Reading a problem’s architecture before reaching for a formula, rebuilding foundations and constructing solutions with increasing independence.
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Violin, mathematics and psychology may appear to occupy entirely different rooms.
One speaks through sound and movement. Another works through quantities, structures and proof. Psychology asks how people attend, remember, avoid, persist and learn.
In my work, however, all three are connected by the same obsession: technical clarity.
I have always been drawn to fields in which improvement cannot be sustained by appearance alone. A confident answer does not become mathematically correct through charisma. A violin movement does not become efficient because it looks dramatic. A study plan is not effective simply because it has been arranged in an attractive table.
The mechanism has to work.
Mathematics appealed to me from middle school onward for precisely that reason. I was fortunate to begin from a position of strength and to study with teachers who developed that strength seriously. They did not present mathematics as a collection of formulas to be recalled on command. They showed me how an argument is built, how one relationship leads to another and why a correct result must survive explanation.
Mathematics has little patience for decorative certainty. I have always appreciated that about it.
During high school, one of my teachers opened an optional mathematics-olympiad course. I attended the lessons, prepared and sat the examination, although I did not earn an official distinction. There is no reason to embroider that part of the story. Its value was elsewhere.
Olympiad-style problems—particularly geometry—taught me to resist the first obvious route. A problem could contain very little information and still demand an extraordinary degree of precision. The solution was often not hidden behind an advanced theorem; it emerged from seeing familiar material in an unfamiliar configuration.
That experience strengthened a view I still carry into teaching: difficulty is not always a sign that the student lacks knowledge. Sometimes the knowledge is present but has not yet been organised into a usable system.
I began explaining mathematics more seriously during my final year of high school while preparing for the 2023 YKS. Friends would bring topics and questions they could not resolve, and we would work through them together.
That was when I discovered that knowing an answer and teaching the route to it are separate abilities.
A person who understands a subject may forget how many invisible steps stand between confusion and clarity. Teaching requires those steps to be restored. The explanation has to begin where the learner is—not where the teacher happens to be standing.
After ranking 1,116th in Türkiye in the Equal Weight track of the 2023 YKS, I began working more regularly with middle- and high-school students. The ranking is relevant, but not because one examination result turns someone into an authority on every academic question. It matters because it emerged from the same method I now teach: rebuilding foundations, identifying priorities, analysing mistakes and constructing a system capable of lasting longer than a burst of motivation.
I did not prepare by beginning at the most impressive chapter. I returned to the beginning, worked systematically and refused to treat unclear material as “probably good enough.”
Unresolved foundations charge interest.
I rarely accept that sentence at face value.
It may describe frustration, but it does not yet identify a cause.
Frequently, I find a student who has memorised procedures without understanding when they apply. Another has accumulated small gaps that now appear everywhere. Some can follow a solution perfectly but cannot reproduce the reasoning alone. Others have been moved from elementary questions to difficult exam material so abruptly that anxiety now arrives before thought has a chance to begin.
Occasionally, the student simply has no interest in mathematics. I do not turn every lack of interest into a hidden passion waiting for a sufficiently inspiring speech. But when a student genuinely wants to learn, the label “bad at maths” is usually far too crude to be useful.
A high-school student I worked with after the YKS period illustrates the distinction. The student had seen most of the relevant topics and could follow worked solutions, yet unfamiliar questions produced immediate paralysis. The assumed problem was insufficient practice.
Practice was part of the answer, but not the central one.
The student was searching for a formula before reading the architecture of the problem. We began separating each question into three decisions:
At first, I supplied the questions. Gradually, the student began asking them independently before touching the algebra.
There was no cinematic transformation and no invented promise that every examination score suddenly doubled. Something more useful changed: an unsolved problem stopped feeling like evidence of personal inadequacy. It became an object that could be inspected.
The student now had a first move.
Some students need a subject taught from the ground up. In that case, I reconstruct the prerequisite knowledge, explain the logic through screen sharing and examples, and encourage questions at every stage. A lesson should not continue through a fog merely because the teacher has reached the next slide.
Many students come for a different reason. They do not want the entire topic presented again. They understand much of it, but their understanding is surrounded by unresolved questions. They bring problems they could not solve, and the lesson becomes a technical examination of those problems.
We identify the mistaken assumption, compare possible methods and examine why one approach works more efficiently than another. The student is not expected to remain a spectator. At some point, they must explain the reasoning themselves.
Following a solution can create a convincing illusion of understanding. Reconstructing it exposes the truth rather quickly.
Mathematics lessons therefore concern the subject itself:
Academic mentoring operates at a different level.
Mentoring looks at the student’s full academic system rather than one mathematical problem.
Meetings may take place once or twice each week, with more intensive structures designed separately when necessary. The work can include weekly planning, mock-exam analysis, prioritisation, error tracking, revision design, accountability and appropriate parent communication.
My psychology education at Koç University gives this process a more precise foundation. Attention, working memory, forgetting, retrieval, reinforcement, feedback, habit formation and self-regulation are not decorative psychological vocabulary added to make a timetable sound scientific. They affect what a student can realistically do and how a plan should be built.
Motivation is a particularly unreliable foundation. It matters, but it has irregular attendance.
A durable system must also operate on the ordinary day when the student is tired, distracted and not feeling remotely transformed.
When work has not been completed, I do not automatically accuse the student of laziness. I examine the system first. Was the task clear? Was the workload realistic? Did an unresolved difficulty create avoidance? Was the week genuinely disrupted?
If the explanation is valid, the plan changes. Life is allowed to happen.
If the work was simply insufficient, I say so clearly. Kindness does not require inaccurate reporting.
Academic mentoring is not therapy, diagnosis or psychological treatment.
It is not completing assignments for the student, forcing them to study, supplying an endless stream of motivational messages or guaranteeing a result. Nor is it taking over the student’s responsibility so completely that the entire system collapses as soon as the mentor steps away.
I understand mentoring as the transfer of a method.
I combine my own examination experience, technical approach, teaching ability and psychology education to help the student read their situation more accurately and act with greater structure.
The aim is not dependence.
The aim is for the student to become progressively better at deciding what matters, recognising why something is not working and taking responsibility for the next move.
The common principle between mathematics and academic mentoring is therefore simple:
We turn uncertainty into components, locate the real problem and build a system that can be used.
I cannot honestly guarantee success. No educator can guarantee an outcome whose production also depends on the student’s work, circumstances and decisions.
What I can offer is something more serious than a promise: a clear method, direct feedback and a structure in which effort is no longer spent at random.
That is why mathematics and academic mentoring belong naturally in my work.
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