The New California Math Framework: Another Step Backwards?

[gleem]

If the current changes mean my grandfather's Mathematics, then I would say, that curriculum would be forced 'tracking'.

I was only thinking of the way that math is to be taught in this framework. As I understand it tracking is de-emphasized in grades one to eight since all but a select group would have to participate in this program.

Maybe not all students will be ready for Calculus in high school. That to me does not mean that "data science" should be a replacement for Calculus. Students could still be working very hard to get through Algebra 1/Algebra 2/Geometry/Trigonometry-Mathematical Analysis.

Again as I understand it, particularly through the links to the criticism of this program since most students would participate in it, moving algebra I to first year HS would be problematic for students who are looking for a STEM career to take Calculus in HS.

Maybe I am missing the point. Could Statistics be one of the options for "College Preparatory Mathematics" courses?

I think that what some say is to forget the data science courses and let aspiring data scientists (along with STEM aspirants) take the current math sequence since how many students out of HS will be hired in this field? With regards to statistics, I think the idea is to provide a math course that can have some positive impact in the non-university bound student's personal life. ". . . how to understand the key concepts of statistics and use them in thinking statistically about whatever real-world problems you find them relevant to." This quote is from a little book by Derek Rowntree: STATISTICS WITHOUT TEARS: A Primer for the Non-Mathematicians: Allyn and Bacon (1981)

 

[Nik_2213]

I still remember my goose-bumps when our 1st-year Uni 'Stats' lecturer addressed distinction between precision and accuracy. Happens I'd sorta-appreciated it, but his examples were utterly terrifying...

Against that, I was unusual as I knew up to my '12x' tables, plus enough of 13x~~19x to get by.
Sadly, despite efforts by school and Uni, my abstracts / calculus hit low glass-ceiling, thwarting several paths...

 

[Hornbein]

I taught entry statistics at a prestigious university and thought it was a waste of the students' time. It was about memorising and executing procedures that a hand calculator can do. Interpretation of the results was neither taught nor tested.

 

[symbolipoint]

I taught entry statistics at a prestigious university and thought it was a waste of the students' time. It was about memorising and executing procedures that a hand calculator can do. Interpretation of the results was neither taught nor tested.

Even some college science courses introduce and make some use of statistics, but my feeling is that the students who study a real Statistics course, such as from their Mathematics department, are the ones who can understand Statistics better. This is mostly my opinion and maybe is not perfect.

 

[bhobba]

If I had kids, I would homeschool and, when they hit 13, start doing some of the easier subjects at the university of open learning. Here in Australia, the easiest way to homeschool is to enrol online in a cheap private school - only about 1k a year. I think the Australian Curriculum is bonkers (for example, Aboriginal perspectives must be included in every subject). Still, it won't hurt a child's development, in my opinion, so I have no issues with using it as a foundation to build on. As an online student, you can still access all the school's social stuff like excursions.

What I need clarification on is why they have these standards at all. Surely, a school, in conjunction with well-qualified teachers and parents, can design the curriculum best suited to their student base. I believe in Finland, their education department consists of a few people who ensure schools meet minimum standards in grades 3, 6 and 9. Here in Aus, grade 10 and above is 'senior school' where students decide whether to pursue a vocational education (e.g. an apprenticeship) or an academic one. There are also pathways sort of in the middle. In nursing, you attend what is called TAFE (similar to a US Community College), complete by year 12 a diploma in Nursing (similar to a US associate degree) and become an Enrolled Nurse. While an Enrolled Nurse, you attend University part-time for three years to become a Registered Nurse.

In Aus, you must complete at least Math A (US precalculus with applications like stats and personal finance) to graduate HS. Nobody seems to worry it is too hard. Grade 7 is like US pre-algebra; we combine US Algebra 1 and Geometry in grades 8 and 9. Algebra 2 is equivalent to grade 10. Combined precalculus and calculus grades 11 and 12, or just precalculus and applications grades 11 and 12. Advanced students compress 7, 8, 9 and 10 math into three years and do precalculus and calculus 10 and 11. In grade 12, they do something like linear algebra and differential equations, although I would teach Boaz.

