6 ms·

I used to be a professor. I did find I got more engagement from students when course material is grounded in reality, but not the same way a lot of posters are

I used to be a professor. I did find I got more engagement from students when course material is grounded in reality, but not the same way a lot of posters are suggesting. Using math to solve real world problems is all well and good, but it has the same problem as teaching math in the abstract. The theorems and techniques are all handed down from on high, like some divine miracle given to humanity by the gods of logic and reason. This works fine for the tippy top of the class who just take the material and run with it (I was once one such), but it loses everyone else. People need context. I tried to, as much as time permitted, give the historical context for the math I was teaching. To show that mere men developed it, that they were trying to solve a specific problem, that they built everything up on what came before. I got great results. I wish I had more time to do it, but, well, when the department standardized end of course test requires that they be able to do n kinds of derivative rules and solve m kinds of integral, I only had so much time to talk about how Isaac Newton invented the cat flap.

newsoul 4y ago
Would love if you could name some books that teach like that, since we can't get you as a teacher.
- travisjungroth 4y ago
  It doesn't go into specific stories but it does explain the process: How to Solve It by George Pólya.
- rootforce 4y ago
  I’m a fan of Mathematics for the Nonmathematician [1] [1] https://a.co/d/grHB5he https://a.co/d/grHB5he
- saityi 4y ago
  I thought William Dunham's Journey through Genius: The Great Theorems of Mathematics did a great job of presenting the very real people and world behind several of results from history, from 400 BC (Hippocrates' Quadrature of the Lune) to recent-ish times (Cantor's transfinites). There's discussions of feuds between mathematicians, how they used to keep results secret and literally duel over ideas (e.g. Cardano's chapter), the historical context and lives of the people who brought theorems into being (like Newton tasting his own chemicals as part of his alchemical research!), etc.
stephc_int13 4y ago
Story telling is very powerful, including for educational purposes. It could clearly be used more often. Doing real-world projects is excellent for engagement but also costly and not always practical.
auxym 4y ago
Agreed. I occasionally teach a strength of materials class, for mechanical engineering students, as a contract lecturer (my main job is research). I love starting the fatigue part of the class with some historical context such as the Versailles/Meudon train accident (https://en.m.wikipedia.org/wiki/Versailles_rail_accident https://en.m.wikipedia.org/wiki/Versailles_rail_accident). I think it really helps to motivate the content and how the "laws", which can be sort of dry and boring out of context, came to be discovered by scientists and engineers who wanted to prevent these kinds of accidents from happening again.
- rawgabbit 4y ago
  I enjoyed your example. When I was a student, these types of stories made the math more relatable. I remember these apocryphal stories; I doubt their authenticity but found them amusing. - Pythagoras was part of what we would call a religious cult. They were trying to discover the secret of the universe when they stumbled on PI and the Pythagorean theorem. - The Sumerians counted in sixes. From them, we have sixty seconds in a minute, sixty minutes in an hour. Don't know why a day only has 24 hours. Maybe the royal mathematician goofed up and got sacrificed to Tiamat. - Today, we count in tens. But you see artifacts of counting by twenty in our language. Lincoln's Gettysburg address begins with Four score and seven years ago our fathers brought forth, upon this continent, a new nation. Four score means four twenties or eighty. - Trigonometry was created by enterprising Greek merchants who had fleets of ships. One problem they had was determining how far a ship was from port. They solved the problem by creating a virtual right triangle. On shore, they marked a "shore line" which they would place two observers. The two observers always stood on the line and at a known distance from one another by means of a fixed rope. The first observer would walk up and down the line. The second observer would adjust his position on the line to keep the same distance from the first. The first observer would walk up and down the line until he thought he was "perpendicular" to the ship which was at sea. The second observer would then write down the estimated angle between the shoreline and the ship. By knowing this angle (theta), the fixed distance between observers (adjacent distance), and the right/90 degree angle... they could calculate the distance to the ship (opposite distance). In other words, the distance to the ship is equal to the tangent of theta multiplied by the adjacent distance.
orangeoxidation 4y ago
> I tried to, as much as time permitted, give the historical context for the math I was teaching. This is great. Funny how teachers generally aim for their students to 'understand' instead of merely 'replicating' (from memory). Yet math is often taught as a complex, fully formed system (especially in university). Teaching math along the same path / outline it was historically developed teaches the 'why' alongside the 'how'.
- VyseofArcadia 4y ago
  Exactly. The why is missing. The how is inadequate in a vacuum. Bright students make the connection on their own, but the others, even highly motivated ones, get left behind. To make the problem worse, quite a lot of my former colleagues don't know the why themselves. They've always thrived on abstraction, and are unable to understand or help when motivated students come to them seeking the why. Bit of a chicken and egg problem, really. The professors who made it did so without the why, and therefore don't understand the need for it. I'm as guilty as anyone. I couldn't tell you much about where my PhD research came from and why. At least my calculus students got some context.
strikelaserclaw 4y ago
teaching the history of science along with science is a much more effective way of teaching for the average student but alas schools are more concerned with operating in an assembly line fashion in which they try to stuff as much knowledge into a person as possible (which the student will undoubtedly forget soon after after they study enough to pass exams)
- UncleMeat 4y ago
  It can be perilous if you don't do it right - where new discoveries and methods are taught as if they are inevitable because you only look at the history when it is related to modern understanding.
EntropyIsAHoax 4y ago
I've always loved math, but one class I didn't expect to like as much as I did was The History of Mathematics. The mathematical content was usually very basic of course, but putting all the things I was learning in my other classes in a historical narrative was eye opening and magical. It also gave me a way better understanding of why we do math the way we do today. Of course mathematical truths are the same regardless of notation and method, but even simple things like the prevalency of the "=" sign are choices we made along the way in history. Today algebra is almost synonymous with math for many people, but it didn't even exist as a branch of mathematics until al-Khwarizmi he just wrote his equations out in words! But we made a concise notation over time and we're all much better for it. And some parts are just funny. Like math "duels" over cubic equations in 1500s Italy
- camjohnson26 4y ago
  Mathematics: From the Birth of Numbers is an illustrated, well written history of mathematics, helped me see how all the different concepts came about. https://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X https://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullber...
rhaway84773 4y ago
I really wish mathematics was taught like a history class. Mathematics, the way it’s taught, rarely ever explains the Why of a concept. For example, I understand that calculus is useful. You’ve shown me a whole bunch of uses for it. But why did we come up with calculus in the first place! Learning about the motivations of the historical actors involved in making discoveries, and learning about the steps that led to those discoveries gave me a far more complete understanding of mathematics. It also removed this massive whiff of arbitrariness that has always existed with mathematics for me.
- markus_zhang 4y ago
  Me too. I think Physics taught as history class would be extremely fun. Say you have to follow the steps of Kepler and do a few observations by yourself.
  - runlevel1 4y ago
    In college, I took a History of Science class about Copernicus and Kepler. It totally could have been adapted into an engaging physics course.
ghufran_syed 4y ago
Time for you to release a set of video lectures! [crosses fingers…]
nerdy_nerd101 4y ago
Absolutely love this approach!
purist33 4y ago
Could it be due to the fact that, college level mathematics are meant to prepare extraordinary students to graduate into research. I imagine research often involves not-so sexy parts of mathematics. I hear a lot of similar sentiments in school level mathematics in the country i live in. The problem comes in the trade-off. Do you cater to the topmost/ most promising students, who will end up contributing a lot in science, or do you cater to the ones who need most help, who will end up getting some skills on this, to make a living ?

