4 ms·

I think the sweet spot is 80% familiar content mixed with 20% new. If you are confronted with chapters that are 100% alien to you, then it's very hard to unders

I think the sweet spot is 80% familiar content mixed with 20% new. If you are confronted with chapters that are 100% alien to you, then it's very hard to understand anything from it and you might just lose the reader.

ivansavz 5y ago
That is very interesting, I would have never thought of using a "duty cycle" as low as 20% in a math/science textbooks. I agree that every chapter should start by connecting the material to past knowledge, and briefly reviewing some of the prerequisites, but then surely the author should get to the new stuff after that? Perhaps your estimate of 20% doesn't include the repetition and worked examples? In general when a new concept X, I try to explain it at least three times, once informally, with terminology and definitions, with formulas, and with extra explanations. In my mind all these repetitions count as "new stuff," since they cover the material at different depth and bring new dimension to the concept. Perhaps you could give some examples of the 20% new max sweet spot? I'd much appreciate.
- hutrdvnj 5y ago
  Recently, I stumbled upon a book "Seven Sketches in Compositionality: An Invitation to Applied Category Theory" where the authors decided to design the difficulty of the chapters like this: https://i.ibb.co/349JLsf/difficulty.jpg https://i.ibb.co/349JLsf/difficulty.jpg (image from the book) I like this approach better, because most math books have some easy introductionary chapters and then it gets harder and harder, because the authors assume that they laid out the basics in the first chapters. The authors might be right technically, but it's very hard for the readers to go through a chapter that is 100% new material. In "Seven Sketches in Compositionality" they try to somewhat reset the difficulty for each chapter by starting again with introduction and motivation for each chapter separately. This makes it much easier for me to get into the material of each chapter and to read the whole book.
  - ivansavz 5y ago
    Thx. That helps a lot. I agree re-contextualizing and smooth-starting each section in a textbook seems like a very good idea. This will probably make the textbook more amenable to "random access" learning too.

ivansavz 5y ago

That is very interesting, I would have never thought of using a "duty cycle" as low as 20% in a math/science textbooks. I agree that every chapter should start by connecting the material to past knowledge, and briefly reviewing some of the prerequisites, but then surely the author should get to the new stuff after that? Perhaps your estimate of 20% doesn't include the repetition and worked examples? In general when a new concept X, I try to explain it at least three times, once informally, with terminology and definitions, with formulas, and with extra explanations. In my mind all these repetitions count as "new stuff," since they cover the material at different depth and bring new dimension to the concept. Perhaps you could give some examples of the 20% new max sweet spot? I'd much appreciate.

hutrdvnj 5y ago
Recently, I stumbled upon a book "Seven Sketches in Compositionality: An Invitation to Applied Category Theory" where the authors decided to design the difficulty of the chapters like this: https://i.ibb.co/349JLsf/difficulty.jpg https://i.ibb.co/349JLsf/difficulty.jpg (image from the book) I like this approach better, because most math books have some easy introductionary chapters and then it gets harder and harder, because the authors assume that they laid out the basics in the first chapters. The authors might be right technically, but it's very hard for the readers to go through a chapter that is 100% new material. In "Seven Sketches in Compositionality" they try to somewhat reset the difficulty for each chapter by starting again with introduction and motivation for each chapter separately. This makes it much easier for me to get into the material of each chapter and to read the whole book.
- ivansavz 5y ago
  Thx. That helps a lot. I agree re-contextualizing and smooth-starting each section in a textbook seems like a very good idea. This will probably make the textbook more amenable to "random access" learning too.