A neat study in

__Educational Studies in Mathematics__(link) points to a familiar yet disturbing characteristic of elementary mathematics texts.There is evidence that the strength and number of cause and purpose connections determine the probability of comprehension and the recall of information read (Britton and Graesser, 1996) and can indicate a teacher's or writer's concern for reasons (Newton and Newton, 2000). Even when writers withhold reasons and provide activities to help children construct them, they cannot assume that this will happen. In books, a concern for reasons, therefore, is often indicated by their presence. Clauses of cause and purpose can, within limits, serve as indicators of this concern (Britton and Graesser, 1996; Newton and Newton, 2000). . . . Clauses are commonly used as units of textual analysis (Weber, 1990). Amongst these clauses, clauses of cause (typically signalled by words likeas, because, since) and purpose (typically signalled byin order to, to, so that) were noted.

Having these data, researchers then compiled the
"reason-giving" statements into seven different categories based on
their "explanatory purpose." The results from the study are shown
below. The labels used are my own.

The first four categories (working
counterclockwise from the largest section) were considered non-mathematical.
Forty percent of the clauses in the sample provided "the purpose of and
instructions for games and other activities intended to provide experience of a
topic"; 22% provided "reasons in stories, real-world examples and applications
and in descriptions of the basis of analogies"; 1.3% provided "the
purpose of text in terms of its learning aims and objectives and could be
described as metadiscourse"; and another 1.3% of the clauses
"justified assertions of a non-mathematical nature." Nearly 65% of
"reason-giving" in the texts was non-mathematical.

The next two categories were considered
mathematical. Just over 13% of the clauses in the sample provided "the
intentions of procedures, operations and algorithms for producing a particular
mathematical end"; and just over 9% "attempted to justify
[mathematical] assertions (e.g., 'It is a square number because 5 × 5 = 25').

Clauses in the final category (symbols) were
considered mathematical or non-mathematical, depending on whether or not the
symbols in question were mathematical ones. These clauses provided "the
purpose of certain words, units, signs, abbreviations, conventions and
non-verbal representations."

This is not to say that writers explain only through clauses of cause and purpose. They may use other devices to the same end and this analysis does not detect them. There is also what the teacher and the child do with the textbook to support understanding, perhaps through practical activity (Entwistle and Smith, 2003). This approach does not detect these directly. The aim of the study, however, is to consider the potential of the children's text to direct a teacher's attention to reasons.

It is important to remember that the results do

**not**tell us that, for example, 40% of the clauses in the sample were instructions. They tell us that 40% of the "reason-giving" clauses were used in instructions. The graph above shows how "reason-giving" statements*were used*in the textbooks.
Although these results are generally supportive
of the conclusions drawn in the study, they also provide further support,
especially in light of these values . . .

Clauses of cause ranged from nil to 3.96% of text (using clauses as the unit) with a mean of 0.68% (s.d. 1.08). Clauses of purpose ranged from nil to 8.03% of text with a mean of 4.77% (s.d. 2.08).

. . . for the long-standing contention that contemporary
elementary mathematics textbooks are, primarily, classroom management tools.

Newton, D., & Newton, L. (2006). Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom? Educational Studies in Mathematics, 64 (1), 69-84 DOI: 10.1007/s10649-005-9015-z