Why students can’t problem solve if they don’t have numeracy

The goal of modern day math classrooms is to equip students to solve everyday math problems.

There are lots of approaches to developing problem solving skills. But without a foundation of numeracy, students won’t be able to reach their full problem-solving potential. Good problem solving is dependent on core numeracy skills.

In some ways, numerical fluency is like reading fluency. Both are building blocks. Reading fluency – being able to decode words – impacts reading comprehension. Many language arts teachers have observed that students with poor phonetic decoding and sight word recognition skills read so slowly that they are unable to understand the very sentence they just read.

Poor numerical fluency has the same negative effect in mathematics. When the child’s numerical ability is lacking, they struggle to solve multi-part math problems. Numerical fluency is the ability to work fluidly with numbers in a variety of mathematical situations.  Kids competent with numeracy have the ability to hold a multi-part problem in their working memory, use their skills to resolve each part, and solve the problem as a whole.

Numerate students are capable of solving multi-step math problems – and importantly – evaluating the reasonableness of the solution.  For example:

Joseph saves pictures in a 4 page photo album. He has 102 pictures in the album – 28 pictures on the first page, and 23 pictures on each of the last two pages. How many pictures are on the second page of Joseph’s photo album?

The numeracy math skills needed to solve this problem are:

  • The ability to double (or multiply by 2) – 23 x 2 = 46
  • Summing two two-digit numbers with carrying:  46 + 28 = 74
  • Subtracting with regrouping: 102 – 74 = 28
  • Evaluating the reasonableness of the solution (adding them all together to verify they sum to 102).

If your students struggle with one of these skills, they’ll be incapable – or extremely slow – to solve the problem as a whole.  Most tests these days are timed – so speed matters.

So what’s a school to do?  Be sure to put a little time into reinforcing the core numeracy skills that your students will need to draw upon to solve the problems they tackle in class.  A little investment in numeracy goes a long way.


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