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AI Technical AptitudeAI Methods9-12.AITA.AIM.6

What This Model Cannot Do

9–12 CS / engineering50 minutes90 minutes (lab extension)

Standard quoted exactly

Evaluate the features and limitations of a machine learning model.

Example from the standards. A decision tree can show feature importance, but it is limited in how it works. Logistic regression, likewise, is a linear classifier that cannot solve the XOR problem.

Student-friendly learning targets

  • I can name a real strength and a real limit for trees, logistic regression, and neural nets.
  • I can show, again in plain language, why a linear classifier cannot solve XOR.
  • I can use feature importance as a tree feature without pretending the tree is unlimited.

Essential questions

  1. If a tree can show which features matter, why not always use a tree?
  2. What exactly can a linear classifier not do?
  3. What can a neural net do that still might be the wrong tool?

Objectives

  1. Evaluate each family with a two-column card: feature (strength) | limitation.
  2. Replot XOR and connect it to logistic regression's linear boundary (tie to DA.6, do not repeat the whole pick-a-model lab).
  3. Read a tiny tree's feature-use counts as 'importance' and then break the tree with a diagonal pattern.
  4. Write an evaluation paragraph that a vendor slide would not write.

Key vocabulary

Feature importance
A report of which inputs a model relied on. Trees can show this from how often/early a feature is used. It is a clue, not a proof of cause.
Linear classifier
Separates classes with one line/plane. Logistic regression is one. XOR's diagonal yes-points cannot be split by that one line.
Axis-aligned split
A typical tree question uses one feature at a time (temp < 32), which draws splits parallel to the axes — awkward on diagonal patterns.
Limitation
Something the model family structurally cannot do well, not just 'needs more data.'
Opaque
Hard to see why an answer happened. A deep net's limitation even when accuracy is high.

Teacher background

The standards example is the lesson spine: trees show feature importance but are limited; logistic cannot XOR. Teach both halves. Strengths: tree — readable, importance; logistic — cheap, probability, few data; net — flexible surfaces, images. Limits: tree — greedy axis-aligned splits, unstable to small data changes, can overfit; logistic — linear, no XOR, weak on raw pixels; net — data/compute, opaque, can be overkill. XOR recap in 4 minutes with the ruler, then move. A 6-node paper tree on wildfire weather can show 'wind and RH used first' as importance. Spreadsheet not required. This is evaluation, not implementation.

Materials and prep

Materials

  • XOR four-point graph and a ruler (from DA.6 kit if you still have it).
  • Paper tree on RH, wind, temp with a tally of which feature appears; a 'importance' bar sketch.
  • Diagonal-pattern overlay that the axis-aligned tree hacks into a staircase.
  • Feature | limitation cards, three families.
  • A fake vendor slide: 'Our logistic model does everything.' for critique.

Before class

  • If DA.6 was weeks ago, refresh XOR in prep so the recap is crisp.
  • Print a tree that overuses one noisy feature so 'importance' can be misleading — a key limitation of the strength.

Instructional sequence

Vendor claim

5 min
  1. Read: 'Our linear model solves every logic problem, including XOR, with enough data.' Students write agree/disagree in one line.
  2. Hold the ruler. We will evaluate, not cheer.

Strengths that come with joints that don't bend

10 min
  1. Logistic: strength = probability + inspectable weights; limitation = one line, therefore XOR is impossible no matter the sample size of those four points.
  2. Tree: strength = questions people can audit + feature importance; limitation = one-feature splits, greedy, jumpy, memorizes.
  3. Net: strength = bent boundaries and pixels; limitation = hunger, opacity, cost. Also not automatic ethics.
  4. Replot XOR. Let a student fail the ruler. Say the sentence from the standard in plain words.

Importance, then a break

12 min
  1. Walk the paper tree. Tally feature uses. Sketch importance bars (wind high, month low).
  2. Show a diagonal cloud. Try to cut it with axis-aligned questions; count how many ugly splits you need.
  3. Ask: is importance a feature or a trap if the feature is a leak (DA.3)? Both — evaluation includes misuse of the strength.

