Grading Freshmen

analogseal18 said:The problem presented here isn't quite suitable for a first-grade assessment, though I suppose it serves as decent practice to teach children that they actually need to engage their brains rather than simply following a template. My own daughter would likely have burst into tears if she couldn't solve it immediately, but if I applied my preferred method—tell her to sit and think for five minutes before calling for help—she would have figured it out on her own.

Nicholas King claims that fourth graders emerge from the classroom completely dazed by data, yet I find myself unable to agree with that assertion. In my specific classroom, nearly half of them are straight-A students, which makes it painfully obvious that the curriculum lacks sufficient rigor. Furthermore, my daughter hasn't even truly studied or mastered the art of learning yet; she simply absorbs everything during class. She isn't some sort of wunderkind; she’s merely attentive, curious, and happens to have encountered most of this information previously through documentaries and encyclopedias. Regarding the lower grades, I feel more a sense of pity for the wasted time and the physical toll of sitting at a desk all day when the child isn't truly gaining any depth. It strikes me that she will struggle significantly once she hits fifth grade, where actual work and discipline become mandatory.

To return to the original topic—I am in favor of grading, provided we also establish clearer standards and raise the bar. If we start early, children will grasp more quickly that being graded isn't a nightmare, but rather an inherent part of life.

I doubt this exact question would show up on an official exam, though if they were working against a clock, it shouldn't be too difficult.

It sounds like those math storybooks that offer great brain teasers for training, even if their actual standardized tests only cover the basics.

Here is an example of a question that actually drove me a little crazy! 😬
Anne has 5 pencils. John has 2 more than her. How many do they have altogether?
Needless to say, most of the answers were just 7, and everyone finished within a minute.
It really just comes down to rushing and not reading for comprehension. 😁

Mary is ten years older than Mark. I suppose you have to consider how much time actually passes—how old will she be compared to him in five years? 😬

15, of course. 😬

I actually really enjoy these kinds of challenges; they prove that math doesn't have to be dry. A perfect example is the Mathematical Kangaroo competition, which focuses on genuine skill rather than just what you can memorize for a standard written exam.

Betty Gray84 said:15, of course. 😬

I actually really enjoy these kinds of challenges; they prove that math doesn't have to be dry. A perfect example is the Mathematical Kangaroo competition, which focuses on genuine skill rather than just what you can memorize for a standard written exam.

Actually, that's incorrect.

5.

Michelle Ward3 said:I don't have an engineering degree, but I have an example for you.🙂

I remembered a specific problem that frustrated me to tears. Even back then, I couldn't figure out how to set up the equation for my sixth grader, and even after asking for help on a forum, nothing clicked.😬
To be honest, I still wouldn't know how to teach it today unless I just told her to "guess!" And when it comes to math, I refuse to resort to that.

It goes like this:

Claire and Sarah picked 20 strawberries.
Sarah says, "If you give me two strawberries, we will both have the same amount."
How many strawberries did Claire pick, and how many did Sarah pick?

The catch is that at that age, kids only know basic addition and subtraction.

It’s basically just guesswork, which is why the numbers stay small. 😁

Or they just end up drawing little strawberries instead of actually solving equations.

Betty Gray84 said:15, of course. 😬

I actually really enjoy these kinds of challenges; they prove that math doesn't have to be dry. A perfect example is the Mathematical Kangaroo competition, which focuses on genuine skill rather than just what you can memorize for a standard written exam.

For the little geniuses out there:
When Mark stands on two legs, he weighs 18 kg. How much does he weigh when he stands on just one leg?

Three passengers are waiting at the bus stop for 30 minutes. How long does a single passenger wait?

And here's one for the fourth graders.

Workers are putting up a fence along one side of a playground.
How many posts do they need to install if the fence is 30 meters long and a post must be placed every 3 meters?

The whole point isn't really about raw knowledge or following a specific formula, but rather about developing logic and that one thing which is absolutely vital to mathematics yet so frequently overlooked—the ability to visualize a problem, or essentially, translating a relatively complex scenario into a relatable, real-world situation...

Nicholas King said:It isn't idiotic to grade them—it's idiotic to grade them poorly.

If I recall correctly, first grade isn't actually "first grade"—kids at that stage are essentially going through a "pre-school transition year," where they are gradually moved from that kindergarten phase of "just playing all day" into a phase where actual learning begins. Besides, if we had school without any kind of grades, it would just feel like another year of daycare for most children (not all, obviously, but enough of them). And frankly, which of us adults takes our jobs seriously if there isn't some sort of accountability mechanism in place?

