Time, Rate and Distance

[UHP]

I thought this excerpt from the teacher's guide for "Reasoning and Writing B" was interesting:

Quote

Children typically have serious knowledge deficits with respect to units of time, rate and distance. Typically, the second grader doesn't understand the difference between "miles" and "miles an hour." They also have trouble with a lot of the concepts associated with these units. For example, children have trouble understanding that if a picture shows two characters racing, the character in front might be going more slowly than the character who is behind. For the children, the faster character is in front. Also, children have great trouble with inverse relationships, the idea that if somebody is faster, that person will finish a race in less time than a slower racer. This fact is particularly paradoxical to many children because the faster racer goes a greater distance during a period of time. (A greater distance has a larger number. So why does the time have a smaller number?)

Much of the work that children will later do in reading, math, science and other content areas assumes knowledge of the concepts of rate, time and distance. Level B teaches how these how these concepts are related.

This is from a program with 70 scripted lessons, the last 25 or so treat these concepts. An earlier track in the program treats map reading. I was interested to see this stuff addressed outside of a math class, in a "language program."

Quote

The track starts with what the children already know about faster and slower and presents a series of graded tasks that introduce different "races."

Lesson 42 presents a race between a mouse and a turtle. the racetrack shows the second markers for each racer. Children indicate where the racers are after a specified number of seconds. Here's the introductory exercise...

I might copy that introductory exercise here later.

Edited October 16, 2021 by UHP

[Gil]

Very interesting. I have long noticed that students struggle with D=RT in math because they don't understand the concept in English, there are a lot of components to the D=RT relationship that are misunderstood.

 

[EKS]

I guess I don't understand why they are calling such a thing a "knowledge deficit" when it comes to second graders.  Eighth graders, yes.

[UHP]

19 minutes ago, EKS said:

I guess I don't understand why they are calling such a thing a "knowledge deficit" when it comes to second graders.

I think this is just a fancy way to say kids usually have a lot to learn about it. My experience with the creators is that they mean no insult to the kids. Earlier in the teacher's guide:

Quote

The development philosophy of Reasoning and Writing is that if teachers or children have trouble with material presented, the program is at fault.

 

[UHP]

9 hours ago, UHP said:

I might copy that introductory exercise here later.

Here it is. Anything in italics is the expected student response to the script.

Quote

1. You're going to work some hard problems that tell how fast characters go. For these problems, you have to understand how much time a second is.

* (Present clock with second hand.) Each line is a second. So each time the hand crosses a line, a second goes by. I'll count the seconds. Watch the hand. 1 ... 2 ... 3 ... 4 ... 5.

2. Your turn: Start with one and count 5 seconds. Get ready. (Signal.) 1 ... 2 ... 3 ... 4 ... 5

Workbook activity

[Here's an attempt to reproduce the diagram in the workbook. "T" stands for a picture of a turtle. "M" stands for a picture of a mouse, "B" for a picture of a barn, "A" for a picture of a tree.

               B         A

   ---1---2---3---4---5---6---7

T|

--------------------------------

M|

     ------1------2------3------4

-UHP.]

1. The picture shows a turtle and a mouse getting ready to race.

* Touch the turtle.

The numbers above the turtles lane show where the turtle will be after the turtle and the mouse have raced for 1 second, for 2 seconds, for 3 seconds, and so forth.

* Touch where the turtle will be after 1 second. To do that, you touch the 1 above the turtles lane.

* Touch where the turtle will be after 2 seconds.

* Go to the end of the turtle's lane and touch the last number for the turtle.

* Everybody, what's the last number for the turtle? Seven

* That means it will take the turtle 7 seconds to get to the finish line.

2. Now touch the mouse.

The numbers below the mouse's lane show where the mouse will be after 1 second, 2 seconds, 3 seconds, and 4 seconds.

* Touch the number that shows where the mouse will be after 1 second. To do that, you touch the 1 below the mouse's lane.

* Touch the number that shows where the mouse will be after 2 seconds.

* Touch the number at the end of the mouse's lane.

* Everybody, what's the number? Four

* That means it will take the mouse 4 seconds to get to the finish line. That mouse goes a lot faster than the turtle.

3. Let's pretend the mouse and the turtle are getting ready to race. I'll count the seconds. When I stop, you'll touch the number for the mouse with one hand and the number for the turtle with the other hand.

* They are getting ready. Go. 1 ... 2.

* Touch where the mouse is after 2 seconds and where the turtle is after 2 seconds.

* Everybody, who is ahead after 2 seconds? The mouse

* One character is at the barn after 2 seconds. Everybody, which character is that? The turtle

* One character is at the tree. Everybody, which character is that? The mouse

4. New race. This time you're going to circle where the characters are. They are at the starting line. They are getting ready. Go. 1 ... 2 ... 3 ... 4.

* Touch where the mouse is after 4 seconds and where the turtle is after 4 seconds.

* Circle the mouse's 4 and the turtle's 4 to show where they are after 4 seconds. Raise your hand when you're finished.

* Everybody, where is the mouse after 4 seconds? At the finish line

* The turtle is next to something after 4 seconds. What is the turtle next to? The tree.

5. Touch the names under the picture. You're going to circle the answer to some items.

* Item A: Who ran faster, the mouse or the turtle? Circle the right name. Circle the mouse or turtle to tell who ran faster. Raise your hand when you're finished.