newsoul 4y ago

Would love if you could name some books that teach like that, since we can't get you as a teacher.

travisjungroth 4y ago
It doesn't go into specific stories but it does explain the process: How to Solve It by George Pólya.
rootforce 4y ago
I’m a fan of Mathematics for the Nonmathematician [1] [1] https://a.co/d/grHB5he https://a.co/d/grHB5he
saityi 4y ago
I thought William Dunham's Journey through Genius: The Great Theorems of Mathematics did a great job of presenting the very real people and world behind several of results from history, from 400 BC (Hippocrates' Quadrature of the Lune) to recent-ish times (Cantor's transfinites). There's discussions of feuds between mathematicians, how they used to keep results secret and literally duel over ideas (e.g. Cardano's chapter), the historical context and lives of the people who brought theorems into being (like Newton tasting his own chemicals as part of his alchemical research!), etc.

stephc_int13 4y ago

Story telling is very powerful, including for educational purposes. It could clearly be used more often. Doing real-world projects is excellent for engagement but also costly and not always practical.

auxym 4y ago

Agreed. I occasionally teach a strength of materials class, for mechanical engineering students, as a contract lecturer (my main job is research). I love starting the fatigue part of the class with some historical context such as the Versailles/Meudon train accident (https://en.m.wikipedia.org/wiki/Versailles_rail_accident https://en.m.wikipedia.org/wiki/Versailles_rail_accident). I think it really helps to motivate the content and how the "laws", which can be sort of dry and boring out of context, came to be discovered by scientists and engineers who wanted to prevent these kinds of accidents from happening again.

