I haven't posted in a long time. I've been studying and trying to learn more about number sense and how to teach number sense. I teach older students, and it seems like number sense is either strong or weak in students before they get to me. What can I do to strengthen number sense later in students' academic careers? When a student is in middle school and does not have good number sense, how do we fix it? If we do not build up number sense, all other mathematics learning will be an uphill battle at best.
Do I teach these students the skills they should have learned before age 6 or 8 now? How do I go about that without making them feel marginalized? Surely most of them would realize that these are skills that their peers already possess. Number sense is such an important foundation for mathematics that I cannot in good conscience ignore these deficits. How do I build these students in a supportive and nurturing way? I want to show these students that they can succeed. They spend enough time believing that they are stupid. I do not want to add to that. I do, however, want to help them fill in the gaps in their understanding so that they can be successful as soon as possible.
I truly believe that if I can build these skills in my students who lack them, they will find success in math classes in general far easier to attain. Am I being naive? Surely it is not "too late" for these kids to get the skills they need. I mean, after all, people can learn to read as adults, so can't I teach a person number sense in middle school? I'm sure going to try.
For those of you who might not be sure exactly what I am seeing, I have a few examples. One student, when asked "If I take two-thirds away, how many thirds remain?" had absolutely no clue what the answer was until I drew a picture for him. Another has to count the faces of a cube each time to figure probabilities using dice. He doesn't "just know" that there are six sides on a cube. Students with poor number sense don't really understand that fractions, decimals and percents can all represent the same thing. When changing 6 1/2 into a decimal, I had a student write 6.12. He can't remember that .5 is the same as 1/2. He has to take 1 and divide it by 2 to get the decimal equivalent, and he's not sure enough in his division skills to do that reliably. He has learned some number skills, and memorized some basic facts and procedures for doing basic arithmetic, but it is not at all intuitive to him. When he looks at a problem, he has no idea if the answer should be closer to 2 or 20,000, so he never looks at his answer and thinks, "That doesn't make sense. I must have made a mistake." This is because none of the math makes sense to him.
Ok, everybody, I'd love some feedback on this. I would love some strategies for nurturing number sense in older children. I'd love to hear where I'm spot on and where I'm way off base.