There is a basic pedagogical framework for Conceptual Math based on building from non-verbal streams.  This means that much of conceptual math is learned through procedural and implicit approaches.  Basically, we are learning by doing.

There are five basic components to "doing" conceptual math.
Most of these exercises are based on the base ten circle.

I always introduce the circle by first indicating the 0 and 5.

This is followed by completing filling in the numbers of the circle.
When students have become familiar with this as each of the multiples is represented, we introduce the array of nine.
The visual system is the starting place, but we move quickly into embodying the Base Ten.
​There are ten basic body positions. In order from one to ten.
Embodied position one. Left arm up by ear, palm facing up.
​Embodied position two.  Hand open fingers outstretched, palm facing forward.
Embodied position three.  Left arm reaching just above hip level, fingers together, palm facing down.
Embodied position four.  ​Hands at side, left leg out.
Embodied position five. Hands at side, feet together.
​Embodied position six.  Hands at side, right foot out.
​Embodied position seven. Palm down, right hand out to side. The inverse of three.
​Embodied position eight. Right hand out just above mid-line, fingers outstretched. The inverse of two.
​Embodied position nine. Palm up, right arm raised to side. The inverse position of one.
​Embodied position ten.  Body stretched tall, arms raised overhead, palms touching.
​Shown are the hand positions for 1 (upper left), 2 (upper middle), 3 (upper right), 7 (lower left), 8 (lower middle), 9 (lower right).  For the numbers 4, 5 and 6 the hands are down by the sides.  For 0, the hands are clapped above the head.