Entrance Slip # 8: Thinking about math textbooks

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As a former student, I don't know that I necessarily thought a lot about the language used in terms of using first/second person in problems. However, I do think the way problems were structured as absolute fact (such as the equations for the male/female height-femur relationship) shaped my attitude towards math. In contrast, I remember complaining about physics problems that told us to "assume friction is negligible," because I thought it was silly for us to be doing a "real-life problem" in a vacuum setting. I admitted I understood it was for simplicity in calculation but it still bothered me. Now I realize math had the same problems, but because the questions were stated as fact while the physics questions admitted their modifications, I hadn't questioned it. I think it also influenced the way I viewed math as more stable than physics or other sciences because we focused more on math "rules" and less on the experimental and uncertain aspects surrounding the situations in the problems we worked on.

As a teacher, I think textbook questions are often manufactured to fit a lesson instead of finding an application of the lesson content and modifying it to fit the skill level of the class. Of course, as mentioned on page 12, textbooks have to make certain assumptions of student knowledge and can't completely cater to a class, but they could still try to base their examples in real-life applications, or give better context. Going back to the femur/height example, I don't know a lot about proportions of the human body and these examples seem like generalizations made up for the sake of tests a math skill, which either should have been stated as such so students knew this wasn't some steadfast rule, or if it is, then that rule should have been explained more to spark interest in students.

In my opinion, textbooks are good for skill building questions, but less helpful in meaningful word problems or activities. In my opinion, word problems should be formed by the teacher so that the teacher can tailor them more to the students, make the problems more applicable to the environment around the students (i.e. where they live, what their context is with respect to the world etc.), and bring some of their own interests and ideas to those problems as this will likely spark more interest and inspiration in students than if the problems seem to come from a faceless source. The textbook may also offer further/alternative explanation to math ideas but I believe students generally turn to the internet for video explanations and easy-to-follow explanations instead of reading through the textbook, which may contain information that is either not being covered in class or is more difficult to follow. However, from what I have observed in classrooms and from my own experiences, workbooks with answer keys are almost better than textbooks because they provide the student a means to make sure they are on the right track. Thus, I think textbooks or workbooks can be useful for testing basic skills and as an additional source of knowledge, but I think classrooms can survive without them if the teacher is able to provide students with strong notes, their own problems that are more applicable, and perhaps use something like Khan Academy as a supplement to skill building problems from the textbook. One of the disadvantages to using something like Khan Academy is if students don't write their work down in a notebook, then they won't be able to refer back to their process at a later date.