I'm assuming your question is asking, do you think current high school math graduation requirements are approapriate?
If so, then yes.
Could they be higher yes, but is this practical in light of NCLB.
Without getting into an endless debate on topics that should/ shoudn't be covered in secondary math, math is useful for calculations and higher thinking later in life. It allows you to examine problems and look at alternative solutions.
Our elementary/ middle school recently swithch to Sinapore Math, any thoughts or opinions on this methodology?
We had a representative from Singapore Math come and speak at one of our professional development opportunities (the Illuminations Summer Institute), and it was definitely interesting! I, too, would be interested to know if others have employed Singapore Math in their classroom!
Another group of great curricula that support the 8 standards of mathematical practice getting at that deep conceptual understanding for K-12 include: Investigations for K-5, Connected Math for middle school, and CPM (College Preparatory Math) for the high school. All of these curricula focus on hands-on, inquiry, sharing of thinking and building to the formulas through modeling, conjectures, and generalizations. The kids aren't given the formulas to memorize. They are provided tasks to have them come to that understanding and formula. WOW, the difference in the approach to learning math is amazing. I have observed all of these curricula in the classroom as a math coach. Along with these curricula, teachers need good professional development on how to change their pedagogy. This isn't something that I have seen happening in the colleges. So teachers need a lot of training and coaching to change how they approach teaching and learning.
As to the graduation requirements - I am concerned with this as along as the math is taught in the traditional methods because many of our students are not good at memorizing and regurgitation. If all students are given an opportunity to understand the math behind the formulas, then the requirements could remain as they are. But what I see happening is the kids that are good at memorizing and using formulas are the ones that move on into the higher level courses and do well with this method of teaching. And those that don't understand why they are doing what they are doing and need to build the understanding are lost and struggle year after year in math and become the math haters of the world. Okay, that was my soapbox for the day.
I like the visual approach to Singapore math and using models to solve problems. Multiple representations are important for kids, and I like that Singapore math helps kids to develop some conceptual understanding about what they're doing with numbers. Seems more "real" and impactful than just teaching them a bunch of facts and algorithms to memorize.