Representation Journal: Cultural Capital in Children's Number Representations

This article is based on an activity within a study in which 50 kindergarten, first and second grade teachers asked each of their students at the beginning of the year to create a sign for the door of the classroom that would tell visitors how many students were in the class. Some students made tallies or wrote numerals while others created graphs, used pictures or even made representations using money. Perhaps most intriguing and surprising to the teachers were the number of students who payed special attention to the race or gender of themselves and their classmates. One drawing included each class member with accurate skin and hair color. Another student created a bar graph including three bars, one for students with white skin, one for students with tan skin, and one for students with brown skin. This activity and others like it help teachers to understand the students ethnicity, culture and home life, which does in fact have an impact on how the student learns mathematical representations.

This is how I found the article to relate to the main points of the process standard of representation:

1) Students need to use traditional methods of representation to solve problems as well as create unique representations that are meaningful to them.

This article shows many examples of student work in which children used their out of school experiences and cultural background in order to create their own unique representation for the number of students in the class. The article also provides some examples of students' explanations of their work, which helps to further understand why the students choose to represent the class in the way that they did (McCulloch, 2009).

2) Students should use representations as a way of organizing and understanding mathematical concepts.

The example activity in this article helped many students to further understand one to one correspondence through the use of inventive representations. Some students also focused on other concepts through their representations such as grouping, charting, graphing and estimating (McCulloch, 2009).

3) Students will be able to apply their understanding of representations not only to mathematics but also to the world around them.

The article proved to teachers of mathematics that this is indeed true through the unique and surprising results of the study performed. Emphasis was placed on the fact that students' experiences out of school have a large impact on their thinking in school (McCulloch, 2009).

4) New technological tools provide additional methods of representation and allow students to better understand more challenging concepts.

The activity done in the article did not include any use of technology. However, teachers could have used technology by having students to create their representation using any number of computer programs that allow students to "draw" or "paint" using the mouse of the computer. This could be done instead of a pencil and paper drawing or in addition to the original representation.


McCulloch, A. W., Marshall, P. L. and DeCuir-Gunby, J. T. (2009). Cultural capital in children’s
number representations: Reflect and discuss. Teaching children mathematics 16(3), 184-
189.