* Item B: Who ran slower, the mouse or the turtle? Circle the right name. Raise your hand when you're finished.

* Item C : Who reached the finish line first, the mouse or the turtle? Circle the right name. Raise your hand when you're finished.

6. For the last items, you'll write numbers. Here's items D. Listen: How many seconds did it take the turtle to get as far as the tree? Listen again: How many seconds did it take the turtle to get as far as the tree? Write the number that shows how many seconds it took the turtle to get to the tree. Raise your hand when you're finished.

* Here's item E. How many seconds did it take the mouse to get as far as the tree? Write the number that shows how many seconds it took the mouse to get to the tree. Raise your hand when you're finished.

7. Let's see how well you did on those questions.

* Item A: Who ran faster? Everybody, what's the answer? The mouse

* Item B: Who ran slower? The turtle

* Item C : Who reached the finish line first? The mouse

* Item D : How many seconds did it take the turtle to reach the tree? Four

* Item E: How many seconds did it take the mouse to reach the tree? Two

* The mouse got to the tree in only 2 seconds, but it took the turtle 4 seconds.

Teaching note.

The children shouldn't have any serious problems with this exercise. The tasks that are presented make it easy for children to track how far each character goes in the same amount of time. This is relatively easy for the children. The questions that are presented after they "act out" different races show that time may be a variable. Items D and E ask how far it took the racers to get to the same place—the tree. By working this and similar problems, children learn that the slower runner has the larger number of seconds. The mouse reached the tree in only two seconds. The turtle reached the tree in four seconds.

What comes next:

Quote

Children work on exercises similar to the race above in lessons 43 and 44. In lesson 45, a new variation of the racetrack is introduced. This racetrack has lines that mark the feet. The children know that the numbers mark the amount of time it takes each racer to reach the finish line. Children first act out the race as they had on previous exercises. Then they deal with the information presented by the feet markers.

[daijobu]

11 hours ago, UHP said:

Typically, the second grader doesn't understand the difference between "miles" and "miles an hour."

This is not a quote from UHP, but from her teacher's guide.  I am curious if anyone else is bothered by the use of "miles an hour" in a document decrying a lack of understanding of the concept.  To my mind, "miles an hour" is not accurate.  One should write "miles per hour" which is consistent with the idea of a ratio or a fraction.  

11 hours ago, UHP said:

For example, children have trouble understanding that if a picture shows two characters racing, the character in front might be going more slowly than the character who is behind. For the children, the faster character is in front.

 I had fun with a group of students explaining Galileo's dictum.  If you are traveling in one space ship with no acceleration, and you see another space ship pass you by, you have no idea whether that space ship is traveling faster than you, or you are going faster than it,  or perhaps you are traveling in  opposite directions.  Minds were blown that afternoon.  I tried repeating it with another group of kids, and they just weren't getting it.  🤷‍♀️

I also enjoy describing how velocity can be negative or positive and layered on top of that you can have a negative or positive acceleration.  It's all fun stuff.  

 

[8filltheheart]

@EKS Count me as I one who doesn't care if a 7 yr old cannot do math equations with miles/hr.   Most 2nd graders are barely learning multiplication, forget about understanding division with units.   

[UHP]

12 minutes ago, daijobu said:

I am curious if anyone else is bothered by the use of "miles an hour" in a document decrying a lack of understanding of the concept.  To my mind, "miles an hour" is not accurate.  One should write "miles per hour" which is consistent with the idea of a ratio or a fraction.  

I think it is just a little bit old-fashioned.

I'm not sure how people in 2021 talk about their wages. "The lawyer charged 500 bucks an hour" rolls off my tongue a little better than any sentence with per in it.

I honestly don't think my teacher's guide is decrying anything.

[EKS]

10 hours ago, daijobu said:

I am curious if anyone else is bothered by the use of "miles an hour" in a document decrying a lack of understanding of the concept. 

YES!  I almost said I wouldn't use a resource that uses this term to teach anything to do with distance, rate, or time, but then decided to limit the criticism to just one area.

[mathmarm]

  

10 hours ago, 8filltheheart said:

@EKS Count me as I one who doesn't care if a 7 yr old cannot do math equations with miles/hr.   Most 2nd graders are barely learning multiplication, forget about understanding division with units.   

This is not a math program. This is a language program that is teaching children to understand the concepts and the language used to convey the concept. The goal of the lessons are not math, but language. Teaching children to understand, use and express rates correctly as a form of language.

This is a useful skill to have as by the end of 2nd, and definitely from 3rd grade on, kids are expected be able to "read to learn", but this is a bit of language that many, many, many kids are missing, so they misunderstand or mentally skip info as they read or converse or just listen to conversation.

Clearly understanding the concepts of Time, Rate and Distance as a function of language will help kids communicate clearly, follow (or participate in) discussion, catch greater meaning from conversations around them. It also allows them to correctly interpret what they're reading about the speeds at which animals run or plants grow, the weather forecasts, discussion about travel plans, read and interpret articles that tell about how something was built or how someone accomplished something difficult over time, or understand adults discussion about travel plans, compare the heights of buildings around the world or understand the rate at which societies were built/advanced, help kids correctly interpret illustrations in books or comics or even plan the correct order to cook a big meal in.

A lot of children's nonfiction just assumes that children understand the language that's being used to share the ideas and facts that it's teaching. This is not so in my experience.

It's a concept that I know a great deal of kids get mixed up. However, it often goes undetected for years--until they get to a math lesson that just assumes that they understand the concept of rates, time and distance as a function of language.

