The mathematical topics, methods, and the exercises are all driven by the need to use mathematics in trades. Topics were selected by seeking input from colleauges who teach the trades and searching textbooks from their classes. As a result the distribution of coverage is different from algebra textbooks. For example, there is more coverage of linear models (especially ratios) than of quadratic models and those are mostly limited to the simplest form.
Methods for solving problems are intended to match how a person would perform the calculation at a job. For example numbers are almost always written in decimal, and rounding is constantly considered. Solving an equation with variables in it, serves limited purpose here, so any values are plugged into the model at the start and simplified before any solving steps. Algebra is a tool rather than a goal here. Correct notation and neatness are still considered important as this impacts accuracy and communication.
Exercises are taken as much as possible directly from textbooks and manuals from the trades. Where deemed useful for skill building, there are still some contextless questions and some applications that are a bit contrived.
In this initial edition there are still some applications with unrealistic parameters where we could not determine a reasonable range. If you can identify one, please contact the author so that can be improved.
MiTaL began as a set of daily class lessons and was extended with the goal of teaching using an active learning approach. In particular it is written with the intent that students will work through examples and checkpoints either as part of a flipped classroom or during class with an instructor and perhaps learning assistants helping students along.
Through classroom testing we have extended the number of examples and level of detail beyond what might be optimal for a flipped classroom. This change was made based on student need and with an eye on making thought processes students should use more clear.
While emphasizes calculations needed for jobs, MiTaL also works to emphasize the importance of thinking critically about models and about results we calculate. Blind following of examples is discouraged (hence exercises without an identical example). Rumination on results is repeatedly required (especially in projects). MiTaL wants readers to always ask, What are the restrictions on the inputs, the results? In which situations does it make sense to use this model?