**MATH
5020/7020**

**Arithmetic
for Middle Grades Teachers**

**University
of Georgia**

**Fall
2014**

Mondays,
Wednesdays, and Fridays, 10:10 – 11 am, room 111 Aderhold
Hall

**Instructor**:

Dr. Sybilla Beckmann, Josiah Meigs Distinguished Teaching Professor of Mathematics

501
Boyd Graduate Studies Building

706-542-2548

email: sybilla@math.uga.edu

Please
contact me as soon as possible (by email or phone) if an illness or emergency
prevents you from attending class.

**Office hours**:
Regular times to be determined. Please donÕt hesitate to e-mail me or call me
with questions or to make an appointment to meet.

**Writing
Intensive Program (WIP) Teaching Assistant**:

Lauren Huckaba

427J
Boyd Graduate Studies Building

542-2722

email: lhuckaba@math.uga.edu

**Office
hours**: Regular
times to be determined.

**Assignments,
test schedules, and announcements**

**This course is part of your preparation to teach
math** in
grades 4 through 8. When you teach, you will select mathematically worthwhile
tasks and problems, ask questions, listen to your studentsÕ mathematical ideas,
orchestrate discussions, and expect students to reason about and make sense of
math. To do so, you must develop a strong and flexible understanding of the
concepts you will teach. Therefore we will go deeply into the ideas about
numbers and arithmetic that students learn in grades 4 – 8.

The course
content is closely linked to the *Common
Core State Standards for Mathematics*, which include **Standards for Mathematical Content** and **Standards for Mathematical Practice**.
When you teach, you will help your students develop habits of mind of
mathematical thinkers by engaging in the mathematical practices. In doing so,
you will help your students develop 21^{st} century competencies, which
include critical thinking, reasoning and argumentation, flexibility,
appreciation for diversity, communication, collaboration, and responsibility
(see the National Research Council report, *Education for Life and
Work: Developing Transferable Knowledge and Skills in the 21 ^{st}
Century*). Therefore, in this course we aim to foster the following
dispositions and practices:

**Adopt
a Ògrowth mindsetÓ**
– Ability is not fixed but is something that can be improved by working
at it. Ò[A] proven intervention is to tell
junior-high-school students that I.Q. is expandable, and that their
intelligence is something they can help shape. Students exposed to that idea
work harder and get better grades. ThatÕs particularly true of girls and math,
apparently because some girls assume that they are genetically disadvantaged at
numbers; deprived of an excuse for failure, they excel.Ó (From the NY Times
4/16/2009 article *How to Raise our I.Q*. by
Nicholas Kristof. See also the Institute of Education
Sciences (of the US Dept. of Education) Practice
Guide, *Encouraging Girls in
Math and Science*, Recommendation 1). And: ÒPeople who believe in the
power of talent tend not to fulfill their potential because theyÕre so
concerned with looking smart and not making mistakes. But people who believe
that talent can be developed are the ones who really push, stretch, confront
their own mistakes and learn from them.Ó (Dr. Carol Dweck,
as quoted in the NY Times 7/6/2008, If YouÕre
Open to Growth You Tend to Grow).

**Engage
actively with mathematical ideas and stretch your thinking about math** – People learn
through active engagement with ideas and by building the ideas in their own
minds. In class, you will often be asked to solve and discuss problems and to
think about mathematical ideas in new or different ways. Make productive and
active use of that time. This includes allowing yourself time to think and
grapple, even when you are stuck or struggling. Throughout the course, try to
think critically about ideas and work towards expressing ideas with greater
precision. Look for interesting connections to other ideas and look for things
that are surprising or neat. Try to ask and answer deep explanatory questions.
There is strong evidence that the practice of asking and answering deep
explanatory questions is important for learning according to the Institute of
Education Sciences (of the US Department of Education) Practice Guide on *Organizing
Instruction and Study to Improve Student Learning*. Understand that
lines of reasoning, explanations, and making sense of concepts and ideas are
just as important in math as skills and procedures. At its core, math is about
ideas.

**Persevere** – Keep trying to
understand an idea or solve a problem even when you donÕt Òget itÓ right away.
Persistence and commitment to continued learning are vital to success in the
long run, much more so than being talented or Òquick.Ó See mistakes as
opportunities to learn. Note that the very first practice standard in the *Common
Core State Standards for Mathematics* (page 6) is ÒMake sense of
problems and persevere in solving them.Ó

**Monitor
your understanding and reflect on the ideas you are learning** – Think about
your thinking and look for ways to extend and improve your learning and
understanding. According to the Institute of Education Sciences (of the US
Department of Education) Practice Guide, *Improving
Mathematical Problem Solving in Grades 4 Through 8*,
there is strong evidence that monitoring and reflecting are important for
learning. Take responsibility for your learning and seek help when you need it.

**Be
an active part of a learning community** – Learn with and from your classmates.
Listen carefully to their ideas, explanations, and problem-solving approaches.
Think critically about what you hear. Listening to others can be difficult and
confusing at times, but itÕs an especially important skill for teachers. As a
teacher you will need to listen closely to your students to determine how they
are thinking about mathematical ideas so that you can build on what your
students know. Recognize that in class we are working together to make sense of
ideas, which will involve some false starts and errors. Incorrect answers are
valuable opportunities to determine where the flaws lie. Be comfortable
agreeing or disagreeing (you may feel more comfortable saying you Òrespectfully
disagreeÓ). Support each otherÕs learning. Nudge each other towards greater
participation and engagement.

**Policies and additional information about this
section of MATH 5020**