Review_Author: Eric Sisofo
Book_Author: Terezinha Nunes, Analucia Dias Schliemann, David William Carraher
Book_Title: Street Mathematics and School Mathematics
Reference: 1993, Cambridge University Press
Time: 4:42:39 PM
Remote Name: 126.96.36.199
Nunes, Schliemann, and Carraher (1993) set out to determine the similarities and differences between school mathematics and street mathematics in this interesting, well written book. Their goal was to establish connections among three types of mathematics: one constructed by children outside of school, one embedded in everyday cultural practices, and another that school aims to teach. In order to do this, a definition of street mathematics had to be formed. The authors defined street mathematics to be method used in problem solving which are not school taught methods (informal). Based on this definition, the authors conducted several studies comparing how street vendors, farmers, and everyday non-schooled people solve problems compared to schooled people. They found some very interesting similarities and differences between street mathematics and school mathematics.
Their first study observed young street vendors who were children in Brazil. The interviewers acted as customers and asked the children questions which made them use arithmetic skills. A week later, a formal test was given to these same children and the questions were similar to the ones asked in the "real" situation. The authors noticed that the children did much better in the "real" situation than in the formal test situation. There are many reasons for this discrepancy. One reason was because the students tried to do the school taught algorithms in the formal test unsuccessfully, but in the "real" situation, they did their arithmetic based on quantity. They were able to keep the meaning of the problem in mind while solving the problem in the "real" situation, but in the formal setting, the meaning of the problem was dropped. Another reason for the discrepancy was because in the "real" situation, arithmetic was done mentally on quantities and during the formal test, arithmetic was done using written symbols. Manipulation of symbols burdened the children on the formal test. In oral mode, "two-hundred-twenty-two" proceeds from larger to smaller and works in ways to preserve the relative value of numbers. In written mode using symbols, when adding "222" to another number, the algorithm starts with the ones, then the tens, etc. which enables children to forget relative value of numbers. This leads to more errors in written arithmetic.
The results were similar with older children when solving problems. School taught children were not able to connect mathematical relations with the meaning of the problem situation. However, street mathematics is practiced orally and one works from the problem situation to mathematical relations quite easily. Thus, since the connection is not made in school, there are more errors made by school taught children. There was evidence which suggested that farmers with no formal schooling performed better than students who were in school for five years because they were able to make this connection between the problem situation and the mathematical relations.
All of the studies done on street mathematics so far have only implemented direct problem solving. The authors wanted to determine if people who used street mathematics could do inverse problems better than school taught children. The research provides evidence that the majority of street mathematics people could solve inverse problems and understood the concept of proportionality much better than school taught people. The reason for this discrepancy, besides the reasons listed above, is because the algorithm to solve proportions contradicts the informal concept of how to solve proportion problems. Calculations across variables are carried out in the algorithm, but in street mathematics, this is never done.
This book illustrated the differences and similarities between street mathematics and school mathematics. It strikingly provided evidence that street mathematics people do much better with calculations than school taugh people. One implication for education that was provided is that realistic mathematics education should be implemented into the curriculum. This type of education lets students confront "real" problems and determine different solution strategies. Another implication is that critical thinking should be implemented in the classroom. We must get the students to think about what is important in the solution of the problem. We must connect the meaning of the problem situation to the mathematical relations so that they can understand the relationship.
I really enjoyed reading this book and recommend it to anyone in the math education field. It supplies the reader with some striking evidence to grapple with and promotes thinking of how we can improve mathematics education in the U.S.