rawgabbit 4y ago
I enjoyed your example. When I was a student, these types of stories made the math more relatable. I remember these apocryphal stories; I doubt their authenticity but found them amusing. - Pythagoras was part of what we would call a religious cult. They were trying to discover the secret of the universe when they stumbled on PI and the Pythagorean theorem. - The Sumerians counted in sixes. From them, we have sixty seconds in a minute, sixty minutes in an hour. Don't know why a day only has 24 hours. Maybe the royal mathematician goofed up and got sacrificed to Tiamat. - Today, we count in tens. But you see artifacts of counting by twenty in our language. Lincoln's Gettysburg address begins with Four score and seven years ago our fathers brought forth, upon this continent, a new nation. Four score means four twenties or eighty. - Trigonometry was created by enterprising Greek merchants who had fleets of ships. One problem they had was determining how far a ship was from port. They solved the problem by creating a virtual right triangle. On shore, they marked a "shore line" which they would place two observers. The two observers always stood on the line and at a known distance from one another by means of a fixed rope. The first observer would walk up and down the line. The second observer would adjust his position on the line to keep the same distance from the first. The first observer would walk up and down the line until he thought he was "perpendicular" to the ship which was at sea. The second observer would then write down the estimated angle between the shoreline and the ship. By knowing this angle (theta), the fixed distance between observers (adjacent distance), and the right/90 degree angle... they could calculate the distance to the ship (opposite distance). In other words, the distance to the ship is equal to the tangent of theta multiplied by the adjacent distance.

orangeoxidation 4y ago

> I tried to, as much as time permitted, give the historical context for the math I was teaching. This is great. Funny how teachers generally aim for their students to 'understand' instead of merely 'replicating' (from memory). Yet math is often taught as a complex, fully formed system (especially in university). Teaching math along the same path / outline it was historically developed teaches the 'why' alongside the 'how'.

VyseofArcadia 4y ago
Exactly. The why is missing. The how is inadequate in a vacuum. Bright students make the connection on their own, but the others, even highly motivated ones, get left behind. To make the problem worse, quite a lot of my former colleagues don't know the why themselves. They've always thrived on abstraction, and are unable to understand or help when motivated students come to them seeking the why. Bit of a chicken and egg problem, really. The professors who made it did so without the why, and therefore don't understand the need for it. I'm as guilty as anyone. I couldn't tell you much about where my PhD research came from and why. At least my calculus students got some context.

strikelaserclaw 4y ago

teaching the history of science along with science is a much more effective way of teaching for the average student but alas schools are more concerned with operating in an assembly line fashion in which they try to stuff as much knowledge into a person as possible (which the student will undoubtedly forget soon after after they study enough to pass exams)

UncleMeat 4y ago
It can be perilous if you don't do it right - where new discoveries and methods are taught as if they are inevitable because you only look at the history when it is related to modern understanding.

EntropyIsAHoax 4y ago

I've always loved math, but one class I didn't expect to like as much as I did was The History of Mathematics. The mathematical content was usually very basic of course, but putting all the things I was learning in my other classes in a historical narrative was eye opening and magical. It also gave me a way better understanding of why we do math the way we do today. Of course mathematical truths are the same regardless of notation and method, but even simple things like the prevalency of the "=" sign are choices we made along the way in history. Today algebra is almost synonymous with math for many people, but it didn't even exist as a branch of mathematics until al-Khwarizmi he just wrote his equations out in words! But we made a concise notation over time and we're all much better for it. And some parts are just funny. Like math "duels" over cubic equations in 1500s Italy

camjohnson26 4y ago
Mathematics: From the Birth of Numbers is an illustrated, well written history of mathematics, helped me see how all the different concepts came about. https://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X https://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullber...

rhaway84773 4y ago

I really wish mathematics was taught like a history class. Mathematics, the way it’s taught, rarely ever explains the Why of a concept. For example, I understand that calculus is useful. You’ve shown me a whole bunch of uses for it. But why did we come up with calculus in the first place! Learning about the motivations of the historical actors involved in making discoveries, and learning about the steps that led to those discoveries gave me a far more complete understanding of mathematics. It also removed this massive whiff of arbitrariness that has always existed with mathematics for me.

markus_zhang 4y ago
Me too. I think Physics taught as history class would be extremely fun. Say you have to follow the steps of Kepler and do a few observations by yourself.
- runlevel1 4y ago
  In college, I took a History of Science class about Copernicus and Kepler. It totally could have been adapted into an engaging physics course.

ghufran_syed 4y ago

Time for you to release a set of video lectures! [crosses fingers…]

nerdy_nerd101 4y ago

Absolutely love this approach!

purist33 4y ago

Could it be due to the fact that, college level mathematics are meant to prepare extraordinary students to graduate into research. I imagine research often involves not-so sexy parts of mathematics. I hear a lot of similar sentiments in school level mathematics in the country i live in. The problem comes in the trade-off. Do you cater to the topmost/ most promising students, who will end up contributing a lot in science, or do you cater to the ones who need most help, who will end up getting some skills on this, to make a living ?