Embodiments of the invention comprise approaches for streamlining and accelerating the communication of applied knowledge to end-users, particularly in science, technology, engineering, and mathematic (STEM) disciplines. Through a framework that leverages consistency and immersive teaching tools, complexity is substantially removed from the knowledge transfer process.

A CPR training device is disclosed comprising a first member including a mouthpiece portion and a first engaging portion, a second member including an output portion and a second engaging portion, and an air passageway. The first engaging portion and the second engaging portion cooperates to form a filter seating arrangement at a filter seat position when assembled together to secure a filter within the CPR training device. The air passageway is open to air outside of the CPR training device only through the mouthpiece portion and the output portion. The filter is disposed in the air passageway at the filter seat position.

A system and method are provided comprising: a) for a specified underlying and tenor, generating a two-dimensional surface showing prices for different strikes at a specific point in time; b) repeating a) for a plurality of points in time; c) connecting the two-dimensional surfaces to generate a three-dimensional block; d) cutting a surface of the three-dimensional block along a spot for each point in time to identifying how pricing has deviated from a Q measure across time; and e) generating a three-dimensional visualization in one or more formats.

A system and method are provided comprising: a) for a specified underlying and tenor, generating a two-dimensional surface showing prices for different strikes at a specific point in time; b) repeating a) for a plurality of points in time; c) connecting the two-dimensional surfaces to generate a three-dimensional block; d) cutting a surface of the three-dimensional block along a spot for each point in time to identifying how pricing has deviated from a Q measure across time; and e) generating a three-dimensional visualization in one or more formats.

Disclosed in this application is a three-dimensional dynamic apparatus that can be configured for illustrating mathematical correlation as in the field of Economics. The three-dimensional dynamic apparatus is comprised of a grid panel with side panels defining one or more three-dimensional spaces for lines to be placed as a three-dimensional dynamic representation of the desired subject matter.

Disclosed in this application is a three-dimensional dynamic apparatus that can be configured for illustrating mathematical correlation as in the field of Economics. The three-dimensional dynamic apparatus is comprised of a grid panel with side panels defining one or more three-dimensional spaces for lines to be placed as a three-dimensional dynamic representation of the desired subject matter.

A system and method for assisted-learning with a portable computing device that includes requesting that a user complete a mathematical challenge by arranging real-world objects in an environment to form an arrangement according to the mathematical challenge, optionally receiving an input from the user that the arrangement is complete, activating a camera of a portable computing device located in the environment with the user to capture an image of the arrangement, wherein the image is received from the portable computing device over a network, evaluating the arrangement using a visual recognition engine to determine whether the arrangement successfully completes the mathematical challenge, and providing at least one of a visual feedback and an audible feedback to the user.

A system and method for assisted-learning with a portable computing device that includes requesting that a user complete a mathematical challenge by arranging real-world objects in an environment to form an arrangement according to the mathematical challenge, optionally receiving an input from the user that the arrangement is complete, activating a camera of a portable computing device located in the environment with the user to capture an image of the arrangement, wherein the image is received from the portable computing device over a network, evaluating the arrangement using a visual recognition engine to determine whether the arrangement successfully completes the mathematical challenge, and providing at least one of a visual feedback and an audible feedback to the user.

Various techniques are disclosed for facilitating distribution of content between a plurality of nodes of a computer network. More particularly, the present disclosure relates to techniques for facilitating distribution of content to a plurality of users having access to an electronic collaborative canvas whiteboard via a computer network.

Templates for identifying equivalent fractions in one example comprise a plate defining a plurality of aligned rows, each row having an equal length and representing a respective fraction. Each row defines a number of slots through the plate, positioned to divide a row into equal parts corresponding to the respective fraction. Slots or markers in respective rows corresponding to equivalent fractions are vertically aligned. An elongated slot may be provided on the template or on a separate template to draw a boundary to mark a fraction, identify equivalent fractions and perform mathematical operations. In another example, a first template includes a plurality of aligned rows with marks to indicate fractions and a second, transparent template for placement over the first template. Fractions may be drawn in a Unit box defined on the second template. Methods of using a template, and virtual templates, are also disclosed.