Table 2.
Direct Effects of Foundational Skills and Processes to Intermediary Skills and Later Higher-Level Mathematics Outcomes (N = 962)
| Intermediary Calculation Accuracy |
Intermediary Calculation Fluency |
Later Word-Problem Solving Skill |
Later Pre-Algebraic Knowledge |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Variable Type/Variable |
path | 95% BCBS CI | β | path | 95% BCBS CI | β | path | 95% BCBS CI | β | path | 95% BCBS CI | β |
| Foundational | ||||||||||||
| Calculation skill |
0.21 | [0.083, 0.343] | 0.14 | 1.75 | [1.382, 2.091] | 0.32 | 0.12 | [−0.034, 0.270] | 0.04 a | 0.37 | [0.155, 0.592] | 0.10 a |
| Number understanding |
0.04 | [0.004, 0.071] | 0.08 | 0.11 | [0.011, 0.210] | 0.07 | 0.12 | [0.079, 0.158] | 0.15 | 0.13 | [0.077, 0.179] | 0.13 |
| Reasoning | 0.05 | [0.003, 0.100] | 0.08 | 0.16 | [0.008, 0.300] | 0.07 | 0.10 | [0.047, 0.164] | 0.09 | 0.13 | [0.048, 0.217] | 0.09 |
| Language comprehension |
−0.06 | [−0.106, −0.009] | −0.09 | −0.07 | [−0.205, 0.077] | −0.03 | 0.17 | [0.116, 0.225] | 0.15 a | 0.08 | [−0.004, 0.147] | 0.05 b |
| Working memory |
0.10 | [0.032, 0.160] | 0.12 | 0.03 | [−0.168, 0.210] | 0.01 | 0.09 | [0.010, 0.167] | 0.06 | 0.14 | [0.029, 0.242] | 0.07 |
| Attentive behavior |
0.03 | [0.006, 0.048] | 0.12 | 0.13 | [0.069, 0.186] | 0.15 | 0.06 | [0.041, 0.087] | 0.15 | 0.09 | [0.063, 0.124] | 0.17 |
| Processing speed |
0.09 | [0.009, 0.172] | 0.08 | 0.36 | [0.101, 0.613] | 0.09 | 0.08 | [−0.016, 0.167] | 0.04 a | 0.21 | [0.074, 0.346] | 0.08 a |
| Intermediary | ||||||||||||
| Calculation accuracy |
0.13 | [0.041, 0.219] | 0.07 | 0.23 | [0.116, 0.346] | 0.10 | ||||||
| Calculation fluency |
0.06 | [0.036, 0.087] | 0.12 | 0.04 | [0.007, 0.081] | 0.07 | ||||||
Note. BCBS CI is bias-corrected bootstrap confidence interval; intervals not including 0 signify the path is significantly different from 0 at α = .05. β is standardized path. Underlined estimates indicate that paths were tested for equality between the outcomes; different letters within a row within an intermediary skill/outcome indicate significant differences between direct effects. Intermediary calculation accuracy is Addition Strategy Assessment. Intermediary calculation fluency is Second-Grade Calculations Battery. Later word-problem solving skill is Iowa Test of Basic Skill-Level 10-Math. Later pre-algebraic knowledge is Test of Pre-Algebraic Knowledge. Calculation skill is Wide Range Achievement Test-Arithmetic. Number understanding is Number Line Estimation (reverse scored). Reasoning is Wechsler Abbreviated Scale of Intelligence-Matrix Reasoning. Language comprehension is Woodcock Diagnostic Reading Battery-Listening Comprehension. Working memory is Working Memory Test Battery for Children-Listening Recall. Attentive behavior is Strengths and Weaknesses of ADHD Symptoms and Normal Behavior Rating Scales. Processing speed is Woodcock-Johnson Tests of Achievement III-Visual Matching.