# Our Method

Although Project SEED is nearly 50 years old, it is still on the cutting edge. Using ** questions** to guide students to the

**of mathematical concepts, Project SEED has always emphasized mathematical reasoning, conceptual understanding, and precise use of language. These skills are at the heart of the Common Core State Standards for Mathematical Practice. Project SEED’s time-tested feedback and involvement strategies actively engage all students in using these skills to explore advanced mathematical topics.**

*discovery*Project SEED’s pedagogy and curricula are adaptable to all grade levels. Topics explored in Project SEED lessons are carefully chosen from Algebra and higher mathematics to engage students’ interest, provide them with challenges and success, build their academic confidence, strengthen their basic skills, and prepare them to succeed in more advanced courses. Well-versed in state standards and local pacing guides, Project SEED Math Specialists work with each district and classroom teacher to embed and reinforce local standards in every lesson.

Project SEED has realigned its curriculum framework for each grade level to reinforce the Common Core State Standards for Mathematics. Our lessons help students directly, while classroom teachers will acquire teaching strategies and lessons for helping their students succeed with the new standards.

In a typical Project SEED lesson, students are posed a challenge problem. As students make conjectures, other students use signals to indicate their agreement or disagreement. Students are continually asked to justify their answers and explain their classmates’ reasoning in their own words. The Math Specialist never tells the students if an answer is right or wrong but instead asks a variety of questions to help the students solve the problem and determine the correct solution. By beginning with easily accessible or known concepts and proceeding to more difficult ones, the lessons help students gain confidence and acquire the skills to guide themselves to the understanding and solution of more challenging problems.

The Standards for Mathematical Practice are not mathematical concepts but are habits of mind. Project SEED lessons continually create opportunities for students to develop and practice these habits. The Math Specialists guide students through a group example of the processes that mathematicians and mathematically proficient students use to solve problems, allowing the students to apply their knowledge and higher-order skills to tackle rigorous mathematical content. Simultaneously, classroom teachers see and receive coaching on how to encourage these practices in their students.

The Standards for Mathematical Practice are student actions. Project SEED’s methodology actively engages students with conceptual mathematics. Over and over again, the students are involved in communicating, reasoning and considering multiple solutions to complex mathematical problems. They practice what the Common Core State Standards preach.

The Standards for Mathematical Practices are an integral part of a typical SEED lesson as shown in this chart:

Mathematical Practices | Examples in SEED Lessons |
---|---|

1. Make sense of problems and persevere in solving them | In each lesson, SEED Math Specialists pose a challenge to the class and ask key questions to help the students analyze the problem. Students then make conjectures and work together toward determining which make sense and are asked to articulate the reasoning associated with their chosen pathway(s) to the solution. Similar yet more challenging problems are then posed and the dialogue continues. Sometimes questions are left open for days while students gather more skills or ideas to solve them. |

2. Reason abstractly and quantitatively | During SEED lessons, students are continually asked to explain and prove their conjectures. Students are asked to draw generalizations from specific examples and justify their reasoning. They discover how to represent generalizations symbolically and apply those generalizations to specific instances. |

3. Construct viable arguments and critique the reasoning of others | In Project SEED lessons students have frequent opportunities to communicate with each other about their reasoning and why they agree or disagree with their classmates ideas. They work at convincing their classmates that their own method works. Hand signals for agreement and disagreement help create a classroom atmosphere of respectful dialogue. |

4. Model with mathematics | Project SEED students apply the mathematics they learn to real life examples. For example, they may use their knowledge of 10 + 17 to solve a problem about temperature change or money. Students might decide to use a chart or graph to solve a problem involving a relationship between two quantities based on a real world situation. |

5. Use appropriate tools strategically | Pencil and paper, charts, tables, graphs and diagrams are examples of the tools that are used in SEED lessons. Occasionally a calculator or a spreadsheet is best. Students choose which to use for particular problems. |

6. Attend to precision | Students are frequently asked to check and justify their reasoning during SEED lessons. Math Specialists introduce and use precise mathematical language and often use literal interpretations of student answers to encourage their students to do the same. For example, if students are asked to correct 3^5=3x3x3x3, and the students say, Add one more three, the specialist will write 3x3x3x3+3. Then students keep revising what they are saying until someone says precisely what they mean. |

7. Look for and make use of structure | SEED students are often asked to solve several problems that follow a particular rule or procedure, and are encouraged to make generalizations and predictions that apply to similar problems. They are asked to use mathematical reasoning to confirm their hypotheses. Often students proudly proclaim, I see a pattern! and then are asked to articulate what they noticed and apply it. |

8. Look for and express regularity in repeated reasoning | SEED lessons often include patterns. Students are asked to discover a pattern and justify their reasoning. When students notice repeated calculations, they look for general methods and shortcuts. |