Is high school-level math really important?

JoyInTheMorning

Mon, Oct 28 2019, 8:49 pm

amother [ OP ] wrote:

Again, there were much nicer ways of saying that.

In fact, I have tried to do the opposite and really believed that growth mindset would help. I don't see a growth mindset helping much when trying to help someone on 3rd or 4th grade level acquire math skills. There's a reason that the attrition rate among math teachers in my school is very high. Obviously that's an issue with the school and not math.

The growth mindset can help only so much. You're not going to get someone who can't dance the hora to become a ballet dancer in six months. You're not going to be able to teach someone algebra in one year if they come into the classroom and aren't competent in fractions or decimals. I'm a strong believer in the growth mindset, but it doesn't work miracles.

Even if you were to teach middle school -- which I am not advising -- and even if you were fantastic at it, and wanted to devote your life to it, the problem is obviously systemic, and will not be solved by one great teacher. If you get your fifth graders up to speed -- which would not be easy to do if they are struggling with borrowing/regrouping, multi-digit multiplication, and long division -- and they continue getting mediocre math education for the next three years, your efforts will most dissipate by the time your students enter high school.

I do know that I was appalled at the math education that my kids got in both elementary school and middle school. (I temporarily transformed myself into a drill sergeant to make sure they learned the basics.) I don't know what has gone so wrong. "New math" was a thing when I was a kid, but somehow we learned the basics. There's a de-emphasis now of learning basic skills in an algorithmically sound (even if non-creative) way and of drill. I think those two contribute to kids just not learning what they need to know to be comfortable doing math.

amother

Mon, Oct 28 2019, 9:22 pm

JoyInTheMorning wrote:

I should show this post to my co-teacher. At least 75% of my students cannot handle fractions and decimals at all.

I guess I am turned off teaching math because of my specific circumstances, but with no options to improve it in a way that makes sense for me, I am going to try a different field that I think I may enjoy more.

nicole81

Mon, Oct 28 2019, 10:27 pm

amother [ OP ] wrote:

You recommend homogeneous or heterogeneous ability groups?

One of the issues I have as an educator is that none of the administrators I have ever encountered truly understand that math is different than other disciplines, or that math education in high school is different than math education elementary and middle school. It seems that you are, but most admins are not and push an agenda in math that makes no sense.

What do you mean by differentiated? I find that many of the methods of differentiation are wonderful and la-di-da during class, but have little impact on how the students actually absorb the material.

That last paragraph- let me amend what I wrote before- sounds exactly like my administrators when they push AP for all. Really? Because research shows that people who take an AP tend to graduate college, so now everyone should take an AP? In my school, we have students who couldn't pass the Geometry Regents taking AP Statistics. If you push enough students like that to take APs, the research will start changing.

But oh, I forgot. Then the DOE will fabricate or skew their own research to suit their agenda. Like playing with the math Regents curve so that a 33% content knowledge gets you a 65 but an 80% content knowledge gets you an 82.

I recommend homogeneous groups; I edited my original post. It's near impossible to make a dent in the achievement gap with heterogeneous math level groupings.

Quick and easy ways to differentiate are giving students choices of problems to work on, giving students who need a clear list of steps and/or a checklist, giving an example worked through as a personal model, giving students partially completed problems with decreasing amount of scaffolding until they're on their own, linking students to a short video explanation of content that they can play and replay as they work through a problem set, providing students with graph paper for non-graph problems so visual processors and less organized students can line up their terms, providing a graph with the axis already there and labeled... and sometimes it's as simple as setting up different stations where kids are grouped according to their gaps and can drill and practice using different methods (videos, flash cards, guided demos activity, direct teacher instruction, etc).

Beyond all of this, however, the students need very regular practice with Regents questions. I've successfully worked with a bunch of kids over the years towards a growth mindset in math, but with all the years of failing, rational thought goes out the window with high stakes assessments and the anxiety kicks in. The kids need confidence, too, and working on Regents questions at least weekly from day one (ok maybe day 10) does wonders for their performance.

