What would be most useful for your student right now?
Same teaching either way. Some students do both: ahead in math, catching up in writing.
A student struggling with fractions may be missing something from years earlier. A reader who stumbles over a chapter may be decoding fine and losing the thread between sentences. Sessions find the idea that never landed and teach it, so the next unit has something to stand on.
This includes ordinary tutoring: homework, unit tests, this week's assignments. The deeper work happens alongside them.
Where a struggle starts
An example of how an earlier idea can affect later work.
Counting & number sense
solid
Place value: what a digit is worth
never fully landed
Multi-digit multiplication
wobbles
Long division & decimals
wobbles
Ratios & pre-algebra
wobbles
↑ the idea that never landed
↑ where help usually gets called
Find the gap. Usually years earlier than the topic on the report card.
Teach it inside this year's work. We revisit the earlier idea where it is needed in the current work, so the student can connect the explanation to the assignment in front of them.
Ask questions. The student does the reasoning, one step at a time.
A 5th grader is struggling with multi-digit multiplication. On the paper: 512 × 21.
Points at the 5. "What number is that?"
Student"Five."
TutorWrites 500 × 2 = 10. "Is that correct?"
Student"No. Obviously not."
Tutor"Why not? If that is a five, and I multiply it by two, why wouldn't it make ten?"
Student"Because it's five hundred."
Tutor"Why? It looks like a 5 to me."
StudentThinks. Reasons it out loud.
Tutor"The digit is 5. Its value here is 500 because it is in the hundreds place."
An idea from 2nd grade, landing in the middle of a 5th-grade lesson.
That question-first way of working is also a program of its own: Critical Thinking & Study Skills.
How a session runs
I ask students to explain what they remember, connect a new idea to something familiar, and try it in a different kind of problem. These activities show me what the student understands and where another explanation or example would help.
We look for changes in the work: the student explains a step, notices an error, or tries an approach without waiting for me to supply it.
I'm Keith Reed, a California-credentialed teacher with a degree in neuroscience and over six years of experience across classroom teaching, small-group instruction, intervention, and private tutoring. I taught fourth- and fifth-grade math and science at a public charter school and served with City Year.
Working ahead
For students with strong grades who want more.
Before Roots of Reason, students working ahead made up most of Keith's private tutoring. Sessions cover three things:
Next year's units. The material school reaches in spring or next fall, taught the first time with the reasoning included.
Depth the class skips. Why a method works, where it breaks, and problems hard enough to be interesting.
Pace set by mastery. As fast as the student owns the material.
A check on foundations
Before moving ahead, I check the ideas the next topic depends on. A student may be ready to move quickly in one area and benefit from a closer look at another.
From there, we can introduce upcoming material, spend more time on an interesting question, or work on problems that require a deeper explanation. We'll discuss what the student is working on and what would be useful next.
Subjects & Grades
Phonics, fluency, comprehension, composition, and essay structure, matched to where the reader is
Number sense through calculus, taught so each step has a reason a student can explain in their own words
Biology, chemistry, physics, and earth science, with lab reports and the thinking behind the experiments
Document analysis, research, and essays that make an argument from the facts
Same-week support on what was assigned, or work beyond the current grade level for students who want it
Test preparation has its own program; motivation and study habits each have theirs. Plans often blend two.