So, instead of learning how to express something mathematically, and using that as a bridge to a new mathematical concept,

kids are confused by the language component of it, the mathematical expression is sense-less and the mathematical concept is obscured because they have 6+ years of misunderstanding/mentally ignoring the concept in English.

Instead of building from clarity in English to clarity in math, too often we're building from confusion in English to confusion in math too.

 

[EKS]

15 minutes ago, mathmarm said:

This is not a math program. This is a language program that is teaching children to understand the concepts and the language used to convey the concept. The goal of the lessons are not math, but language. Teaching children to understand, use and express rates correctly as a form of language.

I understood that, and I stand by my statement.

[mathmarm]

@EKS and @daijobu

I think that "per hour" vs "an hour" is a regional thing.  You can say both. "Slow down! You're going 62 miles an hour when the speed limit is 45!" <--a comment I made just a few days ago.

Here is an interesting discussion to explore the language bit. Merriam Webster lists them both as correct.

As always, the curriculum is not the master.

As teachers, we have to often tweak or adjust something for our needs. It should be easy enough to change a 1-syllable 2-letter word, for a 1-syllable, 3-letter word for your particular needs.

 

11 hours ago, daijobu said:

To my mind, "miles an hour" is not accurate.  One should write "miles per hour" which is consistent with the idea of a ratio or a fraction. 

 

1 hour ago, EKS said:

YES!  I almost said I wouldn't use a resource that uses this term to teach anything to do with distance, rate, or time, but then decided to limit the criticism to just one area.

Edited October 17, 2021 by mathmarm
weird capitalization

[mathmarm]

@UHP I think it's very interesting to see a language program tackling a crucial language concept early on. I really like that RaW focuses on developing this relationship and this understanding. It's something that I've seen my own kids mix up a lot.

Often it's not discovered that people don't actually understand certain grammar constructions or bits of language until they misunderstand something important in context -- ie people saying something ridiculous to a judge or Police Officer and then being confused about it, and often in math class when it's time to learn math for something that they (supposedly) understand in English already.

Many young children struggle with word problems--not because of math, but because of language.
They struggle to interpret relationships so when they read that Tom has 9 more than Joe, they take that as Tom has 9.

Likewise, "Sarah has 3 fewer than Jane" they jump right to Sarah has 3. Or Jane has 3.

Subtraction problems are a beast because "....more than..." or "...less than..." doesn't connect in their head naturally as a relationship between 2 different people or things.

Taking the time to help children linguistically understand the relationships is key.
Typically, you see this addressed in math because it holds kids back and they can't ignore or get around it in math class, but it's not a math problem--it's a language problem. Other subjects are taught in such a way that you can ignore the problem for much longer.

Edited October 17, 2021 by mathmarm

[VminusEplusFis2]

Hmm, I find the strong feelings about "miles an hour" and "miles per hour" very interesting. I was certainly taught both, and I use them interchangeably. I believe "an hour", "a day", etc., is the traditional way of expressing rates in English, which is why it appears in sayings: "an apple a day keeps the doctor a way." I suppose language has evolved towards preferring "per"? Is the concern that it will confuse children? My kids, who are little, understand both without an issue. Feynman uses "miles an hour" in his lectures. Would the ladies who feel strongly about only using "miles per hour" not ever use Feynman? Or is this only a concern when teaching little children for fear they might be confused that there are two ways of expressing the same thing?

[8filltheheart]

39 minutes ago, mathmarm said:

  

This is not a math program. This is a language program that is teaching children to understand the concepts and the language used to convey the concept. The goal of the lessons are not math, but language. Teaching children to understand, use and express rates correctly as a form of language.

 

Thanks for the clarification. I wasn't paying that much attention.  It really doesn't change my personal POV.  I have known way too many little kids who haven't really grasped time in terms of a clock to think it is a big deal for a 2nd grader.  Ever been in a car with kids who ask how much longer and 10 mins later ask if you are almost there when the previous answer had been 5 hrs?  

Use the correct language when speaking with kids?  Absolutely.  But concept-wise, I don't see it as an issue that matters in 2nd grade.  But equally, I have NEVER had a child have a problem differentiating between the concepts of distance and speed (in terms of 2nd graders' daily language).  Nor have I ever seen a child not understand that speed and distance matter in terms of starting point.  I am guessing that kids who don't understand that have never played around racing and giving slower/younger kids a head start in an attempt to level the "playing field."  Some things kids learn just from normal human interaction.  

For kids in language deprived environments, maybe.  But in a healthy environment?  No, I don't see a big deal.

But, equally, I am not someone who latches onto terminology being a big deal in primary grades.

[mathmarm]

11 minutes ago, 8filltheheart said:

For kids in language deprived environments, maybe.  But in a healthy environment?  No, I don't see a big deal.

It's not necessarily a matter of a "language deprived" environment vs a "normal language" environment.

It's just a common misconception and misunderstanding that kids across the socio-economic spectrum can make so the program is trying to preempt that by including this relationship in their language program.

For example, I think any academically minded parent would say that my kids are in a language rich environment. I certainly think so, but my kids still have some of the developmentally appropriate language gaffes for their ages.

Even in the most elite of private schools students experience the same cross-curricular struggles with language that poor kids have. Because their just kids. There are certain misconceptions and misunderstandings that kids have in their native language irrespective of what language they and their community speak.

