What is the purpose of math education?

[lewelma]

I've come to believe that integrated math in 8th, 9th, and 10th grade is a better idea than siloed math by year.  (algebra, geometry, and statistics). That way you can do all the easy topics in 8th grade, leave all the hard ones until 10th grade, and have constant repetition so stuff sinks in.  It is actually a small percentage of kids that are developmentally ready for a proper course in Algebra 1 in 8th grade. This sets kids up for failure and sets teachers up for covering only the most basic drill and kill content so that most kids can pass with an A (or maybe a B lol). Bad all the way around. 

[Heartstrings]

13 minutes ago, lewelma said:

I've come to believe that integrated math in 8th, 9th, and 10th grade is a better idea than siloed math by year.  (algebra, geometry, and statistics). That way you can do all the easy topics in 8th grade, leave all the hard ones until 10th grade, and have constant repetition so stuff sinks in.  It is actually a small percentage of kids that are developmentally ready for a proper course in Algebra 1 in 8th grade. This sets kids up for failure and sets teachers up for covering only the most basic drill and kill content so that most kids can pass with an A (or maybe a B lol). Bad all the way around. 

I think that would be a much better way to do it.  Repetition is really so important. 

[Corraleno]

21 minutes ago, catz said:

This whole grade inflation trend where many kids are getting 100% on every test full of super basic problem sets is not really prepping kids for higher ed or how to really be challenged.

15 minutes ago, lewelma said:

This is what I saw with my nephew that I homeschooled by zoom during covid. He thought he was good at math because he always got top grades. But then we found out that this is only because they were teaching algebra at the most basic level, doing a 2 week unit and taking the test right after it (with no cumulative tests), and all word problems were extra credit.

My niece had straight As in Honors Alg I and Geometry in PS, and then chose to homeschool for the rest of HS, so I sent her a copy of Teaching Textbooks Alg II. She could not even get through the basic review problems at the beginning and sent it back saying the program was far too advanced for her compared to what she'd been doing in school — in honors classes!

This is the same kid whose Honors English 9 class never read a single novel or wrote anything longer than a page, and their big project was a Flat Stanley project and a PowerPoint presentation. I agree that math education in this country really sucks, but honestly so does most of secondary education for far too many students. I think smart students in wealthier areas likely have access to good teachers and challenging coursework, but there also seems to be a significant percentage of the population for whom basic literacy, along with a pathetically basic knowledge of history and science, are just as lacking as decent math education.

[Heartstrings]

This from Feb 2023 popped up on my feed, because the apps are definitely not spying on us.  I don’t remember if we talked about it here then or not.  It’s from Illinois…

 

There are 53 schools statewide where not one kid is proficient in math. The data comes straight from the Illinois State Board of Education. The failure isn't about money, either. Data from the Illinois State Board of Education shows spending at Spry was already at $20,000 per student before the pandemic.

The tables in the article show that this list includes some prep schools that are spending $50k per student. (Douglas Academy High School).   

 

 

Edited February 8 by Heartstrings

[SKL]

38 minutes ago, Corraleno said:

My niece had straight As in Honors Alg I and Geometry in PS, and then chose to homeschool for the rest of HS, so I sent her a copy of Teaching Textbooks Alg II. She could not even get through the basic review problems at the beginning and sent it back saying the program was far too advanced for her compared to what she'd been doing in school — in honors classes!

There have been several times that one of my kids was in an "honors" class while the other was in the non-honors version of the same class.  It is not unusual for the non-honors class to be ahead of the honors class in terms of material covered, and I also don't get the impression that there is more depth or better understanding in the honors classes.  My non-honors kid has had to teach the honors kid some concepts.  So I'm not really sure what's going on with that.

Well, maybe it's because they initially place only accelerated 8th graders into 9th grade honors algebra.  So maybe they are adjusting for the fact that they're teaching a younger group.

Edited February 8 by SKL

[SKL]

28 minutes ago, Heartstrings said:

This from Feb 2023 popped up on my feed, because the apps are definitely not spying on us.  I don’t remember if we talked about it here then or not.  It’s from Illinois…

 

There are 53 schools statewide where not one kid is proficient in math. The data comes straight from the Illinois State Board of Education. The failure isn't about money, either. Data from the Illinois State Board of Education shows spending at Spry was already at $20,000 per student before the pandemic.

The tables in the article show that this list includes some prep schools that are spending $50k per student. (Douglas Academy High School).  

I can't help wondering if the issue is that "proficient" is defined in an unrealistic way.

[Heartstrings]

26 minutes ago, SKL said:

I can't help wondering if the issue is that "proficient" is defined in an unrealistic way.

That might be part of it, but I’m guessing there are other schools that do have kids showing proficiency on the same scale.  To have so many schools with no kids being proficient is a huge systemic failure.  

[regentrude]

9 hours ago, lewelma said:

I've come to believe that integrated math in 8th, 9th, and 10th grade is a better idea than siloed math by year.  (algebra, geometry, and statistics). That way you can do all the easy topics in 8th grade, leave all the hard ones until 10th grade, and have constant repetition so stuff sinks in.  

Absolutely. I have never understood the silo approach in the US, not just to math, but also to sciences - it defies all pedagogical principles. 

[SKL]

8 hours ago, Heartstrings said:

That might be part of it, but I’m guessing there are other schools that do have kids showing proficiency on the same scale.  To have so many schools with no kids being proficient is a huge systemic failure.  

