Inquiry in Mathematics

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Inquiry in Mathematics

What does inquiry look like in Math? What distinguishes the Math classrooms at Cate? What are the main aspects of our Math program?

Foundational Principles and Distinctive Features of the Math Program at Cate

  • The over-arching theme of developing Problem Solving Skills carries through all of our courses.
  • We teach content in the context of problems and help students make connections.
  • We emphasize preparation for future math courses and demonstrate this by developing skills for college-level math and related quantitative courses.
  • We underscore the utility of math through applications, making classes active, relevant, energetic, and enjoyable.
  • We connect multiple representations of functions by using equations (symbolic), tables (data), graphs (visual), words (language), and applications when solving problems.
  • Our sequence of courses includes advanced and honors courses in PBL (problem-based-learning).
  • We incorporate statistics and computational thinking into our core sequence and also have advanced electives for further study.
  • We use internal and external measures to solicit feedback and evaluate our program.
  • The NCTM principles of practice are emphasized and attention is paid to common core standards.

We have a strong program and tradition of math competitions, characterized by energetic and enthusiastic participation in local (Westmont College Math Contest), state (Cal Math League) and national (AMC) contests each year. (More than half of our students annually participate in Cal Math League).

Student Skills and Learning Responsibilities

Cate students will be able to:

  • Formulate and solve problems with proficiency and skill, learning to “take risks” in their thinking.
  • Employ the inquiry skills of asking and developing useful questions.
  • Think deductively, employ mathematical reasoning, see patterns, generalize, and use logic.
  • Create, understand, and develop math models.
  • Communicate mathematically in writing and verbally through questions, discussions, and reflection.
  • Use technology as a problem-solving tool.
  • Demonstrate “number sense” and assess their own problem-solving methods (using reflection).
  • Be active learners, share their thinking, contribute, collaborate, and critique others’ reasoning to develop better models, arguments, & solutions.
  • Take responsibility for their own learning.
  • Attend to precision and persevere in their problem solving.
  • Understand “why” math works through proof.
    Appreciate mathematics as a creative, problem-solving endeavor, think like a mathematician and learn to “do” math in addition to learning valuable content.

Teaching Practices and Pedagogy

Cate Math teachers: “Explore before Explain” by

  • Starting with a problem, question, or dilemma to generate questions and motivate the content.
  • Using “guided discovery” to develop curiosity, engage student learning and “extend” topics.
  • Employing “essential questions” as themes across courses to help students make connections.
  • Structuring class time by using a variety of full-group discussions, cooperative learning groups, pairs, and individuals, with students presenting and sharing work on the white boards or ipads.

Teachers also:

  • Employ the methods and question techniques of Polya (How to Solve it) helping students to ask themselves key questions, recognize patterns, and learn what do do when they get “stuck.”
  • Challenge students to see “why” methods work, deriving and proving formulas and methods to increase understanding.
  • Use technology (Desmos, Geogebra, graphing calculators) as a tool to visualize math.