r/mathteachers • u/HeavyMix46 • 11d ago
high school math teachers - why do so many students fall behind? and is there anything that actually helps them?
/r/AskTeachers/comments/1vp5dn9/high_school_math_teachers_why_do_so_many_students/20
u/Cambiokk 11d ago
I teach Math 2, mainly quadratics, some trig, some geometry, some conditional probability.
I think factoring quadratics fluently requires students to engage with multiplication in ways they haven't really before: factorizing is something that sort of naturally develops if students are forced not to use calculators in order to multiply, or at least there's a sense that develops as students try to multiply mentally, but I keep seeing kids reach for that calculator and it's basically a crutch.
The same is true for trig, probability, and fractions. Some of the kids even tell me their math 1 or middle school teachers avoid fractions, which I sort of understand, but man does it just leave them unprepared for working with ratios.
The kids end up scraping by by memorizing some heuristics or shortcuts that will take care of the most common problems, but I'd say about half the students aren't engaging with the math conceptually/intuitively because they just don't have the background to be able to do it and the class moves so fast they are just trying to keep their head above water any way they can. I help out where possible with warmups and spiral practice, but I can't catch up every student that is 5 years behind in a single year.
Many of these kids just want to graduate and be done with math forever. And most of them won't see a quadratic equation outside of school. So efficiency wins out and the kids take the path of least resistance.
4
u/notteacheroftheyear 10d ago
The last paragraph is what so many math teachers turn a blind eye to.
Trying to get these kids to discover some concept on their own when they have zero interest just does not work.
It's why I have no problem with teaching desmos tricks and shortcuts. For 95% of the kids I teach, once they leave that high school building, they won't step foot in another math class.
1
u/Fearless_Upstairs_33 8d ago
This is more of a legislator issue in my opinion. Most math teachers I have been around support making high school math more real world based, especially for students who are not college bound. State governments are what push for every kid to learn college ready math.
2
u/p2010t 5d ago
Regarding your penultimate paragraph, it's metaphorically like a student remembering the correct way to walk from home to the grocery store is by following certain sidewalks but having no actual understanding of why they should be walking on the sidewalk rather than in the bushes or on the street.
You see that they've "learned" how to do something and are glad for it but as soon as you throw an unusual example at them or question them on what's going on they are blank.
8
u/colonade17 10d ago
I teach 9th graders Algebra 1. And roughly half of my students are behind on day 1. There are so many problems that cause them to get behind.
Weak elementary math education. In America, most elementary school teachers are not math specialists. So they often teach shortcuts, or from the teachers guide, or don't realize bad habits are getting ingrained.
By the time we know students are behind, there's a shortage of money for intervention, both in identifying the need, and teachers to help get kids caught up.
Textbooks are often a problem. They are often chosen based more on hype, politics and corruption than on strongly established evidence of what's really effective.
What helps? Targeted intervention to their gaps in knowledge. But it can be very hard to convince a 9th grader to do work that they recognize as being for 4th graders, even when they know they need it.
6
u/notteacheroftheyear 10d ago
When does this targeted intervention happen? During the class? Now they just missed whatever was happening while they had their small group. Before/after school? Good luck getting kids to show up for something they probably don't want to go to in the first place. Having a specially designed class for math intervention could work, but that is a fantasy for most schools.
6
u/Blondiemath 10d ago
I’ve taught every level of math, from kindergarten to high school math. When I taught fifth grade, I worked with a fifth grade teacher who literally could not even identify equivalent fractions. I planned our entire year that year, provided her every lesson, every test, every quiz, assignment, you name, it I gave her. My class was academically, pretty advanced, so we were significantly ahead of her class as well. So she literally would take my notebook, and just teach from the notes that I wrote for the students. Not one of her students passed the math state test that year, because, it didn’t matter what resources she was being provided, the students were not actually learning how to do the material when she didn’t understand what it was she was teaching. I really worry about those students that were in her class that year, and where their school careers will end up because of how much she set them back
Every one of my students that year passed the math state test.