I hope someone is writing up the actual explanation.  It makes no sense, unless these are schools specifically for struggling students ... which seems unlikely given the number of schools.

[Heartstrings]

1 hour ago, regentrude said:

Absolutely. I have never understood the silo approach in the US, not just to math, but also to sciences - it defies all pedagogical principles. 

Which brings me to the question of "why?"  Why are we doing so many things in education so poorly?  And holding to those poor practices so stubbornly?  It's the sort of thing that breeds conspiratorial thinking because it just boggles the mind that we're simultaneously doing math, science, reading, and writing so poorly in spite of all the evidence. Who benefits from it being done so poorly and why is it allowed to continue this way? 

[ScoutTN]

11 hours ago, lewelma said:

I've come to believe that integrated math in 8th, 9th, and 10th grade is a better idea than siloed math by year.  (algebra, geometry, and statistics). That way you can do all the easy topics in 8th grade, leave all the hard ones until 10th grade, and have constant repetition so stuff sinks in.  It is actually a small percentage of kids that are developmentally ready for a proper course in Algebra 1 in 8th grade. This sets kids up for failure and sets teachers up for covering only the most basic drill and kill content so that most kids can pass with an A (or maybe a B lol). Bad all the way around. 

This model would have been SO much better for my Ds! 

[EKS]

9 hours ago, SKL said:

I can't help wondering if the issue is that "proficient" is defined in an unrealistic way.

I don't know how proficient is defined, but I do know that in general, its only kids at about the 90th percentile and above that have mastered the material taught in the previous year.  So 90th percentile on the fifth grade test means you've mastered fifth grade material.  On the other hand, 50th percentile means you've mastered third grade material.

This also goes the other way.  If you've had a young elementary school student who has gotten what seems to be a hugely inflated grade equivalent score (high school level), if you convert that score to a "mastery" score you'll find that they've mastered fourth or fifth grade material.

Testing companies caution people about over interpreting grade equivalent scores but for the wrong reason.  They say the kid isn't achieving at a high school level, but they make it seem like that is an artifact of the test.  It is not.  The kid is achieving at the level of an average high schooler.  The problem is that the average high schooler has the mastery of fifth grade material (or less).  But no one wants to admit that.

So if proficiency is defined on an absolute scale, I could definitely see how entire schools could have no student who is proficient.

If you think I'm making this up, here is a link to the most recent norms study for the MAP test:  https://teach.mapnwea.org/impl/NormsTables.pdf.  The tables start on page 17.  Note that this was done prior to the pandemic.  Things are probably worse now.

 

 

[SKL]

8 minutes ago, EKS said:

I don't know how proficient is defined, but I do know that in general, its only kids at about the 90th percentile and above that have mastered the material taught in the previous year.  So 90th percentile on the fifth grade test means you've mastered fifth grade material.  On the other hand, 50th percentile means you've mastered third grade material.

This also goes the other way.  If you've had a young elementary school student who has gotten what seems to be a hugely inflated grade equivalent score (high school level), if you convert that score to a "mastery" score you'll find that they've mastered fourth or fifth grade material.

Testing companies caution people about over interpreting grade equivalent scores but for the wrong reason.  They say the kid isn't achieving at a high school level, but they make it seem like that is an artifact of the test.  It is not.  The kid is achieving at the level of an average high schooler.  The problem is that the average high schooler has the mastery of fifth grade material (or less).  But no one wants to admit that.

So if proficiency is defined on an absolute scale, I could definitely see how entire schools could have no student who is proficient.

If you think I'm making this up, here is a link to the most recent norms study for the MAP test:  https://teach.mapnwea.org/impl/NormsTables.pdf.  The tables start on page 17.  Note that this was done prior to the pandemic.  Things are probably worse now.

Yeah it just doesn't seem helpful to ding a school for not having kids in the 90th+ %ile.

In our state, the test result levels are limited, basic, proficient, accelerated, and advanced.  The minimum algebra test score for graduation 684, compared to the "proficient" lower cutoff of 700.  (Kids who don't meet that "required for graduation" score have to keep taking the test every year until they pass, or prove their knowledge in another way as provided by the state.)

Edited February 8 by SKL

[Boymama5]

I think algebra 1 and geometry along with logic and consumer math should be required for all students. Anything above should be choice. IMO those classes would be the most beneficial in the future regardless of job choice. 

[SanDiegoMom]

11 hours ago, lewelma said:

I've come to believe that integrated math in 8th, 9th, and 10th grade is a better idea than siloed math by year.  (algebra, geometry, and statistics). That way you can do all the easy topics in 8th grade, leave all the hard ones until 10th grade, and have constant repetition so stuff sinks in.  It is actually a small percentage of kids that are developmentally ready for a proper course in Algebra 1 in 8th grade. This sets kids up for failure and sets teachers up for covering only the most basic drill and kill content so that most kids can pass with an A (or maybe a B lol). Bad all the way around. 

We have Integrated Math here in CA, but my the textbooks are so bad, so much of it is online, the lower level teachers didn’t teach a lot (especially during Covid) and my daughter struggled greatly.  My son skipped it all and had Calc in 9th grade, and his teacher apologized to the class for anyone who had to struggle through Integrated Math.  I think it’s a combination of bad materials and unprepared teachers. The jumping around REALLY confused my daughter too - she would learn a concept and practice only 1-2 problems and then it would leave it immediately.

