"Intelligent brains take longer to solve difficult problems "
"Do intelligent people think faster?
Researchers ... made the surprising finding that participants with higher intelligence scores were only quicker when tackling simple tasks, while they took longer to solve difficult problems than subjects with lower IQ scores.
...the researchers could determine that brains with reduced synchrony between brain areas literally “jump to conclusions” when making decisions, rather than waiting until upstream brain regions could complete the processing steps needed to solve the problem.
In fact, the brain models for higher score participants also needed more time to solve challenging tasks but made fewer errors. "
Anonymous wrote:Parent here, so a different perspective... In my experience, kids who were in AAP or otherwise advanced in math in ES typically take Honors Algebra in 7th, not Math 7 Honors. Our MS has already moved to an Honors for all strategy so all 7th graders not enrolled in Algebra or a remedial course take Math 7 Honors. Based on what you've stated about your child, I assume they would be fine.
Not even close. I teach seventh grade, including AAP classes. In each AAP class each year, I have about 25-40% in Algebra I Honors, and 60-75% in Math 7 Honors. That breakdown has been pretty consistent for the past 10 years.
Across my non-AAP classes, I usually have only a handful of students in Algebra.
Anonymous wrote:Parent here, so a different perspective... In my experience, kids who were in AAP or otherwise advanced in math in ES typically take Honors Algebra in 7th, not Math 7 Honors. Our MS has already moved to an Honors for all strategy so all 7th graders not enrolled in Algebra or a remedial course take Math 7 Honors. Based on what you've stated about your child, I assume they would be fine.
AAP teacher here.
The above is absolutely incorrect. Approximately 20%-50% of my students, depending on the year, take Algebra HN in 7th grade. The others take Math 7 HN.
Different AAP teacher here. Agree. It also varies year to year. Some years more test in than others. Honestly, if the IAAT wasn’t 10 mins per section, you would see more students qualifying. I hate the Iowa because kids think they are dumb if they can’t work as fast, which is completely false.
That's a very feel-good statement but processing speed has always been considered a major component of intelligence. It is a big contributor to IQ scores. In addition, even in practice (like in a work environment), people who very quickly solve a problem or pick up new information and are able to quickly form a judgment about it are considered by others to be more intelligent. Therefore, if a student cannot solve math problems quickly, they are in fact less intelligent.
This is ridiculous. Speed does not make you more intelligent. I didn’t have to work hard at math but double checked my work and was always good at math. This is why kids think they are bad at math.
I believe the idea is that fluency in calculation and concepts is important in order to be able to succeed in High School math. I could be wrong on that.
IAAT is a lot more than just arithmetic. It's also got questions that involve reading a question and reading data from graphs. Students who skim questions and are trained in grinding out lots of easy questions quickly will do better than students who solve tricky problems and are trained to carefully read the questions and double check their work.
I have been giving the IAAT for years and have never really been surprised by a student's score. Typically, scores match what I would have recommended based on what I see in class. In general, stronger students do well, weaker students do worse.
Anonymous wrote:Parent here, so a different perspective... In my experience, kids who were in AAP or otherwise advanced in math in ES typically take Honors Algebra in 7th, not Math 7 Honors. Our MS has already moved to an Honors for all strategy so all 7th graders not enrolled in Algebra or a remedial course take Math 7 Honors. Based on what you've stated about your child, I assume they would be fine.
AAP teacher here.
The above is absolutely incorrect. Approximately 20%-50% of my students, depending on the year, take Algebra HN in 7th grade. The others take Math 7 HN.
Different AAP teacher here. Agree. It also varies year to year. Some years more test in than others. Honestly, if the IAAT wasn’t 10 mins per section, you would see more students qualifying. I hate the Iowa because kids think they are dumb if they can’t work as fast, which is completely false.
That's a very feel-good statement but processing speed has always been considered a major component of intelligence. It is a big contributor to IQ scores. In addition, even in practice (like in a work environment), people who very quickly solve a problem or pick up new information and are able to quickly form a judgment about it are considered by others to be more intelligent. Therefore, if a student cannot solve math problems quickly, they are in fact less intelligent.