What’s truly problematic—aside from the curriculum being fundamentally misaligned—is that those first four years should be about instilling a foundation for how to approach learning... basically ensuring that even if they don't love it, they at least don't grow to hate school. As it stands now, kids are coming out of fourth grade as nothing more than a mindless heap of memorized facts—and quite often, they're functionally illiterate.

I can say with certainty that some of the questions are abnormal (for that age group).

Can you give me a few examples?

Having an engineering degree from MIT isn't a guarantee that someone can explain math to a six-year-old. No, I'm really not joking.

So, I was looking at this little math riddle earlier—you know, the kind that seems simple enough until you actually sit down to chew on it—and it’s kind of driving me a bit crazy. Here’s the setup: Sarah and Claire went out and picked a total of 20 strawberries together. Then, Sarah hands over 2 of her berries to Claire. After that little swap, they both end up with the exact same amount. I guess the question is... how many did Sarah pick originally, and how many did Claire grab? It sounds like one of those brain teasers meant to trip you up, but if you just break it down, it's actually pretty straightforward. If they ended up even after the swap, they must have had 10 each at the finish line. So, working backward from there—since Sarah gave away 2 to get to 10—she must have started with 12. That leaves Claire with 8. Just a little logic puzzle to pass the time, I suppose.

So, we were looking for the full breakdown—you know, the complete equation and the actual solution. Out of about 30 kids in the class, only one girl actually managed to crack the problem... and even then, it wasn't exactly a smooth ride. She didn't get it on the first try, and I guess you could say she needed a little bit of a nudge to get there. Just one out of thirty. It’s honestly kind of wild.

Look, we all know Claire grabbed 8 and Sarah took 12. That part is easy. But what about the actual equation? I’ll be the first to admit—it took me a minute to wrap my head around it... and if it’s giving me this much trouble, I can only imagine how much of a headache this is going to be for the kids.
Look, I’m asking you—please, just... don't go posting stuff like 12 minus 2 or 8 plus 2. Seriously. 😁

Nicholas King said:It isn't idiotic to grade them—it's idiotic to grade them poorly.

If I recall correctly, first grade isn't actually "first grade"—kids at that stage are essentially going through a "pre-school transition year," where they are gradually moved from that kindergarten phase of "just playing all day" into a phase where actual learning begins. Besides, if we had school without any kind of grades, it would just feel like another year of daycare for most children (not all, obviously, but enough of them). And frankly, which of us adults takes our jobs seriously if there isn't some sort of accountability mechanism in place?

What’s truly problematic—aside from the curriculum being fundamentally misaligned—is that those first four years should be about instilling a foundation for how to approach learning... basically ensuring that even if they don't love it, they at least don't grow to hate school. As it stands now, kids are coming out of fourth grade as nothing more than a mindless heap of memorized facts—and quite often, they're functionally illiterate.

I can say with certainty that some of the questions are abnormal (for that age group).

Can you give me a few examples?

Having an engineering degree from MIT isn't a guarantee that someone can explain math to a six-year-old. No, I'm really not joking.

I get where you're coming from. I agree—but that’s not exactly what I meant. What I was trying to get at is that this task just isn't easy for kids their age. It’s a lot to ask, especially for the ones who are a year younger—they're probably struggling way more than people realize, I guess.
By the way, back when I was at university studying math, I had this one professor—this absolute little mathematical kangaroo—who was a complete and utter lunatic. I mean, seriously... he’d hold office hours at 6:00 AM, and we'd be sitting there tackling these massive "atomic" equations at dawn. It wasn't even about learning at that point; it was just pure, unadulterated chaos. Just straight-up madness, I guess.

The task itself is fine as a logic puzzle—but honestly, any first-grade teacher expecting a kid to solve this by setting up an equation is just being ridiculous.

Nicholas King said:Mary is ten years older than Mark. I suppose you have to consider how much time actually passes—how old will she be compared to him in five years? 😬

Betty Gray84 said:15, of course. 😬

I actually really enjoy these kinds of challenges; they prove that math doesn't have to be dry. A perfect example is the Mathematical Kangaroo competition, which focuses on genuine skill rather than just what you can memorize for a standard written exam.

This was supposed to be a joke.

Nicholas King said:Actually, that's incorrect.

5.

Wait, what's the deal here? It’s the same joke, right? If I just say she won't be older, but instead they'll basically be peers... isn't that just as funny?