I got her through most of AOPS intro to Alg (the first half of the book) before she went to high school.  We pared it down and kept Alcumus at easy level, but any high school math that she had already covered with AOPS she breezes through. She said it was so much clearer than what she did at school. 
 

The best teachers taught Calc, so when she got to Calc she did better too - though still she got A’s mostly because of extra credit.  But she passed the  AP exam with a four, so she’s hopefully done with math! 

[Heartstrings]

10 minutes ago, SKL said:

Yeah it just doesn't seem helpful to ding a school for not having kids in the 90th+ %ile.

In our state, the test result levels are limited, basic, proficient, accelerated, and advanced.  The minimum algebra test score for graduation 684, compared to the "proficient" lower cutoff of 700.  (Kids who don't meet that "required for graduation" score have to keep taking the test every year until they pass, or prove their knowledge in another way as provided by the state.)

I found this digging into a bit and I'm honestly more confused than ever.  The conversations around education are made purposely impossible due to not having standardized language and metrics. 

 

Illinois has decided that in order to be considered “proficient” on its statewide high school test, students will have to earn a higher score on the SAT than the one that’s correlated with college readiness.

The decision has touched a nerve in national testing debates about how states should meaningfully measure high school achievement and report it clearly to parents.

As part of its work to create an accountability system for its schools, the Illinois state board of education decided last month that students will be deemed proficient if they score 540 on each section of the SAT, the exam Illinois uses to measure high school achievement.

Each section of the college-admissions exam is scored from 200 to 800. The College Board considers students “college ready” if they score 480 in English and 530 in math. That means they have a 75 percent chance of earning a C or better in entry-level, credit-bearing college classes.

Other than influencing their chances of college admission, scores below the 540 cutoff won’t affect Illinois students, since their grades and graduation are not linked to their scores.

But Illinois schools have a lot on the line in the new plan; their students’ average SAT scores will count for 20 percent of their academic rating in the report card Illinois issues for each public school.

And early signs suggest cause for concern. In the first statewide administration of the SAT, in the spring of 2017, Illinois juniors averaged a 512 in English/language arts, so only 39.8 percent met the 540 cutoff score. In the math, their average score was 504. Only 36.4 percent met the SAT score cutoff.

[EKS]

8 minutes ago, Heartstrings said:

I found this digging into a bit and I'm honestly more confused than ever.

If we consider "proficient" to mean having mostly mastered Algebra 1 and geometry, then because the SAT really only tests those skills, with a smattering of other topics thrown in, a 540 makes sense for very basic high school proficiency.

The problem is that we need to admit that the majority of high schoolers aren't achieving at a high school level and that the solution to this problem isn't tacking on requirements at the high school level.  The solution is completely revamping how we teach K-8.

[Heartstrings]

3 minutes ago, EKS said:

If we consider "proficient" to mean having mostly mastered Algebra 1 and geometry, then because the SAT really only tests those skills, with a smattering of other topics thrown in, a 540 makes sense for very basic high school proficiency.

The problem is that we need to admit that the majority of high schoolers aren't achieving at a high school level and that the solution to this problem isn't tacking on requirements at the high school level.  The solution is completely revamping how we teach K-8.

It seems silly and arbitrary to set 540 as the standard when the creator of the test says 480 ELA and 530 math is the standard?.  Wouldn't the creator and administrator of the test know better than some people in a government office?  What's the purpose of saying that the levels set by the test creators aren't good enough when most students aren't even reaching the lower bar set by the test?  

 

[frogger]

1 hour ago, Heartstrings said:

Which brings me to the question of "why?"  Why are we doing so many things in education so poorly?  And holding to those poor practices so stubbornly?  It's the sort of thing that breeds conspiratorial thinking because it just boggles the mind that we're simultaneously doing math, science, reading, and writing so poorly in spite of all the evidence. Who benefits from it being done so poorly and why is it allowed to continue this way? 

Well, locally a lot is dictated in the political arena. For example, where I live curriculum decisions at the district level are decided on by the school board. The school board is not made up of experts but rather people who can get themselves voted in by telling voters (predominatly older since they vote in greater numbers) what they want to hear. Something like "we will take schools back to the good old days" is often popular here. Throw lawsuits in the mix, stir it up, and va-la! A mess that teachers and administrators must wade through before they even start thinking about actual teaching. 

ETA: Yes, often teachers or administrators try to get on the school board pointing to their experience but that matters less to voters than if the candidate agrees with them on stuff. 

Edited February 8 by frogger

[TravelingChris]

On 2/6/2024 at 1:07 PM, Catwoman said:

Forget about higher mathematics for a minute, because before they even get to the point of studying those subjects, I think kids need to learn a lot more basic arithmetic skills than they are apparently being taught. 

Seriously, it amazes me when I see people who can't figure out such basics as how to give change, how to calculate how much a 25% off sale would save them, or how to figure out how much the sales tax on a purchase will be. 

I'm a fan of higher math because it makes kids think. And I would disagree that people don't use basic algebra and geometry in their daily lives in everyday situations. We don't really think of it as using those skills because we're not sitting down doing formal equations, but we are still using what we learned.

I went up  through analytical geometry and a teig class in high school then did Calculus 8n first year of college. Also did 1 stat class in undergrad and more in grad school.  

There is a video going around X and probably other media too of some 9ne ask8ng what is 4x15.  None could do that and I know it may very well be selective editing, but how hard is it to ad 15"+15=30  and 30+30=60.