As an illustration, I'm reminded of Beverly Cleary's Ramona books.

There is an instance when Ramona thinks they're singing about the Dawnzer Lee Light when they sing the national anthem.  (Dawns Early Light)

Or when the family schedule requires Ramona to stay home alone one morning, she's told to leave for school at a quarter to 8.
She knows a quarter is 25 cents so she leaves at 8:25. Once she's walking she notices that she's the only one outside on the way to school and is confused, she is confused and unable to explain why she arrived late for school when her teacher asks.

Ramona, like many children, make sense of language based on what they know. The adults in Ramona's world take for granted that because she's fluent in English, she's flawlessly following whatever they're saying. The adults in the real world did that to me and my generation when I was young too. I have caught myself doing the same thing with my own kdis from time to time.

Ramona wasn't from a language deprived home--her parents read the paper, read to her and with her, her sister reads with her and to her, her family has dinner together most nights and discuss things. But like many children, Ramona draws conclusions using her (limited) world knowledge.

She surmises for herself that the Dawnzer is some sort of lamp or light. She's mishearing/misunderstanding. She knows what "dawn" is. She knows what "early" is, but because she misunderstood the words she didn't recognize them. She used good thinking skills, but she still drew the wrong conclusion.

I think that clearly teaching children to understand various grammatical constructs in context is something that's appropriate for the majority of kids.

[EKS]

1 hour ago, mathmarm said:

@EKS and @daijobu

I think that "per hour" vs "an hour" is a regional thing.  You can say both. "Slow down! You're going 62 miles an hour when the speed limit is 45!" <--a comment I made just a few days ago.

Here is an interesting discussion to explore the language bit. Merriam Webster lists them both as correct.

As always, the curriculum is not the master.

As teachers, we have to often tweak or adjust something for our needs. It should be easy enough to change a 1-syllable 2-letter word, for a 1-syllable, 3-letter word for your particular needs.

 

 

The difference is that when you use"an hour" you're generally speaking. Or writing dialogue. It's not appropriate when you're actually writing about science.

When I see mistakes like that, it makes me wonder where else the author is going astray.  To me it shows that the author doesn't actually know what they're talking about when it comes to distance, rate, and time, and that they haven't been exposed to enough scientific writing to know that it is more appropriately written as "per hour" in this context.

 

 

 

 

 

 

[EKS]

59 minutes ago, VminusEplusFis2 said:

Hmm, I find the strong feelings about "miles an hour" and "miles per hour" very interesting. I was certainly taught both, and I use them interchangeably. I believe "an hour", "a day", etc., is the traditional way of expressing rates in English, which is why it appears in sayings: "an apple a day keeps the doctor a way." I suppose language has evolved towards preferring "per"? Is the concern that it will confuse children? My kids, who are little, understand both without an issue. Feynman uses "miles an hour" in his lectures. Would the ladies who feel strongly about only using "miles per hour" not ever use Feynman? Or is this only a concern when teaching little children for fear they might be confused that there are two ways of expressing the same thing?

It has nothing to do with being able to understand both ways of saying it, or even saying it both ways.  It has to do with what is appropriate to say in a scientific context and what is not. It is never appropriate to say "miles an hour" in a scientific context.  It doesn't matter what region of the country you're from.

[mathmarm]

1 minute ago, EKS said:

The difference is that when you use"an hour" you're generally speaking. Or writing dialogue. It's not appropriate when you're actually writing about science.

When I see mistakes like that, it makes me wonder where else the author is going astray.  To me it shows that the author doesn't actually know what they're talking about when it comes to distance, rate, and time, and that they haven't been exposed to enough scientific writing to know that it is more appropriately written as "per hour" in this context.

This excerpt is taken, as you already knew from your very first response, from a language program.
It's focused on helping children to speak and understand spoken language and make statements that convey what they're trying to say.

This is not a science program. This is not a math program. It's a language program for children between 1st and 3rd grade.

[EKS]

Just now, mathmarm said:

This excerpt is taken, as you already knew from your very first response, from a language program.
It's focused on helping children to speak and understand spoken language and make statements that convey what they're trying to say.

This is not a science program. This is not a math program. It's a language program for children between 1st and 3rd grade.

For this particular purpose, it is a language program that's masquerading as a science program. 

[mathmarm]

Just now, EKS said:

For this particular purpose, it is a language program that's masquerading as a science program. 

Wait, what? Are you sure?

Please explain how so? I will admit that I haven't used RaW-A and B, so I don't want to speak with too much authority.

I'd like to first understand why you think so Reasoning and Writing B is masquerading as a science program?

 

[UHP]

1 minute ago, EKS said:

For this particular purpose, it is a language program that's masquerading as a science program. 

What makes you say that?

I don't detect any mask at all, in that passage or elsewhere in the materials I've used and read. It's very up front and explicit about what it's doing and why.

[EKS]

1 minute ago, mathmarm said:

Wait, what? Are you sure?

Please explain how so? I will admit that I haven't used RaW-A and B, so I don't want to speak with too much authority.

I'd like to first understand why you think so Reasoning and Writing B is masquerading as a science program?

 

Well, it's obviously masquerading as a science program in that it's trying to teach distance, rate, and time concepts. I didn't say that the entire thing is a science program.