Can someone break this down for the rest of us? What’s the deal here... why is 15 wrong, but 5 is actually correct? 😕
Is there really any other explanation besides the fact that it was just a failed attempt at a hall?

Just kidding, Anthony, just kidding...

Of course I was joking, dear God 😁

But honestly, you make a fair point. Once you realize more than 70% of the class responds the exact same way (multiple times, no less), the joke definitely loses its charm.

It’s just like how it stops being funny when I ask how many dwarfs are in "Snow White and the 7 Dwarfs" and get any answer other than seven.

And how many minutes does "culture" actually take?

Kids—I’m convinced of this—possess more than enough cognitive capacity on their own. The real issue lies with the adults: both the teachers in the classroom and the parents at home. They seem obsessed with forcing math into rigid, predictable templates instead of... well, if parents aren't capable of doing it themselves, they probably shouldn't be doing it at home, but rather letting schools handle it—letting them actually play with logic puzzles and brain teasers instead.

They certainly do. Plus, once you get through a few of those tasks, your success rate starts to climb. You just have to stick with it.

Nicholas King said:Just kidding, Anthony, just kidding...

Betty Gray84 said:Of course I was joking, dear God 😁

But honestly, you make a fair point. Once you realize more than 70% of the class responds the exact same way (multiple times, no less), the joke definitely loses its charm.

It’s just like how it stops being funny when I ask how many dwarfs are in "Snow White and the 7 Dwarfs" and get any answer other than seven.

Look, those kids are little... if you guys managed to throw me off my game—not that I’m some genius, just a bit older than them—what chance do they have?

So, I'm starting to see that this is all coming from him. Makes you wonder about the whole situation, doesn't it?
How much older will she be in five years? Honestly, what Nicholas King said—it’s the exact same thing. I'm sorry, I didn't quite catch that. What's on your mind? True, if we’re really gonna split hairs about whether the question was clear enough.
So I figured they aren't even real math problems, just total brain teasers where every answer is somehow both right and wrong at the same time. Like, if you go with x, you're still stuck, right? 😛 It’s not just "no," it’s "y." And if you answer with "y," then... what? 😛 Nah, it’s definitely X. It’s like when you ask someone how many fingers they see and they say four—so you have to tell them, "Nope, you're seeing all five."
Not talking about test prep here—this is just for fun. Just some food for thought where there might actually be two right answers. Who knows?
Fair enough... I was wrong there, but the question itself is pretty straightforward. It literally says—how much older is she? From him..
I mean, they're just little kids, right? Only six or seven and barely even started elementary school—maybe it’s not even that big of a deal. It's just weird when you hear those kinds of answers from adults.

It’s just like when things stop being funny. Like, if I ask how many dwarfs are in Snow White and the 7 Dwarfs, and you give me any answer other than seven? Yeah, the joke's over.

Wait, how does that even work? 🤷 So, did you ever figure out how they actually get to those other numbers? Like, does anyone have a real explanation for that?
Maybe... I mean, there've gotta be way more dwarfs out there besides just the seven hanging with Snow White, right? 😁

Rachel Jones8 said:Look, those kids are little... if you guys managed to throw me off my game—not that I’m some genius, just a bit older than them—what chance do they have?

So, I'm starting to see that this is all coming from him. Makes you wonder about the whole situation, doesn't it?
How much older will she be in five years? Honestly, what Nicholas King said—it’s the exact same thing. I'm sorry, I didn't quite catch that. What's on your mind? True, if we’re really gonna split hairs about whether the question was clear enough.
So I figured they aren't even real math problems, just total brain teasers where every answer is somehow both right and wrong at the same time. Like, if you go with x, you're still stuck, right? 😛 It’s not just "no," it’s "y." And if you answer with "y," then... what? 😛 Nah, it’s definitely X. It’s like when you ask someone how many fingers they see and they say four—so you have to tell them, "Nope, you're seeing all five."
Not talking about test prep here—this is just for fun. Just some food for thought where there might actually be two right answers. Who knows?
Fair enough... I was wrong there, but the question itself is pretty straightforward. It literally says—how much older is she? From him..
I mean, they're just little kids, right? Only six or seven and barely even started elementary school—maybe it’s not even that big of a deal. It's just weird when you hear those kinds of answers from adults.

It’s just like when things stop being funny. Like, if I ask how many dwarfs are in Snow White and the 7 Dwarfs, and you give me any answer other than seven? Yeah, the joke's over.