I never thought I would have to use trig until I wanted to build a window seat to go in an alcove.  The only reason we ever got to live in Europe was because the last officer was awful at math  ( It was an account8ng off8ce for NATO) so they decided to require PhD in math or math oriented sciences and my dh is a physicist  who had never had an accounting class or done any accounting. But it sure was easier to teach a person w very good math skills accounting than to have a person bad at math there.

Having a good command of math helps me all the time. I  definitely use algebra alot and even use calculus.

[SKL]

14 minutes ago, Heartstrings said:

It seems silly and arbitrary to set 540 as the standard when the creator of the test says 480 ELA and 530 math is the standard?.  Wouldn't the creator and administrator of the test know better than some people in a government office?  What's the purpose of saying that the levels set by the test creators aren't good enough when most students aren't even reaching the lower bar set by the test? 

So I think it's important that the general public understand that "proficient" in math means pretty good at math; it doesn't mean "will hopefully survive in everyday grown-up transactions."

I think people see "nobody at these schools is proficient at math" and think "nobody at these schools has the math skills to survive life."  That's just unhelpful.

[TravelingChris]

On 2/6/2024 at 1:42 PM, Heartstrings said:

Remedial classes are a joke, full stop.  There is NO effort put into them.  My kid is on his 2nd pre Calc class in a 2nd university in a 2nd state and pre Calc is taught the same way.  Here is Pearson online, good luck.  No live teacher at all. Just 100% Pearson videos with Pearson online problem sets.    Every single problem gets met with “that is the correct answer but the wrong format” and 2 different instructors now can’t tell him how to put the answers in correctly to appease the program.   At this point I’m convinced it’s on purpose because the powers that be would prefer to out source STEM so they can pay foreign workers less.  

 It’s my fault, I mistakenly assumed taking pre Calc at the college with a teacher would be better than fumbling through it with me at home.  

My dd2 took college chemistry where there was online work like you are describing. She wasted so much time w the ccomputer because  she was giving a correct answer but getting it wrong because they wanted ab extra space at the end and other completely idiotic problems. This was in her senior year and led her to pick a college that didn't rely on computer teaching and grading.

[SKL]

Along the lines of college readiness in math ... as I've said, my eldest is pretty bad at math.  She took the SAT last spring, having spent the year studying Algebra II, and her SAT math score was 480.  She took it again in August and her math score was down to 380.  Goes to show how much was actually retained.

The college she's going to does not care about her SAT math score.  They have an online entrance math test, and you have to meet certain benchmarks based on your major / school.  If you flunk it, there are some sort of practice / study aids and you can retake it as many times as you want.  I foresee my kid doing at least a couple iterations of this, which is fine.  I hope it will be a nice refresher of all the basic math skills she's supposedly been taught.  😛

[TravelingChris]

On 2/6/2024 at 2:08 PM, Heartstrings said:

My sociology degree required stats but it wasn’t the same as the stat in the math department.  It was a stats for humanity majors. 

For some odd reason, at University of Cincinnati, the criminal justice dept was in the School of Education except we took zero education classes. However a few future teachers tried our to take our stat class - they all dropped out very quickly. 

I think it is so wrong for education majors to have that as the main degree. All too many teachers don't know not only math but a lot of other subjects too.

[EKS]

32 minutes ago, Heartstrings said:

It seems silly and arbitrary to set 540 as the standard when the creator of the test says 480 ELA and 530 math is the standard?.  Wouldn't the creator and administrator of the test know better than some people in a government office?  What's the purpose of saying that the levels set by the test creators aren't good enough when most students aren't even reaching the lower bar set by the test?  

Note that a score of 480/530 requires that the student get only half of the questions right.   Perhaps college readiness isn't what it used to be.

21 minutes ago, SKL said:

I think people see "nobody at these schools is proficient at math" and think "nobody at these schools has the math skills to survive life."  That's just unhelpful.

This is true.  Again, the average person tops out at 5th grade math.  Basic fractions and decimals.  Note that half of the population is below average.

[Heartstrings]

31 minutes ago, SKL said:

So I think it's important that the general public understand that "proficient" in math means pretty good at math; it doesn't mean "will hopefully survive in everyday grown-up transactions."

I think people see "nobody at these schools is proficient at math" and think "nobody at these schools has the math skills to survive life."  That's just unhelpful.

I think I thought of "proficient" in terms of the Nations Report card use of basic, proficient, and  advanced, with proficient meaning roughly mastery of grade level expectations and skills.  If 0 kids have mastered grade level skills then something has gone wrong somewhere.   Maybe that's in the expectations, or the teaching methods, or parenting, I don't know.  But something has gone wrong. 

 

https://nces.ed.gov/nationsreportcard/ndehelp/webhelp/achievement_levels.htm#:~:text=Basic—This level denotes partial,performance for each grade assessed.

The policy definitions of the levels are:

• Basic—This level denotes partial mastery of prerequisite knowledge and skills that are fundamental for proficient work at each grade.

• Proficient—This level represents solid academic performance for each grade assessed. Students reaching this level have demonstrated competency over challenging subject matter, including subject-matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to the subject matter.

• Advanced—This higher level signifies superior performance.

Edited February 8 by Heartstrings

[EKS]

Here is an example of a fifth grade test: https://www.nysedregents.org/ei/math/2022/english/2022-released-items-math-g5.pdf

Everyone here must know adults, college educated adults at that, who would have trouble with this exam.

