As a teacher, when I observe the image of Figure 1: A hand doing mathematics (Lappan et al., 1998, p. 6), I think the disembodied, generic hand is simple enough to help students understand the process. There is no need to draw a person in that image. The unnecessary part of the graph can confuse the readers. This image is quite detailed, and it positions the students to recall their real-life experience that adding coins to the cup will eventually break the bridge.
As former students, the figure shows a very interesting scenario that someone is trying to test how many coins a paper bridge can hold when each side of the paper bridge has 1 inch on the books. The ”1-inch“ label is a clue. It will make me eager to figure out the paper bridge's holding capacity.
No matter as a teacher or as a former student, I think the textbook is necessary for learning mathematics systematically. Not like some other subjects, such as physical education and language, mathematics involves many concepts, theories, theorems, propositions, etc. We need a book to present them systematically. With a textbook, students could learn mathematics in a rigorous and systematic way. I always think learning Math is like building a skyscraper. The final height of the skyscraper will usually depend on how strong and deep the foundation must be built. To build a skyscraper, we need a guide book (Technical Drawings). Moreover, for Euclid's "Elements" and Euler's "Introduction to the analysis of the infinite", we all know how important these textbooks are.
There is one issue that I concern about. Math textbooks are too expensive to have for most students and schools. Some schools do not have sufficient funds to buy Math textbooks for students. And Math textbooks change versions every several years, so it is another difficulty for school. I observed students in my practicum school are still using Math textbooks in old the version.
Some people suggest digital textbooks or e-textbooks. I think students need to avoid spending too much time with electronic devices. There are many Apps on their electronic devices, so students cannot fully concentrate on the textbook and learning.
In conclusion, I think textbooks should be essential for Math learning, and they still play a fundamental role in schools.
You raise some interesting dilemmas for schools, about the cost and rapid obsolescence of physical textbooks, and yet the problems of too much screen time with e-books. Good point about the helpful role of textbooks as reference books to lay out the systematic structures of mathematics as it is taught.
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