To be clear, the research shows that students who take an AP class and fail the exam are more likely to graduate college than students with the same academic and demographic factors that did not take an AP class. But this isn't just about AP; this is old time ed 101... The higher the standards we hold students to, the higher they will achieve. Will they all reach the bar? Of course not. But they have no chance of ever getting halfway there if the expectation is 10x lower. My school is made up of primarily level 1 and level 2 students. We started giving AP Lit a few years back and while only a couple of kids pass the exam, the class gets 100% Regents pass rates, with many scores over 80. The pass rate and average score were much lower prior to pushing the AP course. The more kids are challenged, the more likely they are to learn along the way, even if they don't meet the goals.

Ftr, because someone said administrators are out of touch because they don't teach, I teach 9th grade algebra to a mixed group of level 1-3 students, and algebra to 10th grade repeaters. Effective teaching in disadvantaged NYC schools is ridiculously hard work and takes way more planning time than the prep period given. Not everyone is cut out for it. But hey, at least we can retire at 55 😁

amother

Denim

Mon, Oct 28 2019, 10:28 pm

🤷‍♀️
I’m a pharmacist, specifically my field/specialty is infectious diseases. My job includes being on top of the ID literature and being able to analyze new antibiotics that come to market and how they compare to the older ones we already are familiar with and whether or not they are in my hospital’s and patients’ best interest to purchase and utilize. I design research protocols to add to available literature and share my findings and experiences so that others can make informed and evidence based decisions for their institutions and patients. I also model absorption and elimination of certain antibiotics to customize dosing regimens for certain antibiotics based on a specific patient’s age, weight, renal function. I am a NY state resident who took the three regent math modules as well as a year of precalc/basic calc. You bet I appreciate every bit of my HS math and wish I had a better statistics background going into my degree instead of needing to catch up to my classmates in that area.
Oh, and my husband is an actuary. Ditto.

amother

Mon, Oct 28 2019, 10:55 pm

amother [ Denim ] wrote:

Again, the need for statistics.

amother

Mon, Oct 28 2019, 11:08 pm

nicole81 wrote:

I recommend homogeneous groups; I edited my original post. It's near impossible to make a dent in the achievement gap with heterogeneous math level groupings.

Agreed, but that's not what my administrators want to see, so that's not what I can do.

nicole81 wrote:

Quick and easy ways to differentiate are giving students choices of problems to work on, giving students who need a clear list of steps and/or a checklist, giving an example worked through as a personal model, giving students partially completed problems with decreasing amount of scaffolding until they're on their own, linking students to a short video explanation of content that they can play and replay as they work through a problem set, providing students with graph paper for non-graph problems so visual processors and less organized students can line up their terms, providing a graph with the axis already there and labeled... and sometimes it's as simple as setting up different stations where kids are grouped according to their gaps and can drill and practice using different methods (videos, flash cards, guided demos activity, direct teacher instruction, etc).

We do most of this in class, but I haven't found that it makes a significant difference. Possibly because of the heterogeneous groupings. But it seems that with the scaffolds, many students can do it, but when they're on their own, they fall back. We just saw this with a quiz on writing one-variable equations to model word problems.

nicole81 wrote:

Beyond all of this, however, the students need very regular practice with Regents questions. I've successfully worked with a bunch of kids over the years towards a growth mindset in math, but with all the years of failing, rational thought goes out the window with high stakes assessments and the anxiety kicks in. The kids need confidence, too, and working on Regents questions at least weekly from day one (ok maybe day 10) does wonders for their performance.

I agree, but how do you do that when your admins want to see inquiry in math every day?

Or how do you do it without paying lip service to inquiry? Many of the Regents problems are hard by any standards. There are very few basic questions; most require 2-3+ skills, especially in Geometry and Algebra II.

nicole81 wrote:

To be clear, the research shows that students who take an AP class and fail the exam are more likely to graduate college than students with the same academic and demographic factors that did not take an AP class. But this isn't just about AP; this is old time ed 101... The higher the standards we hold students to, the higher they will achieve. Will they all reach the bar? Of course not. But they have no chance of ever getting halfway there if the expectation is 10x lower. My school is made up of primarily level 1 and level 2 students. We started giving AP Lit a few years back and while only a couple of kids pass the exam, the class gets 100% Regents pass rates, with many scores over 80. The pass rate and average score were much lower prior to pushing the AP course. The more kids are challenged, the more likely they are to learn along the way, even if they don't meet the goals.

