You are to begin leading an eighth-grade algebra class to solve the equation 4x+1=29 by using one of two sentences: (a) “I am going to ask you to help me solve an algebra problem” or (b) “I am going to show you how to solve this algebra problem.”
Chances are that the college-prep classes your school district’s educators took left the impression that the choice doesn’t matter; that which you picked depended on your teaching style.
But it does matter. Picking sentence A tells the students that they will be involved, so their brains prepare to spring into action.
Sentence B tells the class that they are about to be listening to a stuffed shirt who is full of himself/herself, and they numb their minds so they can endure what is coming.
After choosing sentence A, your second sentence might be, “Does it matter which term I focus on first, or can I just move terms around at random?”
Someone will say that the “4x” should be focused on first because it contains the unknown, and the class will guide the teacher to subtract one from both sides and divide both sides by four, thus leaving the “x” by itself and solving the equation: x equals seven.
Note that a state-mandated standardized test, while it might be an important measurement tool that will be given later, is of no help during these moments of learning.