Begin simple algebra and multiplication by first grade; have every child talk extensively about his or her mathematical reasoning; let students set up their own problems and equations and allow them to use big numbers if they choose; cover few topics in great depth; use lots of visual and hands-on modeling to make math ideas concrete.There are several factors in this approach that coincide with Singapore Math including the use of visual models, covering fewer topics in great depth and introducing algebra concepts as early as 1st grade. Singapore actually introduces algebra in kindergarten though model drawing. Every problem needs to begin by placing the question mark (the unknown variable) in the right place. This allows students to easily transition to algebraic thinking.
One of the observations I had in the article is that students began to develop confidence in their math abilities and teachers were surprised at the capability of their students to grasp more complex problems. Notice the kind of attitude this fostered in one of the Lebanon 3rd graders:
Says 9-year-old Casey McEuen : "Sometimes the problems can be very hard and difficult, but we can figure it out."