What have we done to Number Sense? Part 1

There’s a great deal of time spent in K-2 developing Number Sense in students.  Teachers find all kinds of creative math activities to help the students understand how numbers relate to one another.   But, something happens in the upper grades 3-5 of elementary that often mystifies many teachers.  The older elementary kids seem to “forget” what they have learned about place value and how numbers work together.  They even seem to lack understanding of what really happens with the basic operations of additon, subtraction, multiplication, and division.  When students start manipulating fractions, something happens to even the simplest relationships between halves and fourths.  For 15 years, I wondered what was happening that caused kids to “forget’. That’s when I discovered that it was all related to number sense.

By the time students reach upper elementary many have lost the idea that one item placed with another item became two items;  1 + 1 = 2.   This may be a slight exaggeration, but the idea is that students lost the means to comprehend what 1 + 1 really means.

They somehow forget that 3 x 4 represents three groups of four objects. The older elementary students lose the idea that two fractional amounts put together create a new fraction, whole number, or mixed number.

Starting with second grade, educators emphasized the use of algorithms in computation.  These algorithms for addition, subtraction, multiplication, and division were quick ways to guide students to an acceptable response.  But without realizing it, we destroyed number sense when teaching students to solve by algorithm.  Students lost the value of place in a number.  The lost the meaning of the symbols +, -, x, and / .  Furthermore, they become unable to explain with words what a simple computational expression represents.

Now, let’s not blame the educators.  We were only teaching the way we were taught in elementary school all the way through our college days.  We even earned a teaching degree and took the big certification test that simply required computation without understanding.

Today we understand that in order to maintain number sense, we must develop concepts before we teach algorithms.  Students must be able to verbally communicate what happens to numbers when objects are added, subtracted, multiplied, and divided.  They must be able to provide reasons that their computations work and are valid.  They must be able to use models (manipulatives) to demonstrate their understanding of concepts.  Today, math is much more than manipulatiing symbols.  To develop conceptual understandings that maintain number sense, we must engage students in learning with performance tasks that mimic real world applications.  Let students discover the algorithms with a little help from the teacher.