The IB program is becoming more popular all the time.

I am still determining how much-advanced math is used, even in majors that require it. I did a double major in math and computer science, but even all computer science majors had a significant amount of advanced math (e.g. operations research and numerical analysis). I certainly didn't use any in my job. What it is good for is understanding better what I did use, e.g. the results of statistics programs I maintained and was sometimes asked to write.

I know schools like Citizens HS only require 18 credits to graduate in the US. But they have 12 dual credit college subjects (each worth 3 credits) available, so you do 6 subjects a year and graduate with 36 college credits after 3 years. Then it's off to the college of your choice, although since they don't offer Calculus, I would take calculus elsewhere eg Algebra and Geometry year 9, College Alglegra and Precalculus year 10 and Calculus 1 and 2 year year 11.
https://citizenshighschool.com/

Thanks
Bill

 

[Vanadium 50]

Australia is not the US.

One difference is immigration. Australia has 1.6x as many immigrants per capita thjan the US, but they come from a wide variety of countries. The US has more than half of their immigrants coming from Spanish-speaking nations, although this number is hard to get accurately since so much of this is illegal. One side effect is that students can spend their whole lives in the US in parts of it where English is only spoken in schools. Not at home, not in stores, just schools. This is obviously not ideal.

The total K-12 spending in the US is just under a trillion dollars. People want to see what they are getting for their money. It also tends to be paid via property taxes, so people get one bill per year, which grabs your attention more than a VAT does.

There is a great disparity in outcomes. Since it's funded by property taxes, schools in well-to-do neighborhoods have more money to spend than in less-well-off neighborhoods. The schools in the well-to-do neighborhood tend to do better than the less-well-off, and many people see this as unfair and something needing to be fixed. It is, however, not this cut and dried. There are a number of school districts that are very, very well off: towns with a lot of commercial real estate and few houses, fofr example. Some do very well, others not so much. They are certainly not universally the best.

Catholic-run schools tend to have better outcomes, despite spending less than public schools. This holds true even in schools that preferentially serve people who are not so well off.

Money is a factor, but not the only factor, and certainly not a proxy for performance. So people want to see some sort of measure.

 

[gleem]

About half of HS math teachers have a math degree in the US. Because elementary school teachers tend to teach several different subjects, there are fewer teachers with a math degree or a related one. Considering the non-academic duties of current teachers it is not surprising that there might be a need for standards for math curricula if anything to make their job easier. These standards are not a requirement and can be modified by the state.

 

[bhobba]

Catholic-run schools tend to have better outcomes, despite spending less than public schools. This holds true even in schools that preferentially serve people who are not so well off.

That is the same as Australia. The cost of attending is mostly quite cheap - about $3k (even cheaper if you attend online) - although their flagship school called the Terrace (they are on the street called Gregory Terrace), is $20k.

I always wondered why. Then I spoke to someone who attended a cheap Catholic school called Carmel College. There are no discipline problems - even the most minor infringement and you are out. A girl was sitting in her seat on the bus (she was in grade 12, and they had special seats). She asked nicely, and they refused to get up. It got more heated, and she said angrily, move your black ass. She was kicked out.

Having attended a public school, their discipline, by comparison, was non-existent. I won't regale anyone with what happened to me; I was not the only one. Suffice it to say nobody was ever expelled. In Catholic schools, you have people who want to be there and act accordingly; otherwise, bye.

Thanks
Bill

 

[bhobba]

About half of HS math teachers have a math degree in the US.

Here in Aus, in grades 7, 8, and 9, you don't need a math degree to teach math. A degree in a related area like physics or data science is fine. But once you hit 10, 11 or 12 - you need a math degree, although many have double majors in math and something else. Where I studied, you could only get a degree in math and something else, but that something else could be essentially math such as statistics or operations research. That tends to be encouraged as it makes for a more versatile teacher. There was a push a while back to have a Master's degree, but that proved too hard.