This statement is completely false. Speed is an artificial construct of the standard k-12 curriculum and standardized testing, that's it. It has nothing to do with problem solving abilities and should never be used to assess intelligence. In particular, speed becomes almost meaningless at higher levels where problems are difficult enough to demand insight and ingenuity. Nobody in college, in jobs or academia, or at the IMO olympiad is complaining that they cannot do well because they are too slow. There many other contributing factors but speed is not going to be one of them. It's quite a terrible thing to test children on something as trivial as speed and then suggest that they are not smart enough because they needed a few more minutes because they were not rushing through something. We wouldn't expect our engineers, scientists, and doctors to rush through things and we certainly wouldn't want to deal with the consequences of a rushed solution, so why don't we give children enough time to think?
It's not about whether the kid is smart enough or not. It's about having sufficient fluency to handle the multistep algebra problems. I worked with some AAP students, and surprisingly many of them took forever to do something as simple as two digit multiplication. Either, they didn't have their facts memorized cold, or they were still using very inefficient algorithms. Algebra would have been torture, because every single homework set intended to take 30 minutes would have required 2 hours. The IAAT might be too fast of a test, but at least some test to ensure that the kids are sufficiently fluent and don't require inordinate amounts of time to complete their work would be appropriate.
Or they just didn't understand the concept well enough. But there are other possibilities too, perhaps they were still trying to understand the efficient algorithm because it didn't make sense to them and they didn't want to just memorize it (as instructed by their teacher), and they were comfortable still using a slower but more logical algorithm that made sense to them. For instance, it would be a very rare kid in elementary school who can show a great understanding of how the traditional long division algorithm taught in school actually works; after all almost all adults also do not understand it! But almost everyone can automatically use it... without thinking. So... does being able to do long division very quickly using the traditional algorithm mean they're ready for algebra? Not necessarily. Does it help them score well on that specific portion of that specific exam? Definitely. Does it then mean it's generally a good idea to memorize and become 'fluent' in algorithms without a good understanding? Definitely not, and here's why:
There comes a point where it will not be enough for students to just rely on speed (what many of you here are essentially calling 'fluency') with procedural steps. At some point kids will tackle problems that defy standard algorithms and where they will have to figure out what and how to use a particular tool/algorithm. They will need to slow down a little and rely on their understanding of ideas and concepts and how to put them together to solve the particular problem at hand, much like how one has to use logic and reasoning to solve a puzzle. Maybe this point comes before algebra, but for many kids (many who are 'fast' at calculations), this point tends to occur in algebra (or perhaps geometry, or later in high school). At that point slowing down and focusing on why things work they way they do is immensely helpful in improving one's ability to solve math problems.
Huh? The question isn't whether kids who are fluent with math are smarter than other kids or even are more ready for Algebra. The fluent kids might be ready for Algebra. The non-fluent kids aren't yet ready for Algebra because they still need a bit more fluency. Otherwise, their computations will take forever and they will become very frustrated. They ultimately might become better mathematicians, but they simply aren't ready *now* for that level since they lack the foundational skills.
I don't think you appreciate just how awful some of these kids are with fluency. I've encountered AAP 6th graders who were still counting on their fingers. Or ones that would need like 5 minutes to solve 6/7-3/5. It should be entirely possible to complete the SOLs in like an hour. Some kids take the entire day. Shoving them into Algebra without trying to address whatever underlying gaps in understanding or fluency would be a mistake.
You're correct in that of course there are many kids who do not understand fractions well enough, (if they did, they would know how to make a common denominator why it works, i.e equivalent fractions, etc.), and nobody is saying to rush them to algebra if they're not ready, they should certainly wait. At the same time, there are kids who might be ready from an understanding point of view, but they were close but just not at the cutoff of the test needed to place them in. Those kids could very well do quite well in algebra, but they will not be allowed to take it, because perhaps they couldn't quite calculate certain things quickly enough, or more likely they were spending a few extra minutes checking their work, etc, or just did not take any practice tests to help them move more quickly and manage their time. While being very fast at long division and multi-digit computations might be slightly helpful in learning algebra from a time spent perspective, in the end it doesn't matter that much. Here's what matters much more:
Understanding the rules of algebra and how to correctly use them to solve equations, introducing variables to solve problems with unknown quantities, understanding why the rules of algebra work the way they do (i.e interpreting the rules as keeping an equation balanced, etc), writing out steps logically and cleanly on a sheet a paper when solving multi-step algebra problems so that the critical portion of checking one's work can be done easily, understanding what an informal "proof" is (i.e a logically connected explanation) is... these and others are all critical skills to learning and understanding algebra well. None of these skills necessarily demand being very fast at doing computations. If a kid really understands fractions, really understands place value and can use it to understand multiplication, understands division as repeatedly subtracting multiples and can use their own algorithm to divide, etc... but is not very fast with calculations, it doesn't mean they will necessarily have a hard time with algebra. Maybe they'll take longer working through calculations, but as long as they understand the concepts and ideas well, they will naturally pick up speed along the way.
