Examples of AI-Powered Visual Problem Solving

Mathematics

These examples focus on showing intermediate reasoning, not outsourcing calculation.

Solving a Linear Equation

Problem: A student needs to solve 3x + 5 = 20.
Starting on the canvas: Write each algebraic transformation on a new line and mark the operation applied to both sides.
First question: “Why do I subtract 5 from both sides before dividing by 3?”
AI guidance: Explain equality-preserving operations and connect each step to the written equation.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The student understands why the same operation is applied to both sides.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Quadratic Equations

Problem: A learner is deciding whether to factor or use the quadratic formula.
Starting on the canvas: Place the equation, possible factors, discriminant, and any graph sketch in separate labelled areas.
First question: “What does the discriminant tell me before I solve this?”
AI guidance: Explain what the discriminant indicates about real roots without assuming a chosen method.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner chooses a method with a clearer reason.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Systems of Linear Equations

Problem: Two equations describe related quantities.
Starting on the canvas: Draw each equation and a coordinate sketch showing where their lines might meet.
First question: “What does the intersection represent in this system?”
AI guidance: Connect the algebraic solution to the graph and the meaning of a shared solution.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner sees why substitution or elimination identifies the same point.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Geometry Problem

Problem: A triangle has known angles and side relationships.
Starting on the canvas: Sketch the triangle, label known values, and mark the target angle or side.
First question: “Which relationship is relevant before I calculate?”
AI guidance: Explain the applicable geometric relationship and the assumptions shown in the drawing.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can justify the next step from the diagram.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Trigonometric Identity

Problem: A student is simplifying an expression.
Starting on the canvas: Write the identity, highlight the part being transformed, and note allowed identities.
First question: “Which identity changes this expression most directly?”
AI guidance: Explain the structure of the expression rather than only supplying the final form.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The student recognises a repeatable pattern.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Function and Graph Interpretation

Problem: A graph changes direction and crosses an axis.
Starting on the canvas: Label axes, intercepts, turning points, and a small table of input-output values.
First question: “What does this turning point mean in the context of the function?”
AI guidance: Explain the graph feature and distinguish visual observation from an exact calculation.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner relates algebraic and graphical information.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Physics

Physics examples separate the physical model from the calculation that follows it.

Free-Body Diagram

Problem: A block rests on an inclined plane.
Starting on the canvas: Draw the object, choose axes, and label forces with directions.
First question: “Which forces belong on this diagram, and why?”
AI guidance: Explain the system boundary and distinguish forces from motion.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The student has a defensible model before using equations.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Projectile Motion

Problem: A ball is launched at an angle.
Starting on the canvas: Sketch the path, define axes, and separate horizontal from vertical information.
First question: “Why can horizontal and vertical motion be considered separately?”
AI guidance: Explain the modelling assumption and identify which quantities are shared in time.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can organise the calculation into components.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Simple Electric Circuit

Problem: A battery, switch, and lamp are connected.
Starting on the canvas: Draw a labelled circuit loop and mark the switch state.
First question: “What changes in the circuit when the switch is open?”
AI guidance: Explain the path required for current in a simplified circuit model.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner connects the diagram to the observed lamp behaviour.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Work, Energy and Power

Problem: An object is moved up a ramp.
Starting on the canvas: Draw the object, height change, force direction, and energy labels.
First question: “Which energy changes are relevant here?”
AI guidance: Explain the system and the difference between work, energy, and power.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner chooses quantities that match the physical situation.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Ray Diagram

Problem: A lens forms an image of an object.
Starting on the canvas: Draw the principal axis, focal points, object, and selected rays.
First question: “Which rays are construction rays, and what do they show?”
AI guidance: Explain how the ray intersections locate an image in the model.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner understands the purpose of the diagram.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Newton’s Laws

Problem: A cart accelerates when a force is applied.
Starting on the canvas: Draw the cart, forces, chosen direction, and acceleration arrow.
First question: “How do net force and acceleration relate in this situation?”
AI guidance: Explain that the net force, not an individual force, links to acceleration.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can distinguish balanced and unbalanced cases.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Engineering

These examples use diagrams to clarify systems; they do not treat Enideon as a simulator or design verifier.

Understanding a Block Diagram

Problem: A sensor feeds a controller which drives an actuator.
Starting on the canvas: Draw blocks, inputs, outputs, and arrows with signal labels.
First question: “What information passes through each block?”
AI guidance: Explain the role of each interface and identify assumptions that need specification.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can describe the system flow.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Breaking Down a Mechanical System

Problem: A mechanism transfers force between parts.
Starting on the canvas: Sketch components, joints, directions of motion, and constraints.
First question: “Which component should I analyse first?”
AI guidance: Suggest beginning with a component whose inputs and outputs are clearly defined.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner has a sensible decomposition order.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Analysing a Simple Electrical System

Problem: A source supplies a load through a control element.
Starting on the canvas: Draw source, load, control, and return path with labels.
First question: “What should I check before estimating behaviour?”
AI guidance: Explain the need to identify ratings, topology, and operating conditions before calculation.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner knows which missing information matters.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Understanding Inputs and Outputs

Problem: A process receives material and energy and produces an output.
Starting on the canvas: Draw a boundary, incoming arrows, outgoing arrows, and state variables.
First question: “Which quantities cross the system boundary?”
AI guidance: Explain why boundaries make conservation and interface questions clearer.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can define the scope of analysis.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Breaking a Technical Problem Into Components

Problem: A fault appears somewhere in a multi-stage workflow.
Starting on the canvas: Draw stages, dependencies, and observations at each interface.
First question: “What is the smallest part I can test first?”
AI guidance: Explain how isolating a subsystem narrows uncertainty.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner has a visual troubleshooting plan.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Comparing Two Design Approaches

Problem: Two architectures meet the same objective with different trade-offs.
Starting on the canvas: Place alternatives side by side with constraints, dependencies, and unknowns.
First question: “Which trade-off should drive the comparison?”
AI guidance: Explain how to compare against stated criteria rather than preference alone.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can make a more traceable comparison.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Studying

Study examples use the canvas to reconstruct and test understanding rather than simply collect notes.

