Topic: Mathematical enterprise |
Mathematics |
| Standard 9. Understands the general nature and uses of mathematics |
| | Level II (Grade 3-5) |
| | | Benchmark 2. | Understands that mathematical ideas and concepts can be represented concretely, graphically, and symbolically |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that mathematical ideas can be represented concretely |
| | | | | 2. | Understands that mathematical concepts can be represented graphically |
| | | | | 3. | Understands that mathematical concepts can be represented symbolically |
| | Level III (Grade 6-8) |
| | | Benchmark 2. | Understands that mathematicians often represent real things using abstract ideas like numbers or lines; they then work with these abstractions to learn about the things they represent |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that mathematicians often represent real things using abstract ideas |
| | | | | 2. | Understands that mathematicians work with abstract symbols to learn about the concept those symbols represent |
| | Level IV (Grade 9-12) |
| | | Benchmark 2. | Understands that mathematics began long ago to help solve practical problems; however, it soon focused on abstractions drawn from the world and then on abstract relationships among those abstractions |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that mathematics began long ago to solve practical problems |
| | | | | 2. | Understands that mathematics evolved from a focus on real world problems to relationships between abstractions and the real world |
| | | | | 3. | Understands that mathematics evolved from a focus on abstractions and the real world to the relationships among abstractions |
| | | Benchmark 3. | Understands that in mathematics, as in other sciences, simplicity is one of the highest values; some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that propositions are generated from a small set of rules |
| | | | | 2. | Understands that one of highest values in mathematics is simplicity |
| | | | | 3. | Understands that some mathematicians try to identify the smallest set of explanatory rules |
| | | Benchmark 4. | Understands that theories in mathematics are greatly influenced by practical issues; real-world problems sometimes result in new mathematical theories and pure mathematical theories sometimes have highly practical applications |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that pure mathematical theories sometimes have very practical applications |
| | | | | 2. | Understands that theories in mathematics are influenced by practical issues |
| | | | | 3. | Understands that real world problems sometimes generate new theories |
| | | Benchmark 5. | Understands that new mathematics continues to be invented even today, along with new connections between various components of mathematics |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that new connections are made every day between areas of mathematics |
| | | | | 2. | Understands that new mathematics continues to be invented every day |
| | | Benchmark 6. | Understands that science and mathematics operate under common principles: belief in order, ideals of honesty and openness, the importance of review by colleagues, and the importance of imagination |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that mathematics and science value order |
| | | | | 2. | Understands that mathematics and science value imagination |
| | | | | 3. | Understands that mathematics and science value honesty and openness |
| | | | | 4. | Understands that mathematics and science operate under common principles |
| | | | | 5. | Understands that mathematics and science value collegiality |
| | | Benchmark 10. | Understands that mathematicians commonly operate by choosing an interesting set of rules and then playing according to those rules; the only limit to those rules is that they should not contradict each other |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands that mathematics rules should not contradict each other |
| | | | | 2. | Understands that mathematicians operate by choosing rules and following them |