[prairiewindmomma]

1 hour ago, SKL said:

So I think it's important that the general public understand that "proficient" in math means pretty good at math; it doesn't mean "will hopefully survive in everyday grown-up transactions."

I think people see "nobody at these schools is proficient at math" and think "nobody at these schools has the math skills to survive life."  That's just unhelpful.

Look at the PIACC tests—the international ones that OECD does to test adult functional literacy and numeracy scores. Arguably based on those we have a lot of citizens without the math skills to survive life. 

[Heartstrings]

16 minutes ago, prairiewindmomma said:

Look at the PIACC tests—the international ones that OECD does to test adult functional literacy and numeracy scores. Arguably based on those we have a lot of citizens without the math skills to survive life. 

I've been watching discourse online about whether or not buying in bulk saves money and it struck me partway through that the problem was no one was calculating unit prices. I'm not sure most of them knew it was possible to know mathematically at all, all of the talk was about whether it feels like saving money or not.  This is even more crazy when you think about it, because doing the math yourself isn't even necessary because most items are displayed with the unit price visible  (including online in the apps) so it's really just directly comparing 2 prices, is 15 cents per ounce more or less than 23 cents per ounce.  

Edited February 8 by Heartstrings

[prairiewindmomma]

Yup, Heartstrings. That’s a late 4th grade word problem IRL. 

[Brittany1116]

1 hour ago, EKS said:

Note that a score of 480/530 requires that the student get only half of the questions right.   Perhaps college readiness isn't what it used to be.

This is true.  Again, the average person tops out at 5th grade math.  Basic fractions and decimals.  Note that half of the population is below average.

This also made me think this:

Not everyone who gets a degree does so with flying colors. Many will barely pass. They represent a large percentage of the population/work force as well. 

Goes back to the high achievers don't realize their experience isn't everyone's, I guess. 

Edited February 8 by Brittany1116
Typo

[SKL]

Yeah, funny (?) memory - when I was in law school (selective school), in corporate tax class iirc, the teacher used an example that involved 25% of 400.  I don't know how many of my classmates couldn't tell you, without serious computation, that that meant 100.  I think that was the first time I realized that people with above average intelligence could be entirely clueless about math concepts.

It hadn't been long since I'd decided to see if my then-7yo sister understood fractions at all.  I asked her something like 3 x 1/4, and her answer was, "that would be 75%."  (She was a public school student and I have no idea where she learned this.)  So yeah ... math wiring is a thing.  We can work with it, but we can't pretend it away.

[EKS]

I took the GRE about 5 years ago.  The math is easier than the math on the SAT. 

That should tell you something about grad school bound college graduates and math.

[Heartstrings]

20 minutes ago, EKS said:

I took the GRE about 5 years ago.  The math is easier than the math on the SAT. 

That should tell you something about grad school bound college graduates and math.

I took one of the Praxis tests that elementary teachers take when I was an education major and I'm pretty sure my 6th-grade niece would pass with no problem.  I was shocked to hear so many people complain about how hard it was to pass and how they had to have multiple attempts.  

[SKL]

1 hour ago, EKS said:

I took the GRE about 5 years ago.  The math is easier than the math on the SAT. 

That should tell you something about grad school bound college graduates and math.

I think the same could be said of the math on the GMAT.  I don't recall there being anything beyond geometric formulas (such as finding the volume of a cone).

As for the LSAT, there was zero math per se, but there were some interesting logic puzzles.

Edited February 8 by SKL

[Clarita]

1 hour ago, EKS said:

I took the GRE about 5 years ago.  The math is easier than the math on the SAT. 

That should tell you something about grad school bound college graduates and math.

That's a known thing. I had to take the GRE for admissions to go for my MSEE. I was also told they basically don't look at the score aside from making sure it wasn't ridiculously low. Since the math was much easier than the SATs since most people taking the GREs haven't taken math since high school. 

[Faith-manor]

20 hours ago, prairiewindmomma said:

We sent my severely dyscalcic kid through statistics rather than algebra 2 for high school graduation, but this has knocked him out of some plumbing apprenticeship programs. Higher level math is needed in most of the trades.

This is something many people do not realize. A lot of this math, prior to the the 1950's or so, was most definitely handed down in practical hands-on ways from parent to child or master to apprentice. But, most kids really do not work in practical ways with their parent in trades due to modern liability issues, school days being longer, extra curricular activities, etc. Tech Center here for 10th-12th grades has been entirely dumbed down. Just terrible. There is no where near the level of work now that there was when my brother went to tech center.  Again, the major issue is that the foundation is about as useful as wood rot. 

The 1930 8th grade diploma exit exam had plenty of algebra and geometry based problems on it. Word problems. Everyday problems using practical, higher-level thinking math skills. How did all those 8th graders manage this exam if they couldn't do the work? 

I hear this same argument (nobody needs this in real life) about English. "My kid shouldn't have to write an essay, or a paper, or read a novel, or diagram a sentence in order to graduate." Okay then. Let's just openly declare a high school diploma to be nothing more than fancy toilet paper, and let kids out of school at 13 and hope their parents have half a brain and will finish educating them. Sure. You will not personally have an employer who pays you to diagram a sentence. You will most certainly have employers that will fire you when you can't find a coherent sentence with two hands and a flashlight, write a decent report outlining the data he/she needs to know in order to make important decisions, or read and understand the darn instructions for setting up the new printer. No one wants a CNA, a lab tech, a car mechanic, or anyone else working on their bodies or their expensive things that can't think logically. The methods we have at our disposal in public education for teaching logic are Math, English, and the branches of mathematics, music (which has been cut to the bone in most of the not wealthy districts), wood and metal working (which has been grossly dumbed down at tech center), high school level science (more subjects that too many people think their kids should not have to take), sewing (apparel construction and design, also gone in nearly every single district in my state), technical drawing (drafting, also gone), formal logic and philosophy (geometric proof writing with big words (😁)....what is left if we take high school mathematics out?

