About Singapore Primary math & algebra

[blessedmom3]

For a long time I was wondering how do kids translate their pre-algebra skills taught in Singapore primary to algebra word problems. For ex. my 4th grader just solved this problem posted by Bill in the other thread,using Singapore's bar diagrams. I tried to teach him using algebra, and he says he doesn't understand and can't do such problems without drawing. I tried using algebra with other problems as well, but he can't get it.

 

So how to kids solve algebra problems when they are older,after coming from Singapore? Will they still need to draw bars?

[Spy Car]

I can't really answer, as we've been doing "both" all along (something I think some "Singaporeans" (in the "math" as oppose to "national" sense) might object to as a practice.

 

My son worked out the example I posted both ways, using bar-diagrams and algebra. But I asked him to turn in only the bar diagram method.

 

I will recommend the book Primary Grade Challenge Math by Zaccaro for the very clear introduction to the basics of algebra and problem solving using linear equations for younger students. We have followed up with Zaccaro's Real World Algebra which is like an extension of the 3 chapters in PGCM and is a step up. You could jump in to that as well.

 

I also love the apps DragonBox 5+ and DragonBox 12+ (the first for younger), and the beginning levels of Hands on Equations also comes as a usefull app.

 

Bill

[nmoira]

So how to kids solve algebra problems when they are older,after coming from Singapore? Will they still need to draw bars?

 

The equal segments in the bar diagrams are really the "x" of "Let x be." Once the connection is made, bars are not needed.

[Nan in Mass]

This was a complete non-issue.  Mine still (in college) use the bar diagrams to draw a picture of the problem if they are having trouble figuring out how to set up the problem, but then they solve it using algebra.  Most of the time, they don't bother with the diagrams.  I learned math using the bar diagrams and did the same thing - used bars to see all the pieces of a particularly hard problem but mostly just use algebra.  Mine had a particularly easy time with algebra word problems and I think that was because of all the practice with visual bars first.

 

I wouldn't worry about it.  It is very useful to be able to draw a picture of a problem.  Whether you label it with x's and y's or question marks doesn't really matter.  Algebra is so convenient once you are quick at it that I don't think you need to worry about children clinging to the bar diagrams and not learning their algebra.

 

Nan

[blessedmom3]

The equal segments in the bar diagrams are really the "x" of "Let x be." Once the connection is made, bars are not needed.

That's what I told my son,but he says he needs to see the picture in order to solve the problem.

[blessedmom3]

Sort of hijacking thread, but it's a very simple question: when does Singapore start teaching bar diagrams? My dd is in 2A and I have seen no mention of it, although it's in the Challenging Word Problems for 2nd grade, although there's not any explicit "teaching" of it. I've sort of showed her how to do it, but it's different from how I learned and I'd like some instruction.

I started in 2A with cuisenaire bars. I think Singapore starts teaching the teacher in 2 B, and more in 3A.

[nmoira]

That's what I told my son,but he says he needs to see the picture in order to solve the problem.

It'll click. Just let him use the diagrams as long as necessary. If you have any old, completed CWP books, you can have him revisit the problems using Algebra.

[nansk]

The old Singapore Maths (that homeschoolers in the US are using) started teaching bar diagrams in 3A.

 

My dd is in a Singapore school and their teacher started teaching basic bar diagrams (for numbers upto 20) in Primary 1.

 

Current Maths books used in Singapore start teaching basic algebraic expressions with one variable in grade 6. But, as nmoira said, even with word problems where students draw a bar diagram, they still use basic algebraic expression, only, with a "U" instead of a "x".

[kiana]

I really don't think there's anything to worry about a 4th grader not being able to make the conceptual jump to algebra from bar diagrams. Many, many 4th graders are just not quite developmentally ready.

 

If he still can't do it in 7th grade then I would be concerned.

