No. In third grade, I teach a lot more than three ways.
Thing is, I also demonstrate to my kids that I can do three-digit subtraction in my head faster than they can with a calculator, given different numbers they throw at me, and after I get the right answer, I show them how I analyzed the problem and decided which method to do. I explicitly teach them that they want to have a lot of different methods, for several reasons:
The more methods they master, the better their numerosity–their informed intuition about how numbers work–becomes. Learn the expanded-form method, and you’ll get better about thinking about place value.
Different methods work better or worse for different students. I have some kids who adore number line subtraction, and other kids who hate it.
Different methods work better for different problems. 701-699 takes a lot longer with regrouping than with Zero is your Hero (or, if they’re not into cutesy, with benchmark multiples of ten and 100).
Last and definitely least, they’re gonna be on the test. If they decide not to learn how to subtract in parts, they’re gonna miss a question or two on the EOG, and even though I think it’s a terrible way to test math knowledge, it’s not my choice.
Being able to approach a problem from a lot of angles is useful.
I agree, that’s a good thing. But when these threads or news articles come up, it seems like teachers are only teaching the new way and that’s it.
I only learned one way when I was in school, and it seemed to work pretty well.
If you are teaching several different ways and allow the students to pick which way they want to solve a problem, then that’s great! But it doesn’t seem to be that way when someone posts “Common Core Math is the stupidest ever!”
If you can honestly say that you give subtraction tests and let the students pick which way they want to subtract, then that’s great and I applaud you for that.
It depends on what you are testing doesn’t it? If your goal is to teach several different methods of tackling a problem then at some point you must test the students ability to use each method. In this case the method used is important because it is what is being tested.
It’s like if you were running a course on navigation. Often the easiest way to figure out where you are is to get out your GPS enabled phone and have a look at Google Maps. The navigation course might include a section on using Google Maps, but it also might include celestial navigation, navigation with reference to street signs, paper maps with a variety of different styles of grid reference, triangulation from visual landmarks etc. The navigation test should quite rightly test your ability to use each of the different methods in the course and the student should not be allowed to answer every problem just by getting their phone out.
Your suggestion that a “subtraction test” should let the student use any method they like would be like the navigation test allowing the use of Google Maps and GPS for every problem.
I think you forget that getting the right answer is not all that important in many tests. What is more important is showing that you’ve learned the methods included in the curriculum (hence “show your working”).
I only learned one way as well, probably the same way you learned, but reading this thread I wish I had some more tools in my toolbox because there are subtraction problems mentioned in this thread that I can’t easily do without resorting to pen and paper.
Yep. there’s no such thing a THE easiest method to subtract numbers.
Similarly, when I program the GPS in my car to get me to a destination, it potentially can give me three routes: fastest, fewest miles, and most economical (at least two of these are often the same, but still).
Just like “core curriculum” refers to shoddy new textbooks as well as the core curriculum they claim to represent, many different things are bound up in the term “New Math” Including:
(1) An emphaisi on new material at the expense of traditional material.
(2) An emphasis on understanding instead of skill.
(3) Changes to the method
otation of borrow/carry.
Some of that was a bit misleading: the “New Math” was developed partly in response to a emphasis on “discovery learning” instead of skill. But in any case the picture addresses an aspect of “New Math” as it was seen by the media at the time.
It’s one of those methods that is easier to actually do but looks a bit silly when written out laboriously.
As others have said, it is just analogous to counting out change (which apparently nobody can do these days).
Someone hands over 32 pence for a 12 pence purchase:
First get to the nearest 5:
12p + 3p = 15p.
Then get to the nearest 10:
15p + 5p = 20p.
Then the next 10:
20p + 10p = 30p.
Then up to the actual amount tendered:
30p + 2p = 32p.
Of course, in the real world, the amount tendered will usually be a round figure so you don’t need the last step.
I’m sure most people use a similar, if abbreviated, process to subtract awkward numbers?
What’s 413 - 76?
Round up to 80, then it’s 313 + 20, or 333. Then add the 4 back on to take it down to 76, so the answer is 337. You’re doing most of the same steps in your head, but if you wrote them all down you’d think “That looks ridiculous”:
413 - 76
There’s no outrage to be had when a teacher asks students to borrow :).
For you. The impetus behind this method of teaching is that there’s no one way that works well for everyone. You’ve known adults who say, “I’m no good at math”? Our aim is to reduce the number of kids who grow up saying that, and teaching multiple ways to solve problems helps in that reduction.
I almost always do, with the exception that on the occasional quiz, I’ll say, “We’ve spent the last week solving subtraction problems on a number line. You can solve these problems however you want, but you must also model your answer on a number line, just so I can see you understand how to do it.”
But yeah, overall I teach kids to use any method, as long as:
Oy. Do you think that just because I don’t explain something to 25 students who don’t care doesn’t mean you can’t ask the teacher and I won’t tell you, the one person out of 25 who does care? :rolleyes:
The value to learning how to factor polynomials is that it will help you in later classes (especially the Calculus).
Most of what you learn in Algebra I (other than the valuable skill set related to co-ordinate plane graphing) is taught for the purpose of using in some later class. Yes, some of what is taught is also useful in a primary way (can be used to solve real-world problems), but that’s not really why we teach it. It’s taught so you can learn Algebra II, and that’s taught so you can take Pre-Calculus (or Trigonometry, or Algebra III, or whatever they want to call it). And those are all taught primarily to prepare you to take a three-semester course in Calculus when you get to College.
I know that will cause some controversy, because we’ve gone to great lengths to try and justify teaching all students Algebra I on the basis it’s immediately relevant. But that’s mostly nonsense. And factoring polynomials is a classic example. 90%+ of people who learn to do that in high school will NEVER need to factor a polynomial outside of a later math class. And while the concept of the slope of a linear function is useful, those same people aren’t calculating slopes from standard form linear equations, either. Etc.
But we don’t know when you’re a freshman in high school (or an eighth grader) whether or not you’ll be needing higher-order math, so we teach all freshmen how to do it these days. We’d prefer to be over-inclusive rather than under-inclusive in preparing students to be ready for the type of math that so many STEM careers require (not to mention other careers involving higher math, such as economists). Of course, that’s no guarantee that the individual freshman is going to care about that.
Reporting bias. When the teacher teaches the one method that the parents vaguely remember, and the kid comes home and asks for help with homework, nobody notices. When the teacher teaches a method that the parents weren’t paying attention to when they were in school, and the kid asks for help with homework, and the parents say “What!? That makes no sense!”, that’s when the story goes to the media (including social media).
DSYoungEsq, while preparing students for (ultimately) calculus is certainly part of the value of math education, I wouldn’t say that it’s the most important part. The most important part is in teaching kids how to think logically in general, and that’s a skill that applies to everything in life.
In the late 1970s, I saw store cashiers use abacuses (abaci) to determine the change due. And, yes, in my lifetime, I’ve seen people use their brains to calculate change due. That was actually part of math class for my cohort.
Factoring polynomials is an essential skill, not just in Calculus but also in algebra and trigonometry. Two big things it’s used for are
(1) Solving nonlinear (e.g. quadratic) equations, and
(2) Working with (simplifying, finding common denominators for, etc.) fractional expressions.
You can also treat polynomials to factor as puzzles to solve. I suspect, but cannot prove, that practice in solving such puzzles makes a person more familiar with and better at working with numbers in general.
