By the end of this course, you will be able to think in functions — to look at a quantity that changes and see the machine that changes it, in a table, a graph, an equation, and a sentence all at once. 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 four 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.
- See the family resemblance — transformations do the same thing to every function they meet; learn the recipe once and use it everywhere.
- Model the real thing — a cooling coffee, a Ferris wheel, a savings account: each one is a function wearing a costume, and a good model earns its keep.
- Grow visibly — your Math Journal is where struggle turns into evidence; see How Marks Work.