That is fair. That was Jaime Escalante's view, as someone mentioned earlier.

nicole81 wrote:

Ftr, because someone said administrators are out of touch because they don't teach, I teach 9th grade algebra to a mixed group of level 1-3 students, and algebra to 10th grade repeaters. Effective teaching in disadvantaged NYC schools is ridiculously hard work and takes way more planning time than the prep period given. Not everyone is cut out for it. But hey, at least we can retire at 55 😁

You teach; my admins don't, and they are hopelessly out of touch. They've never taught the demographic that we attempt to teach in our school. They expect us to teach both Regents curriculum and a consortium-style, portfolio-based curriculum. We have presentations three times a year where students need to make a portfolio and defend their growth in a specific subject area, which means that we are committed to project-based learning. At the same time, our students are supposed to be getting over an 80 on the Regents. Come on.

ora_43

Tue, Oct 29 2019, 4:13 am

Thoughts in no particular order:

1. No subject is important if the students aren't listening. Literally nothing. You could have the secret to good relationships, wealth, and lifelong happiness, and it wouldn't matter if the students weren't motivated enough to take it in. Of course inspiring the class is part of teaching, but honestly, there's only so much you can do.

2. No subject is important if it's taught badly. I don't necessarily mean taught badly by you, the teacher - I mean in terms of, say, in math, teaching "to solve the problems on the test, you need to do XYZ. Now practice solving problems exactly like I showed you" vs giving students problems that allow for creativity and that challenge them.

Meaning - baby, bathwater, etc. Just because math taught badly isn't useful, doesn't mean we should do away with math. (again, not saying you personally are making the choice to teach badly, but maybe you're stuck in a system that discourages creative/interesting math).

3. Growth vs innate isn't black and white. Students' potential to learn is a very complex thing. Some parts of it are innate - ie, some people are just born way smarter, or just get a lot more math and logic in early childhood. OTOH, some parts can be taught at older ages. Both "math is mental exercise, and anyone can use it to build a strong brain" and "some people are just good at math, and others just aren't" are way too simplistic.

4. A lot of people who are "bad at math" just missed a step somewhere. I've seen this over and over again in tutoring.

5. To know a thing long-term, you have to learn more than just that thing. To really properly understand algebra, you have to put your algebra skills to use in algebra II or calculus. (This is true everywhere, not just math. If people need to know ABC, you need to teach them ABCDE. And you, the teacher, need to know at least half the alphabet.)

ora_43

Tue, Oct 29 2019, 4:21 am

SO MANY THOUGHTS

6. It's not always enough to know that things work. Look, in a lot of parts of life it's enough to know that something works, without knowing why. I have no idea how microwaves are built, but that doesn't stop me from enjoying tasty reheated coffee.

But IMO it would be a terrible idea to raise a generation of, say, engineers who can solve problems using computer programs but are completely clueless about the math those programs are based on, or social science researchers who can analyze data without understanding basic statistics, or... etc.

Understanding the concepts behind the work you do 1. makes you better at using tools effectively, 2. allows you to understand the new tools when they are introduced, and they will be introduced (this was a big issue in comp sci at one point, where I was at the time - students would leave the degree program early because they knew enough to get a job, only to find that 5-10 years down the line, they didn't have the skills to transition to the new programs being introduced), 3. is what allows us as a society to progress and build better tools. (Even if only 1 in 1,000 professionals advance the tools of their trade by understanding the science behind them, we don't know in advance who that 1 will be. We need to train hundreds of people in order to reach the one person who will have the brains, motive and opportunity to make a real difference.)

7. Making math less scary is huge in itself. Maybe your students will never need to solve a growth problem in daily life. But maybe the fact that they could, if they had to, will make them less inclined to just say "oh, I don't understand all these numbers, whatever you say" when a mortgage broker talks to them about interest rates, or to react to a lack of money at the end of the month by throwing up their hands and saying "I don't know where the money is going, I guess we just have to accept that we can't save for a house right now." And that can be life-changing.

8. High school math is important, but not all individual topics are. I do think that students need to have a basic understanding of functions, statistics, growth problems, percentages, and logic. That's all stuff that everyone uses, not necessarily directly on a conscious level, but indirectly it helps you understand all kinds of things in daily life.

