We need to be teaching algebra earlier, not getting rid of it. I think introducing the idea of symbols as numbers at a younger age would go a long way to helping kids develop critical thinking skills which is one area where we are failing right now. I hate that so much of our education system right now is just memorizing facts. That's not learning. Algebra forces kids to actually think about problems, which is a critical skill in the real world.
I think they have. Our district uses a variation of singapore math and DS had "algebraic" thinking worksheets this past year. He also had logic problems that looked like LSAT logic games and he was only in 1st grade.
I taught in a 1st grade classroom (teaching reading, not math) for a few years, and I saw some of this same stuff. I was really impressed. They had the kids start out with basic addition and subtraction (those that didn't know it from Kindergarten already) and then moved to equations set up like this: 9 + ___ = 13 15 - ___ = 10
The kids had to fill in the blanks. After they got the hang of it they started to sub the ___ for an X or another letter. They have colored manipulative that the kids can use to count up or count down with to compensate for the cognitive difficulty of abstract thinking at that age, but it was very developmentally appropriate and IMO a great basis for algebra later on. When I was in school I don't think I ever even saw an equation like that until pre-algebra in the 7th grade.
Post by shouldbworkin on Jul 29, 2012 14:49:30 GMT -5
Geometry and algebra are important for how they relate to logic and critical thinking. I think that we have waited too long to teach it, until recently, and that is why there is such difficulty with adoption in later grades. It's not a question of stop teaching it, but start teaching simple algebra and geometry earlier to develop logic and critical thinking skills. They end up helping a lot with "everyday math" like personal finances and simple formulas you may need to know for your job.
I've been teaching Algebra and Geometry for twenty years. I think they are the best way to introduce reasoning and critical thinking skills. That is why students don't do well--at first. They are accustomed to regurgitating information. Ask them to solve a problem based on information they know, they sink. The first test is usually a slap in the face. Most kids I teach will rise to the occasion after that. Critical thinking, reasoning, and drawing conclusions while being able to back them up, are important skills no matter what occupation you choose. If you can't do that, how are you supposed to move ahead vs. being told what to do? When my students ask me, "when are we going to use this?" I tell them, You're not. In twenty years, no one will care if you know what an isosceles triangle is. However, you will have a boss, or will be the boss, and the ability to solve problems will be expected of you or your employees. You will need to make business decisions based on data, charts, graphs, and be able to justify your decision. THAT is what math is---puzzles that exercise/develop the logic part of the brain now.
Oh I didn't mean to imply that we should get rid of geometry. Just that I don't see it directly used as much (but then again I sucked at geometry! I remember noticing in HS that usually people excelled at one or the other but not both).
This was me. Sucked in algebra, but trig and geometry were fine. I also didn't have a great time in chemistry, but loved physics. Very odd. I don't know why that was. It could be that the equations gave me trouble, hence why chemistry wasn't my best subject.
As to the article, I don't know that Algebra should be done away with because kids have a hard time with it. I do agree with Pamela that it's like a building block.
I think the way most math is taught needs to change. As pp have mentioned, algebra and other higher level math courses are important for critical thinking, but it is my opinion that rather than requiring the memorization and regurgitation of formulas for testing purposes, achievement should be based on ones ability to understand how when and why a formula or process works.
I think the way most math is taught needs to change. As pp have mentioned, algebra and other higher level math courses are important for critical thinking, but it is my opinion that rather than requiring the memorization and regurgitation of formulas for testing purposes, achievement should be based on ones ability to understand how when and why a formula or process works.
It's funny you say this. My greatest struggle with math was understanding the why. Geometry made perfect sense but the rest of it, pfffft. My last math teacher in highschool (precalc) never ever was able to answer those questions for me, beyond "dude be ause that's what the book says."
Post by mccallister84 on Jul 30, 2012 1:40:19 GMT -5
I teach math, actually algebra, and while I agree that it has the potential to teach critical thinking skills it's not usually presented in the best way. I also agree that students would greatly benefit from a consumer math course.
I was a math major so the traditional path we offer in schools worked for me but lately there has been a big push towards focusing more on statistics. Honestly, the majority I the world does not need trig or calculus but statistics has major real world applications.
Many states are starting to introduce the common core which will integrate more stats and problem solving. It is going to be a rough transition though.
*Algebra* is too complicated and not necessary in daily life? I might argue that for calculus but not algebra (and even there I'm on the fence).
Did you notice the mortgage crisis? Or the number of people who don't understand how securitization works? Why are we considering dumbing down an already math illiterate public? Do we really think this is in our interest? Who doesn't use algebra at least a few times a month in daily life?
