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Northern Kentucky University
College of Education and Human Services
EDMT 544 Methods and Pedagogy in Middle Grades Mathematics
3 credit hours Fall 2011
"Committed to the Development of All Learners"
The students, faculty, staff, and community of the NKU educational programs are committed to the
development of all learners through active collaboration and participation in coursework, projects, and
field experiences. The education programs in the College of Education and Human Services prepare
exemplary helping professionals who demonstrate the personal and professional knowledge, skills, and
dispositions necessary to provide for the developmental needs of all individuals in an increasingly
diverse, complex, and technological society.
KERA Initiatives
As students complete and implement projects and assignments throughout their education programs they
will address all components of the KERA initiatives: Kentucky Learning Goals and Academic
Expectations, the Kentucky Program of Studies, and the Core Content for Assessment.
EPSB Themes
All NKU professional education programs address and affirm the value of diversity in education, the
importance of helping all children develop reading and literacy skills, attaining high levels of skill in
assessing the outcomes of instruction, and using those skills to develop strategies for closing identified
achievement gaps. This course will provide students an opportunity to demonstrate their knowledge,
skills, and dispositions in the particular theme(s) of diversity, assessment, and closing the achievement
gap.
Kentucky Core Academic Standards
Preparation of Kentucky’s students for the demands of the 21st century requires districts and schools to
prepare every student for successful transition to post-secondary education, work, and the
community. The Kentucky Core Academic Standards help ensure that all students throughout Kentucky
are provided with common content and have opportunities to learn at high levels. The purpose of the
Kentucky Core Academic Standards is to outline the minimum content standards required of all students
before graduating from Kentucky public high schools.
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As education candidates complete and implement projects and assignments throughout their education
programs at NKU they will address all components of the Kentucky Core Academic Standards, which are
posted at this link:
http://www.education.ky.gov/users/otl/POS/POS%20with%20CCS%20for%20public%20review.pdf.
The work you do in this course is subject to the NKU Student Honor Code,
http://www.nku.edu/~deanstudents/documents/StudentHonorCode-Fall2007.pdf.
Students in the education programs must also adhere to the education programs’ Code of Ethics:
http://coehs.nku.edu/docs/COEHS_code_ethics_20.doc.
Students With Disabilities
Students with disabilities who require accommodations (academic adjustments, auxiliary aids or services)
for this course must register with the Disability Services Office. Please contact the Disability Service
Office immediately in the University Center, Suite 320 or call 859-572-6373 for more information.
Verification of your disability is required in the Disability Services Office for you to receive reasonable
academic accommodations.
Course Evaluation
Northern Kentucky University takes Instructor and Course Evaluations very seriously. It is an important
responsibility of NKU students as citizens of the University to participate in the instructor and course
evaluation process. During the two weeks* prior to the end of each semester classes, you will be asked to
reflect upon what you have learned in this course, the extent to which you have invested the necessary
effort to maximize your learning, and the role your instructor has played in the learning process. It is very
important that you complete the online evaluations with thoughtfully written comments.
Starting Spring semester 2011, the students who complete an evaluation for a particular course (or opt out
of doing so in the evaluation) will be rewarded for their participation by having access to their course
grade as soon as that grade is submitted by the instructor. On the other hand, any student who does not
complete the course evaluation (or opt out of doing so in the evaluation) should expect to incur a two
week delay in access to his or her course grade beyond the university's official date for grade availability.
To complete online evaluations go to http://eval.nku.edu. Click on "student login" and use the same
USERNAME and PASSWORD as used on campus.
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Course Information
Instructor Information
Sarah Kasten, Ph.D.
Office: BEP 262
Telephone: 572.5233
Office Hours: T, R 9:00 – 11:00, W 1:00 – 3:00 and by appointment
Email: [email protected]
Class Meeting Information
BEP 204
Wednesday 4:50 – 7:35
Course Communication
We will communicate using our NKU email addresses and Blackboard. We will adhere to the COEHS
Code of Ethics in our communication with one another. A NOTE ABOUT EMAIL: I will do my best to
return your emails within 48 hours of receiving them. I rarely check email on the weekend or in the
evening. You must plan ahead if you need to contact me with time sensitive information.
Textbooks/Memberships/Materials
National Council of Teachers of Mathematics Student E-Membership - $39
Join at www.nctm.org
Choose Mathematics Teaching in the Middle School as your journal
Optional Text:
National Council of Teacher of Mathematics. (2000). Principles and standards for school mathematics.
Reston, VA: Author.
