# Math 4 Curriculum

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A bit of philosophy regarding the teaching of mathematics:
Thus a teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking. (Polya, 1945)
The National Research Council identified five strands of mathematical proficiency:
1. Conceptual Understanding: Refers to the "integrated and functional grasp of mathematical ideas", which enables students to learn new ideas by connecting those ideas to what they already know.
2. Procedural Fluency: Defined as the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.
3. Strategic Competence: The ability to formulate, represent, and solve mathematical problems.
4. Adaptive Reasoning: The capacity for logical thought, reflection, explanation and justification.
5. Productive Disposition: The inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one's own efficacy.

Mathematics is the language of physics and many other disciplines, such as finance, economics, computer science and engineering (which has sometimes been referred to as applied physics). But mathematics is much more than that. For many mathematicians, mathematics is purely a human endeavor, similar to that of music for musicians and paintings and sculptures for artists: it is pursued for the joy of gaining insight and making new discoveries.

In this course, we will be exploring the world of mathematics from both perspectives. Much of what we will cover will be learning the language of mathematics and using those skills to solve problems, but we will also explore the more abstract nature of mathematics and (hopefully) develop an appreciation of its inherent elegance and how that elegance can manifest in abstract concepts. This exploration will be undertaken primarily using the resources from the CPM Education Program: Calculus Third Edition, which has a very strong emphasis on problem-based group work (collaboration and mathematical discourse). Other activities and short projects will also be used as a part of this exploration. For example, for each of the enduring understandings, there will be open-ended explorations that give you the opportunity to communicate the depth of your understanding.

In addition to exploring the world of mathematics, we will also focus on preparation for being successful with college-level mathematics. Students will be supported in learning essential skills: following lectures, note-taking, organization, using textbooks , calculator fluency, using office hours, using on-line resources, and so forth.

The work we do in math (and what we will present at Exhibition in December) will also be connected to a yet-to-be-determined over-arching theme of the year. As part of the theme, you will be reflecting on your growth as a mathematician, your growth in understanding what mathematics is, and your growth in being prepared for college-level mathematics.