Structured Derivations

Structured derivation

Structured derivations is a simple language for writing the solution to a math problem, in a way that is easy to understand both by a student and by a computer. The language shows the logical structure of the solution, and requires that each step in the solution is explicitly justified. Structured derivations give a deeper understanding of how mathematics works, of the logic behind a mathematical solution. It guides the student in how to construct a valid mathematical argument that starts from initial assumptions allowed by the problem statement to a final answer for the problem.

Derivation editor

eMathStudio has a special digital derivation editor for constructing and editing structured derivations. The editor uses standard mathematical notation. It guides the student into constructing a syntactically correct derivation, and preserves the correct syntax during editing. The editor allows the student to write down an initial solution to a problem and then improve the solution incrementally, to find a correct answer to the given problem. The solution is automatically saved so the student can return to it later. A solution can also be shared with others for discussion and help.

Automatic checking

The automatic checker reads a structured derivation step by step and checks the correctness of each step. Steps that are proved correct are marked as such with a check mark, while steps that cannot be proved correct are marked with a question mark. The checker gives the student immediate feedback on his/her own solution when it is most needed, when the student is working on the problem. The solution is correct if the checker has proved each step correct. Otherwise, the student needs to go back to the solution and fix the unproved steps. And then check and fix anew, until the checker says that the solution is correct.

How to solve math problems with structured derivations

This video below shows how these three main features, the structured derivation language, the editor, and the checker, work together when we solve a simple calculation problem.

Check out the tutorial for more information.

How to write math in eMathStudio

This video shows how to write mathematical formulas in eMathStudio. You have the option of inputting math symbols from a math panel (slower), or then just text shortcuts to input math symbols (faster).

Check out the tutorial for more information.

Calculating with fractions

Algebraic calculations

We show how to carry out an algebraic calculation

Solving a first order equation

Solving a second order equation

We show how to solve a first order equation

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Solve an equation system

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Solve a word problem

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Another word problem

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Solve a geometry problem

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Logical expressions

Logical connectives

Calculate the solutions to a first degree equation

Calculate solution to a second degree equation

Example derivation

Follow derivation step by step, with explanations