Field 208: Mathematics
Alignment of Test Framework Objectives with State and National Standards
| Illinois Licensure Testing System Framework Objectives for Mathematics | State Board of Education Rules-Title 23 of the Illinois Administrative Code – 27.130 | NCTM/CAEP Standards for Mathematics Teacher Preparation |
|---|---|---|
| Subarea I: Mathematical Practices, Technology, and Disciplinary Literacy | ||
| 0001 Understand mathematical practices. | a2 A; b1; b2 A-B; C1; C2 A-B; d1 A-B; d2 A-B; i3 A-B; i6 A-B | 2a-f |
| 0002 Understand how to select, integrate, and use appropriate technologies in the mathematics classroom. | c2A; e1 A-B; e2 A-B; f4 A-B; j5 B; i6 A | 3c, 4e |
| 0003 Understand the process of reading, and apply knowledge of strategies for promoting students' reading development in the mathematics classroom. | k1 A-H; k2 A-J | |
| Subarea II: Number Systems and Operations | ||
| 0004 Understand the real number system and its operations. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; f1 Ai-iii; f2 A; f3 A i-iii; g1B iii; g3 C I; h1 A1; h4 A I; h5 A I | 1a; 3a-g; 4e; A.1.1; A.1.2; A.1.3 |
| 0005 Understand the properties of complex numbers and linear algebra. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; f1 B; f1 C; 3B-C; h2 C; h4 B; h5 B ii; h6 C | 1a; 3a-g; 4e; A.1.1; A.1.4; A.2.5; A.2.5 |
| Subarea III: Functions and Algebra | ||
| 0006 Understand algebraic techniques. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; f2 B; h1 A i-1v; h1 B; h2 A i-ii; h2 B; h2 C; h5 A i-vii; h5 B I; h5 C iii; h6 A i-ii; h6 B i | 1a; 3a-g; 4e; A.2.1; A.2.2; A.5.3; A.6.1 |
| 0007 Understand functions and the properties of linear relations and functions. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B; h2 A i-ii; h2 B; h2 C; h5 B i-iii; h6 A i-ii; h6 B i-ii | 1a; 3a-g; 4e; A.2.1; A.2.3; A.2.4 |
| 0008 Understand quadratic functions and conic sections. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1. B; h2 A i-ii; h2 B; h2 C; h5 B I, iii; h6 A i-ii; h6 B i-ii | 1a; 3a-g; 4e; A.2.2; A.2.3; A.2.4; A.3.9 |
| 0009 Understand polynomial, absolute value, radical, and rational functions and inequalities. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B; h2 A i-ii; h2 B; h2 C; h5 B I, iii; h6 A i-ii; h6 B i-ii | 1a; 3a-g; 4e; A.2.2; A.2.3; A.2.4 |
| 0010 Understand exponential and logarithmic functions. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B; h2 A i-ii; h2 B; h2 C; h5 B I, iii; h6 A i-ii; h6 B i-iii | 1a; 3a-g; 4e; A.2.2; A.2.3; A.2.4 |
| 0011 Understand trigonometric functions. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B; h2 A i-ii; h2 B; h2 C; h5 B i, iii; h6 A i-ii | 1a; 3a-g; 4e; A.2.2; A.2.3; A.3.5 |
| Subarea IV: Differential and Integral Calculus | ||
| 0012 Understand principles of differential calculus. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B; h3 A i-ii; h3 B ii-iii; h7 A i, ii | 1a; 3a-g; 4e; A.5.1; A.5.5 |
| 0013 Understand principles of integral calculus. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B; h3 A i-ii; h3 B ii-iii; h7 A i, ii | 1a; 3a-g; 4e; A.5.1; A.5.5 |
| Subarea V: Measurement and Geometry | ||
| 0014 Understand principles and applications of measurement. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B | 1a; 3a-g; 4e; g1 A i-ii; g1 B i, iii; g2 A i-iii; g2 B-C; g3 A i-iv; g3 B i; g3 C i-ii; i4 A iii, iv; i4 B; A.3.4; A.3.6; A.3.7 |
| 0015 Understand Euclidean geometry. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; i1-2; i4 A i-iv; i5 A i-ii; i5 C i; i6 C | 1a; 3a-g; 4e; A.3.8; A.3.1; A.3.4; A.3.6; A.3.7 |
| 0016 Understand coordinate and transformational geometry. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; i2; i5 A i-ii; i5 B iv; i6 A | 1a; 3a-g; 4e; A.3.2; A.3.3; A.3.6; A.3.9 |
| Subarea VI: Statistics, Probability, and Discrete Mathematics | ||
| 0017 Understand the process of collecting, organizing, and representing data. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B; h5 B I; j1 A i-iii; j1 B; j2 A i-ii; j3 B; j3 C; j5 A i-iii; j5 B; j6 A i-ii; j6 B; j7 A i-iii; j8 A i-v; j8 B i-ii; j8 C | 1a; 3a-g; 4e; A.4.1; A.4.2; A.4.3 |
| 0018 Understand probability and discrete mathematics. | a1 B; a2 A; a2 C; C2 A; e1 A; e1 B; e2 A; e2 B; h1 B-C; h4 ii; h5 B I; h5 C I; j4 A i-iii | 1a; 3a-g; 4e; A.4.4; A.4.5; A.6.1; A.6.2; A.6.3 |
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