We will explore the content standards using what I call the Vertical Articulation of the standards. In other words, instead of grouping them by grade level they are grouped by content standard to that students can see the progression of the content; a critical element when trying to differentiate instruction.
For the practice standards I have added an additional two practices which I believe to be central to the study of mathematics and which have been totally neglected by the authors of the Common Core. Here they are:
9. Enjoy and celebrate mathematics
Mathematically
proficient students enjoy and appreciate the aesthetics of quantitative and
spatial relationships. They are captivated by the challenges of resolving
mathematical problems and are able to use their mathematical understanding in
creative and novel ways. They will demonstrate genuine curiosity when faced
with novel mathematical situations. Younger students will share their excitement
about finding several different ways of making 6, of understanding why a square
number is so called and that pi is a ratio between the circumference and
diameter of a circle and not just a number that goes on forever. Older students will recognize and celebrate
the artistic elements associated with fractals and the aesthetic
characteristics of algebraic relationships.
10. Recognize linguistic and cultural diversity in mathematics
Mathematically
proficient students will recognize that math is not the same the world over.
Living in diverse communities students will recognize that there are
differences in mathematics and the ways we learn mathematics based on local and
global cultural differences. As they work with students from different cultures
they will be aware of the ways language development, as well as the language
used in mathematics, are major factors
in learning math for all students as well as those who are English Learners.
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