Let’s play a little game. We’ll call it Modern Algebra or Common Core?
For each of the following learning targets, determine whether it comes from my undergraduate Modern Algebra textbook or from the Common Core State Standards for Algebra I.
- Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
- Discuss… exponential functions with continuous domains.
- The polynomial ring…has features that have no analogues in the ring of integers.
- Polynomials form a system analogous to the integers.
- By “abstracting” the common core of essential features…develop a general theory that includes as special cases the integers…and the other familiar systems.
- With each extension of number, the meanings of addition, subtraction, multiplication, and division are extended. In each new number system—integers, rational numbers, real numbers, and complex numbers—the four operations stay the same in two important ways: They have the commutative, associative, and distributive properties and their new meanings are consistent with their previous meanings.
Answers in the comments.
3. Abstract Algebra
5. Abstract Algebra (I was very excited to find a quote with “common core” in it.
I realize that 1&2 might have been better contrasted with an Analysis textbook. But I’ve only so much time.
This activity helped me to notice that the main difference between the two documents is that CCSS always uses system where modern algebra textbooks use ring, field and group.
Interesting dissonance between #3 and #4.