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Module 1 

Problem Solving in Mathematics

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The Common Core State Standards for Mathematics identify eight “Mathematical Practices” — the kinds of expertise that all teachers should try to foster in their students. They go far beyond any particular piece of mathematics content, describing instead what mathematics is really about, and why it is so valuable for students to master. The very first Mathematical Practice is:

“Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.”

This module will help you develop these very important mathematical skills, so that you will be better prepared to help your future students develop them.

Week Objectives

  • Explain the difference between a problem and an exercise in mathematics, and give examples of each.
  • Tackle several challenging problems and persevere in solving them.
  • Catalog, describe, and apply several problem solving strategies.
Activities Icon

Due This Week

  1. Journal

    Due: Friday, January 17, 2014

    Please submit before 5pm

      1. Set up your Google Docs Journal:
        • Open the template.
        • Click on File, then Make a Copy. 
        • Under Enter a New Document Name, use the following format [Math 111 Journal Spring 2014 - First + Last Name].
        • Do NOT click on Share it with same people.
      2. Work on your Journal 1: Your Experiences with Math. See your personal Google doc for full questions.

  2. Post Discussion

    Due: Friday, January 17, 2014

    Please submit before 5pm

      • Post your discussion response after completing Online Session: Part 2.

Assignment Icon

Online Sessions, Readings, and Videos

  1. Part 1

    For first half of week (Sunday to Tuesday). Includes Before We Meet (due before Online Session 1), Online Session 1, External Resources.

    View Session
  2. Part 2

    For second half of week (Wednesday to Friday). Includes Before We Meet (due before Online Session 2), Online Session 2, link to Discussions.

    View Session

Instructions:

  1. Introduce yourself by sharing your full name, place of residence.
  2. Why do you want to become a teacher?
  3. What do you expect to learn from this class?

After posting, reply to at least three other students’ introductions.

This forum activity should be posted in the discussions below before Friday 5pm.

  1. 1. Linda Sakamoto, Kaua’i
    2. I have three younger siblings and helped my mom home-school all of them. Ever since having that experience I decided that I wanted to become a teacher or some kind.
    3. I hope to review some of the fundamentals of math and maybe learn about how to think about math.

    Looking forward to virtually meeting everyone!
    – Linda

  2. 1. Haunani Kendall, Kapa’au, Hawai’i Island
    2. I love kids. Their energy gives me inspiration to teach. I think education is the most important thing you can give to young people.
    3. Basic elementary school level math.

    Thanks
    -Haunani

  3. 1. Elizabeth Nantes, Hagåtña, Guam
    2. My parents are teachers here at the University of Guam and raised me to value education.
    3. Different concepts of math and ways to think about it.

    – Liz