Quadratic and cubic trends significantly improved the linear model of teacher and student behavior, showing the importance of studying nonlinearity¶
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Evidence · 1 study · associationalr1·q2
Currency · newest study 2017 · not yet checked against its sources · not reviewed by a person · overdue for a recheck since 2020: tool and model accuracy changes quickly
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q2 i? For both teachers, adding quadratic and/or cubic terms significantly improved the linear regression model of the behavioral time-series. → Pennings 2017
Evidence¶
Pennings 2017¶
Pennings, H. J. M. (2017). Using a Complexity Approach to Study the Interpersonal Dynamics in Teacher-Student Interactions: A Case Study of Two Teachers. Complicity: An International Journal of Complexity and Education, 14(2). https://complicityjournal.org doi:10.29173/cmplct29338
q2 · i? · associational · r1
Ordinary least squares regression trend analysis of the two classrooms' time-series (Table 2 reports R2 linear and ΔR2 quadratic and cubic terms with significance markers). The article concludes this "shows the importance of studying the nonlinearity".
"Both for Ethan and Sam, the quadratic and/or the cubic terms significantly improved the linear model. This also shows the importance of studying the nonlinearity."
Discussion¶
Related Claims¶
- Fuzzy time series forecasting beats nonlinear regression when only a quadratic term is included, but loses when a cubic term is included — related
- A first-order time-invariant fuzzy time series model produces more precise university enrollment forecasts than linear regression with time as predictor — related
- Phase analysis showed Ethan leading the interaction with sameness in Communion and oppositeness in Agency, while Sam led in Communion but followed in Agency — related
- Teacher-student scaffolding and autonomy support co-evolve into self-reinforcing attractor states over sustained one-on-one instruction — related
- The hypothesis that both teachers can refrain from complementarity when facing hostile student behavior could not be confirmed — related
- Engagement peaked at the middle of the Mindsets program and declined slightly by post-test, showing a significant negative quadratic trend — a narrower finding that bears on this claim
- Content knowledge does not significantly predict the number of experiments conducted; general cognitive ability shows a quadratic association and self-concept a negative linear association — related
- Role identity formation is a self-organizing process in which the system strives toward coherence, moving from repellor states toward attractor states — related
- Ability to Reason (SMP 2) benchmark levels improved linearly across all three time points (d ≈ 0.78) with no significant quadratic trend — related
- Verbal working memory shows non-linear growth from ages 3–19, with the most rapid growth during childhood and a brief accelerated period during early adolescence — related
- When PSID-CDS data are restricted to ages 6–11, backward digit span growth is best characterized by a quadratic (not cubic) function — related
- In a visual-spatial integration task, the interaction between visual-spatial working memory capacity and visual design is quadratic, with the inverted-U progression more strongly accentuated for the dynamic design — a narrower finding that bears on this claim
- Mental effort relates to self-rated certainty in a cubic (declining–flat–declining) rather than linear pattern — related
- Non-linear (Goldilocks) effects of expectations and aspirations on outcomes are small and largely non-significant — related
- Over a full term, aggregated lecture time decreases linearly while independent study time follows a negative quadratic trajectory, rising until the end of the lecture period and then declining — a narrower finding that bears on this claim
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
quadratic-cubic-trends-improve-linear-model-teacher-behavior |
title |
Quadratic and cubic trends significantly improved the linear model of teacher and student behavior, showing the importance of studying nonlinearity |
description |
Quadratic and cubic trends significantly improved the linear model of teacher and student behavior, showing the importance of studying nonlinearity |
status |
review |
evidence_strength |
moderate |
newest_evidence |
2017 |
recheck_by |
2020 |
generated |
by process:wiki-ingest on 2026-09-26 |
trust |
unverified — no one has confirmed this page's content |
sources |
1 — pennings-2017 |
Frontmatter is the page's machine-readable record — see the Schema & Guide.