STEM PRACTICE AND EVIDENCE WORKBENCH
Use first and second differences across equally spaced outputs to audit linear, quadratic, or neither model classifications.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Subtract adjacent outputs to create three first differences. If all three agree within the absolute tolerance, classify linear. Otherwise subtract adjacent first differences to create two second differences. If those agree within tolerance, classify quadratic; if neither test passes, classify neither. The linear test runs first so a constant sequence is not mislabeled quadratic. Supported means the learner classification follows the supplied equally spaced outputs and threshold. This is pattern evidence over four points, not proof of a unique generating process. Inspect the original x-spacing, units, graph shape, measurement precision, residuals, domain, turning behavior, and alternative models. More data and contextual reasoning are needed before forecasting or making a scientific claim.
Confirm the learning question, authoritative source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence and remove learner names or identifiers.
Run the worked example first, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method. Correct input evidence before interpreting a flag.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently, connect the numerical signal with learner reasoning, and document any teaching or laboratory decision outside this tool.
How to interpret the result
Use when learners are choosing a simple model from a table and need visible finite-difference evidence. The diagnostic distinguishes constant first differences from constant second differences over a small bounded sample. It does not infer missing input spacing, fit coefficients, prove global behavior, compare residuals across larger datasets, model exponential change, or decide whether the context justifies extrapolation.
Outputs 2, 5, 8, 11 have constant first differences of 3 and are linear. Values 1, 4, 9, 16 have first differences 3, 5, 7 and constant second differences 2, so they are quadratic. The irregular example is neither. Outputs 0, 1, 4, 9 are quadratic, making the loaded linear claim a deliberate misconception flag.
Subtract adjacent outputs to create three first differences. If all three agree within the absolute tolerance, classify linear. Otherwise subtract adjacent first differences to create two second differences. If those agree within tolerance, classify quadratic; if neither test passes, classify neither. The linear test runs first so a constant sequence is not mislabeled quadratic.
Supported means the learner classification follows the supplied equally spaced outputs and threshold. This is pattern evidence over four points, not proof of a unique generating process. Inspect the original x-spacing, units, graph shape, measurement precision, residuals, domain, turning behavior, and alternative models. More data and contextual reasoning are needed before forecasting or making a scientific claim.
Do not use finite differences when input gaps vary, call increasing differences automatically quadratic, round until differences appear equal, classify a constant first-difference pattern from only the endpoints, assume every curved graph is quadratic, or extrapolate far beyond the evidence. Write the complete difference table and preserve the measurement resolution when choosing tolerance.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish assessment validity, or replace teacher, laboratory, curriculum, accessibility, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the approved school system.
No. It describes entered evidence under one disclosed rule. Review reasoning, uncertainty, access, and several evidence sources.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow course and academic-integrity rules.
YOUR NIRMION
