MTH 143 - Mathematical Reasoning for Education -

Rediscovering Mathematics

Pi King

Spring 2015 - Dylan 3.126
Fall 2011 - Michael:  3.137
Fall 2009 - Kevin:   3.10

Pi Queen

Spring 2015 - Faith 3.137
Fall 2011 - Amanda: 3.139
Fall 2010 - Megan: 3.14136 !!
Fall 2010 - Jen: 3.4128
Spring 2010 - Nicole:  3.138
See Chapter 12 for Details

Professor Shai Simonson

Office: 306 Stanger   
Phone:  (508) 565-1008

Description:   This is the required math course for all education majors in the state of MA.  It is primarily a course on math content, but it should make you a better math teacher.  Through the high school level, mathematics in the US is often taught woodenly and without passion.  Most people never experience mathematics' poetic, experimental, and involved world until it is too late;  and the world of mathematics is misunderstood and under-appreciated.  This course is about how to appreciate, read, discover, and do mathematics.  A few of us have had inspiring math teachers who opened up a world of exploration and excitement, but most of us have been exposed to dull curricula and unmotivated teachers.  What passes for mathematics education in the United States is sometimes a sham and a shame - a collection of dry memorized methods.  This course teaches you how to appreciate mathematics and become one of those inspiring motivating teachers.  You can change the way mathematics is taught and reshape the popular perception of mathematics in the United States - one child at a time.

Goals:  To empower future teachers by inspiring them with a passion for mathematics, grounded in personal experience, and supported with creative materials directly relevant to the classroom.  Mathematical subareas for state of MA requirements will be covered as shown below:
Numbers and Operations:                                                   Chapters 1, 2, 5, 6, and 12.
Functions and Algebra:                                                       Chapters 3, 8, 9, and 11.
Geometry and Measurement:                                              Chapters  8 and 12.
Statistics and Probability:                                                  Introduction and Chapter 10.
Integration of Knowledge and Understanding:                    Introduction, Chapters 6, 11, and 13.

Lectures:  TThF 11:30 - 12:20

Lecture Format:  Each unit is an interactive exploration of a mathematical topic, varying in percentage of lecture versus discussion.  The first lecture of each unit considers a topic or problem and investigates and explores.  Reading assignments with challenges follow for homework.  Your progress on the challenges is the topic of the subsequent lectures.

Text and Readings: All readings for this course come from Rediscovering Mathematics, and appear in the syllabus below.

Special Dates:  April 10, Friday is Passover and I will not be in class.  I will announce alternative plans for that day.

Exams:  There will be occasional quizzes, together worth 20% of your grade.  There will be one final examination worth 30% of your grade.  The best way to study for quizzes and exams is to review the challenges, your journals, and your notes.  Here are some practice challenges.  The final will be Thursday, May 7, 1:30 PM in 001 Stanger, our usual room.

Groups:  Studies have shown that success in mathematics is directly related to how much a student incorporates study into his/her social life. You should find a group of three people with whom you feel comfortable working all semester.  If you prefer, I will assign you to a group.  Try to pick group members with whom you enjoy spending time, and whose study habits you respect.

Journals:  Your journal is worth 30% of your grade.  Journals should be done in groups of three.  At the end of each chapter, I will assign a collection of challenges of varied difficulty.  Your journal should detail your group's attacks on various challenges. You should include a summary of the attempts, dead-ends, and any relevant discussions - whether or not you were able to solve the challenge.  In addition to these notes, whether a challenge is straightforward for you or whether your group learned the solution in class, write up the solution in your own words at the end.  The book's solutions to other challenges can be used as a model for writing solutions.  Always rewrite the challenge in your journal before recording your discussions or solutions, and use figures or drawings if it helps you explain your ideas. 

It is a good idea to rotate the job of the person who records your group's progress on the challenges.  I will collect your journals twice during the semester to grade and give you feedback.  Your group's final journal submission should be edited, and handed in at the end of the semester.  There will be one grade for the entire group.

Class Participation:
Class participation is worth 10% of your grade.  I expect you to interact with me, your group, and the rest of the class. You need not be extroverted, just willing to engage in investigation, conjecture, and discovery. 

Project:  A mini-lesson plan (20 minutes worth) is required in which your group will interactively teach the class a new mathematical idea using exploration and experiment.  Your project is worth 10% of your grade.  Your group should choose a topic using the resources below or you can choose your own topic.  You are encouraged to discuss your choice with me, but whether or not you do, your choice must be approved by me before starting to work on the details.  Projects will be delivered over the last two weeks of the semester.  The grading rubric will be discussed in class and depends on:  organization of lesson, appropriate and effective handouts, math knowledge and expertise of topic, interactive discovery content, and further suggested work in closing.  One grade will be given for the entire group.

Questions based on your presentations may appear on the final exam, so make a special effort to understand each group's work and not just your own.  You are encouraged to hand out a couple of possible problems based on your presentation that I might include on the final.  Your lesson plan and copies of any handouts should be attached to the back of your journal and marked "project".  References you used and links for further investigation should be included.  There should be enough details in your write-up so that another teacher could use and reproduce your lesson-plan.

Grades: Your grade is based on 20% quizzes, 30% final, 10% class participation, 10% project, and 30% journal.  Normally, 90%+ is A, 80%+ is B, etc.  However, I may curve these cut-offs in your favor at the end of the semester, based on class average.

Resources for Projects
Content Focused
  1. Cut The Knot - Best Overall Resource - Start here!
  2. Riddles - Fun
  3. Museum of Math - Great Collection of Puzzles from MOMath
  4. Internet Math Library - Broad and Education-Oriented
  5. Great Puzzle Collection - Michael Shackleford
  6. My Materials - Various
Teaching Focused
  1. Khan Academy - Free Lessons - Huge Variety
  2. Math is Fun - Just What it Says
  3. Rice Math -  Fun and Eclectic Lessons
  4. MathcountsOnline Practice
  5. Math-ManiCS - Lessons for Discrete Math
  6. Math Circle



Starting Out - How does this trick work? And this one?

Introduction How to Read Mathematics - An example using basic probability.
1 Discovery and Experiment in Mathematics - An investigation of long division and repeating decimals.

2 Calculating Tricks - A deeper understanding of arithmetic and algebra.  When and when not to use calculators.  Art Benjamin doing his tricks.  
Here is Art on his soapbox about math education.

3 Infinite: Puzzles and Paradoxes - Euclid and geometric series

5 What's Mathematics Good For? - Finding math in daily life.

8 Pythagoras' Theorem - The relationship of algebra and geometry.
Paulo Porta version of My Pythagoras's Theorem Proofs

Quizzes throughout term
if time allows
Three Averages - Different tools for different problems.

Games and Gambling - Probability and combinatorics at carnivals and the casino.

9 Memorizing Mathematics - The pitfalls of memorizing mathematics:  solving quadratic equations without memorizing.

12 Areas and Pi - A geometric exploration of Pi and its appearance in unexpected places.
Sea of Solomon Slides
if time allows
Soccer Balls and Counting Tricks - Algebra and combinatorics meet graph theory.

13 Think - Putting it all together.

Fun Stuff and Puzzles