Even fields preferred by the math deficient are better served by an educated populace. For example, lawyers should be required to brush up on their math. People who don't understand algebra draft crappy contracts and shouldn't litigate certain cases. There is plenty of basic black letter law you learn first year in law school that would be better understood if you reduce it to an equation. It doesn't cover all the nuance, but it certainly clarifies some things.
I agree that students need the " why" answered and that is way more important than you might think. Students drop out when they realize their why's aren't answered. But give them a means to their end? They'll learn whatever you wanna teach them.
I kicked ass at Algebra. I loved it more than any other math class. I'm not a math whiz.
I don't buy this at all. I don't use Algebra much in my job, we use it some with Earned Value Management. But I use Algebra for finance stuff, buying groceries, even calculating my pace.
Algebra teaches the fundamentals of higher math and if we even want to have a chance of kids pursuing or excelling these subjects, then they need to learn it.
Maybe the answer is that we are not preparing kids for algebra properly if they aren't doing well. More problem solving/logic problems should be integrated into the earlier levels.
I haven't read all the responses cos I have little time today, but I would say the problem is much wider. Simply put, a large amount of what you learn at school is useless. We have a system that treats everyone the same way, when it is blatantly obvious that everyone is not the same. Using myself as an example, I was at best average at school. I left at 16 (thats not dropping out in the UK, its normal if you don't wish to go to college etc) and I have been self employed most of my life, and I have done well by many peoples standards. I have not used much of what I learned at school, other than the absolute basics. But thats just me. My brother is a DNA scientist, and went through all the school system until he was 26. We took radically different paths, but both did well.
I don't know the answer, but picking on algebra when pretty much any subject can be regarded as useless (depending on the individual) seems a little off.
Re-working how algebra is taught? I'm OK with that. I think there are a lot of problems with our current educational paradigm, though I am very pleased to see from this thread that there may be some moves in the right direction with young kids and math. Stopping algebra as a requirement because it is too hard for some people? Absolutely not acceptable.
I am sad that standards have been lowered across the curriculum, but I don't think a lot of people realize just how much of our economic growth in the decades following WWII was driven by technological advancements. Now, we have a culture that often doesn't respect (or at least doesn't understand) science and math, and we are paying the price in our economy and our environment.
We need to be teaching algebra earlier, not getting rid of it. I think introducing the idea of symbols as numbers at a younger age would go a long way to helping kids develop critical thinking skills which is one area where we are failing right now. I hate that so much of our education system right now is just memorizing facts. That's not learning. Algebra forces kids to actually think about problems, which is a critical skill in the real world.
This!!
My DH is constantly trying to incorporate this line of thinking into what we are teaching my girls. Granted he uses complex math at work daily so he finds it to be really important.
I'm a little confused by people that say geometry is used in daily life.
We need to be teaching algebra earlier, not getting rid of it. I think introducing the idea of symbols as numbers at a younger age would go a long way to helping kids develop critical thinking skills which is one area where we are failing right now. I hate that so much of our education system right now is just memorizing facts. That's not learning. Algebra forces kids to actually think about problems, which is a critical skill in the real world.
This!!
My DH is constantly trying to incorporate this line of thinking into what we are teaching my girls. Granted he uses complex math at work daily so he finds it to be really important.
I'm a little confused by people that say geometry is used in daily life.
I use it all the time in crafty stuff and DIY around the house stuff - but I'm not sure that my daily life is really similar to most people's daily life.
Huge dittos to teaching algebraic concepts earlier, not eliminating them. It sounds to me with the "life skills" class suggestions that people undertand how useful algebra is in real life, but are running away from the word algebra itself like it's the problem. Maybe we need to revamp HOW we teach algebra, but eliminating it is a ridiculous idea.
I have always avoided taking algebra. I took algebra 1 in HS (twice....) and then geometry. I prefer geometry. In college I had to start at the dumb dumb level of algebra and work my way up to college algebra. Once I got to that point I ended up taking ideas of mathematics which was a course in probability and very easy math. I have yet to take college algebra (out of college already) and purposely avoided any major that required it for graduation. Yes, I detest it that much. I have no clue what I'm going to do when my kid needs help with her algebra. I couldn't even help her with fractions.
Of course its important. You use almost every concept IRL, even if you don't realize you are. Are some not important? Of course...just like every subject in school. But the general concepts are.
Post by One Girl In All The World on Jul 30, 2012 10:09:49 GMT -5
Can I just say that I am sosososo happy that DH's godmother is a retired calculus teacher who runs a tutoring business (with DH's parents)? Therefore, I have someone who can help my kids with their math homework. Neither DH nor I will be able to. Unless it's geometry, I rock at geometry.