None of this is "You must read Hemingway and Chaucer in order to be successful" or "You must remember the quadratic equation or you will be unemployable." It is all about training brains to think and problem solve, to digest the whole yet see the parts. It is all about having enough skill that if you needed to read Shakespeare to the boss and tell him what it means, you could actually do that. It is all about IF the boss came up with a new plan in your line of work and it meant you had to learn to program a microcontroller, or whatever, you could sit down and figure it out or to take a class and pass it. It is about having a foundation strong enough that a person can learn a new skill if needed. And we are fast embarking on a downward spiral to a functionally, life-illiterate society.

As for trades, I did a quick search for several non-"college" trades programs and what is required on the licensing exams. Solar installer: Algebra2 and Geometry. Solar Technician: Algebra - Trig. Some persons indicated they even use Calc 1 on their job. Electrician: Algebra 1&2, and Geometry. Electrical Journeyman: Algebra - Trig. Cabinetry building - Algebra 1- Trig (yes, there is applied trig used). Paramedic school exam locally tests through Algebra 2 and requires two essays (I would imagine the essays are to determine if the person could actually chart, note, and report with clarity and decent sentence structure.)  Welding (welder, not a technician or robotic welding programmer) - algebra and geometry. Robotics technician (2 year certification course that is not a degree seeking program) - Algebra - Trig and also a statistics course. Since trades and public safety go hand in hand, higher level thinking about math will always be required.

Do we have a problem with how math is taught? Absolutely. Seriously, we could be getting kids excited about and embracing math if we didn't teach it in such stupid ways. Believe me, I have taken numerous teams of middle schoolers and high schoolers, young high schoolers, through Battle of the Rockets and NASA Student Launch, college level engineering competitions, and taught them to calculate the following: Barrowman's Equations (Algebra 2, and have taught kids how to do it that hadn't even had algebra 1 yet), Descent Rates, Center of Gravity, Thrust Equations, Kinetic Energy (force at landing per ft/lb), Ideal Gas Law (calculating ejection charges), Exit Rail Velocity (we didn't push them into calculus, but they definitely used algebraic skills based on an assumption of consistent acceleration), Drift Analysis, Altitude calculations (trigonometry). Though there were computer simulators that could have spit numbers out to them, we made them do it all by hand so they would understand how this data is created. Some of them got so good at it, they could do a lot of this higher level math in their heads. They also learned the Design Life Cycle and wrote the technical documentation for it, some of their documents exceeding 135 pages in length produced by 6 students half of whom were middle school age. More than one kid who entered the program told us they were "no good at math", " not smart", "can't understand hard things" and came out the other side with a whole knew outlook on their own abilities, a positive outlook.

Lest you think we had geniuses, we only had one ever whose IQ could be pegged as gifted or highly gifted. The others were just regular kids hovering around the average, not advanced, not the top 10-20% of their schools, and until they completed the program, not certain they were smart enough to do whatever their hearts' dreamed of in life. They found out they were capable of anything. Now that said, none of them had diagnosed LD's. I am talking neurotypical kids.

In terms of humanities, I can tell you that the students who thought "I sing well and play my instrument pretty decent so I am going to be a musician or music teacher because I hate math!", flunked straight out of the music major in college. Mathematics is the language of the universe, and music is the poetry of that language. Four semesters of music theory, and most music majors flunk out in year one. They don't make it past theory 2. They barely make it through theory 1. Writing a 32 measure two part invention in the style of Bach (Theory 2) or a 20 measure 12 tone row piece of music for piano (Theory 3) is NOTHING more than a brain twisting exercise in mathematical precision, and the opportunity for error is not much different than that of a calculus problem that takes an entire page,front and back, of a legal pad. You just pray the professor is having a happy go-lucky-aren't-my-students-lovely day when he/she grades it because you are so far in the weeds you need partial credit in order to not tank your GPA.

I think if we are going to talk about jobs that do not require higher order math thinking, then we need to talk about jobs that require no skill beyond 8th grade and a driver's license. Some of these jobs are vital, very vital, much needed jobs. None of these positions and the people who fulfill them should be looked down upon for doing them. But historically, no one has been willing to pay a living wage for this work. Of course that is a different problem for sure. However, if we are going to say "Hey, we will no longer require x,y,z high order thinking skills in order to graduate high school", let's at least be brutally honest with what these kids face.

We have so completely compartmentalized the subject matter of math that swaths of people do not realize they use their algebra brain very routinely at work.

I am all for the option of letting them out at 10th grade with a solid, very solid foundation and let the chips fall where they may because keeping them at that age when so reluctant to learn is making teachers crazy. But the foundation is trash at the moment so we aren't doing them any favors. I am also in favor of saying, " Hey. The journey is its own reward, and you don't have to be GOOD at all of it." But we can't just keep lowering the bar. 

And the only reason four year college is now a practical default is because the foundation sucks eggs. So we need to go back to kindergarten and start talking about math differently, teaching math differently, and work our way up. 

