An apparatus for teaching statistics concepts includes a simulation module that generates a simulation of subject elements moving from a first portion of a simulated space to a second portion of the simulated space, where the simulated space has a treatment path and a non-treatment path. A propensity module utilizes one or more propensity inputs to the simulation module to affect a propensity of the subject elements to move on the treatment path to have treatment functions applied. A treatment module applies the treatment functions to the subject elements moving on the treatment path, where the treatment functions are configured to affect at least one output measure of the subject elements. A display module displays the simulation of the subject elements having the propensity inputs applied, application of the treatment functions, and the at least one output measure.

A tile instructional system for presenting a linear growth problem and for allowing the linear growth problem to be solved comprises an input tray having at least a first tile and a second tile. The first tile has a first marking and the second tile has a second marking. Each of the first tile and the second tile is configured to selectively expand in accordance with its respective marking. The system includes a tile bed comprising a plurality of tile slots. Each of the plurality of tile slots is configured to receive a tile. The linear growth problem is solvable by situating in the tile bed at least one of the first tile and the second tile and by causing each tile situated in the tile bed to expand in accordance with its respective marking to fill the tile bed.

A tile instructional system for presenting a linear growth problem and for allowing the linear growth problem to be solved comprises an input tray having at least a first tile and a second tile. The first tile has a first marking and the second tile has a second marking. Each of the first tile and the second tile is configured to selectively expand in accordance with its respective marking. The system includes a tile bed comprising a plurality of tile slots. Each of the plurality of tile slots is configured to receive a tile. The linear growth problem is solvable by situating in the tile bed at least one of the first tile and the second tile and by causing each tile situated in the tile bed to expand in accordance with its respective marking to fill the tile bed.

A system and method for the automatic grading of mathematical expressions includes importing a hand-written answer, converting the hand-written answer to a LaTeX formula, creating a model with noise to compare one or more mathematical expressions, checking the correctness of derivations between the mathematical expressions, applying machine learning and/or state estimation theory to determine the mistakes, and suggesting correct coefficients for the derivation. The system and method may further include identifying the handwriting of students using machine learning to determine whether cheating or copying has occurred.

A system and method for the automatic grading of mathematical expressions includes importing a hand-written answer, converting the hand-written answer to a LaTeX formula, creating a model with noise to compare one or more mathematical expressions, checking the correctness of derivations between the mathematical expressions, applying machine learning and/or state estimation theory to determine the mistakes, and suggesting correct coefficients for the derivation. The system and method may further include identifying the handwriting of students using machine learning to determine whether cheating or copying has occurred.

A system and method for teaching and learning mathematics. The system includes a plurality of modules including a first module having blocks for assembling into different configurations, a second module having a plurality of sheets of predetermined mathematical equations, a third module having a plurality of dice having numbers and mathematical operation symbols, and a fourth module having a deck of playing cards. At least one of the modules is implemented with augmented or virtual reality. The blocks of the first module comprise blocks of differing geometric shapes. The sheets of the second module comprise at least addition, subtraction, multiplication, and division operations. The third module includes dice having a plurality of sides, with two dice having a number on each side and one dice having a different mathematical operation symbol on each side. The deck of the fourth module contains playing cards with numbers on both sides.

A system for rendering interactive simulations is provided. The system includes an interactive display screen and one or more physical nodes to which users can selectively assign values. The interactive display screen is enabled to provide a visual representation of a simulation for a systemic model which may be driven by one or more mathematical equations. Each model, by way of one or more mathematical equations, has one or more parameters. The interactive display screen is enabled to define one or more node location for each parameter. The interactive display screen provides one-way communication via each node location. As a result, when a node is physically placed on a node location, the one-way communication assigns or configures that node to a simulation parameter. The user may then select a value for that simulation parameter, which in turn influences the simulation being represented on the interactive display screen.

A system for rendering interactive simulations is provided. The system includes an interactive display screen and one or more physical nodes to which users can selectively assign values. The interactive display screen is enabled to provide a visual representation of a simulation for a systemic model which may be driven by one or more mathematical equations. Each model, by way of one or more mathematical equations, has one or more parameters. The interactive display screen is enabled to define one or more node location for each parameter. The interactive display screen provides one-way communication via each node location. As a result, when a node is physically placed on a node location, the one-way communication assigns or configures that node to a simulation parameter. The user may then select a value for that simulation parameter, which in turn influences the simulation being represented on the interactive display screen.

The present invention relates to a mathematics and geometry device for visually impaired (1) comprising retractable push-buttons (2) at least one button body (4) which enable the push-button to be placed on the socket (3) and making a linear movement towards the inside-outside of the device when the push-buttons are pressed; and at least one lock system which is located on the button body and which enables the button body to be locked in upper and lower positions; when the button body is locked in the upper position, the push-button becomes an open button; when the button body is locked in the lower position, the push-button becomes a closed button.

Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface finishes, such as color, shading, cross-hatching or real or apparent texture.