This text can be purchased on the NCTM website after you have joined for a discounted rate.
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Course Description and Objectives
Learning to teach is not something that can take place in a semester, a year or even three years. Good
teachers are still engaged in considering how to improve their practice even after many years in the
classroom, searching for new ways to craft instruction to enable all of their students to learn. My goal for
this course is to provide you with frameworks for your continued exploration of what it means to teach
and how to do so well. In particular, my goals for this course are for you to:
▪ Deepen and connect mathematical content knowledge with student mathematical understanding. Being
able to do middle school mathematics is different from being able to teach it. A teacher needs a
different kind of understanding of mathematics content in order to make the math meaningful and
understandable to students, including the ability to clearly articulate specific mathematical goals for
each lesson and how these goals fit into the larger mathematical landscape of a course.
▪ Analyze from a new perspective what mathematics is and what it means to learn, do and teach
mathematics. Mathematics is a fascinating discipline that involves representing a mathematical concept
concretely and working through a problem to find a solution where the pathways are not well defined
and the solution involves combining existing knowledge in new ways. One of the beauties of
mathematics as a whole is the interplay between various areas of the subject. A particular way of
representing a problem may lead to an especially efficient or enlightening result. The job of a
mathematics teacher is to convey this sense of mathematics to students so they will come to value and
enjoy learning how mathematics works.
▪ Learn to listen to and look at students’ work as a way to inform teaching, using evidence from these to
make decisions. Teaching is about what students learn, and the only way you can understand what
students are learning is to focus on what students are doing. What does it mean for a student to “get” an
idea in mathematics? How can a teacher determine whether or not a student understands? How can
what you observe about what students do and say about mathematics help shape your instruction? What
kinds of tasks or assessments are the most effective in helping teachers evaluate student understanding?
▪ Learn to design and implement lessons in ways that engage students in learning (tasks, sequence,
discourse, questioning, use of technology) Professionals in any field share an emphasis on planning,
implementing and evaluating what they do; teachers are no different. Successful teachers create careful
and thoughtful plans for their lessons and use a range of teaching techniques that can be drawn upon to
help their students develop understanding and know when one technique may be more appropriate than
another. And successful teachers choose tasks and manage discussions so that all students have the
opportunity to learn.
▪ Learn to reflect on your practice – both from your perspective as a teacher, as a researcher, as a
learner, and from the perspective of what you see students learn. After implementing a lesson,
successful teachers evaluate whether their objectives have been met and use this information in an
ongoing way to shape their teaching so that all students learn in meaningful ways. They think about
teaching as ongoing research about their practice and use what they have learned to continue to grow as
a teacher. Successful teachers also recognize that they belong to a profession and use the resources
provided by their profession, journals, conferences, and colleagues, to support their growing
understanding of teaching.
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▪ Recognize what is meant by equity and access to quality mathematics for students, parents and
communities (including attention to policy) Opportunities for all students to learn high quality and
challenging mathematics vary from school to school and even from teacher to teacher. Recognizing
this and developing strategies to work with students from different backgrounds, cultures, and social
and economic contexts and to ensure they all have the same opportunities to learn the same
mathematics is a responsibility for all teachers, in particular mathematics teachers because of the unique
role of mathematics as a potential gatekeeper in schools and society.
The course addresses these Kentucky Teacher Standards as a part of in-class course activities, including
the final exam, and through course assignments (course assignments related to each standard are in
boldface):
STANDARD 1: THE TEACHER DEMONSTRATES APPLIED CONTENT
KNOWLEDGE.
(Interview Assignment, PTR Lesson, Leading a Math Problem Discussion)
STANDARD 2: THE TEACHER DESIGNS AND PLANS INSTRUCTION
(Interview Assignment , PTR Lesson)
STANDARD 4: THE TEACHER IMPLEMENTS AND MANAGES INSTRUCTION
(Interview Assignment, PTR Lesson, Leading a Math Problem Discussion)
STANDARD 5: THE TEACHER ASSESSES AND COMMUNICATES LEARNING RESULTS
(Interview Assignment, PTR Lesson, Leading a Math Problem Discussion)
STANDARD 6: THE TEACHER DEMONSTRATES THE IMPLEMENTATION OF TECHNOLOGY
(PTR Lesson, Expert Presentation)
STANDARD 7: REFLECTS ON AND EVALUATES TEACHING AND LEARNING
(Interview Assignment, PTR Lesson
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Student Activities, Evaluation, and Grading Policy
Students will attend all class meetings and participate in class discussion and group activities. In addition,
students will complete and earn credit for the following assignments and activities:
Interview Assignment
150
Plan-Teach-Reflect (PTR) Lesson *
150
Leading a Reading Discussion
50
Threading a Process Standard
150
Expert Presentation*
40
Weekly Journal & Math Problem
110
Midterm
150
Final Exam
250
Total 1050
Assignments indicated with * are acceptable for inclusion in a student’s portfolio.
