Schedule of Classes, Readings and Assignments
The Teaching of Algebra 7-12: Credit Hours: 3.0
MTHED 1045/2035 Tuesdays: 5:30 – 7:10 Bldg: East Room:403
Professor:
Anne Burgunder
Email: [email protected]
Phone: 908-407-8364
Required Text(s):
•
Boaler and Humphreys, Connection Mathematical Ideas. Heinemann, 2005
•
Driscoll, Fostering Algebraic Thinking: A Guide for Teachers Grades 6-10, Heinemann, 1999
•
Fosnot, Catherine Twomey., and Bill Jacob. Young Mathematicians at Work. Constructing Algebra. Portsmouth,
NH: Heinemann, 2010.
Optional Text(s):
• Jacobs, Harold R. Mathematics, a Human Endeavor: San Francisco: W.H. Freeman, 1982 or later.
Class Number/
Date / Topic / Activity
1: (Jan 28, 2014)
Readings prior to class
Assignments Due
Syllabus Review
Come to class (every week).
Participate in activities and discussion.
Read:
Writing Assignment:
Typed summary of your reading:
2 pages max!
Chapter 1: You should be able to identify and
react to Fosnots’s beliefs about what algebra
is and how it should be developed.
Foundations of Algebra:
Seeing Structure
Factor Problem
Handshake Problem
2: (February 4, 2014)
Movement Problems:
Keeping Track of Change
Fosnot, Chapters 1-2
Holding a Math Congress.
Charles – Big Ideas
Locker Problem
Crossing the River Problem
Chapter 2: You should be able to compare
and contrast Big ideas – (Charles) with
Landscapes (Fosnot)
(updated 20140125)
3: (February 11, 2014)
Read:
Writing Assignment:
Developing Big Ideas Around
Equivalence Through Rich
Tasks
Fosnot, Chapter 4: The Role
of Contexts and Models.
According to Fosnot, why are contexts and
Models important?
Driscoll, Chapter 1: A
Framework for Classroom
Questions.
According to Driscoll, What is Algebraic
thinking and how do habits of mind and
teacher questioning facilitate its development?
Cube Problem
No more than 2 pages, 1.5 spaced.
Problems Due: Locker Problem
Part 1) Most of you realized that the perfect
square lockers were the ones that would be
left closed.
Explain why, in terms of the locker context,
(in terms of people walking through and
opening and closing locker doors) why this
happens.
Part 2) Think about what prompt you might
give if you were going to use this problem
with students and what materials you might
make available to students, and why.
(updated 20140125)
4: (February 18. 2014)
Read:
Writing Assignment:
Tools for Developing Ideas for
Combining and Decomposing.
Driscoll, Chapter 2:
Transition to Algebra through
Algebraic Thinking.
1) By reading VanAmeron, you will begin to
thing more deeply about what is algebra, the
approaches of algebra, the difficulties students
face and role of models. Make note of the
important ideas in this reading – bullet points
are fine, but be prepared to incorporate some
of these ideas into the rationale for choosing
the four problems below.
Algebra Lab Gear.
Border Problem – Design the
Border Problem
VanAmeron, Reinvention of
Early Algebra, pages 1-32
Common Core Practices
Area Model
Multiplying and Factoring.
Finding area, perimeter, volume
2) According to Driscoll, what is the bridge
between arithmetic and algebra? How does
this relate to the development of Algebra?
Choose 4 problems from this chapter that you
would give to and 8th grade class. Think about
the prompt that you would use and work out
what you think student work will look like (3
or more strategies would be ideal). Provide a
rational for choosing each problem that
connects meaningfully to the reading you
have done so far. (This may be done with a
partner.)
3) Think about the problems we engaged in so
far in class. Then, read the Common Core
Practices – one line at a time. Explain which
Common Core Practices we engaged in by
quoting the exact phrase from the practice and
giving precise examples of when we engaged
in each of the practices.
Problems Due:
In addition to the selection of problems from
Driscoll above, Think about 8 different
strategies for finding the number of edge
cubes on any size cube.
Explain how you would sequence out a share
and why. In other words, imagine that you
have walked around the room and you noticed
which students were doing the different
strategies. Which strategy would you
highlight first, second, third etc., in whole
class discussion? Why?
(updated 20140125)
5: (Feb 25, 2014)
Growth Problems:
Logo Problems:
Tree Growth Problem.
Double Your Money Problem
Read:
Driscoll, Chapter 3: Building
on Number Sense and
Number Theory
Driscoll, Chapter 4:
Expressing Generalizations
About Structure
Writing Assignment:
Reflect on ways in which the activities we
have done so far in class connect to the
Common Core Practices. Name exact
sentences from each of the Practices and give
precise examples of when we have engaged I
those practices.
Problems Due:
Cuisenaire Trains
CCSS Practices
6: (March 4. 2014) Raising
Consciousness about the
Common Core Practices.
Read:
Case Study
Response to case study questions due.
7: (March 11. 2014)
Topics for Research in
Teaching and Learning
Algebra ICME Mock Research
Conference
Scan and Choose 2 ICME
Articles to Read.
Read 2 additional articles
from the bibliographies of
each of the chosen articles.
Present Research.
8 (March 25. 2014)
Parent Functions
and Transformations
Read:
Writing Assignment: (2-3 pages): What are
the “big ideas” of CCSS in Algebra? How do
these ideas connect to other readings and
experiences you have had throughout this
course?
Developing Properties of
Equality.
Systems of Equations
Balance Scales
Computer Games
Green Globs
Driscoll, Chapter 5:
Expressing Generalizations
about Functional Relations
Driscoll Ch 7: Linking
Multiple Representations.
CCSS
9: (April 1. 2014)
Mini-lessons, Tasks and
Experiments in the
Math Classroom.
Fosnot Ch 8: Comparing
Quantities and Relations.
Writing Assignment: What is the role of
mini-lessons, tasks and experiments in the
math classroom?
Fosnot Ch 9: Mini-Lessons
Paper-folding experiments Jacobs Chapter 6
(updated 20140125)
10 (April 8. 2014)
Curriculum Materials
for Teaching Algebra.
Lesson Planning Design
Examine Curriculum Materials according to
focus groups.
Assessment.
11: (April 15. 2014)
World Café: Sharing topics
across focus groups.
Curriculum Materials of your
Choice.
12: (April 22, 2014)
Read EdTPA Guidelines
ED TPA
Video Cases
Boaler and Humphries
Chapters 2 and 3.
13: (April 29, 2014)
Fosnot, Ch 10: Proof
Proof
Handshake Problem
14
(May 6, 2014)
Last Class
Issues Raised from the Field
FINAL Exam, May ?, 2014
Examine Curriculum Materials according to
focus groups.
Watch the video: Respond to prompts
(aligned to EdTPA, then read chapters
Written Reflection.
Boaler, Ch 5 and 6
Loose ends.
Presentations
Final paper and presentation due.
First Week/ Month of School Assignment Due
(updated 20140125)