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MATHEMATICO PWA

Universal Multimodal Mathematics Diagnostic Engine

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Hybrid Knowledge Space Theory (DAG) + 3PL Multidimensional IRT + Digital Ink, Voice & Manipulative Fusion

0 / ≤25 adaptive items
Tier 3 · Secondary Math · UI Mode: STEM_STANDARD
IRT (a=2.2, b=0.3)
Target Concept Node: Quadratic Transformations, Binomial Expansion & Roots
Expand and simplify f(x) = (x + 3)^2 - 4 into standard polynomial form.
Expand and simplify f(x)=(x+3)2−4 into standard polynomial form ax2+bx+c.\text{Expand and simplify } f(x) = (x + 3)^2 - 4 \text{ into standard polynomial form } ax^2 + bx + c.
Psychometric Router: Macro-tier funnel: anchor for Tier 3 (Quadratic Transformations, Binomial Expansion & Roots) maximising expected tier-posterior entropy reduction · Fisher Info I(θ)=0.98275 · ΔH=0.59737b
Interactive Mathematical Sandbox · COORDINATE PLANE FUNCTIONVerify vertex at (-3, -4) and roots at x = -5 and x = -1 on the coordinate plane.
−8−8−6−6−4−4−2−222446688xy−5−15
Vertex h−3
Vertex k−4
Vertex: (−3, −4) · axis x = −3
Vertex form: y = (x + 3)² − 4
Standard form: y = x² + 6x + 5
x-intercepts: −5, −1 · y-intercept: 5

Drag the vertex dot (snaps to whole units) or focus it and use the arrow keys; Shift moves ×5. Use the slider for a.

Or select a structured response (mapped to Misconception Taxonomy):
Digital Ink Scratchpad (60Hz Stylus/Touch)· 0 strokes · 0 hesitation pauses
Freehand scratchpad canvas. Your browser does not support canvas; type your reasoning in the think-aloud box instead.

This freehand scratchpad is optional visual working space for stylus, touch or mouse. It is not required to answer: use the typed answer field and the think-aloud text box to describe your reasoning instead. Press Control or Command plus Z to undo and Shift plus Z to redo.

Voice Think-Aloud & Metacognitive Probe
0 time-synced reasoning notes

Live Knowledge Space DAG & Psychometric Belief State (Tiers 0–7)

Phase: MACRO_TIER_FUNNEL · Estimated Tier: Tier 3 · Mean Graph Entropy: 0.90 bits

Mastered / Inner FringeOuter Fringe (Ready to Learn)Uncertain FrontierPrerequisite BlockedSolid edge = Hard prereq · Dashed = Soft transfer
Number Sense & Arithm…Ratios & ProportionsAlgebra & EquationsFunctions & ModelingGeometry & TopologyMeasurement & DataProbability & Inferen…Discrete Logic & Proo…Calculus & AnalysisLinear AlgebraAbstract Algebra & Nu…Differential Equation…Tier 0Tier 1Tier 2Tier 3 ★Tier 4Tier 5Tier 6Tier 7T0 · P(M)=94%H=0.31bCounting Sequence, Cou…T0 · P(M)=91%H=0.45bNumber Composition, De…T0 · P(M)=92%H=0.39bSubitizing, Counting &…T1 · P(M)=80%H=0.73bFraction Magnitude & U…T1 · P(M)=81%H=0.70bMultiplicative Arrays,…T1 · P(M)=83%H=0.66bBase-Ten Place Value B…T2 · P(M)=71%H=0.87bSigned Integer & Ratio…T1 · P(M)=78%H=0.76bMultiplicative Compari…T2 · P(M)=69%H=0.89bProportional Relations…T2 · P(M)=67%H=0.91bLinear Equations with …T3 · P(M)=56%H=0.99bLaws of Exponents, Rad…T3 · P(M)=58%H=0.98bSystems of Linear Equa…T3 · P(M)=54%H=0.99bFunction Composition, …T3 · P(M)=55%H=0.99bQuadratic Transformati…T4 · P(M)=44%H=0.99bLogarithmic Laws, Chan…T4 · P(M)=45%H=0.99bUnit Circle Radian Mea…T0 · P(M)=91%H=0.42bShape Recognition & At…T2 · P(M)=66%H=0.92bPythagorean Theorem & …T3 · P(M)=55%H=0.99bGeometric Similarity, …T7 · P(M)=11%H=0.51bGeneral Topology: Comp…T0 · P(M)=93%H=0.37bComparing Quantities &…T1 · P(M)=79%H=0.75bLinear Measurement, Ar…T2 · P(M)=68%H=0.90bMeasures of Center, Sp…T4 · P(M)=42%H=0.98bConditional Probabilit…T7 · P(M)=10%H=0.46bMeasure-Theoretic Mart…T0 · P(M)=89%H=0.49bRepeating Patterns & S…T4 · P(M)=46%H=0.99bCombinatorial Counting…T5 · P(M)=31%H=0.89bChain Rule Composition…T5 · P(M)=33%H=0.91bInfinite Series Conver…T5 · P(M)=35%H=0.93bLimits, Continuity & L…T6 · P(M)=22%H=0.75bSup-Norm Uniform Conve…T6 · P(M)=20%H=0.71bEpsilon-Delta Quantifi…T7 · P(M)=12%H=0.52bComplex Analysis: Cauc…T7 · P(M)=11%H=0.49bLebesgue Integration: …T4 · P(M)=44%H=0.99bComplex Arithmetic, 2D…T5 · P(M)=33%H=0.91bEigenvalues, Character…T6 · P(M)=21%H=0.75bInner Product Spaces, …T7 · P(M)=10%H=0.48bFunctional Analysis: R…T6 · P(M)=22%H=0.77bGroup Theory: Lagrange…T6 · P(M)=21%H=0.74bRings, Maximal & Prime…T5 · P(M)=32%H=0.90bSeparable First-Order …
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