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Thinking from practice, for practice

Essays and reflections from Mr. Raj on mathematics education, assessment, Lesson Study and school leadership.

Assessment · AI

By Mr. Raj

3 minute read

When Answers Become Cheap

If a machine can produce the answer in seconds, what exactly are we assessing?

For most of the history of schooling, producing a correct answer was reasonable evidence of understanding. A student who could solve the equation probably understood something about equations. That link has now been broken. Any student with a phone can produce a correct answer, a full worked solution and a fluent explanation of it, none of which passed through their own thinking.

The temptation is to respond with policing: detection tools, locked-down rooms, a return to pen and paper for everything. Some of that has its place. But it treats the symptom. The deeper question is what our assessments were really measuring all along. If a task collapses the moment students gain access to AI, it was probably measuring the production of answers rather than the quality of thinking.

The more durable response is to redesign the task. Ask students to choose between two plausible solutions and defend the choice. Ask them to find the error in a confident, fluent and wrong piece of reasoning. Ask them to explain why a method works, where it breaks and what it assumes. These are things a student cannot outsource without the outsourcing being visible.

Answers have become cheap. Reasoning has not. Assessment now has to ask for the expensive thing.

Mathematics

By Mr. Raj

3 minute read

The Bar Model Is Not the Magic

Schools around the world import Singapore mathematics as a set of techniques. The techniques are the most visible part and the least important.

When schools adopt Singapore mathematics, the first thing they usually reach for is the bar model. It is visual, learnable and impressive in demonstration lessons. Yet I have seen schools train every teacher in model drawing and change almost nothing about how students learn mathematics.

The bar model works in Singapore because it sits inside a coherent system. Concepts are developed from concrete experience through pictorial representation to abstract notation, in a deliberate progression that runs across grades, not within a single lesson. Problem solving is the organising goal of the curriculum, not an enrichment activity for Friday afternoons. Teachers are expected to understand not just how a method works but why it appears at that point in the progression.

Take a technique out of that system and it becomes one more procedure for students to memorise, which is precisely the outcome it was designed to prevent.

Adopting Singapore mathematics means adopting its coherence. The tools travel easily. It is the thinking behind them that has to be unpacked, adapted and taught. That is where the real work of any adoption lies.

Lesson Study

By Mr. Raj

3 minute read

What Lesson Study Actually Takes

Many schools run Lesson Study for a year and quietly stop. The problem is rarely the teachers.

Lesson Study looks deceptively simple: teachers plan a lesson together, one of them teaches it while the others observe and the group discusses what happened. Plenty of schools do exactly this and see little change. What is missing is usually invisible from the outside.

The first missing piece is kyozai kenkyu, the deep study of the content and curriculum materials before any lesson is planned. Without it, planning meetings drift into logistics and the research lesson has nothing to test. The second is the discipline of observing students rather than the teacher. The question in the room is not whether the lesson was delivered well but what individual students were thinking, attempting and misunderstanding as it unfolded. The third is a post-lesson discussion anchored in evidence, where claims must point to something a student said, wrote or did.

None of this survives without leadership. Time must be protected, not borrowed. The first cycles must be allowed to be imperfect. And the school must treat Lesson Study as its way of improving teaching, not as this year's programme.

Lesson Study is a culture that grows under certain conditions. The schools that sustain it for a decade are the ones whose leaders built those conditions first.

Leadership

By Mr. Raj

3 minute read

The Most Underused Seat in a School

Between the principal's vision and the classroom's reality sits the head of department. Almost everything depends on how that seat is used.

School improvement plans are written at the top and enacted at the bottom, but they are translated in the middle. A head of department decides what a school priority actually means for Tuesday's lesson, which parts of the plan reach classrooms intact and which arrive diluted beyond recognition. In my experience, no single role has more leverage over the quality of teaching and no single role is prepared for less of it.

Most middle leaders are promoted for being excellent teachers, then handed timetables, budgets and administration. The work that matters most, leading the professional conversations that change how colleagues teach, is the work they receive the least preparation for. It is also the most uncomfortable, because it must be done with peers, without the authority of the principalship and often with friends.

Schools serious about improvement invest here first. Give middle leaders the tools of instructional leadership: how to observe developmentally rather than judgementally, how to give feedback that improves practice, how to use departmental data to ask better questions rather than assign blame.

Strengthen the middle and the whole school moves. Neglect it and the finest strategic plan remains a document.

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