By the end of this course, you will hold the two ideas this course was built to deliver: the derivative — the instant, made precise, after a year of circling it — and the vector, an arrow that does algebra. You will use the first to read any function’s story (where it climbs, where it turns, where it should stop) and the second to do geometry in three dimensions without drawing a single picture. And you will work the way mathematicians work: investigate, conjecture, verify, defend. The curriculum names seven processes that run through everything we do:
Mathematical Process Expectations
The mathematical processes are to be integrated into student learning in all areas of this course. Throughout this course, students will:
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- Problem Solving: develop, select, apply, compare, and adapt a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;
- Reasoning and Proving: develop and apply reasoning skills (e.g., use of inductive reasoning, deductive reasoning, and counter-examples; construction of proofs) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
- Reflecting: demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);
- Selecting Tools and Computational Strategies: select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
- Connecting: make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
- Representing: create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
- Communicating: communicate mathematical thinking orally, visually, and in writing, using precise mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.
The full set — every overall and specific expectation across the three strands — lives in the Curriculum folder, and each task page links to exactly the expectations it addresses.
Put plainly, week to week that means:
- Think on your feet — work problems you have not been shown how to do, at the whiteboards, in a room built for it.
- Conjecture the rules — the derivative’s toolbox is discovered here, pattern first, proof after, never handed down.
- Optimize honestly — the best box, the cheapest route, the smoothest landing: calculus answers “what is best” only after you say what “best” means.
- Grow visibly — your Math Journal is where struggle turns into evidence; see How Marks Work.