Wait, how does that even work? 🤷 So, did you ever figure out how they actually get to those other numbers? Like, does anyone have a real explanation for that?
Maybe... I mean, there've gotta be way more dwarfs out there besides just the seven hanging with Snow White, right? 😁

Of course! The simplest explanation is that they just listed whoever they could remember. There might even be fictional dwarfs or characters from different fairy tales mixed in. 🙂

Kids will be kids, right? They just do whatever they want. 🙂

It’s honestly quite adorable when they try to explain their reasoning. 😍
The funniest part is when you ask them the title of the fairy tale they just described; they'll repeat it back to you and look genuinely baffled by the question since the answer is so obvious. 😁

What entertaining little exercises. I’m practically itching to test these out with my own little girl (who's about five and a half). It’s all about practical application, isn't it? After all, what’s the point of any of this if they don't understand how to share strawberries, or whatever else they happen to be enjoying with a friend?

I assume we aren't actually looking for complex equations here. Just hand them some buttons, some beans, maybe some nails or candies along with two dolls and ten minutes of free time. I am convinced that any child of average ability could solve these types of problems, provided they have enough motivation, naturally.

The most endearing tasks are the ones that bypass math entirely in favor of pure logic. For instance, how much older will someone be in five years 🙂?

I remember a kid—a friend of my oldest daughter back in the day—who, at just four years old, could unerringly tell you exactly how many wheels a truck or a semi-trailer had, even if he was only seeing it from the side. He’d answer with total certainty. Yet, if you asked him what 6 times 2 was, he wouldn't have the slightest clue.

Then there was the case of a boy who was stuck in the eighth grade. He struggled with the basics whenever a problem became abstract; the multiplication table was such a nightmare for him that he’d practically break into a sweat trying to figure out 7 times 8. But, interestingly enough, he was an absolute pro at converting dollars to euros (his parents ran a local grocery store where he helped out from time to time).

As for grading in general, I find it largely unnecessary, particularly during those first three grades (and honestly, even later on).
In first grade, I truly believe it can do more harm than good for a child. A single letter grade simply cannot capture the nuances of a child's progress. There are so many other ways to express growth that are far more meaningful.
Well done, you drew that quite nicely. Just add some wheels and then your car might actually drive. (I wonder, what grade would that earn?)
Yes, you answered correctly; March is essentially still a winter month—most of its days fall under winter, even if spring starts creeping in during the second half. (And what grade would that get you?)

wanderinggardener12 said:What entertaining little exercises. I’m practically itching to test these out with my own little girl (who's about five and a half). It’s all about practical application, isn't it? After all, what’s the point of any of this if they don't understand how to share strawberries, or whatever else they happen to be enjoying with a friend?

I assume we aren't actually looking for complex equations here. Just hand them some buttons, some beans, maybe some nails or candies along with two dolls and ten minutes of free time. I am convinced that any child of average ability could solve these types of problems, provided they have enough motivation, naturally.

The most endearing tasks are the ones that bypass math entirely in favor of pure logic. For instance, how much older will someone be in five years 🙂?

I remember a kid—a friend of my oldest daughter back in the day—who, at just four years old, could unerringly tell you exactly how many wheels a truck or a semi-trailer had, even if he was only seeing it from the side. He’d answer with total certainty. Yet, if you asked him what 6 times 2 was, he wouldn't have the slightest clue.

Then there was the case of a boy who was stuck in the eighth grade. He struggled with the basics whenever a problem became abstract; the multiplication table was such a nightmare for him that he’d practically break into a sweat trying to figure out 7 times 8. But, interestingly enough, he was an absolute pro at converting dollars to euros (his parents ran a local grocery store where he helped out from time to time).

As for grading in general, I find it largely unnecessary, particularly during those first three grades (and honestly, even later on).
In first grade, I truly believe it can do more harm than good for a child. A single letter grade simply cannot capture the nuances of a child's progress. There are so many other ways to express growth that are far more meaningful.
Well done, you drew that quite nicely. Just add some wheels and then your car might actually drive. (I wonder, what grade would that earn?)
Yes, you answered correctly; March is essentially still a winter month—most of its days fall under winter, even if spring starts creeping in during the second half. (And what grade would that get you?)

The example I used comes straight from an official school textbook... or rather, a workbook. In every single one of those problems, you're expected to write out the calculation or equation first, and then provide the written answer.

You're acting like it’s some kind of high-stakes crisis... honestly, this is child's play. I guess about 90% of them end up with honors... and then God help us when they actually hit the real world. Of course, all the parents will be beaming with pride. Hahaha 🤣