[8filltheheart]

@mathmarm I agree 100% that teaching in context is appropriate.  It is also what happens in a normal, healthy environment.  The example you used is an example of a mistake that little kids could easily make.  It doesn't mean that in a couple of yrs they will still be making the same mistake in a normal, healthy environment (and I am not referring to SES status at all.  I am simply referring to normal, healthy human interaction).   That same scenario would not read as at all plausible with an older child bc most readers would immediately dismiss the idea that older kids would make that mistake.

[VminusEplusFis2]

34 minutes ago, EKS said:

It has nothing to do with being able to understand both ways of saying it, or even saying it both ways.  It has to do with what is appropriate to say in a scientific context and what is not. It is never appropriate to say "miles an hour" in a scientific context.  It doesn't matter what region of the country you're from.

Hmm, so I understand that you believe it, but I'm not sure why. If everyone understands that those two expressions mean the same thing, why does it matter which one you use? Not only that, but both have been used by native speakers of English for a long time, so it's not a matter of one of them being somehow incorrect. Is there an official body that determines what sort of language is appropriate to use in all scientific contexts, during conferences, during physics lectures? And if so, on what grounds? Isn't the most important thing effective communication, and is the effectiveness of communication somehow affected by using "an hour"? Feynman lecturing about physics at a university seems like a sufficiently scientific context, by the way, and he didn't seem to care about using "miles an hour", since he used this expression himself, presumably because it means the exact same thing as "miles per hour" and there was no way his students would misunderstand him. I'll be honest, nitpicking about this seems like unnecessary rigidity to me, but I'm genuinely curious if there is a good argument for being this strict about this issue.

In the context of a language program, it is definitely appropriate to use "miles an hour" because it's an accurate representation of how the English language works, and it's important for students to learn about it.

Edited October 17, 2021 by VminusEplusFis2

[UHP]

34 minutes ago, EKS said:

The difference is that when you use"an hour" you're generally speaking. Or writing dialogue. It's not appropriate when you're actually writing about science.

I think you're mistaken. E.g. the nytimes this august opened an article (this one) with "Hurricane Ida, which struck the Louisiana coast on Sunday with winds of 150 miles an hour..."

[EKS]

I stand by my statement.  

ETA: I'm glad I've been able to provide a source of entertainment for mathmarm this morning!

Edited October 17, 2021 by EKS

[VminusEplusFis2]

@EKS, I apologize if I made you feel piled-on. I'm very interested in language and I also learned to talk about physics in English partially by reading Feynman, so that's why I kept posting about this issue. Given that I'm not a native English speaker, I appreciate hearing people's opinions on how to talk about science. If you ever felt like coming back to this subject and explaining why using "miles per hour" is so important in scientific contexts, I will be very curious to read your explanation. And if not, that's fine, too! I will stop pestering you about it now. 🙂

[mathmarm]

 

18 minutes ago, 8filltheheart said:

@mathmarm I agree 100% that teaching in context is appropriate.  It is also what happens in a normal, healthy environment.  The example you used is an example of a mistake that little kids could easily make.  It doesn't mean that in a couple of yrs they will still be making the same mistake in a normal, healthy environment (and I am not referring to SES status at all.  I am simply referring to normal, healthy human interaction).   That same scenario would not read as at all plausible with an older child bc most readers would immediately dismiss the idea that older kids would make that mistake.

Woops! Point taken. I incorrectly moved your comment re the "environment" to "SES" connection in your statements--my apologies.

However, adults mishear and misunderstand widely too. Mondegreens and other occur outside of songs and poems and the occur at every age as well. Little Kids are not the only ones who easily misunderstand. Teens and adults easily misunderstand as well.

However, good instruction has to take into account mistakes that students can make or misconceptions that students may have or may develop while learning a later skill.

The Teacher Guide for Reasoning and Writing B says:

Quote

All the skills taught in Reasoning and Writing B are important. These skills (a) are assumed by later work in reading, writing and content areas; (b) are typically not taught in any form; (c) can be taught uniformly to children who qualify for entering Level B.

 

[mathmarm]

1 hour ago, UHP said:

I think you're mistaken. E.g. the nytimes this august opened an article (this one) with "Hurricane Ida, which struck the Louisiana coast on Sunday with winds of 150 miles an hour..."

According to the interview I linked, miles an hour was standard and widely used before the 1950s. However, journalism standards still use "an hour" rather than "per hour"

 

@VminusEplusFis2 As for "per hour" vs "an hour" it sounds like there was a shift in usage and acceptability of saying "per hour". Originally Americans thought that "per hour" was wrong, because "per" is from Latin/French and is part of set phrases. (ie "per diem"). It was counted as incorrect to take just "per", it seems like.

So, if you were born, raised and educated prior to the 1950s, you probably learned that "per hour" was incorrect and only used "an hour".

Feymann, who was born in 1918, grew up hearing, using and being taught "an hour" and it doesn't even sound like "per hour" had yet entered the scene. He was over 30 years old before "per hour" was introduced as acceptable so odds are he was set in his way and continued.

Zig Englemann, who was born in 1931, grew up hearing, using and being taught "an hour" and was 20+ years old by the time "per hour" became acceptable. Odds are that he was set in his way and continued.

During the 1950s, once "per hour" became an option, it was just that a new option. I think that "an hour" was still widely used and definitely acceptable and so both just continued to be used in the scientific as well as non-scientific manner throughout society.

If Some Group Some Where decided that a set phrase--such as "Logging On" should be done away with, and only "Logging In" should be allowed, then they'd put it in a book somewhere, but its not going to stop "Logging On" from being used and understood. It doesn't make saying "logging on" wrong.

