Farmer provided scientific explanations of the chemical processes that occur in food during cooking, and also helped to standardize the system of measurements used in cooking in the USA. Before the Cookbook’s publication, other American recipes frequently called for amounts such as “a piece of butter the size of an egg” or “a teacup of milk.” Farmer’s systematic discussion of measurement — “A cupful is measured level … A tablespoonful is measured level. A teaspoonful is measured level.” — led to her being named “the mother of level measurements.”
Doesn’t explain why it’s still done that way, of course.
I had the exact same problem with teachers way back when: Negative numbers simply “didn’t exist”.
However I do know what caused this ridiculous statement back then: We only operated in Natural Numbers. Not the full set of Integers. This may seem like a largely hair-splitting difference but in many cases it’s actually an important distinction.
I really wish my teacher back then would have told me: “For Natural Numbers that doesn’t work.”, hinting at there being more later down the line. That would also have been the fully correct answer. But alas they didn’t.
The worst class I ever taught was Math for Elementary School Teachers. Half the students had absolutely no clue about the math they were supposed to teach. I can’t believe they ever made it to university. I later taught in a public high school and even there, where the teachers were certified in their specialty, a large percentage just didn’t understand math.
The commutativity of multiplication is an important concept and makes computation much more convenient. Embrace it! If you want to blatter about non-commutative operations you have to go no further than subtraction or division. I always found that a good excuse to promote adding a negative or multiplying by a fraction instead to get back to a nice, friendly, commutative operation.
I think that the teacher is wrong here, but your last sentence: “Here is the rule that all math teachers should always obey: full marks for the right answer.” is just dangerous.
There’s and old saying, “Even a blind hog finds an acorn once in a while.” That doesn’t mean we should encourage their bumbling.
Yeah, I’m not that worried about it. If a student really doesn’t know what they are doing it’s going to show up. Imagine a student in a calculus class doesn’t know how to take a derivative. I think we could use something called “math” to help us estimate the probability that they pass by simply guessing the correct answers and find that it is acceptably low. On the flip side, there is a student in almost every class who is frustrated by losing part marks for skipping steps that seem trivial to them and that will be regarded as trivial a few years on.
This is why I couldn’t go to my Dad for math homework help in highschool.
He was an electrical engineer. He’d look at my grade 11 equations and go “thats dumb and too long, do this instead” which I would do, and lose half the marks because “you have to show your work” (but only on the equations they taught you, not ones you brought from home, apparently).
Semantically, the “form” is incorrect, as is the teacher. M x T is not represented by 5 x 3. It is actually the reverse from a logical perspective. The child had it right.
I often had partial grades when I didn’t memorize the “correct” way to reach a solution, even when I reached the right answer through unapproved methods.
I guess rote memorization: good and figuring things out on your own under a deadline: bad. Ask me which skill is more useful in life.
What it really comes down to is that most of your math teachers in public school didn’t know how to do math. Your math teachers in high school might have known some math, the ones in the upper years who taught real math subjects probably knew math. You have to go a lot of years through your education before you can reliably bet that the person who is teaching the class has done more than memorize the method themselves.
My research into this subject (how people mentally do math problems) has shown me that people perform math calculations many different ways. If you ask a room full of people how they solve a problem, you will get back many different answers if not a unique one for each person in the room.
Channeling kids into one distinct way of thinking about how to do problems is 1. counterproductive 2. suited more to the teacher than the student 3. totally expected of cookie-cutter education.
I encourage my kids to learn it both ways: how the teacher & school want them to, and also how it works best for them. I encourage my grad students to do it their way and I will only step in when it’s clear they are misguided or stuck and need help.
Who the F cares that you multiply 3 and 5 the same way every time? Heck, I don’t always do math operations the same way every time. It can change around, and yeah, I can even make simple mistakes sometimes even though I’m very mathy. It happens. I’m not a computer. I’m a thinker.
As a high-schooler I regularly failed high school math, all throughout my high school career, and I would then take it in summer school where I would get 90s.
The difference? Summer school was taught by the same woman each year (all my school teachers were men) and most of the students were girls. While highly personal anecdotes are not data, it has always stuck with me when talking to kids now that claim they’re “bad at math” - I will always think they just didn’t have the right teacher and environment.
My math marks went up over 15 percent from highschool to university. You can get very poor marks and understand things very well, and very good marks while understanding things poorly. Marks, I believe, are strongly correlated with the ability to get marks in the future, and not very correlated at all with anything else.
Of course, your teacher may have been dumb as hell.
Ironically, this belief that there are many different ways to do math, and that different brains work differently, was probably at the heart of the curriculum that this quiz was based on. Somewhere in a galaxy far, far away from standardized testing administrative hierarchies, there were probably some well-meaning curriculum developers and educational theorists who thought “wouldn’t it be great if we introduced many ways of thinking to the kids, so that we can have a formal process for helping them to discover the best way for themselves.” This then got fed through a system full of standardization mongers who mangled it into a quiz, where points are removed if each kid doesn’t learn each method perfectly, and regurgitate it letter-by-letter.
Yeah. I was lucky enough to have very good math teachers. The best one in high school was math consultant to the school board; the best in university was the head of the department, who actually liked to teach (and was superb at it).
Both were women. Co-inky-dink? Probably not. I’m coming to think we may have moved backwards for women in STEM since I was a lad in the '60s.
