ED 526A: Learning and Assessment in Elementary
Mathematics
appelbaum@arcadia.edu;
215-572-4476
As
described in the course catalog, this is a seminar/workshop emphasizing the use
of a variety of instructional materials in the teaching of mathematics, grades
K through 8, including manipulatives, calculators, and other non-textbook
resources. Keep this in mind: Not all materials are "things." Some
tools are "ideas," or ways of thinking about what could be happening
during an educational encounter.
This semester, you will develop:
· a conception of mathematics as an
evolving literacy
· notions of how to integrate mathematics
with other subjects in the school curriculum
· a comprehension of the expectations
that people hold for mathematics N-8
· effective strategies of achieving the
first two goals through or in spite of the third
We will spend a lot of time thinking about teaching as ongoing assessment (gathering information that helps you learn about your students, make decisions, and reflect on your own practice). (This is different from "evaluation," by which I mean judging, rating, or grading the quality of student performance.) As part of our course, you will practice working as a mathematician, lead a small group of children through a mathematics unit where they work as mathematicians, and find ways to connect mathematics education theory with the world outside of Arcadia.
Enjoy yourself! The purpose of this semester is to re-think what it means to do mathematics, what it means to think mathematically, what it means to live mathematically ... how to connect with the mathematical in your own and your students' everyday lives ... how to help people to cherish and nourish the mathematics ... how to seek mathematical challenges ... [you get the idea...]
This course is also
designed to help students seeking elementary certification to demonstrate the
following State Standards:
I.D. Mathematics instruction at the elementary level in accordance
with the Pennsylvania Academic Standards including:
·
Prenumber concepts, number
sense, whole numbers, fractional numbers, measurement, algebra, geometry,
estimation, probability, statistics, reasoning, and problem solving
·
Use of developmentally
appropriate manipulatives, calculators, computers, and emergent technologies
II.B. Planning of instruction based upon knowledge
of the subject matter, learning theory, classroom environment, students, the
community and the Pennsylvania Academic Standards including:
·
Alignment of curriculum, instruction, and assessment
·
Multidisciplinary curriculum integration
·
Collaborating with appropriate subject area
specialist
II.D. Selecting, implementing and adapting effective
instructional strategies, curriculum resources and technologies in
collaboration with other educators to meet the needs of diverse learners
including:
·
Assessing, identifying and building on the students’
prior knowledge, experiences and skills in each content area
·
Problem analysis, creativity, problem-solving, and
decision-making skills
·
Inquiry, direct instruction and cooperative learning
·
II.E. Developing, utilizing, and communicating
appropriate measurement and evaluation procedures in the instructional program
II.F. Monitoring students’
understanding of content, providing feedback to students and adjusting
instructional strategies as needed
III.A.
Professional organizations and professional journals
III.C.
Establishing and maintaining collaborative relationship with basic and higher
education colleagues, families and the community agencies to meet the needs of
diverse learnersIII.D. Communicating effectively with parents/guardians, other
agencies and the community at large to support leaning and elementary education
Required Texts:
Cathcart, George, Pothier,
et al. 2006. Learning Mathematics in
Elementary and Middle Schools: A Learner-Centered Approach. FOURTH EDITION
(Multimedia Edition). Pearson, Merrill; Prentice Hall. ISBN 0-13-170059-6.
Appelbaum, Peter. In press.
Embracing mathematics: On Becoming a
Teacher and Changing with Mathematics. Manuscript copies will be
distributed in class.
Office
Hours: M W
2:00-3:30 & by appointment (especially before and after class)
Please make the following arrangements in order to meet
the requirements of this course:
- You’ll need to find 2-3 children to work with as
a teacher twice a week for 60 minutes February 23 through April 13. Start
now making contacts, so that you will be ready by the end of February. Any
K-8 students meeting at any location on any days of the week is
satisfactory for this part of the course. You will work with the same
children for a total of ten sessions, leading them through a mathematics
investigation unit. I encourage you to work in pairs with 4-6 children
together; this is not required if it is too difficult to arrange.
