"Carrying" and "Borrowing" Let's Stop the Rot...

I'm just going to jump right in a start by saying It’s time to build mathematics programmes that instil understanding and confidence in all, engage and empower, unencumbered by the discriminatory shackles of computational algorithms. (Kinda like computer programs which are also called algorithms – algorithms are step by step rules of how to get something done.) It’s time to banish these vestiges of yesteryear from our schools and from our tests! 

I am so eager to end our obsessive love affair with pencil-and-paper computation as we were to move on from outhouses and sundials! No more demanding mastery of increasingly complex computational procedures - most often taught and learned in mindless, rote fashion  I really believe  that these methods are outdated and obsolete in light of everyday societal realities!

Mindless procedures like “carrying threes into the tens column,” “six times seven is 42, put down two and carry the four,” and “eight from two, can’t do, cross out the five, make it a four, and borrow 10.” It’s also about memorised rules like “yours is not to reason why, just invert and multiply” that, for most learners, meaninglessly enter one ear and leave the other.

Continuing to teach these methods is failing both kids and the society that so desperately needs a far more mathematically powerful citizenry.

There has to be a better way...and there is!

A question...  Do we want our learners to just memorise or mimic maths procedures OR do we want learners LEARNING and DOING/ APPLYING MATHS? 

To learn, we have to THINK! So we have to provide tasks and learning that is worth thinking about. 

A few short years ago we had few or no alternatives to pencil-and-paper computation. A few short years ago we could even justify the pain and frustration we witnessed in our classes as necessary parts of learning what were then important skills. Today there are alternatives and there is no honest way to justify the psychic toll it takes. We need to admit that drill and practice of computational algorithms devour an incredibly large proportion of instructional time, precluding any real chance for actually applying mathematics and developing the conceptual understanding that underlies mathematical literacy. 

In her book The Harmful Effects of Algorithms, Constance Kamii, describes why we don’t want kids learning algorithms. She lists out 3 reasons why teaching algorithms in the primary grades is harmful:

• Algorithms force children to give up their own numerical thinking.

• They “unteach” place value and hinder children’s development of number sense.

• They make children dependent on the spatial arrangement of digits (or paper and pencil) and on other people

"Algorithms enable children to produce correct answers, but the side effect is the erosion of self-reliance.”

Helping kids build place value and number sense, gives them the ability to create their own ways of solving problems and helps them become self-reliant.  They are not waiting on you to tell them how to solve a problem.  They can use their own numerical thinking!

 So why do we continue to impose these skills on our learners and teachers?

Because despite all the powerful reasons for change, schools are equally powerful perpetuators of what they’ve always done! Ask an educator why long division is still taught and you will hear that it’s in the text,

on the test,

part of the curriculum,

and/or has always been taught.

Never do you hear that it’s needed or that it’s important.

Usually this is all it takes to start an avalanche of dismay. The most common reactions are: “But weren’t those rules and procedures good enough for us?” “Isn’t this just the ‘new math’ all over again?” “But what if the calculator is lost or the batteries die?” And “What about the basics?”

If we really want to help our learners become fluent and flexible with numbers  then the course is clear: 

 Here's an idea: True fluency in maths doesn’t come by following rules and procedures it comes from being a flexible thinker.

And how do you help nurture flexible thinking in maths, I hear you ask?

Good question. I love to celebrate the creative and imaginative capacity of children. And it is my job as a teacher to expose mathematical structures to make abstract processes concrete and clear. I help learners develop their own ways of solving problems respecting their views and their preferred ways of working. This is why I prioritise NUMBER SENSE. 

It is now naturally and logically time to abandon the teaching of computational algorithms. If you want to help your children build a deep sense of numbers in maths you need to read our MINI SERIES on MAKING SENSE OF NUMBERS... Because number sense leads to fluency with numbers.

You can read about that here:

I'd love to know your thoughts.  

Other resources and references that might be of interest to you...

The Harmful Effects of “Carrying” and “Borrowing” in Grades 1-4* Constance Kamii (1998)