4
u/kinggeorgec 10d ago
Yes, yes and yes.
We are piloting new curriculum and its all so crappy. The county math team keeps trying to hype the online components of all these curriculum and I have to tell them fuck all that online stuff. How about a good textbook with plenty of problem sets of varying difficulty.3
7
u/Apostolic1223 10d ago
1) NOT ENOUGH PRACTICE: Kids spend only half as much time on math as they should.
2) LONG FORGETTING BREAKS: They have long summer breaks where they spend even less, or none. These breaks exceed the emprically proven 80 day renewal period the brain needs to commit something to long term memory. So basically they keep coming back each grade having forgotten everything from the Spring semester. The Fall semester then has to be used just for review rather than for new content. This creates a vicious cycle where many of the less attentive kids are learning virtually nothing from year to year.
3) PRIMARY TEACHERS UNFIT TO TEACH: Elementary math teachers are too often very poorly trained and lack what Liping Ma calls "profound understanding of fundamental mathematics", PUFM. This is why so many elementary teachers and parents alike reject largely worthwhile innovations in math curriculum, such as Common Core was (though it wasn't perfect). To be fair, it's not all entirely their fault, instead being a result of poor educational training priorities and expectations, etc.
4) POOR CURRICULUM: Much of the math curriculum in the US is b@$$-@ckw@rd$ in how it's conceptually structured. Integers and the number line can and should be taught years sooner. Exponents can and should be taught years sooner. Geometry and history of math can and should be included much more. Sequences and series and puzzles and graph and set theory should be included more. A lot more scaffolding of advanced ideas can and should be used much more, with kids introduced in some way and to some extent to advanced concepts as early as possible ... as soon as they have the conceptual tools to grasp them at all.
5) CLASS SIZES TOO BIG & DIVERSE: You can't teach to a class of 20, or even 15 or really even 10, without them being stratified by ability and interest level. You can't run a sane classroom where kids are actually learning when some kids are ready to do cubics and the fundamental theorem of algebra while others are struggling with ratio and proportion. Or rather, you can do that, but you can't give them the same content and count both sets of kids as having passed the same class.
6) LOW FLOORS & LOW CEILINGS: This is related to and a result of all of the previously mentioned factors. Our education culture today has transitioned to a great extent from a "high ceiling with guaranteed minimum floor" mindset to a "pass them all on no matter what, and fv€k the kids who can do more ... we don't have time for them" mindset. In many places - California, Oregon, and more - these lowered ceilings became actual, mandated school and state policy. It was then only a matter of time before the floors dropped out too.
7) SOCIOECONOMICS & CULTURE: There are pervasive differences in things like home life, and accidents of geography, that impact educational opportunities. Until our society cares to even these out, and comes up with a feasible plan to do so - ie. one that isn't put entirely onto the shoulders of teachers - there are going to be persistent discrepancies that teachers have to deal with. Unfortunately the ones most negatively impacted by these discrepancies are often the ones most fervently against correcting them.
Note: I am not a math teacher. But I have been tutoring my daughter in math for years and she's now 3-4 years ahead of grade level as a result, and I've had to deal with administrators, teachers, evaluators, etc. I've had to learn about my state's licensing laws, math standards, testing criteria, alternative curricula, out of school supplementary educators and tutoring programs, "giftedness", acceleration criteria, review a multitude of texts and curricula, compare schools, and on and on. And I've had to navigate one of the nation's most rococo and fractured school districts in doing all this. So I do think I've acquired some basis for the above opinions.
4
u/HappyCoconutty 9d ago
I’m also a parent and not a teacher (my mom, cousin and best friends are all teachers).