Thanks
Bill

 

[MidgetDwarf]

That is the same as Australia. The cost of attending is mostly quite cheap - about $3k (even cheaper if you attend online) - although their flagship school called the Terrace (they are on the street called Gregory Terrace), is $20k.

I always wondered why. Then I spoke to someone who attended a cheap Catholic school called Carmel College. There are no discipline problems - even the most minor infringement and you are out. A girl was sitting in her seat on the bus (she was in grade 12, and they had special seats). She asked nicely, and they refused to get up. It got more heated, and she said angrily, move your black ass. She was kicked out.

Having attended a public school, their discipline, by comparison, was non-existent. I won't regale anyone with what happened to me; I was not the only one. Suffice it to say nobody was ever expelled. In Catholic schools, you have people who want to be there and act accordingly; otherwise, bye.

Thanks
Bill

It is not because children in catholic schools do better because they want to be there. It's a combination of factors. Having worked at both a Catholic school, and a public in California. I can share a bit of light on this.

There are public schools in CA, that have a questionable policy regarding discipline. Ie., you are not allowed to send an unruly child out the classroom in some schools, Kipp schools are a prime example.

Catholic schools have a bit more flexibility in dealing with students. Schools are smaller so it is more common for administration to know the students, and interact with them frequently. They also visit mass once a week during school hours, and are constantly drilled in "morality." (We can agree or disagree if Catholic dogma is itself moral, but they get the "FEAR" of god drilled into them)

Again, since classrooms are smaller, it is easier for children to receive more individual attention. A large class size would be considered 20-24 students. I was able to lecture for 15 minutes, make students work problems on the board and give them immediate feedback, and also sit down next to every student and help them for a few minutes during class time. From this, I could gauge whether I needed to explain again, or go into more detail in tackle challenging problems. Something which was not possible at the public school due to the large class size. So students at the catholic school learned more, were better prepared for the next course, and better behaved. Because I could give them more attention.

I found it puzzling that parents at the public put a greater emphasize on academics than the private (in my experience). There was a bit of pushback at the beginning when I assigned math homework everyday. Parents were more worried about enrolling the child into extracurriculars for bragging rights among their friend group, then kids practicing and retaining the math concepts they had received. One would assume that the private school parents would value education more, since on average, they themselves were educated. The majority of my students parents had graduate degrees. Contrast that to the no diploma, or GED recipient at the public in Compton.

Returning to behavior.

Some of the private school kids were just awful in terms of having decent human decency. They would gossip constantly about each other. A behavior common in todays world, but at least the public school kids knew that this behavior could lead to physical altercations, or even worse. Ie., if you talked about Pedreto or Tyrone, you probably getting stomped out at next recess. Many other examples such as the concept of sharing was lost with the private school kids.

A select few were even allowed to do whatever they wanted, since the parents donated large sums of cash to the parish. It was not uncommon for parents to also bully the teachers.

Because the parents paying for an education, may also have the means to hire a tutor to further help a child. So a kid does not act out, because they are lost and confused. Moreover, parents talked the language or had more time to sit with them to complete work. An issue that many first generation students face, is not having the means to hire a tutor, or parents knowing English to help them.


Private schools are also more flexible in the hiring process. At least for mathematics, one could teach at a catholic school having only a BS in a stem degree. You need a teaching credential otherwise for public schools. Teaching credential cost money and time, and in some cases you work for free for 6 months. Typically takes two years, the time required for an MS, so you may end up teachers that are not competent in mathematics, and did the bare minimum to be qualified by the state of california to teach it...

 

[symbolipoint]

Private schools are also more flexible in the hiring process. At least for mathematics, one could teach at a catholic school having only a BS in a stem degree.

That goes for public schools in California, too (regarding k-12). (Or, it did, a few years ago still.)

 

[symbolipoint]

Teaching credential cost money and time, and in some cases you work for free for 6 months.

That's often called an "internship", but depending on the part of the system, teacher must do work as a teacher for some number of terms (yes, paid employed) to get past the "preliminary" credential.

