Solving problems is not only a goal of learning mathematics but also a major means of doing so. It is an integral part of mathematics, not an isolated piece of the mathematics program. Students require frequent opportunities to formulate, grapple with, and solve complex problems that involve a significant amount of effort. They are to be encouraged to reﬂect on their thinking during the problem solving process so that they can apply and adapt the strategies they develop to other problems and in other contexts. By solving mathematical problems, students acquire ways of thinking, habits of persistence and curiosity, and conﬁdence in unfamiliar situations that serve them well outside the mathematics classroom.
Use appropriate technology (including graphing calculators and computer spreadsheets) to solve problems, recognize patterns and collect and analyze data.
Explore vectors as a numeric system, focusing on graphic representations and the properties of the operation.
Scaffolded (Unpacked) Ideas
Develop, record, explain, and critique different strategies for solving computational problems.
Students should evaluate problem situations to determine whether an estimate or an exact answer is needed and be able to give a rationale for their decision.
Calculators should be available at appropriate times as computational tools, particularly when many or cumbersome computations are needed to solve problems.
Developing fluency requires a balance and connection between conceptual understanding and computational proficiency.
Computational methods that are over-practiced without understanding are often forgotten or remembered incorrectly (Hiebert 1999).
Part of being able to compute fluently means making smart choices about which tools to use and when.
Academic Vocabulary
Tennessee Academic Vocabulary for Problem Solving |
Algebra I