Evaluate all three

10 min
  1. Pairs complete feature|limitation cards for all three families with an Idaho sentence each.
  2. They rewrite the vendor claim so it is true: 'Logistic is strong on small binary problems with linear-ish structure; it cannot solve XOR.'
  3. Offline: cards and XOR plot only.

Real-world examples

  • Logistic frost alarms fail if the true pattern is an interaction (warm but radiative cooling on still nights) — XOR-like interactions.
  • A 20-questions nutrient tree looks important on 'leaf color' because that question is first, not because color caused the yield.
  • A neural net smoke detector cannot explain itself to a incident commander at 2 a.m. — opacity as a limitation even if recall is high.
  • Energy load: a linear model cannot capture a holiday × temperature bend without extra features; a tree might split 'is_holiday' but will miss smooth curves.

Hands-on activity

Limitation museum

8 min
  1. Each pair posts one limitation with a tiny sketch (failed line, staircase tree, black-box net).
  2. Gallery: steal a better XOR sentence from a neighbor if yours used jargon only.
  3. Vote: which limitation would matter most to a fire dispatcher vs. a researcher.

Discussion questions

  1. Can more data ever make logistic solve the four XOR points? (No. The family cannot draw the shape.)
  2. If a tree's top important feature is an ID number, what limitation just showed up?
  3. Is opacity a feature (harder to game) or a limitation (harder to trust)? For whom?
  4. How is this evaluation different from AIM.5's comparison table? (We stress failure modes.)

Differentiation

Support

  • XOR plot pre-labeled; student only writes 'one line cannot split the diagonal.'
  • Two families only (logistic + tree) if needed.

Challenge

  • Explain that a small net or a tree ensemble can solve XOR, and still justify shipping the IF rule on a pump (DA.6 + AIM.4).
  • Critique feature importance vs. causation using the leaky column from DA.3.

Multilingual learners

  • limitation / strength / linear / importance glossary.
  • Sketch-first, then a sentence stem.

IEP / 504

  • Physical ruler XOR is the assessment; cards can be dictated.
  • Avoid extra algebra on logistic scores.

Assessment

Formative

  • Vendor-claim disagree line.
  • Feature-use tally on the paper tree.

Summative

  • Three feature|limitation cards plus a true rewrite of the vendor sentence including XOR.
  • Tree card must mention both importance (feature) and a limit (axis-aligned / overfit / instability).

Success criteria

  • Student explains XOR vs. linear classifiers in ordinary language.
  • Student treats feature importance as a tree strength with a caveat.
  • Student names a neural-net limitation other than 'it's hard.'

Responsible use, ethics, and privacy

Responsible use

Evaluating limits is how you refuse a vendor model that cannot do the job even with 'more data.'

Ethics

A limitation that falls on one group (a linear screen that cannot capture a legitimate interaction) is a fairness issue, not only a math one.

Privacy

No student-performance data to 'show feature importance of attendance.' Use weather and crop toys.

Reflection

  1. Which limitation will you actually use in a design review?
  2. How would you explain XOR to a parent in 20 seconds?
  3. When is a model's strength the thing that will trick you?

Homework

One page: evaluate logistic, tree, and net. For each, one feature, one limitation, one Idaho job to avoid. XOR paragraph required in ordinary language. Graph may be copied from class.

Closing

Trees can show importance and still cut the world into rectangles. Logistic is honest, cheap, and cannot XOR. Nets bend and hide. Evaluation means saying the second sentence, not only the first. Next we plan the human gates so those limits do not run unsupervised.

Extensions and cross-curricular links

Go further

  • 90-minute block: try to hand-build a staircase tree for XOR (it can, awkwardly) vs. the one-line rule; write which limitation you still care about.
  • Python extension: logistic on XOR (fails); decision tree on XOR (can pass); print importances — notebook extra.
  • Card-sort 'feature' vs. 'limitation' claims, including traps ('more layers always help').
  • Printed XOR tracing for subs.
Geometry
Linear separability and axis-aligned rectangles are visual, not mystical.
Statistics
Variable importance is not causation; same lecture as confounding.
Engineering
Choosing a family is choosing which failures you can live with.