What is Number Sense and How Do I Get It For My Students?

What is number sense?  I hear from school to school, teacher to teacher that kids don't have number sense or know their basic facts.  I've often wondered, not knowing the basic facts, is it the problem or the symptom of a greater problem.   I've come to the conclusion that not knowing the basic facts is a much deeper problem of not having strong number sense.  So what is number sense?

There are many building blocks to number sense. Some blocks are so intuitive, that as adults, we have forgotten just how complex our number system actually is.  Why do we call "22" twenty two but we don't call "12" ten two?  Does it matter the order in which we count objects?  Does the order in which we count, one, two, three matter?  What does division really mean?  Did you know there are two different types of division problems?  How does division of fractions work?  Do we know why?  There are so many concepts of number sense that needs to be explored with our students.  Do we as educators understand all of these stepping stones so that we can agree if a student has number sense and to what degree?  If students are missing critical components do we know how to address these?

I just attended a Numeracy conference that exposed many components of number sense.  It was at that point I realized the math strategies and presentations we support at ESSDACK fit perfectly into the research on number sense.  Number sense extends from simple one-to-one correspondence and runs through subitizing, unitizing, hierarchical inclusion, place value, and to understanding relationships between numbers and operations.  All of these skills are visited and explored in my Developing and Assessing Number Sense DVD and Teacher's guide.   I have just finished the Teacher's Guide and Diagnostic Tools to check for students understanding and to what level of number sense the student is displaying.  Included in the teacher's guide are backline masters, such as games, tens frames, number lines, and 200 charts.  These are all great tool to help with many skills of number sense including subitizing, addition, hierarchical inclusion, decomposing numbers, etc.  This Teacher's Guide should be uploaded and ready to for sell in the next few weeks.  I have been using this assessment tool in my work with El Dorado and am looking forward to sharing this tool in Arkansas in April.

Cognitively Guided Instruction is another wonderful strategy that we offer at ESSDACK.  It includes leveraging the "visual" system of our brain to move from the concrete to the representational (pictorial) to the abstract (symbols).  The role of the teacher is crucial to the CGI strategy to help make these connections through teacher questioning.  CGI is a strategy that focuses on problem solving.  This is important because there is a direct correlation between number sense and problem solving.   Problem solving needs to be strategic, tools need to be provided, scaffolding, and students discussing and comparing strategies is central to the strategy. Schema based instruction is also embedded within the program.  There are fourteen different problem types that include the different structures of addition/subtraction and multiplication/division problems.