The ingredient that math needs most is love.
The coach’s biggest challenge is balancing guidance with discovery. The appropriate balance is different for every student.
About the love: this is pretty clear, I hope. Math without love is a sad, sad story.
About the balance: it’s unreasonable to expect people to discover everything on their own. People get a lot out of targeted doses of exposition and demonstration.
On the other hand, it’s fun and exciting to discover solutions and connections by oneself.
In general coaches can follow a policy of letting kids read the book and try to decipher it. Encourage them to ask one another for clarification. Sometimes a coach has to demonstrate and clarify.
All of the material in the workbooks can be done with elementary level techniques. This is especially important to keep in mind in the Related Numbers chapter, which has a set of problems that many adults think of as “algebra problems”. Full blown symbolic algebra is not needed to solve these problems. Furthermore it’s not desirable. Students need opportunities to use what they know in a challenging context. And, it’s very important that coaches and teachers motivate the skills and shortcuts of algebra–this only happens by spending time with problems.
Encourage different modes of learning: diagramming (visuals), talking, modeling, moving physical objects.
How to deal with a struggling student: find out what the student knows about anything at all related to the problem. Build from there. Keep asking questions the student can answer, and gradually ask harder and harder problems. This is a technique they will learn to do for themselves: breaking a harder problem into smaller easier ones.
How to deal with a student who needs challenge:
Ask them to pose questions. Ask them to pose questions they can answer, or could in theory answer. Ask them to pose questions they cannot answer, and have them work on those questions.