On the first day back after the winter holiday, you are visiting with your fourth-grade class before getting down to work. You ask whether anyone received any "mathematical" presents. One boy says that he was given a mathematics game from his uncle's country. He says that the game is very interesting and has lots of variations and asks whether he may show how it is played.

What would you do? Would you let him go ahead and see what develops? Would you say, "That would be nice, but we do not have time to do it now--maybe later," or perhaps, "Excellent, show me after class, and I will decide then whether we can play it." Are mathematical games a part of your curriculum? More than likely, you would make a choice about the game in the way that you normally do and not think much more about it. But the fact remains that you must make a choice, and that choice depends on your values.

Consider the following situation, which occurred in my classroom many years ago and has stayed in my memory. I was working on fractions with a lively class of youngsters and asked them to name a fraction between 1/2 and 3/4. One particularly eager student offered the answer 2/3. When I asked how she knew that 2/3 lies between the other two fractions, she answered, "You can see that on the top, the numbers go 1,2,3, and on the bottom, they go 2, 3, 4. The 2 is between the 1 and the 3, and on the bottom, the 3 lies between the 2 and the 4, so 2/3 must be between the other two fractions!" That answer was certainly interesting, but how would you react to it? Would you say, "No, that is not the right reason," or "Yes, very interesting, but I do not think that will work for any two factions," or "Very interesting. Let's see whether that will be true for any two fractions?"

Consider this final situation: As the teacher, you ask your students to think of a mathematical problem that can be linked with a photograph of a woman selling produce at a rural market. One student, Miguel, suggests that the question is a trick! He states, "There is no mathematics problem here. The woman has never been to school, and she does not know any mathematics." How would you react to Miguel's comment? What would you do if the class agreed with him? Suppose that only the boys in the class agreed with him; what would you do? Whatever decisions you make depend on your values, and through the choices you make, you are implicitly shaping the values of your students.

In this article, I share some ideas from research that examines the connection between mathematics and culture, focusing particularly on the values that we convey when teaching mathematics and on how we do so.

Mathematics, Culture, and Values

Human beings everywhere and throughout time have used mathematics (Bishop...

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