I am interested in educators real-world experience or being pointed to any research in this area.
I have a student whose arithmetic skills are weak for his/her age. The student counts on his/her fingers when attempting to multiply, struggles to add two integers with a total greater than 20, cannot compare the relative size of fractions with different denominators, etc. These are skills which I understand "most" students would hope to master several years earlier than this student. I believe this student has fallen into a comfortable routine of (i) finger-counting or (ii) guessing or (iii) giving up on a question. Not to be critical of finger-counting, it is just that even the most basic of exam questions are inaccessible to this student.
I have used a number of tools such as Cuisenaire rods (which I think are extremely powerful and flexible teaching aids) to develop his/her number sense and skills in basic arithmetic. However, I decided to enter the student for an exam where basic electronic calculators are permitted, i.e. there are no non-calculator papers.
My sense/ instinct is that if a "number/arithmetic sense" is not developed then handing a student a calculator is pointless because the student has not feel for expressions and questions like "the ratio of the lengths is 2:5" or "this cost has increased by 20%" or "the sale discount is 15% what is the selling price?" or "how much should we distribute £1m grant money if we want to distribute it equally between 7 organisations?" etc. etc. My sense is that "teaching how to answer the question" is a very "fragile" form of learning since a question can be rephrased slightly and the student can feel he/she hasn't been taught how to answer that question.
So do people have evidence that routinely using electronic calculators helps or harms development of basic/fundamental mathematical problem-solving skills?