There is an analogy to chess, many chess players think that playing a lot of blitz (speed chess) will help improve their chess skill. But by itself it does not at all. In reality, playing lots of slow chess games (at time controls 10x or greater than speed chess) is what leads to great improvement at blitz chess. The reason is that improving at chess first and foremost requires improving one's understanding of the game, and to do that one has to think about things (especially lost games, what went wrong, how to fix mistakes, how to avoid similar mistakes in the future, etc, basically undergo the learning process). The wonderful thing is if one does this, their chess skill improves... and with it their blitz chess skill also naturally improves, even if they did not play much blitz chess. This is because speed is naturally acquired through pattern recognition, which is naturally built up from understanding of ideas and concepts.
I notice you responded to all the unsupported arguments with your own unsupported arguments, but you still have not responded to the scientific articles I cited which prove you wrong. Go figure
Randomly googled internet links don't really warrant anything here because they are not important, but I can certainly respond if you would like to share some coherent thoughts of your own I think my point stands that attributing speed to having great intelligence is quite silly. It's even more dangerous and detrimental to instill/suggest that idea to your child, as it will likely be detrimental to their growth if they believe that they cannot accomplish things if they are not fast enough.
You're setting up a straw man argument. I didn't say speed = intelligence. I said it's correlated. And that point is absolutely 100% true.
Here's the concluding sentence of your original claim, which is definitely disinformation: "Therefore, if a student cannot solve math problems quickly, they are in fact less intelligent." You're clearly implying causality here and that's just silly. There are many kids who enjoy thinking about things more deeply, are you saying they're less intelligent? There are many adults who like to consider things before they pass judgement or make assumptions, they may be perceived as slow.. are they any less intelligent?
Correlation is not the same as causation, this is a key idea in statistics.
I do statistics for a living my friend. And I hate to tell you, but whether causal or not, when one thing is correlated with another, a reduction in one means a reduction in the other. That's kinda how correlations work. Okay I'm obviously arguing with someone who didn't pass the Iowa test lol
Ice cream sales are correlated with the temperature. If we stop selling ice cream, does that mean the temperature will go down?
Anonymous wrote:Parent here, so a different perspective... In my experience, kids who were in AAP or otherwise advanced in math in ES typically take Honors Algebra in 7th, not Math 7 Honors. Our MS has already moved to an Honors for all strategy so all 7th graders not enrolled in Algebra or a remedial course take Math 7 Honors. Based on what you've stated about your child, I assume they would be fine.
Very few kids from our small AAP center go into Algebra for 7th.
I am hoping some middle school math teachers can weigh in - what has the experience been like for students who were not in FCPS advanced math at their elementary school but then elected to take Math 7 honors? (I am assuming you can tell/review what math the student completed in 6th grade?)
Will a student not be successful if they weren’t in Advanced Math during ES, especially during 6th grade?
Would a student who has had consistently strong scores on tests, 4s on report cards, 475 or higher on SOLs for “gen ed” math struggle?
Any insight would be appreciated.
I’m not a teacher, but my DS took Math 7 HN in 7th grade while not taking advanced math in 6th and did well! If your student can grasp concepts fairly well, then they will be fine.
Anonymous wrote:(though M7H generally leads to algebra honors and M7 to algebra)
If M6H is M7, and M7 usually leads to non-honors algebra, why is honors algebra the standard course after M6H?
There is no option for 7th graders to take standard algebra. Whoever makes the rules for FCPS decided many years ago that if you are advanced enough to take 7th grade algebra it should be honors, else you should take prealgebra to shore up foundations first.
Anonymous wrote:Parent here, so a different perspective... In my experience, kids who were in AAP or otherwise advanced in math in ES typically take Honors Algebra in 7th, not Math 7 Honors. Our MS has already moved to an Honors for all strategy so all 7th graders not enrolled in Algebra or a remedial course take Math 7 Honors. Based on what you've stated about your child, I assume they would be fine.
AAP teacher here.
The above is absolutely incorrect. Approximately 20%-50% of my students, depending on the year, take Algebra HN in 7th grade. The others take Math 7 HN.
