On Thinking About Math Textbooks

Textbook use is a tricky subject. On one hand hand, they can contain relevant academic examples that can be difficult to find, such as the equation of human height and femur length; also, at the grade school level, they contain plenty of exercise question for honing mechanical proficiency. On the other hand, as the authors have pointed out, textbooks can overvalue the formal and deductive approach to a fault (experiments and observations have their role in mathematics), give the impression of issuing commands to the reader in a top-down fashion, and promote detachment in spite of drawing from real-life examples (apersonification versus depersonification).

Speaking of which, when I went through junior high and high school, I do not think I saw much textbook use; custom handouts were already prevalent. Still, if the technology is inadequate or papers are difficult to come by, I suppose there is little choice.

As for the examples (height and femur equation algebra with Figure 2, hand dropping coins with Figure 1, word choice for problems),

as a student:

• Figure 2 would actually lead me astray, thinking that height is a scalar multiple of femur length, when it is not exactly so
• I actually visualized myself doing the experiment in Figure 1 without difficulty.
• Not that mechanical practice is unimportant, but I suppose I might feel like a soldier going through orders when it comes to how exercises are worded

as a teacher:

• I would actually highly value the height and femur equation- here is a Diophantine equation being used for anatomy in real life! I would try to present a diagram drawn by myself based on Figure 2 rather than presenting it as-is.
• Figure 1 could potentially be interpreted as "the teacher" or "the author" doing the experiment. Thus, it may do me well to prompt students with phrases like "visualize yourself..."
• Knowing that language is important for promoting engagement, as far as mandatory worksheets go, I would probably create my own with words chosen deliberately towards that end.