“Some schools are trying to help parents adjust to Common Core by holding classes that teach them how to help their children with math homework.” …
Excellent! That’s the math intuition we should try to develop in students.
The linked story talks about ‘the new vocabulary of math, including “doubles,” “count on,” and “bridge to 10.”’ I didn’t know what those were. Here’s an expanded version of the linked story, that includes definitions of those terms:
http://bigstory.ap.org/article/05d35d51bec644d9b178909c874bf5d4/help-homework-help-teaching-parents-common-core-math
Nobody ever taught me any of those strategies, but I do “bridge to 10” (or 100, or 1000) all the time when I’m adding numbers in my head.
Cardinal Fang - In my mind, there’s no question that many of the techniques taught as part of common-core math are good things to know and can help build arithmetical intuition if they are mastered. But I think that’s the wrong standard to apply.
The question isn’t “is it good math?”; the question is “is it good pedagogy?”. Teaching very young students who have a wide range of ability levels is very tricky. I have no idea whether “bridge to 10”, “doubles”, etc. will confuse or enlighten the average 2nd grader.
[ul]
[li]If I had to guess, being taught these techniques will help the top 5-10% of typical 2nd graders. [/li]
[li]I am certain that I have no idea whatsoever if it will help or hurt the average student, much less the bottom 10% of the class. However, I do suspect it will hurt the bottom 10% of students.[/li]
[li]I am almost as certain that the people who developed the common core have no idea if it will help the average student either (despite the supposed “research” they have done). Just as with the “New Math”, I suspect it will take 10-15 years for us to find out the answer.[/li][/ul]
My kids are too old for it to affect them. By the time my grand-kids are in 2nd grade we will probably know whether this latest fad is a good thing or a bad thing, though there will probably be another fad by then …
I don’t know. I was never a math whiz, but I was able to help my kids with math up to Algebra 2 in high school.
My son had a very good math book in 7th grade. It had an online version and interactive tutorials.
When I didn’t know how to do something it would explain a concept step by step and I was then able to help explain it to my child.
I have watched average mixes of 2nd and 3rd graders using these strategies successfully in our local schools. It is not just for the top students.
Our teachers use “Number Talks,” with the goal of getting students comfortable with using multiple ways to solve the same problem using mental math. This is new in the past 2-3 years. The kids sit on the floor in a group at the front without paper. The teacher puts an equation on the board that’s appropriate for the grade level. For example, two digit addition for some grades and two digit multiplication for other grades.
Kids hold up fingers to indicate how many ways they’ve thought of for solving the problem mentally. For example, subtracting from one number and adding to the other to make numbers easier to add is essentially “bridge to 10”. Or, using distributive property for multiplication.
The teacher calls on students to have them explain their solutions. The teacher writes the solution method on the board and says something like “I see, Susie is using doubling with bridge to 10.” That way, the kids see multiple solutions, and the advanced students typically come up with more complex ways to solve problems. We have trained the teachers in the names for these strategies, including strategies that kids might discover early but that are normally introduced in higher grades.
al2simon, I don’t think the strategies are aimed at the top 10%. Those kids, like you and I, were going to figure out the strategies anyway. I’m guessing they were aimed at developing math intuition for the average students. The average student, the one at the 50th percentile, comes out of an American school with horrible math skills. I’d like to think we can do better.
The bottom 10%? That’s harder. But since our current strategies aren’t working for the bottom 10%, new strategies probably aren’t going to make the situation worse.
So many people, women especially, are afraid of the most routine applications of math. You have a sock pattern with 60 stitches around, to fit a woman with an ankle measurement of 8". You want to knit the sock for your husband whose ankle measures 9". How many stitches around do you need? Now round it to the nearest four stitches because of your ribbing pattern. This is not a hard problem, and it’s the kind of real problem that real knitters face, but many knitters can’t do it. Wouldn’t it be better if they could? I hope this kind of math instruction could develop better math intuition for knitters.
Is anyone keeping an eye on the teachers? My kids realized by fourth or fifth grade that some of their elementary math teachers had very weak math skills and could not keep pace with the more capable students.
A couple of times, they asked my advice on whether or how to correct teachers, or what to do if they were told they were wrong when they gave an “out of the box” method for getting a correct answer.
Good districts are giving teachers extra training and having teachers work collaboratively to develop these skills. It’s true that many people who go into elementary education are better and more comfortable at teaching reading/writing than at math/science.
Good teachers are not adamant about ways to solve a math problem when a kid comes up with a novel solution. Common Core makes clear that there are multiple ways of solving single problems–whether by using the standard algorithm, graphically, or some other way. So, teachers with that training should be open to “out of the box” methods.
Sometimes advanced kids aren’t very good at explaining their “out of the box” methods, and that is something they need to learn how to do. Common Core places more emphasis on explaining how a problem was solved than previous standards. This is a skill that is probably more important to kids who will go on to advanced math than people who will mainly only use math for knitting, making consumer purchase decisions, etc.