That said I'd be all for leaving geometry (and geometry-related concepts in algebra II and calculus) and most of calculus for the math/science track students (who absolutely do need it, it's a crucial part of understanding differential equations, which are important to literally every field in science) and adding in more programming and data and strengthening statistics and logic.

9. We can't afford to give up on logic. Or statistics/probability. (Or history, or writing...) Yes, not all students get it. Some people take ages to understand even basic concepts. But these are the building blocks of society. Put bluntly, a stupid population is going to make stupid decisions.

(no, not understanding math doesn't make someone stupid - but if someone can't grasp the difference between correlation and causation (logic), or the fact that "it's risky" doesn't mean the results are bad every single time (statistics), people with bad intentions will find it easy to convince them of some pretty stupid things.)

ora_43

Tue, Oct 29 2019, 4:32 am

OK, one last thought, but maybe the most important:

10. Keep the individual in mind.

Sure, on a systemic level, maybe it would make more sense for non-math-inclined high school students to be doing less SAT-style math, and more math that's going to help them in daily life, or that's specifically designed to improve logical thinking and argumentation.

No arguments here.

But the individual student, or the individual class, needs to know the math on the SATs. Maybe it doesn't make sense. Maybe it's not fair. Maybe it's ultimately all part of a system that keeps the rich rich and the poor, poor. But if they don't learn the math, all that happens is that they, personally, suffer.

Sometimes the rules of the game are bad, but leaving the game entirely is worse.

Not saying that you, OP, should feel bad about leaving teaching. But teaching students to thrive in a less-than-ideal system isn't pointless.

small bean

Tue, Oct 29 2019, 11:01 am

I love math and I do use a lot of high school math and the reasoning skills. My job is in business.

I think math is extremely important. I take issue with the way it is taught as rules and not logic.

A friend of mine, recently started understanding the concept of borrowing in subtraction (1rst grade math). She never understood the concept of place value and it's ramifications.

How many kids suffer when they get to 5th grade and the concept of positive, and negative numbers are introduced. They've been working with that all their lives.

How many people dont understand the logic behind simple algebra equations

How many people don't understand what they are doing when calculating square feet, area and perimeter.

I think teaching maths logic is extremely important and makes it attainable for most people as well as gives tools to succeed in every career.

Mommyg8

Tue, Oct 29 2019, 11:27 am

small bean wrote:

These are all examples of elementary school math, not high school math. My kids learn basic algebra in elementary school. Not a high level school at all.

DrMom

Tue, Oct 29 2019, 11:50 am

small bean wrote:

It sounds like you had horrible teachers -- or teachers who were obligated to use terrible teaching methods -- if you have so many acquaintances who cannot subtract, calculate areas or perimeters, etc.

These are not exactly advanced mathematical concepts.

What's going on in our schools???

small bean

Tue, Oct 29 2019, 3:20 pm

I only mentioned one friend and we were not in school together. Also she is not dumb, it just went over her head and she followed the rules. Teachers are not explaining the logic. They are just teaching steps.

I have tutored many people in math over the years and have seen that those that struggle with high school math, it's because they didn't understand what they were doing before high school. They were subtracting following rules. They were adding following rules. They were solving equations following rules.

And my point on the low level math, was that if you missed elementary school math than you definitely can not move up as the logic builds. OP mentioned a lot of her students can't do it, the reason they can't is not because you need to be smart to do the math (I'm not a genius and have taken actuary tests, with self study and no schooling), it's because they don't understand what they are doing, and the rules are confusing. For example how many people understand why an exponent to the 0 power is 1 - ask your kids to explain it (5th grade math), if you don't understand that, how are you expected to understand further math.

In my girls school they are taught to use what they know to build the next concept on their own. My boys are taught everything is a rule and when we do homework I explain the logic behind it (they role their eyes)

DrMom

Tue, Oct 29 2019, 3:44 pm

small bean wrote:

My lessons in public elementary school always emphasized exhaustive and varied explanations of the reasoning behind rules (then again, I went to school when "new math" was in vogue). My kids' books and HW all include explanations as well, not just rules.

Is not explaining reasoning behind mathematical operations some new pedagogical fad in the US? Is this a tenet of the "Common Core" methodology (I thought it was supposed to be the opposite)?

Or is the problem poor math teaching?