Early man discovered math concepts as part of understanding the processes in life, and experimented with applications, finding new uses over time, developing science and engineering, and increasing the sophistication of the math information processing system as the need arose.
The U.S. has lost the ability to continue this historical process because of the removal of concepts from the curriculum and teacher training programs the last 50 years.
Not only have science and engineering programs become dependent on international students to keep up standards (and hope they stay in the country to work), but training programs have added applied math courses and continue to struggle with student skill sets in math applications.
Companies are having trouble finding employees with basic algebra skills for training.
Problems finding employees with basic skill sets was recently driven home for my brother, an electrical engineer who also conducts training classes for linemen in trig applications. He has never understood why the employees understand his explanations of the applied trig processes to their work but cannot get the algebra right.
I sent him a link to a web site that explains the present-day concept-void memorized steps of “order of operations” to solve equations. He checked it out and went ballistic because it completely fails to explain the information being processed for an understanding of the results.
When the U.S. replaced math concepts with algorithms about 50 years ago, it became necessary to memorize specific ordered steps instead of using the concepts of application to organize the information for processing.
Equations explain relationships by showing what factors are involved in the relationship and how they are related.
For understanding the results of the processing for application, the use of algorithms is a proven failure (evidenced by low test scores for concepts and the inability to apply concepts).
I can supply a list of nine links with great math curriculum programs (for apps, computers, DS games, etc.), which I did for my brother to help train employees, and which I have done for others who requested them.
Another example of processing information for decision-making is the accounting equation. Businesses use this to make critical decisions for conducting operations.
When a business begins, it usually needs start-up money, which comes in the form of loans (liabilities) and/or stock (equity in the business) in order to purchase assets to conduct business. The relationship for this is expressed in the equation: assets = liabilities + equity.
Anytime a business wants to know what their equity is, they can subtract liabilities from both sides of the equation (which is done in this manner to maintain the concept of the equal sign as a scale showing the combination of what is on each side is in balance). Taking this step would result in: assets – liabilities = equity.
This relationship forms the balance sheet for the business, guiding decisions until the business is either closed (zeroing the accounts) or sold (when the accounts become part of the purchaser balance sheet).
There is an added part to the accounting equation that forms the income statement, an annual report that is closed at the end of each fiscal year, adding the profits to equity or subtracting losses from equity in the balance sheet. This makes the complete accounting equation: assets = liabilities + equity + revenues – expenses.
Understanding the impact business decisions make to other accounts in the balanced equation is important in preventing what might appear to be a good decision for one thing but a bad one for a related factor.
Other countries experimented with algorithms (as they have with other ideas to improve curriculum) but when they were unable to maintain student achievement, they dropped the idea and went back to what was provably working while they still had teachers trained to effectively teach those concepts. Only in the U.S. has the practice of eliminating concepts from curriculum and teacher training programs continued for 50 years.
The reason for this lies with the adoption of the bogus defective student theory in 1968 — blaming the victims for failure rather than the curriculum or teaching.