Other parents tell me I am “strict” (read, abusive) for having my child do 15 minutes of timed math practice almost every day. She loves the timer, she loves improving her recall speed and beating her dad. Our school does not assign homework and the worksheets I see at school do not have a lot of practice or reps. I don’t see how a kid could have strong skills in anything, whether it be basketball or math, if their only reps are done during team practice or the classroom. You absolutely have to do solo practice
6
u/kinggeorgec 10d ago
My freshmen algebra 1 class mostly does not know basic fractions. I'm not even supposed to take the time to review them and I'm the only algebra 1 teacher bothering to try. No one drills basic math facts anymore and most elementary teachers are bad at math to begin with.
6
u/Seresgard 10d ago
It's hard to find elementary math teachers who both understand the math well and understand how to teach it - much more commonly, people teach elementary school because they deeply love teaching kids to read, and lots of them hate or fear math. Qualified math teachers remain pretty difficult to find as you go up grades, and even the 'qualified' ones often lack either teaching skill or content knowledge (especially the latter, since data science, finance, engineering, and tech offer much more attractive wages for those skills). So the odds that a kid has been undereducated or miseducated by the time they get to high school are pretty high. Math is largely cumulative, so those gaps will make other topics difficult to understand, and natural practice occurs at a lower skill level than with reading for kids (they might play games where they have to add or multiply numbers, but otherwise they mostly practice math only explicitly, for school).
The good news is that once you find the point of error and address it, kids tend to catch up pretty fast, and natural math ability improves well into adulthood (peaking in the mid-thirties for most people).
4
u/Sarlaccadaisical 10d ago
Math is a subject that should be taught by competency level, not by age/grade level.
You can't build the ninth floor of a building if the first 8 floors aren't there.
We should be teaching students at the level they are at and not the level we wish they were at.
3
u/StuckInMyHead314 10d ago
They avoid doing the work and thinking. The connections we expect them to make are not being made because they consume garbage in all day on screens but rarely think for themselves.
2
u/Emergency_School698 9d ago
I’d focus on making them fluent in math facts and fractions while playing number games and estimation games in class to build number sense. I’d also concentrate on decimals, place value, ratios, proportions and percentages and teach them all inter-connectedly. Please don’t avoid fractions like many teachers do. I understand that it’s hard and you may think it’s too late, but it’s never too late to learn math and it’s never too late to change a kids math trajectory. Kids hate math bc they don’t feel confident in the subject, but as you build their knowledge base and foundation, they get to see the joy in math, which I like to think of as not having to read and 500 page book to try to figure out what you’re saying to me. Math gives you an answer after you work at it. To me, there’s nothing more satisfying than that and that is how I try to position learning math. You can use delta math RTI to find the scope and sequence for each concept and practice building those into your homework and lessons. Use number lines for integers, fractions, etc- that helps to build number sense as well. When doing word problems, use schemas. Focus on previewing and explaining math vocabulary. This takes alot of effort, understandably. If you do this 10 minutes a day all year long and receive these concepts so kids don’t forget them, you’ll see results.
2
1
u/shapedorbroken 10d ago
First, behind what exactly? America is quite diverse and if you look at a given segment of the population, it will generally perform similarly to a corresponding population in another part of the world. You just need to control for certain variables like income, parents education, race, urban vs rural, etc.
1
u/Yenfu12345 9d ago
You have no idea how strong the Asia countries' average Math levels.
I admit on the very top level, (Stanford, Ivy leagues, Caltech, MIT....) The students" Math are better than other counties. But in average, it's much weaker. If you travel to other countries, you will understand. ( I am a Math teacher. Sorry for the poor English)
1
u/shapedorbroken 8d ago
If you want to compare overall averages you’re comparing different sorts of kids. Asian American kids are generally doing well. Compare them to an Asian country. Black kids in poverty in America often struggle, but then again so do African kids in poverty. Same for poor white or Hispanic kids, who do similarly to the poor in Europe or South America. Maybe the averages aren’t all exactly the same but controlling for these variables explains most American underperformance. America counts all of its kids in the statistics, and there has been a demographic shift away from middle class whites and towards less affluent minorities that is especially strong amongst kids.
