AMDM: The Purposeful Maths Course

Before I begin, I would like to give a shoutout to all the LHS AMDM teachers of 2021 (especially to Mr. Cortez). Words can’t describe the amount of hard work you’ve put into making this year successful. This will be one of my most memorable classes, and I can’t thank you enough. I wish you all the best for the coming years, and I hope to see the course develop into something that everyone at Lakeside takes.

There were some days when I sat in a maths class and asked, “Why am I learning this?” I bet we’ve all asked this before. When course selections came around last year, I wanted to make sure that I was preparing for college with classes like AP Calculus and AP Chemistry. But I also wanted to apply what I was learning outside of class. I debated whether it was worth dropping a sixth AP class in favor of AMDM. When my dad, a doctor, encouraged me to look into AMDM as one of my two senior maths courses, and after hearing what the class was about, especially that it was the only class offered at Lakeside with a complete finance unit in the syllabus, I decided to give it a shot.

Advanced Mathematical Decision Making is essentially what I dub as “the IRL maths class,” because it takes all of the concepts that students learned in previous years (up to Algebra II) such as functions and basic geometry and applies them in ways that aren’t necessarily discussed in a traditional maths class. From some of the more basic topics such as calculating the size of computer and phone screens to creating a monthly budget for a dream career, AMDM has topics that range from “Oh, that’s cool to see how what I’ve learned is used,” to “Wow, I will actually use this for the rest of life.” Outside of regular maths courses, these topics would barely show up.

Contrary to the name, the maths required in this class isn’t necessarily all that difficult – the most you need to be ready for the course is to have a good understanding of algebra and general arithmetic. I recall talking to my calculus teacher and discussing that many of the students in the class can’t do basic trigonometry. One of my friends also noted that it would be a definite drop in rigor. I wouldn’t be surprised if, by taking this one “easy class” my senior year, I made myself look less stellar to college admissions officers than others who went out with a whole suite of AP and dual enrollment classes to show off.

But let’s face it: Many of our day-to-day encounters with mathematics don’t require non-right-angle trigonometry or the summation of infinitely small increments of change. While I feel those things do need to be appreciated and have their place in the real world, there are plenty of fields that only require simple maths to approach even complex matters such as finding final grades at the end of the year. We might consider how we can use technology to make each step of calculating easier – everyone loves using calculators. Other times, you can’t just go off pure mathematics to make a choice on complex matters: you get the numbers and calculate the long-term debt for different college loans or a financed car, but you must make the decision in the end.

This is where AMDM comes into play. It’s not calculus, but it can’t be reduced to just pure and simple arithmetic either. It’s not a class where you’re just given a bunch of random numbers smashed into a bunch of words and are supposed to get a numerical result.

AMDM requires deeper logic than deciding off a number. For cases like finance where there is no wrong answer or there are many factors to consider, the actual coursework demands that you stop and think about the results and possible options once you come to an answer, then conclude with your own personal reasoning. During this process, you have to use every possible resource you can to obtain those answers, such as using the good old paper-pencil, the TVM solver on your calculator, filling a spreadsheet’s cells with numbers and formulas, or conducting research through the internet and talking with adults.

Consider the 2-meter social distancing rule, for example. How would one determine the greatest possible number of masked students that could fit in the school cafeteria with an initial floor area of approximately 880 square meters?

After some careful thought, you might narrow your approach to two different ways. One is to approximate the area required for each person with a square, where the squares cannot overlap each other but are touching to maximize the amount of space. If you use this approach – let each side of the square be two meters since the combined distance between two people is two meters, then divide the available area by the area of the square – you should land at an answer of 220 persons.

However, another answer you might have obtained was 280 persons. This would have been made by using a circle instead of a square and letting the person stand in the middle, where the radius of the circle is one meter since two circles touching each other will have a combined radius of two meters. Again, we find the area of the circle, divide the area available by the amount of space each person takes up, then round down since we can have neither a part of nor any more of a person without reducing the two meters.

Did this feel too simple? You’re right. In fact, this is not where the problem should end. What happens when we need to consider the vending machines, tables, chairs, or cashier counters, since each of these takes up some amount of floor space? Would it make more sense to estimate numbers with squares, and have the calculations be easy, but have a lower capacity than what’s possible? Or do we use technology to get a more exact number with a larger capacity without considering anything else? How would things change if people were moving instead of being fixed at one point in the room?

While I can’t give a whole assessment of the course compared to other years due to three out of the seven units being cut out due to COVID-19, this type of thinking is what’s required at the end of many problems that we encounter, and thus, when taking the class. Again, the maths itself is not difficult, but training yourself to reason towards something that makes sense based on the big picture is something that I find is unfortunately lacking in many of our maths classes here at Lakeside. AMDM allows an easy yet complex introduction into the numerous ways of how and why we model the world around us beyond the application of algebraic formulas.

There are moments when, as a former calculus student, I facepalmed behind the computer screen at how terribly easy the problems were to solve when others had trouble doing things like adding fractions. But I have to remember that, despite the setback, the course has skills that those students will be able to have for the rest of their lives and it takes time to master them. Quite frankly, it might be the last maths class they’ll ever take in their lives.

So the next time you look at the course selection sheet, consider adding AMDM as a class to take at Lakeside. We’ve got the harder calculus and statistics classes, but what about something more directly purposeful? It’s slow and simple to all the rest, but I definitely enjoyed taking it this past senior year.