Systems and methods using mathematical reasoning blocks

Abstract

This invention supplies a method to make the abstract, step-by-step logic of math problems visible via the use of digitized mathematical reasoning blocks, which can be used to construct an interactive teaching program that allows a student to select problem sets from an index of problems, allows the student to view a brief instructional video pertaining to that skill if desired, allows the student to chose the mode of problem presentation (i.e., various learning or test modes), allows the student to work randomly generated problems from within the chosen mode and set by picking mathematical reasoning blocks that represent the various necessary / possible sub-steps in route to the solution of that problem.

Description

STATEMENT OF RELATED CASES[0001]This is a continuation of co-pending application Ser. No. 13 / 683,408, filed on Nov. 21, 12, which claims the benefit of U.S. Provisional Patent Application No. 61 / 563,272, filed on Nov. 23, 2011, the teachings of both of which are incorporated herein by reference in their entirety.BACKGROUNDField[0002]The present disclosure relates generally to automated systems and methods for student instruction and teacher training and, more specifically but not exclusively, to systems and methods using mathematical reasoning blocks.Description of the Related Art[0003]This section introduces aspects that may help facilitate a better understanding of the embodiments disclosed herein. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art.[0004]American elementary school math students score among the top children from industrialized countries on...

AI Technical Summary

Benefits of technology

[0023]In yet another embodiment, mathematical reasoning blocks do not exist in a set template. Thus, a user has the freedom to attempt dragging and dropping them in any sequence desired to solve a problem. In contrast, because of the way the axioms, theorems, and procedural functions, which underlie them logically interlock, the ways in which the blocks can be arranged in route to a problem solution are constrained. Thus, one result of certain embodiments is freedom bounded by constraint, allowing the blocks to supply a strong alternative to the imbalances prevalent in current multi-choice and template-driven, algebraic teaching systems.

[0033]Although the mathematical reasoning block interface is designed to be highly intuitive, the knowledge for teaching math embedded in that system is not. As the program mediates the interaction between students and their teachers, it continuously exposes these users to an automated, expert system that is designed to (i) help users break the problems down into appropriate “knowledge-size” pieces, (ii) tutor users to spot the typical errors made by students, and (iii) aid some users, e.g., teachers, to give differentiated instruction that appropriately connects students' interests and cognitive levels to the problem-solving tasks at hand.

Problems solved by technology

Yet, by the end of high school, they find themselves among the lowest performers on such standardized tests.

An inability to balance intuitive, whole-language approaches to teaching mathematics with more-traditional, analytic approaches is, in many ways, at the root of the entire problem.

Whether because of student laziness, poor teacher pedagogy, technological limitations or the failure of imagination, mathematics often ends up being taught and grasped in large, memorized chunks.

The problem becomes that students who memorize math problem solutions like phrases in a phrase book often find themselves lacking a sense of the individual parts making up the solutions as wholes.

They fail to acquire knowledge of how to rearrange these smaller constituent parts to express new ideas or solve new problems.

It occurs at the surface of the subject, resulting in multiple-choice environments that are overly mechanical and prone to intuitive guess-work on the part of students—a complete overemphasis on intuitive wholes.

But current attempts at success with this mode have resulted in rigid, unalterable templates that eliminate flexibility in the solution of problems.

For despite the widespread acceptance of reform-math approaches, no one has been able to scale theory up into widespread practice in a way that produces measureable results.

Images