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The historical development of the structure of the continuum part 4: Newton and Leibniz
Newton uses procedural infinitesimals, fluxions generated by motion, and limits via prime and ultimate ratios, while Leibniz uses infinitesimals as…
Jan 11
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Dylan Wiliam
5
2
1
How do we prepare students for a world we cannot imagine?
This is the original text of a paper prepared for the 2011 Salzburg Seminar on Optimizing Talent: Closing Educational Gaps Worldwide, and published by…
Jan 7
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Dylan Wiliam
18
1
5
The historical development of the structure of the continuum part 3: Europe in the 17th Century
Galileo’s ideas, developed by Cavalieri, Torricelli and others, spread across Europe through competing geometric and arithmetic approaches, using…
Jan 5
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Dylan Wiliam
3
1
The historical development of the structure of the continuum part 2: The Middle Ages
Calculus concepts develop slowly through Indian arithmetic, quantitative theories of motion and infinitesimal geometry, culminating in Stevin, Valerio…
Jan 1
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Dylan Wiliam
2
The historical development of the structure of the continuum part 1: Ancient Greece
The influence of atomism on Greek mathematics, Zeno’s paradoxes, Aristotelian continuity, indivisibles and Eudoxus’ method of exhaustion.
Jan 1
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Dylan Wiliam
6
2
Is the history of mathematics useful for teaching it?
A series of posts about how understanding the history of one aspect of mathematics might help us understand the difficulties encountered by our…
Jan 1
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Dylan Wiliam
24
4
5
December 2025
What does education need next?
A contribution to the SSAT's 'Beyond manifestos'—a collection of reflections on the priorities for the English education system in the run-up to the…
Dec 30, 2025
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Dylan Wiliam
15
2
1
Learning from international comparisons
Introduction
Dec 30, 2025
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Dylan Wiliam
7
1
Liff in Educational Research
This is the text of a presentation I gave at the "Triennial Travesties" session during the 2019 AERA conference held in April in Toronto, Canada.
Dec 30, 2025
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Dylan Wiliam
3
3
Formative Assessment, Feedback, and Self-Regulated Learning: Making Learning Visible, Equitable, and Sustainable
This is ChatGPT's summary of the slide deck that I used for my presentation at St Kentigern, New Zealand on September 13th, 2025, and shared via DropBox…
Dec 28, 2025
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Dylan Wiliam
and
ChatGPT
13
3
6
Artificial Intelligence and Education: What Will Change — and What Will Not
This is ChatGPT's summary of the slide deck that I used for my presentation for Learning Network New Zealand on September 12th, 2025, and shared via…
Dec 28, 2025
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ChatGPT
and
Dylan Wiliam
21
1
5
Combining student scores
It turns out that aggregating student scores across different subjects is much trickier than most people imagine
Dec 17, 2025
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Dylan Wiliam
9
13
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