Testing, calculators and numeracy...

Had an interesting question raised on one of the many communities I pay attention to, "Along with the practices calling for use of mathematical tools, do you think calculators should be allowed on the state testing?"

I feel we, as math teachers, must not get sucked into one answer about calculators and their use.  We must stop the pendulum between all or nothing, reform and traditional, there is a middle position!  That means some amount of non-calculator numeracy and the ability to use tools. (And if you think a TI-84 or 92 is a real world tool, you need to hang out in a production facility of some sort -- it is spreadsheets, databases, etc....)

I believe that numeracy is learned, any math instructor of any amount of time has seen something like this -- a student take 3 times 6  on their calculator, they miss the 6, hit 9 and fully accept the answer of 27 versus 18.  This is a by-product of instruction that only focuses on solutions and processes, it also demonstrates a huge numeracy deficiency.  I believe that numeracy is mostly learned with practice without a calculator, and when using a calculator a student must make an estimate to make sure they are getting a reasonable solution.

So what about the all mighty state tests...  If they are going to measure anything that approaches usable data, they would include no calculator through the grades where basic processes are learned, approximately 5th grade.  They would then include portions of the exam that allow any tool to solve problems, computer, calcualtor, etc for a portion of the test in 6th-10th grades.  As the grade level raises the longer the calculator/tool section, by 10th or 11th grade the non-calculator portion should be really short, about 15 minutes. 

In my room, 9th graders are not allowed calculators on tests/quizzes (tests are also designed so multiplying 15953.23*129.482 is not required).  10th graders and up do get to use calculators most of the time, with a small portion of quizzes being no calculator.  I do not use TI-84s until AP Calculus, all other classes use Microsoft excel for graphing and problem solving (a real world tool).

The real problem is we get caught in this discussion about calculators and other technology and miss the point that some amount of time needs to be on numeracy, processes and skills & more time on concepts, problem solving and math's interconnections.  I teach high school and I divide that time at about 30% skills, 50% concepts and 20% problem solving. 

At this ratio there are many topics I do not get to, yet my students are consistently testing into college math (not remedial), scoring well on the ACT and have worked through many large projects which they cannot see solutions to  --   that is our job.   Nowadays students are able to look up everything and calculators are an easily acceptable tool, thus we need to let students use them.  The real question is whether they will have the tenacity and understanding to find acceptable solutions to today's & tomorrow's problems.