Language is dynamic and alive. It changes, it grows, and it's flexible.

Until the 1950s, it doesn't seem like educated people were saying "per" anything if they weren't speaking set Latin phrases or expressions, but that's changed.

ETA: And in the 1950s, once "per hour" became accepted, its' not like you could update every book, speech or text that'd been written using the "an hour" term with the push of a few buttons to make that change. "an hour" would've continued to be used widely for a long time afterward, because the educated adults who were alive in the 1950s, were all just that--adults who'd already been educated. They continued to use the language that they'd been brought up and trained to use.

Imagine how silly you'd be to rush up to scientists and science professors around the country and begin scolding them for not immediately switching their speech to incorporate Syllable 2.0 instead of still using Syllable 1.0?

I think that Some Group allowing "per hour" to be used meant was that it changed the conversation teachers and students had from "per hour" is wrong, to "per hour" is also acceptable.

As cars dashboards read MPH and speed limit signs read MPH, I think that's why it took over and entered many peoples mind as the default and "correct" way. But that's just one instance used repeatedly.

I certainly grew up using both.

However, my colleagues--the ones who teach physics and chemistry--certainly use both, among others, in speech and lecture.

Edited October 17, 2021 by mathmarm

[daijobu]

3 hours ago, VminusEplusFis2 said:

Hmm, I find the strong feelings about "miles an hour" and "miles per hour" very interesting. I was certainly taught both, and I use them interchangeably. I believe "an hour", "a day", etc., is the traditional way of expressing rates in English, which is why it appears in sayings: "an apple a day keeps the doctor a way." I suppose language has evolved towards preferring "per"? Is the concern that it will confuse children? My kids, who are little, understand both without an issue. Feynman uses "miles an hour" in his lectures. Would the ladies who feel strongly about only using "miles per hour" not ever use Feynman? Or is this only a concern when teaching little children for fear they might be confused that there are two ways of expressing the same thing?

Yes, I will use both interchangeably, "mile an hour" colloquially or with advanced students, but "miles per hour" in academic context, particularly with young students who are learning rate/time/distance for the first time.  

It isn't typical to see rate/time/distance taught in a writing curriculum, but I think it's a worthwhile endeavor because there are nice equivalences between English and mathematics, and the word "per" as an indication of a ratio is a good one.  This is typically discussed in math or physics classes, but I welcome the English department to describe this continuity as well.  

If I am teaching a  younger student about rate/time/distance, I might explain that people will often say "miles an hour" when they really mean "miles per hour" and explain the use of the word "per."   

The Feynman Lectures on Physics are based on Richard Feynman's lectures to CalTech students in the 1960s.  I have not read Feynman, and did not use the Feynman Lectures to teach rate/time/distance to my own students.  I'm fairly certain Prof. Feynman is not introducing CalTech students  to time/rate/distance, but like I said I haven't read the book, so I could be wrong.  I'm guessing CalTech undergraduates ought to have understood this concept long before they arrived on campus.  (My Wikipedia article lists  mechanics, but also radiation, heat, electromagnetism, quantum mechanics.)   

[daijobu]

@VminusEplusFis2  From the Wikipedia article:

 

The Feynman Lectures are considered to be one of the most sophisticated and comprehensive college-level introductions to physics.^[5] Feynman himself stated in his original preface that he was “pessimistic” with regard to his success in reaching all of his students. The Feynman lectures were written “to maintain the interest of very enthusiastic and rather smart students coming out of high schools and into Caltech”. Feynman was targeting the lectures to students who, “at the end of two years of our previous course, [were] very discouraged because there were really very few grand, new, modern ideas presented to them”. As a result, some physics students find the lectures more valuable after they have obtained a good grasp of physics by studying more traditional texts, and the books are sometimes seen as more helpful for teachers than for students.

And a link to the Feynman treatment of speed and acceleration.

Edited October 17, 2021 by daijobu

[Gil]

2 hours ago, EKS said:

Well, it's obviously masquerading as a science program in that it's trying to teach distance, rate, and time concepts. I didn't say that the entire thing is a science program.

Seriously?

If you're that strict about language use in science, then you wouldn't even be using miles per hour in a science lesson since the official SI unit for speed is meters per second.

Its' perfectly fine that you don't like the program or its authors or a poster on the forum, but I think you're going too far and trying to be arbitrarily rigid with this particular issue.

Your comments in this thread are full of logical fallacies and poor reasoning and I think that you know it.

[VminusEplusFis2]

Thank you, @mathmarm, that was very comprehensive.

And thank you, @daijobu.

ETA: To clarify, I wasn't suggesting Feynman's lectures were an introduction to the subject, and I only brought them up because they contain an example of "miles an hour" used by a great scientist in a physics lecture. I had personally studied physics in a different language and only started reading excerpts from Feynman when trying to acquire some fluency in speaking about physics in English.

Edited October 20, 2021 by VminusEplusFis2

[mom2bee]

On 10/16/2021 at 9:34 PM, daijobu said:

... To my mind, "miles an hour" is not accurate.  One should write "miles per hour" which is consistent with the idea of a ratio or a fraction.

Wait, I am confused. I'm not attacking you, but I have two questions.

How do you use "per" re: fractions?

How do you use "per" re: ratios?

[daijobu]

4 hours ago, mom2bee said:

How do you use "per" re: fractions?