Different AAP teacher here. Agree. It also varies year to year. Some years more test in than others. Honestly, if the IAAT wasn’t 10 mins per section, you would see more students qualifying. I hate the Iowa because kids think they are dumb if they can’t work as fast, which is completely false.
That's a very feel-good statement but processing speed has always been considered a major component of intelligence. It is a big contributor to IQ scores. In addition, even in practice (like in a work environment), people who very quickly solve a problem or pick up new information and are able to quickly form a judgment about it are considered by others to be more intelligent. Therefore, if a student cannot solve math problems quickly, they are in fact less intelligent.
This statement is completely false. Speed is an artificial construct of the standard k-12 curriculum and standardized testing, that's it. It has nothing to do with problem solving abilities and should never be used to assess intelligence. In particular, speed becomes almost meaningless at higher levels where problems are difficult enough to demand insight and ingenuity. Nobody in college, in jobs or academia, or at the IMO olympiad is complaining that they cannot do well because they are too slow. There many other contributing factors but speed is not going to be one of them. It's quite a terrible thing to test children on something as trivial as speed and then suggest that they are not smart enough because they needed a few more minutes because they were not rushing through something. We wouldn't expect our engineers, scientists, and doctors to rush through things and we certainly wouldn't want to deal with the consequences of a rushed solution, so why don't we give children enough time to think?
It's not about whether the kid is smart enough or not. It's about having sufficient fluency to handle the multistep algebra problems. I worked with some AAP students, and surprisingly many of them took forever to do something as simple as two digit multiplication. Either, they didn't have their facts memorized cold, or they were still using very inefficient algorithms. Algebra would have been torture, because every single homework set intended to take 30 minutes would have required 2 hours. The IAAT might be too fast of a test, but at least some test to ensure that the kids are sufficiently fluent and don't require inordinate amounts of time to complete their work would be appropriate.
Or they just didn't understand the concept well enough. But there are other possibilities too, perhaps they were still trying to understand the efficient algorithm because it didn't make sense to them and they didn't want to just memorize it (as instructed by their teacher), and they were comfortable still using a slower but more logical algorithm that made sense to them. For instance, it would be a very rare kid in elementary school who can show a great understanding of how the traditional long division algorithm taught in school actually works; after all almost all adults also do not understand it! But almost everyone can automatically use it... without thinking. So... does being able to do long division very quickly using the traditional algorithm mean they're ready for algebra? Not necessarily. Does it help them score well on that specific portion of that specific exam? Definitely. Does it then mean it's generally a good idea to memorize and become 'fluent' in algorithms without a good understanding? Definitely not, and here's why:
There comes a point where it will not be enough for students to just rely on speed (what many of you here are essentially calling 'fluency') with procedural steps. At some point kids will tackle problems that defy standard algorithms and where they will have to figure out what and how to use a particular tool/algorithm. They will need to slow down a little and rely on their understanding of ideas and concepts and how to put them together to solve the particular problem at hand, much like how one has to use logic and reasoning to solve a puzzle. Maybe this point comes before algebra, but for many kids (many who are 'fast' at calculations), this point tends to occur in algebra (or perhaps geometry, or later in high school). At that point slowing down and focusing on why things work they way they do is immensely helpful in improving one's ability to solve math problems.
Huh? The question isn't whether kids who are fluent with math are smarter than other kids or even are more ready for Algebra. The fluent kids might be ready for Algebra. The non-fluent kids aren't yet ready for Algebra because they still need a bit more fluency. Otherwise, their computations will take forever and they will become very frustrated. They ultimately might become better mathematicians, but they simply aren't ready *now* for that level since they lack the foundational skills.
I don't think you appreciate just how awful some of these kids are with fluency. I've encountered AAP 6th graders who were still counting on their fingers. Or ones that would need like 5 minutes to solve 6/7-3/5. It should be entirely possible to complete the SOLs in like an hour. Some kids take the entire day. Shoving them into Algebra without trying to address whatever underlying gaps in understanding or fluency would be a mistake.