- Find access to a videocamera and a digital camera
for your work with the children; if you do not own these and can’t find
anyone to borrow from, you may be able to use an
- Please check your personal calendar for any
potential conflicts in attending weekly class meetings now, before the semester starts, so
you can work out alternatives is possible.
- If you do not know how to access your
- Our textbook comes with a useful CD of video
excerpts that you will need to view as part of your reading. You’ll need
to find a way to view these videos, either on a home computer, on
Assignments:
Your grade in this course will be based on four parts:
1. Participation and Contributions. A classroom community is made by people who do more
than show up. The nature of this course requires that you get involved
and try things. Just being here is not enough. You must throw yourself
into the experiences, and share your thoughts. Only by talking to others about
what you are thinking about, and by listening to the ways that others are
thinking, will you begin to articulate for yourself and others what the
complexities are, what the issues are for you, how other people might
interpret what you would like to make possible for young people. Now, some people
are not comfortable talking in class, and others think it unfair to put someone
else "on the spot." So we need to expand our notion of
"participation and contributions;" this might entail looking over
this week's television guide and coming to class with a printed list of good
shows to watch this week; or videotaping a news segment that we can watch
together; or clipping an article out of the newspaper; or just making sure to
ask the questions you want answered -- as many times as necessary in order to get
us to address the important points. Feel free to suggest ways that people can
contribute other than just talking a lot, even though talking a lot will be a
good thing. We also need to think about not talking and listening: how
to help each other to facilitate somebody else's developing idea, as this will
be a valuable skill in teaching. More than two absences from class,
consistently late arrival, and/or consistent need to leave early will result in
a maximum grade of C- for this part of the course.
2. Mathematician’s Notebook. Our
course begins with an opportunity to explore what it means to be a
mathematician. We will do this by pursuing mathematical investigations as
groups and individuals. Your mathematician’s notebook provides tools to pursue
these investigations. It also prepares you to utilize this kind of notebook
with your students. The criteria for this notebook is described on the Notebook
Specification Sheet; we will discuss it in detail in class.
3. Teacher
Portfolio. In the second part of the
semester, you will maintain a teaching portfolio as you work outside of class
leading a small group of children through a mathematics investigation unit. The
portfolio is a way of organizing your work and making your process transparent.
It will be organized around the following processes and products: Planning,
Assessment, and Inquiry/Research. This portfolio is described in detail on the
Portfolio Specification sheet. When you turn in your portfolio include a brief
letter of introduction (no more than two pages is necessary). This letter
should help orient me to the work that you have done while in the field. In
this letter, please answer the following questions: a) What five things out of
all the things you have done have you pulled out and placed at the front of the
portfolio? b) Why have you chosen these five things? Together, what do they say
about you as a teacher? Or, what do they say or not say about teaching and
learning? c) How do you want me to be a reader of your work? How can I be a
part of your work? What kind of feedback would be useful in supporting your
work as a teacher in training? I will respond to your letter as part of my
evaluation of your portfolio.
4. The
Final Action Project. You will
build this third project out of much of the work that is in your Teacher
Portfolio. The final part of the class (the archaeology) is dedicated to
supporting the identification of significant aspects of your current and future
work as a teacher, and connecting the related ideas and possibilities with an
appropriate audience. This is another archaeological opportunity for you to
take the ideas and experiences of this course and take action through them in a
way that is most relevant to your immediate and long-term goals. The final
event of our course will be shaped by our action proejcts.