I am normally not a book burning kind of person, but honestly if my local school district would provide their math textbooks for K-6, I would host the weenie roast!

Wow! That was a long rant! 😂😂😂 Sorry about that.

[prairiewindmomma]

Exactly, Faith Manor. This kid needed to be in public high school, and has had excellent hands on vo tech classes but the math instruction in the district is shaky at best. We’re planning on doing some remedial math with him to get him ready for his professional coursework and exams—but, really, NO ONE should NEED remediation coming out of k-12 schools. If someone does, that is school failure. 
 

My next in line kid is getting straight high As in her math and sciences honors coursework, but her problem sets in her physics and algebra classes are far weaker than what we did with our homeschooled oldest. OTOH, she’s getting to do all kinds of hands on practical things I cant offer her from home and in the community.

For all of the time and money and energy we throw at this, we are exceptionally bad as a nation in improving. Teacher education needs to improve. We need teachers who are strong in math in elementary.

 

[SKL]

1 hour ago, Faith-manor said:

I think if we are going to talk about jobs that do not require higher order math thinking, ... Some of these jobs are vital, very vital, much needed jobs. None of these positions and the people who fulfill them should be looked down upon for doing them. But historically, no one has been willing to pay a living wage for this work. Of course that is a different problem for sure. However, if we are going to say "Hey, we will no longer require x,y,z high order thinking skills in order to graduate high school", let's at least be brutally honest with what these kids face.

Yeah all that is true whether those kids get proficient in higher math or not.

At least they can spend time practicing other things if higher math isn't going to be their future.  Writing, working, volunteering, managing money and time ....

A person can suck at math and still be a good thinker / communicator.  I think it's OK to admit that different people have different but useful talents.

Edited February 8 by SKL

[BronzeTurtle]

 

What I think happens in most places is that kids aren't ready for a couple concepts (manipulating fractions being the big, huge one, dealing with exponents is another) and instead of developing mastery and making sure the kid understands those thngs, the kid is shoved along in a pipeline and by the time they get midway through algebra they think they suck at math and hate it when really they've just never learned proper arithmetic in late grade school/early middle school.

Also if a kid doesn't master whatever a pre-algebra text their school uses and is passed regardless they will suck at math for the rest of their educational career.
 

[KungFuPanda]

On 2/7/2024 at 4:26 PM, Faith-manor said:

The number one problem with high school mathematics has nothing to do with the difficulty of high school mathematics and whether or not requirements are too difficult. It has everything to with the colossal incompetence in teaching mathematics at the elementary level, a fundamental lack of understanding of foundational principles. Most neurotypical kids would not struggle with Algebra 1 and 2 nor geometry IF the foundation has been decent, and they have a work ethic. I have spent too much time with elementary teachers who don't know what 10% of $30 is to have any faith that the issue is "are graduation requirements too hard."  Nope. They aren't though I would argue that I would prefer the foundation to be so good that we could allow students to have a vocational diploma at 16/10th grade and then options for continuing education like Tech Center full time instead of half days. 

We are being left behind in the dust by most of the industrialized world living in the age of technology. the answer is not to lower the bar. We need to fix the base.

I don’t think I know any adults, much less school teachers, who don’t know what 10% of 30 is. That seems like an extreme example. I don’t think it’s my suburban bubble because I have some serious rural connections. I absolutely believe you spent time with elementary teachers who can’t handle it, so I’m not doubting your word. I’m just stunned that this is the case. How did they get through basic freshman classes? Elementary ed requires more math than non-math secondary ed. 

[Faith-manor]

27 minutes ago, KungFuPanda said:

I don’t think I know any adults, much less school teachers, who don’t know what 10% of 30 is. That seems like an extreme example. I don’t think it’s my suburban bubble because I have some serious rural connections. I absolutely believe you spent time with elementary teachers who can’t handle it, so I’m not doubting your word. I’m just stunned that this is the case. How did they get through basic freshman classes? Elementary ed requires more math than non-math secondary ed. 

In my state, they eliminated the test of basic skills. It was considered too hard and discouraged elementary ed majors. It required a 70% in order to pass, and tested at its highest, most basic algebra 1. I gave my homeschooled not particularly mathy 7th grader the practice exam in 2010. He scored a 96%. Eliminated.

We have more than one state university with very low bars for entrance to elementary ed, and in one of those programs, the only math (so long as a 410 on SAT math or 17 ACT is achieved) require no math classes in college except to meet a single Gen Ed requirement with a class specifically for early childhood ed and elementary ed which spends a lot of time talking about making creative flashcards, and bulletin boards with math facts and symbols. Same school also had a "history through nursery rhymes" class for GEN ed history for the football team, and I won't regale you with the horrors of what that class actually was, suffice it to say that my lazy brother - a comp sci major in 1982 - petitioned to get into the class so he wouldn't have to take a real history class. He didn't get in. But his college, known locally as Crappy U, was and still is one of the top providers of new elementary ed teachers.

I am in a state that has decided that any 18 year old with a high school diploma can substitute teach, even long term subbing. Let the blind lead the blind.

Basic lifeskills math illiteracy is actually kind of normal in many of our rural schools because the pay is low. The most qualified teachers land in wealthier towns like Frankenmuth and Traverse City, Ann Arbor, West Bloomfield, etc.

