Thinking about math textbooks

My responses to the textbook content (texts and images) are not entirely in the model constructed in the paper by Wagner & Herbel-Eisenmann. In my view, the primary purpose of the text and image selected by the authors in a section of mathematics textbook is usually to demonstrate the theory in that particular section. For example, pre-calculus textbook printed by McGraw-Hill Ryerson in 2012 has the following text and image in the section of logarithmic and exponential equations.

Using this equation, students see the application of logarithmic functions and practise using them. After playing the position of learners, students and teachers can play the positions of the inquirers. 

A: Directly related to the text and image

(1) How this equation was developed?
(2) When and where this equation was developed?
(3) What mammals were used in the research that arrived at this equation?
(4) Is it approximation over some types of dogs (particularly white dogs from the image)?
(5) What is the precision in relation with the range of m-values?
(6) Would this equation be still valid in the future or in the regions outside of the research area?
(7) Why they choose white dog for the image?

B: Expanding the inquiry

(1) Would that kind of research be done to develop other equations?
(2) Can we approximate the total amount of food per day needed to feed the domestic dogs all over the world that fulfil the calories requirement?
(3) Can we approximate how much money is spent by the dog owners per day buying this magnitude of food per day?
(4) What about the production, from farm-to-mouth processes, business activities involved in making this amount of food available to all domestic dogs?
(5) With respect to the processes and materials involved, what are the environmental consequences?
(6) What about the social conflict or inequality that could emerge because we have students who own dogs and students who do not have dog in class? Or, could this be an opportunity for making a peaceful constructive discussion for our future?
(7) Can we do this kind of math-work for human being with all such inquiries repeated?
(8) Then, how do we compare the people who eat more and the people who eat less with respect to any context of our choice?

The role of teacher is helping expand the idea contained in the ‘texts and images’ not only in the textbook but also from external resources relevant to the topic under study. Teacher listens to the way students view the content and make productive and meaningful discussion possible. Students change position between learner and inquirers.

The diversity in the students in the class would make diversity of such inquiry. Each student brings to the class the culture, knowledge and environment in which the student grows up. Environmentally conscious student would like to inquiry about the relationship between the text/image and environmental matters. Culturally sensitive student would like to ask relationship to the breed of mammal. 

Students who own a dog and students who do not own a dog could have different inquiry or debate over certain point of view. The location of the school can also play a role. The inquiry on ‘where’ the research was done in developing the equation in the text tells us about this.

Let us look at the example in the paper:

This example seems to be demonstrating the application of linear functions. Outside of this scope there is again a large world for inquiry. We can make similar questions as above. Due to two equations involved we can add inquiries with respect to gender.

This time it is related to human being. The image used is of a male can be of a certain ethnic group. This image can create diverse cultural discussions. The accompanying text does not say if these two equations are for all ethnic groups or for some. In addition to the purely mathematical inquiries as above we can add more depending on the experience of teachers and students and level of freedom or comfort they enjoy in public matter discussion.

1) Are these two equations valid only for the ethnic group of the person described in the image?
2) If students think yes to question (1), then more questions arise on the equations for other ethnic groups?
3) What about the geographic, climate, food and life style differences on these equations?
4) If we write the generalized equation as H = a + bF, then what values of ‘a’ and ‘b’ would be advantageous for a particular type of sports?
5) Using more complex formulas and knowledge, will future human genetic engineers, under certain leadership, attempt to modify the genetic design of us? Will that be a disaster in genetic, ecology and entire world? How do we prevent such kind of events?
6) If the ‘a’ and ‘b’ values of certain group of people are significantly different from these two equations, are the people of this particular group abnormal in some sense?
7) Suppose there is a physically handicapped student in the class. Will this study create feeling of inequality? What shall we talk when we arrive at this page in the textbook?

We can also inquiry about authors who make decision on what to include in the textbook.
1) Can the authors of the textbook explain to the public on their selection criteria?
2) Who choose the authors? Do members of the public participate in this? How can a public participation in school textbook design be possible?
3) Can we look at job advertisements or detail descriptions of the works of authors?
4) Are there stories on ‘from thinking and feeling to printing’ processes of actual design of content written by authors of school textbooks that we can read?
5) Do businesses dominate the design of school textbooks? What are the consequences?
6) What is the relationship between authors, textbooks, teachers, teaching resources actually used in class, class discussions, student families, and their future world?

Conclusion

The role of textbook is complex and diverse. Making of textbooks and how they are used are important because of their contributions to future. In general, educators (authors, schools, authorities, teachers inclusive) should be mature, well experienced in their subject matter plus in general knowledge, logical, and diversity-minded persons. Any piece of public work should not be done by a group of people. Diversity-involved discussions and decision making are needed. Diverse, deep, wide, logical and critical thinking should be promoted in class because today students will become leaders, authors, publishers, business owners, politicians, and decision makers in the future. 

Here are some reasons for using a certain content of the text book:
(1) Relevant to the curriculum
(2) Enough amount of resource provided (e.g. time)
(3) No content that could create atmosphere of social inequality, below is an example from an exercise problem in a textbook. This is the type of content to avoid using in teaching

(4) Content offers critical thinking, generalization, and discussion for the betterment of the future
(5) No better alternative available