Feb 18, 2018 | Cambridge

Many math teachers and books spend a lot of time teaching algorithms. In fact, for most of us that is all we learned about math. An algorithm is any memorized step by step process for solving a math problem. Here is an example of a common algorithm used for teaching addition of numbers with multiple digits.

Start by adding the digits farthest to the right, or those in the ones place. Write the answer and take the ones digit of that number and write it underneath the line and carry the tens digit of that number to the tens place. Next, add the tens column. Continue from the right to the left until the process is completed. Then look to see the answer.

Tens Place Ones place

1

38

+ 39 8+9= 17

---------

77

Does this seem complex? It is. Is it any wonder that the seven year olds trying to remember this algorithm get confused?

**5 Problems with Algorithms Even if They Help Get the Right Answer**

- Algorithms are hard to remember. Keeping every step straight is a challenge if you don’t know why it works. Can you recite the algorithm you learned for converting a mixed fraction into a decimal? If not, you can probably still figure out how to convert a mixed fraction into a decimal if you understand the concept.
- Children relying solely on algorithms won’t be able to apply the concept in a variety of situations. For example, some kids get thrown when the sum of the ones place is a number over 19 (as it would be in 29+29+35) because they are so used to “carrying the one” they don’t know what to do when they should carry any other number that is not a "one". Additionally, seeing a problem in a manner that does not look like the algorithm (such as horizontal addition) can confuse many children, some of whom say "it can't be done."
- Many algorithms are difficult to perform mentally. Look at the above problem and solve it mentally. You probably used a different process than the algorithm explained earlier, ie. stack the numbers so the place values align, then add the ones place, write the ones amount, carry the tens amount, add the tens place, etc.. Here is one approach to mentally solving it. 29 is 1 less than 30, and 35 is 5 less than 40. 30+30+40= 100. 1+1+5 =7, and 100-7=93 so 29+29+35 = 93. Or here is another approach: 30 x 3=90. 90-1-1=88+5=93. Ask five different people how to solve a math problem and you are likely to get five different methods. Children who depend solely on algorithms to solve problems forget to look for short cuts, try a problem mentally or don’t have the confidence to use short cuts and mental math.
- Some kids get so bogged down remembering each step to an algorithm they learned, they forget to check if their answer makes sense. Everybody makes mistakes, but children who lack mathematical reasoning often don’t catch their mistakes.
- Algorithms don’t inspire creative thinking. They provide a step by step process which deprives children from creating their own process. Mathematicians agree that schools have been so focused on problem solving they forget to encourage creative thinking.

**Should Schools Stop Teaching Algorithms?**

No. Algorithms have their place. ALL methods that solve the problem are valid. Algorithms taught in school are ONE way to solve a math problem not THE way to solve a math problem.

Children need to have numerical fluency, number sense and mathematical reasoning to really understand the math they are doing. Curricula that cover a lot of topics quickly often sacrifice developing strong mathematical foundations and children become over reliant on algorithms to solve problems. Teachers using curricula of breadth instead of depth (which is what most of our schools currently face) struggle to make time for teaching higher order thinking skills like mathematical reasoning, number sense, and numerical fluency. Armed with these foundational skills students can still solve the problem even if they forget a specific algorithm.

**Worried Your Child Lacks Fundamental Math Skills?**

At Mathnasium of Cambridge, we provide instruction on the five most important elements of math and ensure your child develops number sense, numerical fluency and mathematical reasoning. Make sure your child can solve problems in a variety of ways, call us at 519-623-6668. For more information about our philosophy and methodology please read these articles or call our centre.

Is Mathematical Understanding Really Necessary?

Why “Number Sense” Is Important

Mathnasium Operates on Core Belief That Every Child Can Become Great at Math