Every prep company in the country sells the same promise in slightly different words. We teach students how to think. We build critical reasoning. We develop problem-solvers. It is an appealing pitch, because it turns a test-score purchase into something that sounds like an investment in the child.
The problem is that the thing being sold does not appear to exist. Christodoulou’s claim, from the opening piece of her new series, is blunt: skills like creativity, problem-solving, communication and critical thinking are tied to domain knowledge. A person can be a brilliant creative thinker in one field and a poor one in the next. There is no generic exercise that lifts a skill across every domain.
For a parent deciding where to put money and a junior’s remaining free hours, that is the most useful idea available.
The Evidence
Fifty years of failing to find transfer
Three of these four numbers come from published research. The fourth is ours.
of students noticed that a second problem used the same underlying math as one they had just been shown
Willingham, Critical Thinking: Why Is It So Hard to Teach?
people trained on brain-training tasks for six weeks. Gains on the trained tasks, no transfer to untrained ones
Owen et al., Nature, 2010
students tracked from age 10 to high school. Fractions and long division predicted later algebra
Siegler et al., Psychological Science, 2012
general thinking skills we claim to teach your child
Corngold Prep
Where the idea breaks
The chess masters who lost their memory
Chess is the cleanest demonstration. In 1973, Chase and Simon showed masters a board for five seconds and asked them to rebuild it from memory. They did it easily. Novices could not come close. The obvious reading is that chess players have trained a general skill, and that memory is the skill.
Then the researchers scattered the pieces at random and ran it again. The masters’ advantage collapsed to roughly nothing. They had never possessed better memory. They had chess knowledge, and it worked only on positions that could actually occur in a game.
Daniel Willingham documents the same pattern in classrooms. In one study, students were walked through the solution to a problem and then handed a second problem built on identical underlying math, dressed in unfamiliar surface details. Nineteen percent spotted the connection. Not a failure of reasoning ability. Reasoning runs on what you already know about the subject in front of you, and these students did not yet know the subject well enough to see past the costume.
Willingham’s summary of forty years of this research fits in one line: the processes of thinking are intertwined with the content of thought.
Daisy Christodoulou
It is possible to be a brilliant creative thinker in one specific domain, and a terribly uncreative thinker in another domain.
No More Marking, September 2026
The consumer version
Brain training got tested at scale, and lost
The commercial form of the transferable-skills myth is brain training, and it was tested properly. Owen and colleagues put 11,430 people through six weeks of it and published the result in Nature. Participants improved on the games they practiced. Transfer to untrained tasks came out at zero. The authors reported no evidence that regular brain training improves general cognitive functioning beyond the tasks being trained.
People got better at the thing they did. They did not get better at thinking. That is the finding, repeated across chess, physics, reading, and now consumer software, and it is the finding that a “critical reasoning” prep curriculum has to explain away.
What it means for the test
The SAT is called a reasoning test. The math section is a knowledge test.
Parents hear “reasoning” and reasonably conclude their child needs to be taught reasoning. What the math sections measure is whether a student knows a specific, finite body of content cold and can retrieve it against a clock. The reasoning is real, and it is built on top of the content. It cannot be installed underneath it.
Siegler and colleagues followed 4,276 students in the United States and the United Kingdom. Knowledge of fractions and long division at age 10 predicted algebra achievement and overall math achievement in high school — after controlling for IQ, working memory, reading comprehension, family income, and parents’ education. The foundation set the ceiling, and it set it years in advance.
In practice
Three reasons a junior keeps missing systems of equations
None of them is a shortage of problem-solving ability, and none of them is fixed by a lesson on how to think.
Cause one
Fact retrieval isn’t automatic
A student computing 7×8 by counting is spending working memory that the setup needs. The algebra is not the problem. The arithmetic underneath it is eating the capacity the algebra requires.
- What it looks like: correct method, wrong number, on questions the student can explain perfectly out loud.
- The fix: five minutes of fact drilling daily until retrieval costs nothing. Not optional, and not negotiable by age.
Cause two
Question type isn’t recognized
The student knows every rule involved and still cannot tell which one this question is asking for. This is Willingham’s 19 percent, sitting in a chair on a Tuesday.
- What it looks like: long pauses, a started-and-abandoned setup, and the right method arriving thirty seconds after the answer was needed.
- The fix: Bluebook practice sorted by question type and by error pattern, not by “did some math today.”
Cause three
The clock is the leak
Content and recognition are both fine. The student is spending ninety seconds on a question that should take forty, and Module 2 arrives with nothing left.
- What it looks like: a strong untimed score and a weak timed one, with the misses clustered at the end.
- The fix: timed sets of five to ten questions, plus Desmos on the questions where graphing beats algebra.
What actually moves the score
- Named gaps — circle theorems, exponent rules, percent multipliers. Question types, not chapters.
- Fluency underneath them, so working memory is available for the reasoning.
- Reps that get reviewed while the memory of the attempt is still warm.
- Strategy taught on real questions, because that is the only place it exists.
What sells well and does nothing
- “Critical thinking” modules with no named content behind them.
- Brain-training apps and logic puzzles bought to raise a math score.
- Generic problem-solving frameworks that apply to any subject and therefore to none.
- More material handed to a student whose actual leak is pacing.
Where Corngold Prep Stands
The part of this that cuts against tutoring
If skills are domain-bound, then test-taking strategy is domain-bound too. Elimination, smart skipping and pacing on the SAT are not general life skills. They are SAT skills, they have to be taught on SAT questions, and they do not follow a student into a chemistry final.
That is a real limit on what any tutor can honestly claim, including this one. A student who gets sharper on Bluebook question types is getting sharper at Bluebook question types. Worth paying for, and not the same thing as becoming a better thinker.
Which is fine, because that was never the job. The families who get the most out of prep are the ones who stop buying a transformation and start buying a specific, boring, checkable set of repairs.
Despite how good the alternative pitch sounds, the honest one is more useful: find the actual gaps, rebuild the fundamentals underneath them, and teach strategy on the real test rather than in the abstract. Before you hire anyone, ask which question types your child is missing, which concepts sit underneath them, and how the work gets checked between sessions. If nobody can produce that list, they are selling the myth.
Your kid does not need to become a better thinker by March. They need the math.
From Corngold Prep
Want the list of what your student is actually missing?
It starts with a diagnostic and an error log, not a package. For focused SAT and ACT preparation built around the gaps a diagnostic actually shows, we’re always glad to talk.