[Monica_in_Switzerland]

Sort of hijacking thread, but it's a very simple question: when does Singapore start teaching bar diagrams? My dd is in 2A and I have seen no mention of it, although it's in the Challenging Word Problems for 2nd grade, although there's not any explicit "teaching" of it. I've sort of showed her how to do it, but it's different from how I learned and I'd like some instruction.

 

I think it's in 3a.  If you have any cuisinaire rods, it's a snap to switch to bar diagrams.  I started by introducing them something like this:

"We don't have a rod that is 127 units long, so let's just draw an imaginary rod.  Now let's draw an imaginary 56 rod under it.  Now let's find the missing rod."  We did imaginary rods for about a week, then I started calling them bar diagrams.  :-)

[Nan in Mass]

I can't say this strongly enough: there is nothing wrong with drawing a picture to help you solve a word problem.  In engineering, they encourage students to draw pictures to solve things.  If the student arrives at college already knowing how to draw the picture, GREAT!  WONDERFUL!  That will give them an edge over the students who don't know how to draw a picture to represent things.  Drawing a picture is a recognized method of solving word problems around the world.  This is a list from a US community college: http://www.jccc.edu/files/pdf/academics/mathematics/math-problem-solving.pdf  This is a standard list of strategies for word problems: http://library.thinkquest.org/4471/learn.htm  Here's a list of strategies to teach students from a college in Turkey: http://pred.boun.edu.tr/ps/   The list in the front of the Singapore NEM (algebra) book contains a list very like this. All these lists contain something like "draw a diagram" or "draw a picture" as a strategy along with "guess and check", etc.  The first step of solving a problem is to figure out what you know and what you don't know ("givens" and "unknowns") and determining the relationship between those things.  Bar diagrams are a way of doing this for certain types of problems.  This is not the sort of tool that one hopes a child outgrows, like a multiplication chart, but a tool that will be useful for life.  Difficult math problems require all sorts of approaches and "tools" to solve.  You can see this if you look at the math competition problems.  Some of them are "simplify this equation" but some are complex word problems, ones that you sort of have to muck around with for awhile before the steps for solving them become apparent.

 

I understand what you are worried about.  You are worried that your child will use bars INSTEAD of algebra to solve simple word problems.  I don't think you need to.  By the time your child has gone through an algebra program, algebra will seem like a shortcut for those sorts of problems, and in the end, being able to draw a picture of a problem to show the relationships between the variables will be valuable.  He will substitute a variable name for "unit".  He will be able to solve more complicated problems with more unknowns by drawing bars to show the relationships and labeling his unknowns x, y, a, b, etc.   Unless he has gone through an algebra program, the bars are going to seem easier and he is likely to balk at having to use an unfamiliar method instead. : )  Eventually, laziness will take over and he will stop drawing the bars for the easy problems.  If, when you are working through an algebra book, he clings a little too hard to the bars, you can just tell him that you know the problems are easy enough to be solved with the bars but books always use easy problems, ones that you can solve another way, to show you a new way of solving the problem and the object of the lesson is to learn the new way, not to get the answers - when he is solving problems that aren't in this textbook, he is welcome to solve them however he likes because then the goal IS to get the answer.  I had this conversation with mine many, many times sigh, not over the bars but over other things.

 

Nan

 

ETA- Reading this over again, it sounds rather scoldy to me.  I didn't mean it that way at all.  I meant it to be encouraging.  I CAN see why you might wonder about this.  I just happen to know from my own schooling and teaching my children that it isn't, in the end, and I also know that if you ask me to solve a problem without a picture, I tend to balk, too, unless they are very simple, and I'm actually a rather good problem-solver, when it comes to math word problems.  I think this might have something to do with brain wiring as well as early training.  There are few situations where you CAN'T draw a picture to solve a problem, and having grown up with engineers, I think of it as a mathy thing rather than a kid thing. : )

 

[WVNA]

I immediately thought of this video, which is of one of my scientific heroes, when I read the OP's questions.

 

Also, as somebody else above said, "there is nothing wrong with drawing a picture to help you solve a word problem."  I can't stress enough the importance and truthfulness of this statement.