Turning a Chapter Into a Concept Map

Problem: A chapter introduces several connected ideas.
Starting on the canvas: Place the central concept in the middle and connect definitions, causes, and examples.
First question: “Which connection is still unclear?”
AI guidance: Help identify a relationship that deserves a focused explanation.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner turns a chapter into an inspectable map.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Preparing for an Exam

Problem: A learner needs to review several topics.
Starting on the canvas: Create a board area per topic with known formulas, diagrams, and weak points.
First question: “Which topic should I review first?”
AI guidance: Use visible gaps and dependencies to make a review order.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner has an evidence-based revision plan.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Understanding a Difficult Concept

Problem: A definition feels abstract.
Starting on the canvas: Draw a concrete example, a non-example, and the relationship between terms.
First question: “Can you explain why this example fits the definition?”
AI guidance: Explain using the drawn case and identify the defining property.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner links terminology to an example.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Learning From a Mistake

Problem: A solution has an unexpected result.
Starting on the canvas: Write the original steps and mark the first uncertain transformation.
First question: “Where might my reasoning first have diverged?”
AI guidance: Help inspect the earliest questionable assumption or calculation.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner identifies a reusable check.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Active Recall With a Whiteboard

Problem: A learner wants to test memory.
Starting on the canvas: Rebuild a concept map from memory, leaving unknown areas blank.
First question: “What important relationship did I leave out?”
AI guidance: Use the visible gaps to guide targeted review.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner turns recall into a diagnosis of understanding.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Explaining a Topic Back to the AI

Problem: A learner thinks they understand a process.
Starting on the canvas: Draw the process and add a short explanation beside each stage.
First question: “Does this explanation skip a necessary step?”
AI guidance: Ask for a check of clarity and missing relationships, not a replacement explanation.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner strengthens their own explanation.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Brainstorming

These examples use diagrams to structure a rough idea before selecting a direction.

Breaking Down a Project Idea

Problem: A broad project idea has unclear parts.
Starting on the canvas: Map goal, users, assumptions, risks, and next questions.
First question: “Which assumption should I validate first?”
AI guidance: Help separate high-impact assumptions from background detail.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The idea becomes a testable set of questions.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Planning a Technical Project

Problem: A project has several components and milestones.
Starting on the canvas: Draw components, interfaces, dependencies, and decision points.
First question: “Which dependency could block the project earliest?”
AI guidance: Explain how to look for upstream dependencies and uncertain interfaces.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The plan identifies an early risk.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Mapping Dependencies

Problem: Tasks cannot all begin at once.
Starting on the canvas: Use nodes for tasks and arrows for prerequisites.
First question: “Which task is on the critical path?”
AI guidance: Explain how to trace the chain that constrains later work.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can prioritise a dependency.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Comparing Possible Solutions

Problem: Several approaches solve part of the same problem.
Starting on the canvas: Create columns for criteria, benefits, risks, and unanswered questions.
First question: “What evidence would distinguish these options?”
AI guidance: Suggest a question or test tied to a stated criterion.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The comparison moves beyond vague preference.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Structuring an Unclear Idea

Problem: Notes are scattered and repetitive.
Starting on the canvas: Group notes into themes, then draw relationships between themes.
First question: “What should be the central question of this map?”
AI guidance: Help identify a single organising question from the visible notes.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The board becomes a coherent starting model.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Voice Workflows

Voice examples focus on short, contextual exchanges while visual work remains on the canvas.

Talking Through a Difficult Problem

Problem: A learner is unsure where a derivation changes direction.
Starting on the canvas: Show the derivation and mark the first confusing line.
First question: “Why does this term appear at this point?”
AI guidance: Provide a spoken explanation tied to the named step.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner can continue the derivation with a clearer model.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Asking Follow-Ups While Drawing

Problem: A system sketch evolves during a conversation.
Starting on the canvas: Keep adding labels as each component is discussed.
First question: “What should this arrow represent?”
AI guidance: Clarify the relationship and prompt a label or assumption.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The board improves as the conversation progresses.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Correcting the AI Mid-Conversation

Problem: The assistant interprets a component incorrectly.
Starting on the canvas: Point to the component and add a concise correction label.
First question: “I mean this block is a sensor, not an output—how does that change the flow?”
AI guidance: Reframe the explanation using the corrected context.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner practises correcting an imperfect interpretation.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Exploring Multiple Approaches

Problem: There are several ways to begin a problem.
Starting on the canvas: Draw a branch for each approach with its first assumption.
First question: “What is the advantage of starting with this approach?”
AI guidance: Compare methods by the information they require and the checks they enable.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner selects a method intentionally.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

Explaining Your Own Reasoning

Problem: A learner wants feedback on a method.
Starting on the canvas: Write the reasoning as numbered steps and mark uncertain assumptions.
First question: “Can you check whether step four follows from the earlier steps?”
AI guidance: Inspect the stated relationship and request clarification where needed.
Follow-up and revision: Ask what assumption, relationship, or intermediate step should be checked next. Add labels, arrows, or the next calculation step so the revised reasoning is visible.
Result: The learner receives feedback on reasoning, not just the answer.
What this demonstrates: Use the canvas to make the relevant information visible, then use a focused question to guide the next revision.

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