I recall one time I was grading timed math tests for my son’s 2nd grade class. The class was doing something similar to the Number Talks I explained earlier, even though that was long before Common Core. (“Come up with an equation that equals today’s date.”) My son proposed something with negative numbers or a square root or something–he saw that part of the day as his challenge to show off. His explanation must have been particularly confusing, because the teacher looked questioningly at me, and I nodded to confirm that what he’d done and tried to explain worked.
These changes came to our elementary school when my youngest was in 4th grade. My H and I were discussing this thread and how we remember struggling to help S with his homework. He brought home problems of simple addition like 42+89 and we would explain about carrying, etc, and work it out with him. He would get frustrated with us and say, “Yes, I know how to do it that way and I know the answer, but we have to do it this way or it gets marked wrong”—and he starts talking about adding by 10s and arrays and writing paragraphs to explain each step, etc.
We didn’t have a clue. It boggled my mind that he could have the answer correct but because he used the “wrong” method, it was marked incorrect or 1/2 credit. Why can’t kids use whatever method comes easiest? Some kids can do it in their heads–so what? He would often end up working backwards from the answer and plugging in the common core stuff instead of using these new ways to GET the answer in the first place.
I was glad when he got to algebra, because as far as I can tell, it is the same as when I learned it back in the day and it is much easier for us to help him now.
Some kids, and my son is one, have great intuitions about math, but struggle when the problems get just enough harder that their intuitions stop working. They need to be required to learn the method that generalizes to more difficult problems, even though they resist at every step.
One of the big problems with people who rely on cookbook algorithms to solve math problems is that they don’t realize it when they come up with the wrong answer because they got a step wrong.
Those ideas are definitely not knew. The verbiage surrounding the ideas might be new, but ideas behind the methods have existed for as long as I have been teaching elementary math (which is since the 1990s.) Young children can learn those methods very easily. I have taught them to every single one of my kids.
I personally don’t think the issue is with the concepts being taught, but in the way they are taught and trying to make simple ideas complex or asking little kids to think in terms of providing a proof vs. just letting them demonstrate that they understand what they are doing. Older kids…definitely proofs are appropriate. But little kids??
“'In bridge to 10, students break one of the other numbers up to form a combination that makes 10. In 7+6, break up the 6 to make 3+3. Then, 7+3=10. 10+3=13.” This is supposed to be new? Isn’t this how addition with carrying is explained to kids?
I have taught a college engineering course in Mechanics a number of times. After some simple 2-dimensional problems using trigonometry, I do the same types of problems using vectors. It is not uncommon for a student to pipe up and suggest that I am “making it harder than it needs to be”. Well, yes, if the world were limited to 2 dimensions, that would probably be true. As soon as we extend to 3 dimensions they usually see the usefulness of a vector approach.
LEARNING the various methods is a different thing than later choosing whatever of those methods one finds easiest for a particular problem. The process is important, not the 15.
I think there’s also value in figuring things out with your kid. When I was helping my D through chemistry, I would sit next to her and read the textbook to figure how to do the homework. Sure it was painful, but in the process my D saw that the textbook actually did explain things if you put some work into it. Once I read the text and figured things out, I’d go over it again with her and basically say, “see, this part of the text is applying that that step in the homework, and here’s what it’s saying to do.”
Once my W asked D, “did Daddy know how to do the homework?” And D replied, “Not right away but somehow he’s always able to figure it out.” That ability to “figure it out” is what I tried to teach my D, moreso than how to solve a particular bit of homework.
I think that’s a different aspect of the same principle sylvan8798 is saying above.
I still have a 5th grader who has been doing common core math for the last couple years. I’m a former home-schooler, math/test prep tutor, and have taught Algebra in the classroom. What I don’t like about this method at the lower levels is that more practice (drill) has been replaced with fewer problems and sentences/paragraphs of explaining how the problem was solved. Kids need to develop speed and accuracy in basic arithmetic. They can’t do this when there are only 5 problems per page instead of 30+. At the elementary level, getting the right answer is usually proof enough that the kid knew how to solve the problem. One of the biggest issues I’ve seen with Algebra students is that they don’t know their times tables, can’t do basic addition/subtraction without a calculator. Students shouldn’t have to think about these simple operations. They should be automatic. The only way to memorize this stuff is through more practice. Now we’ve gone from less drill in the early years to even LESS drill. A mistake, IMO. One more gripe–some of the problems are badly written/textbooks poorly edited that students/parents can’t tell what the problems are asking. Another issue is that many elementary school teachers are not good at math. Sometimes they can barely explain the lesson/get it wrong themselves.
Are these schools that are holding math classes for parents the same ones who complain about helicopter parents?