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Mathematical Depth in Grasple

From first-year calculus to advanced engineering mathematics

Grasple - diagonalize - diagonalizable 3x3 matrix - 3 differenet eigenvalues (2)

Grasple is best known for supporting university mathematics and statistics courses, but its mathematical engine is not limited to any particular level.

Grasple’s mathematical capabilities support a wide range of university programmes, from research methods to quantum mechanics.

Our platform offers dedicated Mathematical and Physics answer check methods to support learning at all levels. Grasple's interpreter operates on mathematics, symbolic expressions, vectors, matrices, and solution spaces. It supports this breadth by design. 

Beyond simply validating a student's final answer, these mathematical check methods also make it possible to recognise common mistakes, enabling targeted, mathematically-grounded feedback that is tailored to each student's approach.

Teachers stay in control

We know that, even though an answer is algebraically equivalent, that doesn't mean it achieves the learning goal. That's why we give you a wide variety of check types and conditions, so you can configure your exercises to match the level of precision required in your subject and at your students' level. 

 

 

Grasple reads math as math, not text

Grasple recognises algebraically equivalent expressions and considers them equal by default.

 

Grasple Levels - Advanced math + Answer rules (3)

 

 

Advanced STEM questions

Unit type questions are perfect for advanced physics, engineering, and more. Decide whether equivalent units are accepted or demand precision in the question's notation.

 

Math levels - Algebraically Equivalent

 

 

Create unique answer rules 

Tell Grasple's CAS what to do with specific student answers, giving you control over which answers and which forms are accepted. Plus, you can give specific feedback to your students to correct common errors. 

 

Units + Equivalencies (1)

Mathematical capabilities

At the core of Grasple is a mathematical interpreter that evaluates student input as mathematics, not as text. Answers are checked for mathematical meaning, so students can enter any correct form of an answer, and instructors can decide exactly how strict the comparison should be.

Grasple currently supports the following answer-check methods:

Comparison and numerical checks

Defined, greater/less than (or equal to), and numerical evaluation to a (complex) number.

Comparison and numerical checks Defined, greater/less than (or equal to), and numerical evaluation to a (complex) number.

Same ordered collection

Compares ordered lists of numbers, formulas, vectors, or matrices element by element.

Same ordered collection Compares ordered lists of numbers, formulas, vectors, or matrices element by element.

Same exact form

Requires mathematical equality and the same written form, useful when the notation itself is the learning goal (e.g. a fully simplified expression).

Same exact form Requires mathematical equality and the same written form, useful when the notation itself is the learning goal (e.g. a fully simplified expression).

Algebraic equivalence

Default checks whether two expressions are indeed mathematically equal (e.g. x + x ≡ 2x). Works for exact numbers (including constants such as π), formulas, vectors, matrices, and unordered collections.

Algebraic equivalence Default checks whether two expressions are indeed mathematically equal (e.g. x + x ≡ 2x). Works for exact numbers (including constants such as π), formulas, vectors, matrices, and unordered collections.

Specialised linear algebra checks

Parallel vector, same basis, same orthogonal basis, same orthonormal basis, same solution to a system of equations (including solutions with free variables), and is-diagonal-matrix. These allow grading of answers that are correct but not unique, a basis, for instance, can be written in infinitely many valid ways.

Specialised linear algebra checks Parallel vector, same basis, same orthogonal basis, same orthonormal basis, same solution to a system of equations (including solutions with free variables), and is-diagonal-matrix. These allow grading of answers that are correct but not unique, a basis, for instance, can be written in infinitely many valid ways.

New checks

Because checks operate on genuine mathematical objects, symbolic expressions, complex numbers, vectors, matrices, sets and solution spaces, instructors can build exercises with targeted, answer-specific feedback at any level of mathematics. The set of check methods is actively being expanded, and new methods can be added based on partner and customer needs.

New checks Because checks operate on genuine mathematical objects, symbolic expressions, complex numbers, vectors, matrices, sets and solution spaces, instructors can build exercises with targeted, answer-specific feedback at any level of mathematics. The set of check methods is actively being expanded, and new methods can be added based on partner and customer needs.
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