Unit 1: Teaching Number and Operation Sense

Topic 5: Rational Numbers

In alternating weeks we will pause in our discussion of mathematical concepts to discuss the teaching of those concepts. We will provide mathematics education readings or activities related to the mathematics concepts discussed the previous week. Many of these readings will be provided in electronic form, where you simply click and download the article. The activities will fall into the following categories.

  • Teaching Strategies:
  • Activities or articles that provide methods of teaching mathematical concepts or skills
  • Actual curriculum modules, units, or lessons that can be used in the classroom
  • Web sites that provide interactive applets, lesson plans, or history (demos of these sites will be provided using short Centra sessions that you can view anytime between Monday after 5:00 and Thursday)
  • Research in Mathematics Learning
  • Action research reflecting the study of classroom practice
  • Theory related to practice which provides insight into student difficulties in learning mathematical concepts and skills, and provides methods for overcoming those difficulties

A group discussion bulletin board will be provided on WebCT so you can share your views on the readings. The assignments will be posted Friday. You are to comment on the focus questions for the readings by Thursday night. You are to read your classmates comments and post at least one reflection on a classmate’s comment. These are open discussions on teaching and I will not subject them to right or wrong grading, however, you must participate in the discussion to receive credit for the assignment. On Thursday night we will hold a virtual office hour on Centra to discuss the assignment and questions on the Centra session posted on Monday.

1.1Article Reflection: Read and reflect on the following articles posted on WebCT

  • Connected Mathematics –Bits and Pieces II: Investigation 7: Dividing Fractions. Focus on division by fractions.
  • FOCUS: What would be the pros and cons of using this lesson in your classroom?
  • FOCUS: Using the discussion in the research reading below, identify at least one problem that illustrates methods supported by research and one problem that does not. Support your answer.
  • A Research Companion to PSSM –Chap 7: Fractions and Multiplicative Reasoning. Focus on conceptual understanding versus algorithmic approach.
  • FOCUS: Select one of the following dichotomies then explain how they are different and what implications it has for teaching: multiplicative reasoning versus additive reasoning, numeric versus quantity equations, magnitude of quantity versus measure of quantity, comparison versus inclusion.
  • FOCUS: What student difficulty identified in this article have you experienced with your students?

1.2Centra Teacher Resource Session: A Centra session will be posted by Monday of each week which provides a brief discussion of the assigned readings and a demonstration of websites related to teaching the topic of the week. View this session before the Thursday Virtual Office Hour. We will discuss questions on both the readings and Centra session on Thursdays.