This is a picture of a page of the alegbra 1 textbook my school uses. The students are learning about linear equations.

The book provides lots of worked out sample problems. What is frustrating about this book is that it references the sample problems right next to the actual problems students are supposed to do for practice (“See example 2, p. 356”). The sample problems are identical in structure to the practice problems, with different numbers.

For many of my students, when they see a problem that isn’t structurally identical to a previously-worked-out question, they tend to get very upset and are unable to make any progress on the question without some additional prodding. For many of the students I tutor, they rarely (if ever) encounter “un-taught” questions in their math class.

This plug-and-chug model of teaching math makes absolutely no sense: why would we possibly care if students are able to mimic an example problem and plug in different numbers? This textbook is explicitly encouraging students to just regurgitate a meaningless procedure they have practiced a bunch of times.

In most other books where there are worked out examples (but not a box next to every problem pointing to an analogous worked-out problem), students at least have to look through multiple example questions. If nothing else, they gain some exposure to all of the techniques in the section and (just as importantly) they practice being able to discern enough about an in-progress problem to decide which sample problem(s) provide the relevant information.

All of the push for higher standards and for more rigorous curricula is utterly meaningless if math is taught in this way. If math students aren’t learning how to THINK deeply, rigorously, and originally, I really don’t know what the point is of making them sit in math class every day….

We can do better than to teach our students from books/curricula like this.