Education professionals said that the increased use of modern technology – such as smartphones, tablets and laptops – has resulted in a reduced dependence on the pen.
Members of the ATL, meeting at their annual conference in Liverpool, heard that children with poor handwriting skills were being "unfairly challenged", while others were having the quality of their work overlooked by the fact that its written presentation was below-par.
Teachers have called for extra focus to be placed on tidying up sloppy handwriting and poor pencil grips across the country's classrooms.
Surrey teacher Penny Goddin, who presented a motion calling for a survey into current standards of handwriting, said that very few pupils were reaching the end of primary-school education with the classic "tripod" grip, which involves using the index finger for stabilising, and the thumb and middle finger for mobility.
Ms Goddin added: "Children who have difficulty writing are often poorly understood. I wonder how many children have already suffered the consequences of bad handwriting – how many have been labelled underachievers when they simply needed help holding their pencils?
"How many have we failed by allowing them to develop the wrong techniques? What is happening in the classroom today has vast implications. A third of children are leaving primary school without the required standard of handwriting."
She added: "It (the survey) will be the start of what could be a major shift in the overall approach towards education, ultimately helping to build a better society and stronger economy. "
Using a comedy-size pencil as a prop as she addressed delegates during her speech, Ms Goddin asked: "Will one of these implements only ever be seen in 100 years' time in a time capsule?"
ATL members voted in favour of the survey, which will use evidence to challenge opinion and to champion good practice.