How do you use "per" re: ratios?

Good questions.  You can represent ratios as fractions.  "50 miles per hour" can be written as  with the fraction bar replacing "per."  Or in the context of pediatric medication dosing, on can write "20 milliliters per kilogram" as .  I think of "per" as a synonym of "for every."  

It's similar to using "of" to represent multiplication.  Have 2 of a quantity is akin to have 2 times a quantity.  

[mom2bee]

On 10/19/2021 at 10:32 PM, daijobu said:

Good questions.  You can represent ratios as fractions.  "50 miles per hour" can be written as  with the fraction bar replacing "per."  Or in the context of pediatric medication dosing, on can write "20 milliliters per kilogram" as .  I think of "per" as a synonym of "for every."  

It's similar to using "of" to represent multiplication.  Have 2 of a quantity is akin to have 2 times a quantity.  

Those are both rates--the units are different. Neither of those is a ratio or a fraction--I mean, yes, it uses "fraction notation" but it's not a fraction (ie, rational number, or representative of a single quantity)
 

[mom2bee]

@daijobu The more I think about this, the more I am sure that one can't use the word "per" in ratios.
In English (maybe only American English)  the word "to" is used for ratios, I have never seen any variation in the wording accepted.

In rates, however, there are 2 units and the wording can vary with either "per" or "a(n)".

 

On 10/17/2021 at 10:33 AM, EKS said:

It has nothing to do with being able to understand both ways of saying it, or even saying it both ways.  It has to do with what is appropriate to say in a scientific context and what is not. It is never appropriate to say "miles an hour" in a scientific context.  It doesn't matter what region of the country you're from.

I disagree. You're trying to force a "hard and fast" rule where it doesn't exist nor would the rule actually apply.

 

On 10/17/2021 at 10:30 AM, EKS said:

When I see mistakes like that, it makes me wonder where else the author is going astray.  To me it shows that the author doesn't actually know what they're talking about when it comes to distance, rate, and time, and that they haven't been exposed to enough scientific writing to know that it is more appropriately written as "per hour" in this context.

I have a physics textbook from 1856 and another from 1919 and they use both "per hour" and "an hour" throughout. It looks like "an hour" might be a little more common, but I'm not counting exactly.

It's likely that the author grew up reading scientific texts that used both "per hour" and "an hour" or perhaps he grew up reading texts that phrased it "an hour" only. He's dead now, so we can't really ask him.

Edited October 21, 2021 by mom2bee
I have a 1919 textbook too.

[EKS]

3 hours ago, mom2bee said:

It's likely that the author grew up reading scientific texts that used both "per hour" and "an hour" or perhaps he grew up reading texts that phrased it "an hour" only. He's dead now, so we can't really ask him.

If this is an older text, that makes things different. 

But I would say that it's likely that the author isn't/wasn't a scientist, but is/was, instead, an English teacher or a writer or something of that ilk, and didn't even think about the difference.

And just to be clear, I don't put this issue in the I-would-never-use-this-resource-because-of-this category.  Daijobu asked if it pinged anyone else's radar, and I made the mistake of saying yes, and then trying to explain why.

ETA: I just discovered that the author was likely Zig Engelmann, so the entire thing is making a lot more sense.  

Edited October 21, 2021 by EKS

[Not_a_Number]

Not to muddle things, but fractions and ratios are the same thing anyway 😛 

[Gil]

21 hours ago, Not_a_Number said:

Not to muddle things, but fractions and ratios are the same thing anyway 😛 

No they aren't.

The same notation that is used for fractions can be used for ratios, but ratios are not fractions.

Fractions are numbers. A fraction stands for a quantity.
You can eat 1/2 of an apple or you can sell 3/4 of a herd of cows or have to refund tickets to 1/9 of a crowd of people.
You can plot a fraction on the number line. Take the unit between 4 and 5, divide into into 7ths and you can plot the mixed number 4 and 2/7 or 30/7.

A ratio is a comparison of different units. (such as dogs to cats, or yellow flowers to pink flowers or a persons height to foot size).
You can observe that someone owns 1 dog for every 2 cats(1/2) , or that there are 3 yellow flowers to 4 pink flowers(3/4) , or a persons  height is 9 times greater than the length of their foot. (9/1).

The context of 1/9 determines if it's a fraction or a ratio.

[Not_a_Number]

1 hour ago, Gil said:

No they aren't.

The same notation that is used for fractions can be used for ratios, but ratios are not fractions.

Fractions are numbers. A fraction stands for a quantity.
You can eat 1/2 of an apple or you can sell 3/4 of a herd of cows or have to refund tickets to 1/9 of a crowd of people.
You can plot a fraction on the number line. Take the unit between 4 and 5, divide into into 7ths and you can plot the mixed number 4 and 2/7 or 30/7.

A ratio is a comparison of different units. (such as dogs to cats, or yellow flowers to pink flowers or a persons height to foot size).
You can observe that someone owns 1 dog for every 2 cats(1/2) , or that there are 3 yellow flowers to 4 pink flowers(3/4) , or a persons  height is 9 times greater than the length of their foot. (9/1).

The context of 1/9 determines if it's a fraction or a ratio.

I guess I don't see anything wrong with saying that it's a fraction that measures something with specific units, and those units are quotients themselves? So you can have 1/9 dogs/cats, for example. The unit is "dogs per cats." 

