involving absolute value- Linear equations and linear inequalities- Quadratic equations and  inequalities- System of linear equations (22) – Polynomials.

• Basic Functions

Linear function- Quadratic function- Absolute value function- Square root function- Inverse function.

• Natural logarithm & exponential

Properties: Formulas, identities, equations and inequalities.

Calculus:

• Limits, continuity & differentiation
• Numerical functions

Study of the following functions (graph, tangents and asymptotes):
Rational, irrational, trigonometric, natural logarithm & exponential.

Geometry:

• Classical  Geometry

Pythagorean theorem- Areas of triangles & parallelograms

• Plane Analytic Geometry

Lines - Circles- Vectors & Scalar product.

Trigonometry:
Solving a triangle- Trigonometric identities- Trigonometric equations- Trigonometric functions- Metric relations in a triangle- Calculation of areas.

Data Analysis & Statistics:

• Data

Data Collection- Data Representation

• Elementary Statistics

Mean- Median- Mode- Variance & Standard Deviation.

1- Analysis:

1. Describe the roots of a quadratic equation (Descriptive).
2. Explain why a quadratic function has a maximum or minimum (Explanatory).
3. What is the effect of a translation (of a given vector) on a geometric figure? (Causal).
4. Distinguish between an unknown and a parameter (Discriminatory).
5. What is the locus of the points M, when N describes a given curve? (Inferential).

2- Criterial thinking:

1. Compare two numbers containing radicals (Comparison).
2. Discuss according to a parameter the solutions of an equation (Classification).

c. Calculate the radius of the circumscribed circle about a triangle (Measurement).
d. Estimate an approximate value of a real number (Estimation).
e. Follow the steps in A to solve B (Analogical reasoning).

3- Relational thinking:

1. Conclude the final result, by using all the last parts of the problem (Synthesis).
2. Under which transformation, Y is the image of X? (Correlation).
3. How X and Y are connected in a geometric figure? (Syntax).
4. Using a derivative function, interpret a given situation in Physics (Transfer).
5. Use complex numbers to study geometric transformations? (Extrapolation).

4- Logical thinking:

1. Justify why two lines are parallel (Justification).
2. Deduce a result from another (Deduction).
3. Demonstrate a statement X by using hypothesis Y (Proof).
4. Based on your answer to the last part, give an expression for X (Conjecturing).

e.Given all you know in situations X, infer what happens in situation B (Induction).

5- Communication:

1. Illustrate graphically the solution of a given system (Semantics).
2. Give the algebraic solutions of an inequality containing absolute value, and graph it on the Real Line (Multiple representations).

c. Represent a Sequence by a table (Correspondence).
d. Graphic interpretation of the behavior of a function (Graphic expression).
e. Coordinate between different graphical representations of certain data distributions (Coordination).