You're correct in that of course there are many kids who do not understand fractions well enough, (if they did, they would know how to make a common denominator why it works, i.e equivalent fractions, etc.), and nobody is saying to rush them to algebra if they're not ready, they should certainly wait. At the same time, there are kids who might be ready from an understanding point of view, but they were close but just not at the cutoff of the test needed to place them in. Those kids could very well do quite well in algebra, but they will not be allowed to take it, because perhaps they couldn't quite calculate certain things quickly enough, or more likely they were spending a few extra minutes checking their work, etc, or just did not take any practice tests to help them move more quickly and manage their time. While being very fast at long division and multi-digit computations might be slightly helpful in learning algebra from a time spent perspective, in the end it doesn't matter that much. Here's what matters much more:
Understanding the rules of algebra and how to correctly use them to solve equations, introducing variables to solve problems with unknown quantities, understanding why the rules of algebra work the way they do (i.e interpreting the rules as keeping an equation balanced, etc), writing out steps logically and cleanly on a sheet a paper when solving multi-step algebra problems so that the critical portion of checking one's work can be done easily, understanding what an informal "proof" is (i.e a logically connected explanation) is... these and others are all critical skills to learning and understanding algebra well. None of these skills necessarily demand being very fast at doing computations. If a kid really understands fractions, really understands place value and can use it to understand multiplication, understands division as repeatedly subtracting multiples and can use their own algorithm to divide, etc... but is not very fast with calculations, it doesn't mean they will necessarily have a hard time with algebra. Maybe they'll take longer working through calculations, but as long as they understand the concepts and ideas well, they will naturally pick up speed along the way.
There is an analogy to chess, many chess players think that playing a lot of blitz (speed chess) will help improve their chess skill. But by itself it does not at all. In reality, playing lots of slow chess games (at time controls 10x or greater than speed chess) is what leads to great improvement at blitz chess. The reason is that improving at chess first and foremost requires improving one's understanding of the game, and to do that one has to think about things (especially lost games, what went wrong, how to fix mistakes, how to avoid similar mistakes in the future, etc, basically undergo the learning process). The wonderful thing is if one does this, their chess skill improves... and with it their blitz chess skill also naturally improves, even if they did not play much blitz chess. This is because speed is naturally acquired through pattern recognition, which is naturally built up from understanding of ideas and concepts.
I notice you responded to all the unsupported arguments with your own unsupported arguments, but you still have not responded to the scientific articles I cited which prove you wrong. Go figure
Randomly googled internet links don't really warrant anything here because they are not important, but I can certainly respond if you would like to share some coherent thoughts of your own I think my point stands that attributing speed to having great intelligence is quite silly. It's even more dangerous and detrimental to instill/suggest that idea to your child, as it will likely be detrimental to their growth if they believe that they cannot accomplish things if they are not fast enough.
You're setting up a straw man argument. I didn't say speed = intelligence. I said it's correlated. And that point is absolutely 100% true.
Here's the concluding sentence of your original claim, which is definitely disinformation: "Therefore, if a student cannot solve math problems quickly, they are in fact less intelligent." You're clearly implying causality here and that's just silly. There are many kids who enjoy thinking about things more deeply, are you saying they're less intelligent? There are many adults who like to consider things before they pass judgement or make assumptions, they may be perceived as slow.. are they any less intelligent?
Correlation is not the same as causation, this is a key idea in statistics.
I do statistics for a living my friend. And I hate to tell you, but whether causal or not, when one thing is correlated with another, a reduction in one means a reduction in the other. That's kinda how correlations work. Okay I'm obviously arguing with someone who didn't pass the Iowa test lol
Ice cream sales are correlated with the temperature. If we stop selling ice cream, does that mean the temperature will go down?
Anonymous wrote:Parent here, so a different perspective... In my experience, kids who were in AAP or otherwise advanced in math in ES typically take Honors Algebra in 7th, not Math 7 Honors. Our MS has already moved to an Honors for all strategy so all 7th graders not enrolled in Algebra or a remedial course take Math 7 Honors. Based on what you've stated about your child, I assume they would be fine.
Not even close. I teach seventh grade, including AAP classes. In each AAP class each year, I have about 25-40% in Algebra I Honors, and 60-75% in Math 7 Honors. That breakdown has been pretty consistent for the past 10 years.
Across my non-AAP classes, I usually have only a handful of students in Algebra.
I teach AAP 6th and this matches what I see. I usually have 6-10 kids (depending on the year) test in. Some test in and decide to take Pre Algebra instead.
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I think my point stands that attributing speed to having great intelligence is quite silly. It's even more dangerous and detrimental to instill/suggest that idea to your child, as it will likely be detrimental to their growth if they believe that they cannot accomplish things if they are not fast enough.