Personally, I've found it pedagogically more useful to treat things as the same rather than different. So, personally, I've always taught ratios like they are fractions, and I've always taught fractions as quotients, and I've never made any difference between them. It has worked well for me so far. 

Edited November 2, 2021 by Not_a_Number

[Gil]

8 hours ago, Not_a_Number said:

I guess I don't see anything wrong with saying that it's a fraction that measures something with specific units, and those units are quotients themselves? So you can have 1/9 dogs/cats, for example. The unit is "dogs per cats." 

Fractions, being numbers, can be operated on. You can perform exponentiation, multiplication or addition on a fraction.

In math, "equality" has 3 conditions. When we say that ratios are the same thing as fractions, we're saying that ratios = fractions. That's simply not true.
Ratios ALWAYS have a unit attached and so

1/9 the ratio can't be universally substituted into an equation for 1/9 the fraction. 

1/9 the ratio doesn't satisfy the Reflexive property either. 1A/9B =/= 1/9 the number

etc.

Quote

Personally, I've found it pedagogically more useful to treat things as the same rather than different. So, personally, I've always taught ratios like they are fractions, and I've always taught fractions as quotients, and I've never made any difference between them. It has worked well for me so far. 

It's your homeschool so you can do whatever you want.  But it doesn't change mathematical reality, nor does it mean that what you do is Best Practice.

There is a long-established tradition of telling lies*to students in math class to help them do well on topic D or to just because the lie seems to hold as they progress from A-F, without concern for what comes after.

*conditional-truths, without ever making the conditions known are as good as lies.

[Not_a_Number]

Pretty much anything with a unit attached can't be used without the unit. It doesn't make sense. Would you say a speed of 1/9 mph is also not being measured by a fraction?

You can have a ratio of things with the same unit, in which case there's no unit on the ratio. For instance, the ratio of side lengths of similar triangles is a unitless ratio, and one does sometimes profitably do arithmetic operations such as squaring on it. 

Perhaps to be more precise, I've told DD9 that if a:b = c:d, then a/b = c/d. I think that is a precise statement that does not ever lead to problems in the future, because they are true in exactly the same cases. Can you give me an example where that understanding would be a problem? 

[Gil]

8 hours ago, Not_a_Number said:

Pretty much anything with a unit attached can't be used without the unit. It doesn't make sense. Would you say a speed of 1/9 mph is also not being measured by a fraction?

1/9 mph is a rate.
Unless you're meaning 1/9 of a mile is traveled in an hour [iow, it would take 9 hours to travel 1 mile.]
Then the 1/9 is a quantity (the amount of a mile traveled) and it's still a part of the rate.

Again, your home school, your rules. You can teach whatever you want and how you like.

What we decide to do in our home schools isn't anything more than what we do. That doesn't make what we're doing Best Practice.

 

8 hours ago, Not_a_Number said:

Perhaps to be more precise, I've told DD9 that if a:b = c:d, then a/b = c/d. I think that is a precise statement that does not ever lead to problems in the future, because they are true in exactly the same cases. Can you give me an example where that understanding would be a problem? 

This is just saying that you can write a ratio using a colon, or a fraction bar. (I'll ignore the proportion for now)

I have already said that Fraction Notation can be used to express ratios.
I have already said that Fractions =\= ratios.

The meaning and correct way to pronounce this word: OBJECT depends entirely on the context.

The meaning and correct way to pronounce this word: ESTIMATE depends entirely on the context.

The meaning and correct way to read and use a/b depends entirely on the context.

[Gil]

9 hours ago, Not_a_Number said:

You can have a ratio of things with the same unit, in which case there's no unit on the ratio.

You're right and I did make a mistake that I need to correct. A ratio is a comparison of different quantities or units.

But you're right that one can take a ratio of quantities, in which case there is not additional units attached.

 

[Clemsondana]

This isn't something that I've thought deeply about or care a lot about, but in many cases I think of ratios and fractions as related but not the same.  Most genetics books will talk about the outcomes of a cross having a 3:1 ratio, so 3/4 of the offspring have one phenotype and 1/4 have a different phenotype.  Almost everything involving simple crosses results in something based on 4s because for 2 genes you can usually have 4, 8, or 16 possible genotypes (fewer phenotypes).  Most texts or classes explicitly talk about needing to choose whether to refer to something as a ratio (1:2:1) or a fraction (1/4, 1/2, and 1/4) or for students to make sure that they answer the question being asked - either 'What is the genotypic ratio?' or 'What fraction of offspring have the AaBb genotype?'.  This may be context-specific, but then again most of my thinking about ratios and fractions is in this context.  🙂  

[Not_a_Number]

14 hours ago, Gil said:

I have already said that Fraction Notation can be used to express ratios.
I have already said that Fractions =\= ratios.

Ah yes, you did SAY that. Of course, that doesn't make it TRUE. 😂

I love the fact that one can get into fights about ratios versus fraction on this forum! Let's agree to disagree, then 😄 

[Gil]

4 minutes ago, Not_a_Number said:

Ah yes, you did SAY that. Of course, that doesn't make it TRUE. 😂

I love the fact that one can get into fights about ratios versus fraction on this forum! Let's agree to disagree, then 😄 

I'm not fighting. I was simply participating in the discussion.

[Not_a_Number]

8 minutes ago, Gil said:

I'm not fighting. I was simply participating in the discussion.

Let me rephrase that to "have spirited discussions," then 😂