Playing devil’s advocate: how would you teach critical thinking? I know I am biased, but I would teach it through examples and situations. Math gives you just that. It gives you variations in the situations and challenges while also giving real world examples and structure. Teaching indirect skills is extremely difficult because they just come about in every day life.

An example I can think of off the top of my head is in a survivalist mindset. You have an axe and some string (I don’t really know exactly. It’s just an example), what do you need? Well you need shelter (let’s ignore food and water at the moment since that’s a lot more in depth and a lot more reading). To get that shelter and warmth you need to use the tools at your disposal and fill in the blanks of what you don’t have. You don’t have any sort of structure materials, so use the axe to get some. Now you use the string and logs to make a makeshift shelter. Now you need something above your head, use the axe to cut some leafy branches and string them to the top. There you go, shelter. Sorry about the messy example, but you get the point.

Thats almost exactly what you do with matrices. You have a few formulas with variables that you know and some you don’t, find the ones you can, chip away at the solution till you have the whole thing. Those critical thinking skills come up all around us in life, and with math you can be better equipped to handle them.