syllabus13

University of Massachusetts at Boston
College of Advancing and Professional StudiesCritical and Creative ThinkingMathematical Thinking - Fall 2013

Instructor: Karen M. Crounse
Phone: 617-775-4087 (cell)
E-mail: kcrounse@hotmail.com
Class Time: Wednesdays, September 4 – December 11, 2013, 4:00 – 6:45pm
Class Room: To Be Determined
Website: http://crcrth650.wikispaces.umb.edu

Course Overview

What are the critical and creative thinking skills used by mathematicians to understand concepts and solve problems? How do we develop these skills? In this course, we will begin with an exploration of our own backgrounds in mathematics to understand where our perceptions of and emotions toward mathematics began. We will then focus on different topics in mathematics allowing us to delve into problem solving and reflect on our thinking. Through experiential learning, students will build their understanding of mathematical ideas and highlight their own thinking skills. Next, we will explore the development of skills including math education historically and around the world. Readings, discussion, research and problem-solving are used to understand both historical and present-day understandings of what is important in mathematics learning. Finally, students will synthesize their understanding of mathematical thinking in a culminating in-class presentation on a mathematics topic of interest. The objective of this course is for students to build an understanding of and appreciation for mathematical thinking and incorporate these skills into their own

Learning Outcomes

At the end of this course, students will be able to
  1. Reflect on their own mathematical development and perceptions
  2. Describe key critical and creative thinking skills used in mathematical problem solving
  3. Describe Polya's problem solving strategy and apply his questioning techniques to solve problems
  4. Describe Hyde's braid model of problem solving and apply it to solve problems
  5. Explain how the brain learns mathematics
  6. Describe different points of view in mathematics education
  7. Explore an area or solve a problem in mathematics and describe the mathematical thinking skills required

Accommodations

Sections 504 and the Americans with Disabilities Act of 1990 offer guidelines for curriculum modifications and adaptations for students with documented disabilities. If applicable, students may obtain adaptation recommendations from the RossCenter (287-7430). The student must present these recommendations to each professor within a reasonable period, preferably by the end of the Drop/Add period. If you have a disability that may have some impact on your work in this class and for which you may require accommodations, please contact the RossCenter for Disability Services. The RossCenter for Disability Services is located in the CampusCenter, UL 211. You can contact them by calling: 617-287-7430 or sending an email to: ross.center@umb.edu. Once you have received your accommodation letters, please meet with the instructor to discuss the provisions of those accommodations as soon as possible.

Overview of Classes

Part I: Introduction to Mathematical Thinking
Class Date
 Topics/Activities
 Assignments Due
Class 1:
September 4, 2013
 Theme: What is Mathematics?
  • Overview of Course/Syllabus
  • Problem Solving Activity – Crossing Over
  • Exploring Mathematics Anxiety
  • Introducing Four 4's
  • Mathematics Autobiographies
 Reading:
Tobias, Sheila, Overcoming Math Anxiety, Chapter 2
Class 2:
September 11, 2013
 Theme: Historical Problems in Mathematics
  • Student Presentations
  • History of Math - Video
  • Stations – Historical Problems and Solutions
  • Overview of Thinking Skills
Class 3:
September 18, 2013
 Theme: What do Mathematicians Do?
  • Math Anxiety - Reflecting on our Actions
  • Speaker – Mathematics Professor
  • Student Presentations
  • Overview of Thinking Skills
Class 4:
September 25, 2013
 Theme: Introduction to Problem Solving
  • Student Presentations
  • Complete History Activities
  • Polya - Key Quotes
Class 5:
October 2 , 2013
 Theme: More Problem Solving
  • Student Presentations
  • Introduce Ten Students in a Boat


