I have few school memories from my childhood, but one that I do remember is learning multiplication. My elementary school was considered a fairly progressive site, and the techniques they were using then are still some of the best! In one particular lesson, we learned multiplication by using counters, and making a matrix of three rows by four columns to illustrate 3 x 4 = 12.
Using "stuff" to help students learn the concepts of mathematics is still a very valid and recommended approach! The fear many teachers have is that they will lose control of their students after passing out the materials. Never fear! If passing out long rolls of paper for a number line lesson, consider giving students a little time to decorate one side of the paper before turning it over for the real business of math that day. The younger the students, the more they may need to play with any manipulatives before acting out the math. Give first graders a chance to really look at geometric solids before beginning a lesson on three-dimensional figures. Kindergartners may want to play with their tangrams before you have them turn them into pictures. And it's not a bad idea to give young students lots of time exploring pictures of symmetrical objects before they cut their own!