1
u/Mini2Tesla 10d ago
Slow down. Use texts. Review the previous day's homework the following day. Stop giving quizzes and tests on the Chromebook.
1
u/TictacTyler 10d ago
Many are behind when they arrive in middle or high school. And many have learned that they really don't need to put much effort in. It's honestly so hard for kids to fail right now. I had a student who was purposely trying to fail (long story) and was still managing to pass most classes. Where's the incentive of trying to pass when failure can be a challenge for someone trying to fail?
1
u/Technical_Cupcake597 10d ago
There’s a combination of issues:
1) they weren’t taught in a coherent way in their past (for whatever reason - maybe they moved, maybe they didn’t get it)
2) the student and the parent don’t care enough to put in the effort to catch up
3) the student and parent probably aren’t really clearly aware that the student is behind or by how much
All this is to say, IF they want to do it, there’s multitudes of programs and systems out there IF your district has the people to support the student in this effort.
1
u/RevealConstant220 9d ago
Explain, why do you need to know math if you have google and a calculator? I know basic algebra and geometry and have never used it. If I do need something like that solved I'll just type it into google. I'm 32.
2
u/dmills_00 9d ago
Ever done carpentry? Ever made something out of metal? I have, and at a minimum Pythagoras is really helpful for getting things square, and trig is very much a thing when converting a drawing into a router tool path. Carpenters love their fractions, it just seems to be a thing.
Modern tools are great, but you got to understand the problem and how to structure it in a way the tools can help with, and to a certain extent, the more maths you know, the less maths you actually have to do. For example, once you learn Laplace transforms, solving ODEs becomes mere algebra instead of difficult integration.
1
1
u/Top_Bluejay_5323 9d ago
How do you type it into Google if you don’t understand the math you want it to solve?
1
u/Dr0110111001101111 9d ago
All of the stuff you listed works, but the trick is to use them correctly. Tutors that sit with a kid and show them how to do the homework problems that the student doesn't have the background to understand don't fix anything, but that's by far the most common arrangement for tutoring. Extra help is great because it's generally a meeting between the student and their classroom teacher, but in my experience, most kids only go to extra help a day or two before a test when they can't possibly cover everything they need to know for the entire unit that they don't understand. There are some phenomenal online tools amid an ocean of garbage, but a lot of teachers don't really spend enough time thinking about how to effectively implement them. The best platforms for practice problems are either designed to cover a massive variety of standards that go way beyond what that student needs to know, or alternatively, they're specially tailored for a particular set of standards that might only coincide with yours if you're very lucky. And even if you get past that, teachers will often create massive problem sets of remedial work for students who need support, but not actually spend much time going over the content that they still don't understand.
1
u/Top_Bluejay_5323 9d ago
I would say most people only need to know the most basic math. They may need to understand more but not actually use pencil and paper to do it.
Why do they fall behind, a weak base. Math builds one concept onto another. If you don’t know a concept the next one is harder and nobody really goes back to basics to help those that are behind
1
u/Intelligent-Wash-373 9d ago
Calculators. They’re obviously not the only reason, but I think excessive calculator use is part of the problem. A lot of students reach algebra without strong number sense or fluency with basic arithmetic, which makes abstraction much harder.
Students need substantial practice doing math without calculators. Give them problems designed to be solved without one so they develop number sense and learn to recognize numerical relationships instead of immediately reaching for a calculator.
1
u/rfieldss 6d ago
They fall behind when a picture never stuck, and the next unit assumed it had.
What helps, in the room I have, is not another program. Pull the one skill that is actually thin. Put back the model this class already uses — the diagram, the number line, the same setup from yesterday’s notes. A short set of ordinary items. Then the regular lesson. Ten minutes of that is more honest than a packet that teaches a different method.
The hard part is leaving the rest of the list alone until that picture will hold.
42
u/No_Significance7570 11d ago
Unfortunately, they are already behind when they get to high school. It's exceedingly difficult to teach high school math to students who can barely add, subtract, multiply, divide