Does Your SAT Tutor Have Mathematical Knowledge for Teaching?

By Dr. Daniel Brink, Ph.D. in Mathematics Education, University of Georgia · October 6, 2026

My Ph.D. is in Mathematics Education. Before that, I was mathematics department chair at the largest boys-only boarding school in South Africa. The school counts two Nobel Prize winners and Elon Musk among its alumni, so the standards are high, and the teachers work hard to keep them there. As chair, I kept asking one question: what can we do so our boys learn mathematics better and enjoy it more?

At the University of Georgia, that question led me to Mathematical Knowledge for Teaching, or MKT. The idea comes from Deborah Ball, Heather Hill and their colleagues at the University of Michigan. MKT is the body of knowledge a teacher or tutor needs in order to teach mathematics well, which is different from simply knowing mathematics. I saw pieces of it in my colleagues every day, and I wanted to study how it affects student learning.

The six parts of MKT

Subject matter knowledge

1. Common content knowledge. The math any educated adult uses, such as solving the problem correctly. On the SAT, this means getting the answer right. A tutor who scored 1580 clearly has this, and it matters. You cannot teach what you cannot do.
2. Specialized content knowledge. Math that only teachers need. A student solves $3(x+2)=12$ by dividing both sides by $3$ first instead of distributing. Is that legitimate? Does it always work? A good tutor knows immediately, and can explain why. Knowing how to solve a problem yourself is one skill. Knowing why someone else's method works, or fails, is another.
3. Knowledge at the mathematical horizon. Knowing where today's topic leads. The Pythagorean theorem is not an isolated fact. It becomes the distance formula, and then the equation of a circle, $(x-h)^2+(y-k)^2=r^2$, which the SAT tests regularly. A tutor who sees these connections teaches one idea where a student would otherwise memorize three.

Pedagogical content knowledge

4. Knowledge of content and students. Knowing what students will find hard and which mistakes they will make. When a student solves $x^2=9$ and writes only $x=3$, an experienced tutor recognizes a pattern seen hundreds of times, not a one-off slip. The SAT is built around these patterns. Its wrong answer choices are often exactly the answers students get when they make the common mistakes.
5. Knowledge of content and teaching. Knowing how to sequence a topic, which example to use, and when to stop and look closely at what a student just said. Should a student learn to graph a line by hand before using Desmos? Which example will show that "flip the fraction and change the sign" breaks down for horizontal lines? These are teaching decisions, and they come from experience.
6. Knowledge of curriculum. Knowing the materials, programs and progressions for a topic. A good tutor knows what a student most likely learned in Algebra 1, what they may have missed, and which practice materials match the real test.

How can anyone know all of this?

This is a mouthful. How can any human being have all of this knowledge at once? The truth is that we all have some of it, and we can all grow in it. Teaching experience is what builds it, often in ways we do not notice until we look back.

The encouraging part is that the more MKT a teacher has, the more their students benefit. Hill, Rowan and Ball (2005) found that teachers' MKT predicted how much their students' math scores grew. Students gain in measurable ways because they meet mathematics in a rich, connected way. They often gain in another way too: they start to enjoy the subject, because someone taught it to them in a way that made sense.

So what should an SAT tutor know?

Is it enough for a tutor to point to their own 1580? Unfortunately, no. A great SAT score, or Calculus III at a well-known university, shows strong common content knowledge. That is the first of the six parts. The other five take years of working with students to develop, and like most things worth having, they cannot be rushed.

This is not a criticism of young tutors. Many are bright and caring, and some grow into excellent teachers quickly. But parents should know what they are paying for.

Three questions to ask a tutor

1. "What is the most common mistake students make on this kind of question?" A tutor with MKT answers right away.
2. "My child solved this in a different way. Does that method always work?" Listen for an explanation, not just "use my way."
3. "What should my child work on first, and why?" A good answer is based on what your child actually got wrong, not on a fixed program.

Every question on freepracticesat.com is built on all six components of MKT. Each wrong answer choice is tied to the specific common mistake that produces it, so a student's results show more than a score. They show which misunderstandings are costing points. The explanations are designed the same way: they draw on knowledge of the curriculum, the mathematical horizon and the student, and on the most effective way to explain each idea.

Dr. Brink

More from the blog: the 5 math gaps that hold back SAT Math scores, and every skill the SAT Math section is built on.