Table 3.
Specific Indirect Effects of Foundational Skills through Intermediary Calculation Skills on Later Higher-Level Math Outcomes (N = 962)
| through Intermediary Accuracy |
||||||
|---|---|---|---|---|---|---|
| to Later Word-Problem Solving Skill |
to Later Pre-Algebraic Knowledge |
|||||
| Foundational Skill/Process | path | 95% BCBS CI | β | path | 95% BCBS CI | β |
| Calculation skill | 0.028 | [0.007, 0.063] | 0.010 | 0.049 | [0.019, 0.100] | 0.014 |
| Number understanding | 0.005 | [0.001, 0.012] | 0.006 | 0.008 | [0.001, 0.019] | 0.008 |
| Reasoning | 0.006 | [0.001, 0.017] | 0.005 | 0.011 | [0.001, 0.027] | 0.008 |
| Language comprehension | −0.008 | [−0.019, −0.001] | −0.007 | −0.013 | [−0.029, −0.003] | −0.009 |
| Working memory | 0.012 | [0.003, 0.028] | 0.008 | 0.022 | [0.007, 0.046] | 0.012 |
| Attentive behavior | 0.004 | [0.001, 0.009] | 0.008 | 0.006 | [0.001, 0.014] | 0.012 |
| Processing speed | 0.012 | [0.002, 0.029] | 0.006 | 0.021 | [0.004, 0.048] | 0.008 |
| through Intermediary Fluency |
||||||
| Calculation skill | 0.106 | [0.060, 0.166] | 0.038 | 0.076 | [0.013, 0.150] | 0.021 |
| Number understanding | 0.007 | [0.001, 0.015] | 0.009 | 0.005 | [0.001, 0.014] | 0.005 |
| Reasoning | 0.010 | [0.001, 0.022] | 0.008 | 0.007 | [0.001, 0.019] | 0.005 |
| Language comprehension | −0.004 | [−0.014, 0.004] | −0.004 | −0.003 | [−0.012, 0.002] | −0.002 |
| Working memory | 0.002 | [−0.011, 0.014] | 0.001 | 0.001 | [−0.007, 0.013] | 0.001 |
| Attentive behavior | 0.008 | [0.004, 0.013] | 0.018 | 0.006 | [0.001, 0.013] | 0.010 |
| Processing speed | 0.022 | [0.007, 0.046] | 0.011 | 0.016 | [0.002, 0.040] | 0.006 |
Note. Three decimal places are reported for indirect effects to help readers distinguish among such small values. 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. Intermediary Calculation accuracy is Addition Strategy Assessment. 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. Intermediary calculation fluency is end of grade 2 Second-Grade Calculations Battery.