Algebra is necessary so that people know that this is not the correct way to draft a math problem:
5 + 5 + 5 - 5 + 5 + 5 - 5 + 5 x 0 =
Shpladow!!!!
On this topic, I'm a big poopyhead who can't take a joke, but seriously this answer actually annoys me more than all the "math is hard" whining that always comes out of these threads. I know, I know, you're half kidding and also your husband is supah-smart and said it, blah blah blah.
don't care. it's not wrong. it's just not. Is it confusing to people who are expecting some sort of trick or just glance at it without thinking or flat forget order of operations? maybe. But it's not wrong.
And yes, I do occasionally write things out in a similar format when I'm doing quick calcs for myself. When I flip back through my notes to check things, I'm not going to stare at that and wonder what in the world I was thinking. And neither would anybody else in my office who was trying to work from my notes. Because it's NOT wrong.
We need to be teaching algebra earlier, not getting rid of it. I think introducing the idea of symbols as numbers at a younger age would go a long way to helping kids develop critical thinking skills which is one area where we are failing right now. I hate that so much of our education system right now is just memorizing facts. That's not learning. Algebra forces kids to actually think about problems, which is a critical skill in the real world.
This!!
My DH is constantly trying to incorporate this line of thinking into what we are teaching my girls. Granted he uses complex math at work daily so he finds it to be really important. I'm a little confused by people that say geometry is used in daily life.
oh and yes, much of geometry is used in daily life.
Do most people need to know the relationship between an inscribed angle and the arc it intersects? no. But many other parts of geometry are used daily. Heck, there is a ton of geometry in parallel parking (my students do a project on that, its pretty cool)
My DH is constantly trying to incorporate this line of thinking into what we are teaching my girls. Granted he uses complex math at work daily so he finds it to be really important. I'm a little confused by people that say geometry is used in daily life.
Do you not play Angry Birds?
Nope but I also don't proof my own posts.
I really, really meant to say "I'm a little confused by people that say geometry <b>isn't</b> used in daily life." I was thinking of the stuff that Wawa mentioned (gardening, DIY, etc.) I
But many other parts of geometry are used daily. Heck, there is a ton of geometry in parallel parking (my students do a project on that, its pretty cool)
I don't know why I never thought about this connection. I'm not very good at geometry, and I'm not very good at parallel parking, either. I think my brain just doesn't work that way. My HS geometry teacher actually asked if I'd ever been tested for dyslexia because I did all my proofs backwards. This also might explain why I'm the only person in the world who finds parallel parking on the left side of the street to be easier than doing it on the right side.
On this topic, I'm a big poopyhead who can't take a joke, but seriously this answer actually annoys me more than all the "math is hard" whining that always comes out of these threads. I know, I know, you're half kidding and also your husband is supah-smart and said it, blah blah blah.
don't care. it's not wrong. it's just not. Is it confusing to people who are expecting some sort of trick or just glance at it without thinking or flat forget order of operations? maybe. But it's not wrong.
And yes, I do occasionally write things out in a similar format when I'm doing quick calcs for myself. When I flip back through my notes to check things, I'm not going to stare at that and wonder what in the world I was thinking. And neither would anybody else in my office who was trying to work from my notes. Because it's NOT wrong.
What can I say? I love the Oxford comma, double spaces after periods, commas after all dates, and neat, tidy math problems.
If I were going to be serious, though, I would say that yes we need algebra because it effectively improves one's ability to problem solve and to recognize patterns. I was not even particularly good at algebra and I see it in my every day life... well... every day. Hell, one could argue that the logic problems on the LSAT require some algebraic competence (which explains my LSAT score). I think this whole idea that you don't need to understand something because you can use a computer to get the "right" answer is bullshit (is that what the article is suggesting?). I think there are people who have trouble grasping the difference between learning and understanding. Or maybe they don't think that difference is important. I do. I think there are some dates you should know by heart and if you can't get the exact date, you should be able to at least get the right damn century; I think geometry and algebra are enormously important for actually understanding our world; and I think everyone should be able to read and write cursive even if you don't ever use it.
I realize this places me outside of today's mainstream. Whatever.
I 'll step outside with you. You have to know that the computer is doing it right. Does your formula make sense? Is the outcome logical, etc?
I didn't read all of the replies but here is a link to the new Common Core math standards. Someone mentioned that they were sick of kids just learning straight facts in math. This is far from what is happening in math education these days. As you can see, algebraic thinking is a domain in the new standards.
I linked to second grade standards, but you can look at the others as well.