But ya. The test of basic skills was too hard. 😠

When I worked in the quilt store, the lack of math skills of local elementary teachers was pretty darn appalling. I tried to explain to a 3rd grade teacher why 1/8 of a yard of fabric was 4.5" by the width of fabric. Her response was, "I never understood fractions." Well thank the universe she didn't teach 5th grade!

[regentrude]

1 hour ago, BronzeTurtle said:

Th a kid doesn't master whatever a pre-algebra text their school uses and is passed regardless they will suck at math for the rest of their educational career.

This. Passing a kid with lack of mastery on to the next math level by giving them a low grade makes zero sense because they can't possibly understand the next thing. 

The grouping by age is convenient and stupid. 

 

 

[EKS]

2 hours ago, prairiewindmomma said:

We need teachers who are strong in math in elementary.

The problem is that people majoring in elementary education are literally running away from serious study.  They are fugitives from math and science and probably everything else that requires any thought.

So given that, I think what we need are math specialists.  Just like we have art, library, and PE specialists--why I don't know, because I think that elementary ed majors could probably deal with those things.  

[Clarita]

11 minutes ago, EKS said:

The problem is that people majoring in elementary education are literally running away from serious study.  They are fugitives from math and science and probably everything else that requires any thought.

So given that, I think what we need are math specialists.  Just like we have art, library, and PE specialists--why I don't know, because I think that elementary ed majors could probably deal with those things.

The flipside of that is why would someone who is good at math and is a "math specialist" want to be a teacher considering the other jobs they could have. 

[Faith-manor]

Just now, EKS said:

The problem is that people majoring in elementary education are literally running away from serious study.  They are fugitives from math and science and probably everything else that requires any thought.

So given that, I think what we need are math specialists.  Just like we have art, library, and PE specialists--why I don't know, because I think that elementary ed majors could probably deal with those things.  

I agree with this. I really prefer subject matter experts for everything. I would rather have a childhood health and wellness expert teach PE in elementary school than the typical PE major. In many states, the El Ed major is actually two minors or "areas of emphasis", and in some colleges, El Ed majors take different classes in those minors than other students, ones that do not have skills prerequisites that must be met to get into the class. At my alma masters the freshman English literature class for El Ed was far easier than the equivalent for actual English majors. I get that they do very much need a literature for young readers class in which there is analysis of what makes good lit for young readers, what is available at that time, how to interest children in reading, what to expect at each age of development. But there is something wrong with the system when freshman English lit is considered too hard or unnecessary for El Ed majors with a Language Arts emphasis. 

A 2018 National Survey of Math and Science Educators found that only 3% of k-6 teachers had a math degree.

It is one thing for a homeschool mom to shore up her own skills and self study to prepare for the next level of math for her child, often outsourcing it to dual enrollment or tutors at the high school level if she doesn't have the confidence to tackle it. It is quite another for someone in that same skill set to be tasked with forming the foundation of mathematics in 30 students year in and year out on behalf of society and the state. The consequences are far worse in the 2nd scenario. 

I am pro teacher, all things considered. They have their backs against the wall in a system so broken it needs to be relegated to the scrap heap and start over. They get no respect, the responsibility is grave, and the pay sucks. And all of that is part and parcel of fixing the foundation. We need teacher qualifications at all ages and in all subjects to be tough and competitive, we need to then pay these experts to teach, and we need to pay them very well and respect the heck out of them until they do something that proves themselves unworthy of respect. It should be a highly esteemed profession that any proud to be "mathy" or "sciency" or "book nerd" person would not be considered "less than" to pursue.

[SKL]

11 minutes ago, regentrude said:

This. Passing a kid with lack of mastery on to the next math level by giving them a low grade makes zero sense because they can't possibly understand the next thing. 

The grouping by age is convenient and stupid.

Yeah, this is basically what I mean when I say they need to offer non-algebra math to 9th graders.

I wouldn't mind requiring algebra if it wasn't required to be taught in 9th grade (or earlier) regardless of prior math mastery.  I could see having math stragglers do 9th grade arithmetic, 10th grade consumer math, and then some mixture of algebra / geometry / stats.

I would add that kids should have access to math instruction (or at least meaningful practice) over the summer, because a lot can be lost in 2.5 months of vacation.  Like maybe a kid who doesn't really master 8th grade math should have to do a part-time math summer course, so at least they don't lose half of what they "learned" in 8th grade.

(I actually tried to sign my kids up for summer school classes at the high school, but they were only for kids who flunked during the year.)

[EKS]

31 minutes ago, regentrude said:

The grouping by age is convenient and stupid. 

Unfortunately, when you group by achievement, you will get things like 8 year olds in with 18 year olds, which is a whole nother can of worms.

[SKL]

23 minutes ago, EKS said:

The problem is that people majoring in elementary education are literally running away from serious study.  They are fugitives from math and science and probably everything else that requires any thought.

So given that, I think what we need are math specialists.  Just like we have art, library, and PE specialists--why I don't know, because I think that elementary ed majors could probably deal with those things.  

Well, maybe not at first.  I was an education major, because I actually loved academics and wanted to share that with kids.  I think that isn't unusual.  But when I realized how stifling the schools were for creative teachers (at least back then), I changed my major.  I knew I'd be frustrated on top of being poorly paid.

But, I agree that having math specialists would be a good idea.  They would have to be able to teach kids though.  I know lots of people who were born knowing math, but have no idea how to explain it to those who weren't.

[EKS]

2 minutes ago, SKL said:

Well, maybe not at first.

I think mostly at first.  You are unusual.

Edited February 9 by EKS