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According to the National Assessment of Educational Progress (nces.ed.gov), 33% of Wisconsin 8th graders scored “proficient” in math. Meanwhile, occupational pay data (e.g., payscale.com) shows that the top earning disciplines tend to be in STEM—science technology engineering and math—plus STEM-adjacent application areas like economics, finance, statistics and computer science.
How can students be convinced during their K-12 years, when math is introduced and skills and talent discovered and developed, that serious study of the subject and its applications will likely enhance future payoff? How can a greater percentage of students find interest in the subject and reason to prepare for careers in fields requiring working knowledge of quantitative methods? AI offers a way to augment the math curriculum that might convince more students that the effort is worth it.
Part of math instruction is a “tool kit” of technique, the manipulation of equations or recollection of formulas, with numerous exercises. Learning this toolkit is absolutely necessary student work but often does not convey the importance of mastery.
Resolving Issues, Reaching Solutions
By contrast, word problems take math to a higher level. They are verbal descriptions of situations with a problem posed for the student to solve. Such problems require nuanced reading, decisions about relevant facts and how they inter-relate, and choosing the mathematical techniques to resolve issues and reach solutions.
By careful choice of narrative description, a word problem can serve a dual purpose, first as a meaningful math exercise for the student and second as a description of a real situation encountered in business or government or other organizations. Each problem is a small project; each solution a step toward a problem-solving skill.
Through word problems, students can get a sampling of how established disciplines use math.
Economics: Demonstrate how import tariffs are paid by the consumers living in the importing country.
Engineering: How to build an electric hybrid vehicle to cut fossil fuel usage.
Chemistry: How to modify the formula for concrete so that it will sequester rather than emit carbon into the atmosphere.
Astrophysics: How to rescue stranded astronauts from the International Space Station.
Law: How to calculate the money damages suffered in accidents, or broken agreements, or defamation.
Medicine: How to estimate the laminar flow of blood through an artificial heart valve.
Political Science: How rules of probability can be used to interpret opinion surveys.
Philosophy: How to apply the principles of logic to civil argument.
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Real World Problems
A shift toward more real-world word problems requires very high cost in terms of time and effort. To properly grade word problems the teacher must perform diagnostic effort that is painstaking and time-consuming. The logic and accuracy of each step the student takes in the process of setting up and solving a word problem must be examined, and the student must be shown any errors in logic and better ways to approach a problem. However, class sizes are large, and teachers are already stretched; new resources are needed.
Fortunately, developments in AI teaching assistance and AI-based tutoring can reduce these costs, performing many of these tasks and never run out of energy and patience. For a pioneering example of a well-developed AI-based assistant, click on Khan Academy (khanacademy.org). Khan Academy has long provided courses and video instruction, and in the last few years has added an AI-based assistant, Khanmigo.
This assistant guides students through problem sets, providing prompts and suggestions. It can also generate the word problems that illustrate the wide applicability of math through challenging assignments. By reducing the time and money cost of formulating the problems and the required intense grading, AI can accommodate a curriculum shift toward more word problems. Student practice would enhance the development of skill and interest, and the confidence to enroll in advanced courses and succeed in them.