Part II: Developing Mathematical Thinking – Movements in Mathematics Education

Class 6:
October 9, 2013
 Theme: Introducing Hyde
  • Student Presentation
  • Finish Ten Students in a Boat
  • Group Summaries of Hyde
*
  • Class Reflection
  • Paired Problems Due
Class 7:
October 16, 2013
 Theme: Hyde and the Learning Cycle
  • Student Presentation
  • Group Summaries of Hyde/Discussion
  • Further Work of Hyde
  • Applying Hyde - The Rendezvous of Two Spies
  • The Learning Cycle - Text-Based Discussion
  • Four 4's
Class 8:
October 23, 201
 Theme: How do we develop Mathematical Thinking?
  • Student Presentation
  • Mathematical Thinking - Summarizing and Connecting Ideas
  • Four 4's
  • Learning Target Tracker
Class 9:
October 30, 2013
 Theme: History and Themes in Mathematics Education
  • Student Presentation
  • Math Education Timeline
  • Constructivist Approach - The Chef's Story
  • Four 4's
Class 10:
November 6, 2013
 Theme: Alternative Views of Mathematics Education
  • Student Presentation
  • In-Class Debate
  • Alternative Models of Mathematics Education
Class 11:
November 13, 2013
 Theme: Current Trends in Math Education
  • Speaker: Department of Education, PARCC
  • Student Final Project Presentation
 Opinion Paper - Models of Mathematics Education
Class 12:
November 20, 2013
 Student Final Project Presentations

Part III: Application of Mathematical Thinking Skills

Class 13:
December 4, 2013
 Student Final Project Presentations
  • Final project with written assignment
Class 14:
December 11, 2013
 Student Final Project Presentation
End of Course Reflection
Course Evaluation
http://bit.ly/CCTEval

Grading System

Students will be assessed based on the following assignments:

Math Autobiography (20 points)
Your perceptions of math and your mathematical thinking skills are colored from your own education and experiences in mathematics. This essay provides a starting point for your analysis of and development of mathematical thinking.

Class Reflections (10 points each/ 100 points total)
Through reflecting on the mathematics and methods in each class, students will gain a deeper understanding of how they understand mathematics. The journal should be written as a weekly reflection of class activities. The journal should include your reaction to class activities and thoughts about your own understanding of the ideas presented.

Opinion Paper – Models of Mathematics Education (50 points)
Several models of mathematics education will be discussed in class. In this opinion essay, you will examine the models to answer the question “How should mathematical thinking be taught?” Although this is an opinion piece, be sure to use resources and research to support your opinion.

Mathematics Problem Presentation and Written Assignment (100 points)
The final presentation should be in the form of a lesson about a problem; students will present to the class about a specific situation in mathematics. Ideas for topics can be selected from one of the on-line class resources provided. In addition, if you have a topic in mind and need resources, please ask! I have a library of mathematics book available for use. The written portion of the Student Presentation includes a summary of your presentation and the types of mathematical thinking required for your problem.

End of Course Reflection (25 points)
The end of course reflection should focus on the question “What are mathematical thinking skills and how are they developed?” This paper should include general reflections about class activities as a whole as well as your reflection about understanding mathematics thinking and how it developed throughout the course.

Your grade for the semester is based on the percentage of points that you earn. The total number of points possible is 295 points. The following are percentage thresholds for each letter grade:
A Range
 A 95%
A- 90%
B Range
 B+ 87%
B 83%
B- 80%
C Range
 C+ 77%
C 73%

Resources for Math Problems

Illustrative Mathematics
http://www.illustrativemathematics.org/

Mathematics Assessment Project/MARS
http://map.mathshell.org/materials/index.php

Linking Math with Art Through the Elements of Design
http://www.share2learn.com/asilomar07packet.pdf

OhioResourceCenter's Problem Corner
http://www.ohiorc.org/for/math/problem_corner/

NRICH: Enriching Mathematics
http://nrich.maths.org/frontpage

The Math Forum @ Drexel
http://mathforum.org

The Problem Site
http://www.theproblemsite.com/problems/mathhs/

Mathwire
http://www.mathwire.com/problemsolving/probs.html

Balanced Assessment
http://balancedassessment.concord.org/

National Council of Teachers of Mathematics - Illuminations
http://illuminations.nctm.org