It is vitally important that a math teacher elicit a stream of continuous feedback from the class while teaching at the board. This feedback allows the teacher to learn immediately if the students are understanding the material and tailor her explanations and questions to reach everyone in the class.

Here is a list of the hand and arm signals I recommend teaching the class on the first day. The signals should be briskly practiced for a few minutes at the beginning of each class until all the children have mastered them.

• “I agree.” (Pumping arms.)

• “I disagree.” (Scissoring arms.)

• “I partly agree and partly disagree.” (One arm pumping and the other doing a sideways motion.)

• “I don’t know.” (Hands held palms up.)

• “Stolen answer.” (One hand grabbing fistfuls of air.)

• “Stop! I’m confused!” (One hand held in a stop sign, the other held palm up, eyebrows raised.)

• “Confusion breaker.” (Meaning, “I can clear up the confusion,” and shown with a silent snapping forward of the arms as if to break a thin sheet of ice.)

• “I’m starting to understand.” (One lightbulb, formed with thumb and forefinger, held over the head.)

• “I really understand.” (Two lightbulbs held over the head.)

• “I’ve had a total breakthrough!” (Two bouncing lightbulbs held over the head.)

• “I have a question.” (One arm and hand curved in a question mark, the other hand in a fist below. The bottom hand can alternate between being the dot at the bottom of the question mark and pointing to the person the child wants to question, or a circling motion indicating a desire to pose a question to the whole class.)

• “I have a theory to propose.” (Arms forming a big “T”.)

• “Please repeat your last statement.” (Both hands making a gesture toward oneself.)

• “Please turn up the volume.” (A twisting motion with one hand to indicate that one cannot hear what is being said.)

• “I can’t see the blackboard.” (Flat hands moving back and forth over eyes.)

• “Algebra applause.” (Vigourous silent clapping, with the palms not quite touching, to indicate appreciation of someone else’s great idea or insight or explanation.)

“I just changed my mind.” (Fingers of both hands touching temples, then shifting sideways, as if a set of thoughts has just been moved out of the mind.)

In addition, students should be asked frequently during the lesson to use their fingers (or arms) to show:

• numbers

• operations (addition, subtraction, multiplication, division)

• directions

• shapes

• brackets