(1) Rationale. The middle-level Mathematics program prepares teachers to use the Alabama Course of Study: Mathematics and other guides to provide instruction in mathematics. The standards build upon the Alabama Core Teaching Standards and are guided by tenets of the Association for Middle Level Education.
(2) Program Curriculum. In addition to meeting Rules 290-3-3-.02(6) (a)1. -4., 290-3-3-.02(6) (e) 1. and 2 . (i) - (iii), 290-3-3-.03, 290-3-3-.04, and 290-3-3-.07(1) (a)1. and (2), the program shall prepare prospective middle-level mathematics teachers who demonstrate knowledge of the number system, expressions and equations, geometry, measurement and data, proportional relationships, and statistics and probability.
(a) Number System. Prior to program completion, prospective teachers demonstrate knowledge of:
1. How to develop fluency with efficient procedures for operations on the real number system.
2. How to create models for operations of the real number system.
3. Operations and properties of the real number system to solve problems.
4. How to develop and use the meaning of unit fractions in the operations of fractions.
5. Relationships among fractions, decimals, and percent.
6. How to solve application problems with fractions, decimals, percentages, and proportions.
7. Numbers that are not rational, and how to approximate them by rational numbers.
8. How to use basic concepts of number theory (e.g., divisibility, prime factorization, multiples) to solve problems.
9. A variety of strategies to determine the reasonableness of results.
(b) Expressions and Equations. Prior to program completion, prospective teachers demonstrate ability to:
1. Reason about and solve one-variable equations and inequalities.
2. Represent and analyze quantitative relationships between dependent and independent variables.
3. Use properties of operation to general equivalent expressions.
4. Solve real-life mathematical problems using numerical and algebraic expressions and equations.
5. Work with radicals and integer exponents.
6. Understand the connections among proportional relationships, lines, and linear equations.
7. Analyze and solve linear equations and pairs of simultaneous linear equations.
8. Define, evaluate, and compare functions.
9. Use functions to model relationships between quantities.
(c) Geometry. Prior to program completion, prospective teachers demonstrate ability to:
1. Graph points on the coordinate plane to solve real-world and mathematical problems.
2. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
3. Draw, construct, and describe geometrical figures and describe the relationships among them.
4. Understand congruence and similarity using physical models, transparencies, and/or geometry software.
5. Understand and apply the Pythagorean Theorem.
(d) Measurement and Data. Prior to program completion, prospective teachers demonstrate ability to:
1. Represent and interpret data.
2. Solve real-world and mathematical problems involving measurements (e.g., angle, area, surface area, and volume, including cylinders, cones, and spheres).
3. Convert units within a given measurement system.
(e) Proportional Relationships. Prior to program completion, prospective teachers demonstrate ability to:
1. Develop ratio concepts and reasoning to solve problems.
2. Analyze proportional relationships and use that ability to solve real-world and mathematical problems.
(f) Statistics and Probability. Prior to program completion, prospective teachers demonstrate ability to:
1. Understand statistical variability.
2. Summarize and describe distributions.
3. Use random sampling to draw inferences about a population.
4. Draw informal comparative inferences about two populations.
5. Investigate chance processes and develop, use, and evaluate probability models.
6. Investigate patterns of association in bivariate data.
(g) Mathematics Instruction. Prior to program completion, prospective teachers demonstrate ability to use the Alabama Course of Study: Mathematics and other guides to provide research-based instruction so that students are able to:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.