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No, not PEMDAS, but the idea that the order and grouping of the addends doesn't matter (i.e., the Associative Property). In any case, Nybbler's post inspired me to think more deeply about the example problem and its purpose. Exposure to the idea that taking away from one side and adding to the other side to "re-group" the addends would lead naturally into balancing equations when the students tackle Algebra.
Whether or not this technique is appropriate for the average six-year-old is another matter entirely, and it's a question best left up to child development types. I am certainly not qualified to make that determination. But I think I understand how mastering the concept illustrated in the problem would be helpful as students as tackle more difficult concepts later on in their math education.
But that is not the curriculum taught in schools.
How many parents are going to "think deeply" and teach that algebraic reasoning to 6 year olds ?
The majority of 6 year olds are not developed enough to understand that.
The slow switch to algebraic thinking starts in middle school.
And I haven't seen any research saying Paiget's theories are all wrong.
I don't understand. I thought the sample problem was an example of the current elementary math curriculum.
How many parents are going to "think deeply" and teach that algebraic reasoning to 6 year olds ?
I can't speak to that, but I did so.
The majority of 6 year olds are not developed enough to understand that.
Okay. I'll take your word for it.
The slow switch to algebraic thinking starts in middle school.
I think it starts in earnest around fifth grade where my kids go to school, at least that was my experience with my youngest, now a sixth grader.
And I haven't seen any research saying Paiget's theories are all wrong.
I understand that young children are concrete thinkers. If I had a six-year-old facing that particular problem, I would demonstrate the solution using manipulatives, i.e., put a group of fourteen coins on the table, divide them into groups of eight and six, and have them rearrange the coins until they can replicate one of the other sets of addends.
No, not PEMDAS, but the idea that the order and grouping of the addends doesn't matter (i.e., the Associative Property). In any case, Nybbler's post inspired me to think more deeply about the example problem and its purpose. Exposure to the idea that taking away from one side and adding to the other side to "re-group" the addends would lead naturally into balancing equations when the students tackle Algebra.
Whether or not this technique is appropriate for the average six-year-old is another matter entirely, and it's a question best left up to child development types. I am certainly not qualified to make that determination. But I think I understand how mastering the concept illustrated in the problem would be helpful as students as tackle more difficult concepts later on in their math education.
It isn't, hence the title of this thread. I agree learning to think this way is helpful - to a middle school student. It is not concrete enough prior to that point. They will eventually discover this system does not work for most kids and will discard it, but not before 5 to 10 years worth of kids are frustrated by it.
It isn't, hence the title of this thread. I agree learning to think this way is helpful - to a middle school student. It is not concrete enough prior to that point. They will eventually discover this system does not work for most kids and will discard it, but not before 10 years worth of kids are frustrated by it.
One Math item they moved earlier in education was division.
Students coming into 6th grade always put the big number inside the division bracket..always.
That is what they were taught.."the bigger number goes inside".
Now try to teach them fractions, decimals using division.
It's extremely hard to undo what was previously taught as what was previously taught did not leave the door open to the next level of learning.
These students did't learn to think about division and what it means. They learned "the bigger number goes inside".
I thought division was taught in elementary school, with the expectation that students had basic division mastered by fourth grade. Long division was introduced in fourth grade with mastery by fifth grade. Is that not the case any longer?
I agree that it's not intuitive. My daughter is in second grade and I am concerned about the way that math is being taught. It's hard to help her with her math homework because the way that she is taught in class is very different then the way that my husband and I learned and when she needs help she gets very frustrated and confused because she learns one way in class (overly complicated, imo) and we try to help her the way we know, at home. I also feel that some of the developmentally inappropriate concepts are too confusing for her and others in the class so she feels like she's not smart enough and is already saying that she "hates math". To me, that is concerning. A second grader should be building the basics, so that they will have a strong foundation. I often feel that the math program is causing more harm then good.
I don't think this has anything to do with friendly numbers, it looks like it comes from the school of "pre algebraic thought" (if that's what it's called), where people think its a great idea to teach the logic behind numbers early so kids will understand advanced math later on. In theory. In practice it can be quite confusing for kids especially when the teachers themselves don't really understand it and haven't had real training on how to teach it.
I THINK they are supposed to teach traditional methods then show students the other ways as alternatives, then after a while let the kid choose the method they prefer. Or something like that. A math teacher on here would know for sure.
But I do agree its a stupid way to do this.
ETA: to clarify I'm talking about the original example, not what old hag just posted. I was talking about the common core question.
It does have to do with "friendly" numbers. This is how my son's school explained the rationale in a math leaflet for parents. It was black on white.
We were also told we might want to consider leaving the math teaching/math help exclusively to the school because many of us just don't understand very well how math is now done - the "new way". We were also advised to focus more on social studies and things like that if we insist on helping the kids with their homework.
I also find the "new math" to be far more confusing then the old way. I don't think rote memorization is a good for things like learning abut history, but I do think it's very useful for learning things like addition, subtraction, multiplication, etc.
You would just kind of hope that schools would be able to distinguish between those situations where rote memorization is called for and those where it is a terrible idea.
Whoever doesn't see the difference in memorizing additions up to 20 or multiplication table vs. memorizing historical events brainlessly...should certainly not have anything to do with the process of education.
I thought division was taught in elementary school, with the expectation that students had basic division mastered by fourth grade. Long division was introduced in fourth grade with mastery by fifth grade. Is that not the case any longer?
Looks like I stand corrected.
I'm more familiar with middle and high school math.
I didn't realize that elementary is the one undergoing huge changes.
From the standards..this is what they master by 3rd grade:
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