 

[Vanadium 50]

The educationalists will tell you "a good teacher can teach any subject". It is possible to be certified a high school science teacher in 48 states without taking any STEM courses beyond what you needed for a degree.

A quick check of course catalogs show that one can teach high school calculus math with high school geometry and a single college class, "Mathematics for Elementary School Teachers". No advanced algebra. No trig. No calculus. Because "a good teacher can teach any subject".

(Note: I don't know that anyone has actually done this, or been hired to do this, just that it's not precluded by any rules)

 

[gleem]

The educationalists will tell you "a good teacher can teach any subject". It is possible to be certified a high school science teacher in 48 states without taking any STEM courses beyond what you needed for a degree.

"Nor does the non-expert teach the non-expert—any more than the blind can lead the blind.
Sextus Empiricus (160 – 210 CE)

 

[MidgetDwarf]

That's often called an "internship", but depending on the part of the system, teacher must do work as a teacher for some number of terms (yes, paid employed) to get past the "preliminary" credential.

Yes, I know its called an internship. But I chose to write work for free, to emphasize that you are doing the job of an actual teacher as soon as you first step into the classroom and continue to do so, and running around getting doughnuts and snacks for the workers.

 

[WWGD]

Yes, I know its called an internship. But I chose to write work for free, to emphasize that you are doing the job of an actual teacher as soon as you first step into the classroom and continue to do so, and running around getting doughnuts and snacks for the workers.

Erm, they're called " Caffeine Supply Engineers". I was one myself at one point.

 

[symbolipoint]

Yes, I know its called an internship. But I chose to write work for free, to emphasize that you are doing the job of an actual teacher as soon as you first step into the classroom and continue to do so, and running around getting doughnuts and snacks for the workers.

The intent of the internship is training. The other parts, running around getting doughnuts for workers needs to be somebody else's task; not that of the intern -- oh wait, the person who is working for free. If that part of the free worker is interfering enough with the teaching and tutorial component, then this school risks loosing this free teacher.

 

[symbolipoint]

The intent of the internship is training. The other parts, running around getting doughnuts for workers needs to be somebody else's task; not that of the intern -- oh wait, the person who is working for free. If that part of the free worker is interfering enough with the teaching and tutorial component, then this school risks loosing this free teacher.

I need to think about that response a little more carefully.
If a teacher candidate or teacher in training, is in an official internship, this person is not a chore-runner for things like running around to get coffee or doughnuts for any group of people. The intern is in a much more serious position than to do little convenience chores.

 

[MidgetDwarf]

I need to think about that response a little more carefully.
If a teacher candidate or teacher in training, is in an official internship, this person is not a chore-runner for things like running around to get coffee or doughnuts for any group of people. The intern is in a much more serious position than to do little convenience chores.

my response had a typo. There should be a not... My point still stands.

 

[MidgetDwarf]

The educationalists will tell you "a good teacher can teach any subject". It is possible to be certified a high school science teacher in 48 states without taking any STEM courses beyond what you needed for a degree.

A quick check of course catalogs show that one can teach high school calculus math with high school geometry and a single college class, "Mathematics for Elementary School Teachers". No advanced algebra. No trig. No calculus. Because "a good teacher can teach any subject".

(Note: I don't know that anyone has actually done this, or been hired to do this, just that it's not precluded by any rules)

We had a shortage of teachers due to covid, or at least California did. I do not watch the news.

Anyhow, the lady who taught arithmetic and pre-algebra at the Catholic high school I would sub for (down the street from the middle school I worked at), was forced to teach calculus due to no teacher availability. She did exactly as you described earning the minimum to teach math. In terms of teaching arithmetic and algebra, she was decent. But the calculus class was a wreck.

The school payed me half salary of what they typically pay a teacher. To act as a consultant. Ie., explain the concepts to the teacher, and help with lesson plans. It worked, not an ideal situation for the children, but they were able to get something out of it. The majority of the students got AP credit ( I hate the AP system). But I did recommend those majoring in STEM to retake Calculus the first semester of college.