Your Course Grade:
|
Participation and
Contributions |
15% |
|
Mathematician’s Notebook |
25% |
|
Teacher Portfolio |
35% |
|
The Final Action Project |
25% |
Tentative Schedule:
|
Date |
Topic |
In-Class |
Preparation for
Today |
|
January 19 |
Welcome! What is mathematics? What is teaching/learning
mathematics? Working as a Mathematician
I: Opening |
Setting the course agenda Math investigations |
|
|
26 |
Working as a Mathematician II:
Developing Investigation Polya’s 4 Phases Mason’s
Specializing/Generalizing |
Math investigations |
Read:
Appelbaum, Prologue; Work on explorations 0-4
for at least one hour; bring all rough work and supplies to class to continue
the investigations |
|
Tuesday 31 |
Teachers
and Mathematics Curriculum Materials: Janine Remillard, Ph.D.,
Assoc. Prof. of Educ.; Co-P.I., MetroMath: |
Toward a
Theory of Participatory Use The Center for Mathematics
in America’s Cities, Graduate School of Education, University of Pennsylvania |
Castle
Mirror Room 7:00 –
9:00 |
|
February 2 |
Planning and Assessment Working as a Mathematician
III: Doing Investigation Brown & Walter Problem
Posing |
Math investigations Mini-lessons as needed |
Read:
Appelbaum, Chapter 1; Cathcart, Ch.2 Polya phases at least 4X Mason Spec/Gen at least 2X |
|
9 |
Working as a Mathematician
III: more doing investigation IV: Putting Work back Out
into World |
Math Investigations Mini-lessons as needed |
Read:
Appelbaum, Chapter 3; Cathcart, ch.4 Polya phases at least 3X Spec/Gen at least 2X Problem Posing at least 2X *Identify an aspect of your
work so far |
|
16 |
A Psychoanalytic
Perspective Working as a Mathematician IV:
Puttting Work back Out Into World |
Clinical interviewing/ listening |
Read:
Appelbaum, Chapter 2 Work Out into World: Write: what you did; What
did you learn? What potential new
directions? |
|
23 |
Critical Thinking Working as a Mathematician V:
Archaeology |
New Contexts; puzzles;
extensions Prep for Teaching: opening |
Read:
Appelbaum, Chapter 4; Cathcart, Ch.3 Mathematician’s Notebook DUE |
|
March 2 |
Consumer Culture Working as a Teacher of
Mathematics |
Prep for Teaching: developing
invest.; observation sheets |
Read:
Appelbaum, Chapter 5: Cathcart, as relevant 2 teaching sessions |
|
9 |
Metaphors for the Classroom
Space Working as a Teacher Observation Assessment |
Prep for Teaching: doing invest.;
analysis of work samples; letters to students |
Read:
Appelbaum, Chapter 6; Cathcart, as relevant 2 teaching sessions Introduce obs.
sheets |
|
|
|
Spring
vacation |
|
|
23 |
Places Where People Learn
Mathematics Analyzing Student Work |
Prep for Teaching:
mini-lessons; work out to world; interviews |
Read:
Appelbaum, Chapter 7; Cathcart, as relevant 2 teaching sessions Ready to report on letter
conversations |
|
30 |
When Students Don’t Learn Facts, Procedures, Concepts Models & Representations
1 |
Prep for Teaching:;
archaeology Arithmetic & number facts |
Read:
Appelbaum, Chapter 8; Cathcart, as relevant 2 teaching sessions Work out encounter Ready to report on interviews |
|
April
6 |
TBA/AERA/AAACS |
|
Read: Cathcart,
as relevant 2 teaching sessions archaeology |
|
13 |
Models &
Representations 2 Workshop on Final Action |
Fractions |
Read: Back
to the Basics Work on Action Project Teaching Portfolio DUE |
|
20 |
Strands not yet covered Workshop on Final Action |
Ratio |
Read: Back
to the Basics Work on Action Project |
|
27 |
Strands not yet covered Workshop on Final Action |
Geometry? |
Work on Action Project |
|
May 4 |
Conference on Teaching
& Learning |
|
Final Action DUE |
Resources:
Peter’s Math Education
Weblinks: http://gargoyle.arcadia.edu/appelbaum/matheduc/mathweb.htm