Writing and Reading Mathematics

This unit identifies mathematics topics for consideration, discusses the topics and offers suggestions about writing assignments that might support the topic, the learning about the topic, processes used in performing the mathematics, or activities that support on-going writing in the classroom.

The presentation of the authors material works well, but I am less than pleased with the discussion of the mathematical content. The content is almost exclusively discussed from a procedural perspective. For example the discussion of part-whole relationships (fractions) is approached from five different topics. The first topic, What is a fraction?, does not present a strong conceptual perspective. Fractions are discussed symbolically, and modeled as circles and rectangles. One writing activity for this topic is: "Draw and cut out a square. Divide the square into two equal parts, measure the parts and explain their relation to the square with words and numbers. Repeat the process, dividing by four, eight and so forth." (pg. 31, Activities #2)

The writing activity is a fine activity to think about comparing the fractional size of objects. The basis of the assignment is using circles and rectangles and research indicates that if the primary focus of understanding is based on just those shapes and if the exploration of the shapes of the pieces isn't varied then student understanding of the concept will be very limited. The use of the writing assignment will hopefully help bridge the transfer gap but the writing activity would be much stronger if it were presented in conjunction with strong visual development.

The rest of the fraction topics, as are most of the topics in this unit, are treated from a procedural point of view. I understand that the authors are not writing a text book but a book about how to support instruction through writing. I believe they are making a decision to treat the topics traditionally to show how writing can support the learning of the mathematics. I just find it difficult to gloss over the approach that they are using. By presenting the material procedurally with little connection, they are espousing the traditional procedural approach that I think leads to teaching that does not value conceptual understanding. Additionally, it seems that by approaching the material from this perspective the authors are

I don't think that many of the activities embrace a deeper understanding of the content, which is as important to the development of student understanding as the writing is.