I was reading a blog about the culture of teaching. The author commented on how the changes in the culture of teaching from the 60's to now have influenced and changed what is expected but because the current teachers tend to use what ever culture we were raised in.
This lead me to thinking that this is not the only culture that effects our students and their learning. Think about the students who are raised in homes where they hear "I was never good in math." or "I couldn't do math when I was in school." from their parents when they ask for homework help. These answers reinforce the idea that you are born with the ability to do math. It is a shame when students think early on that they won't be able to do it because their parents have issues from childhood. My dad always said "I didn't learn it that way but I'll try my best." I thought that was an encouraging answer.
What about students who grow up in a culture where math is more intuitive or less formalized such as in many native cultures where they use their body parts to create clothing that fits the person properly. In many Alaskan Cultures they use fingers to measure certain things because the finished product will be proportional to the wearer rather than relying on one size fits all.
In addition, they might build a fish drying rack that is based on the height of the primary user or creating netting with wholes that are say 4 fingers wide. They do not use rulers, measuring tapes or any other type of tool. What about those people who navigate by the stars. It is said the polynesians who sailed to Hawaii used the currents and the starts to get there!
All of these students are good at mathematics but not with the formal variety. I've been trying to figure out ways to help students learn they are good at it and are able to do math by trying to create or find a bridge between their cultural math and formal math. Some good resources for Alaska Native math include Math in a Cultural Context, and Village Math.
For other students who are in to building things or art, I would look at activities that would all them to see the math in each topic and the math its associated with. The problem is that we can't always teach math the way we want due to everyone elses demand.