Assignments will be given a letter grade based on departmental grading policy and the scoring guidelines
which accompany each assignment.
Graduate Plus – Minus scale
Letter
% Equal to or
Grade Point
Grade
Greater than
A
95-100
4.00
A93-94.99
3.67
B+
91-92.99
3.33
B
87-90.99
3.00
B85-86.99
2.67
C+
83-84.99
2.33
C
77-82.99
2.00
F
0-76.99
0
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Attendance
Attendance matters. It matters to me as the instructor, it matters to peers who count on your support and
feedback, and it matters to your development and experience in this course. I expect you to attend all class
sessions of this course.
If you know you are going to miss a class, please talk with me instructor prior to that time, just as you do
or will do when you are a teacher. Make a plan for getting a record of that session from another student in
the class. If a serious illness strikes you more suddenly, e-mail me and/or and call my office and leave a
message on voice mail.
More than one absence will impact your grade. Two absences will result in a lowering of your final grade
by half a letter grade (e.g. B+ to a B), two and a half or three absence will result in a lowering or your
letter grade by a full letter grade. More than three absences will result in failure of the course. [At that
point you have missed more than 25% of the course and you would need to retake it to be able to receive
the full benefit of the experience.]
Coming late to class and leaving early are a form of being absent. No matter the amount of time missed,
being late or leaving early will be counted as a “half absence” from class.
If you are going to be absent for the midterm or final exam you must let me know in advance in order to
be able to make up the test.
Quality of Work
All work completed outside of class and submitted for evaluation must be typed (double spaced and 12
point font). The work should reflect proper grammar and evidence of proofreading. By placing his/her
name on an assignment, the student is verifying that the work is the original, independent product of
his/her individual effort.
The instructor reserves the right to return, ungraded, any work that is not acceptable for final submission
(excessive mechanical errors, obvious lack of effort, lesson plans missing KTIP or math lesson plan
components, etc.). Returned assignments must be reworked by the student and submitted within one week
of when it was returned to the student. If not resubmitted by one week you will earn a grade of 0 for the
assignment
All work is expected to be submitted by the due date. If your work is late you will automatically receive
half-credit for the assignment. No work will be accepted more than one week after the due date. Similarly,
if you have questions about your grade you have one week after you receive the assignment back to
contact me to discuss the grade.
Professionalism, Preparation, & Participation
Professionalism, preparation, and participation are key components of this course due to their importance
in establishing professional teaching communities. Professionalism and participation in this course
include attending and engaging in all class meetings and working with your instructors and other students
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in a professional manner that contributes to the development of a community based on respect, trust, and
high expectations.
Lack of professionalism includes but is not limited to: not being prepared for weekly reading discussions,
being late for class, reading newspapers or other material not related to the course in class, using objects,
e.g. watches, cell phones, that beep or ring in class, having private conversations or text messaging during
class time, leaving class early (if for some reason you must leave class early, please inform your instructor
before the start of class, and please leave class quietly), contacting other faculty or students with concerns
about the class without consulting the professor, being disrespectful to peers, or any other behavior that
would be considered unprofessional in a school setting. If I feel that you are being unprofessional in class
in any way I will contact you individually so that we can arrange a time to talk about your behavior.
In the event that you have an issue with any professor, professional norms requires that you discuss that
issue with the professor face-to-face. If you are unable to go to the professor’s office hours, contact the
professor by e-mail or telephone and request an appointment. If, after discussing the issue face-to-face
with the professor, you are unsatisfied and wish to take the issue to a higher authority, you may contact
the department chair, Dr. Shawn Faulkner. If, after discussing the issue face-to-face with the department
chair, you are unsatisfied and wish to take the issue to a higher authority, you may contact the dean, Dr.
Mark Wasicsko. Following the chain-of-command is a commonly accepted professional practice to which
you are expected to adhere.
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Tentative Schedule
Note: The instructor reserves the right to make changes in the syllabus and/or class calendar if
circumstances so dictate.
Week
Date
Topics
Week 1
Aug. 24
Visions of teaching and learning
mathematics; NCTM Standards
Week 2
Aug. 31
Facilitating mathematical
discussion; Setting goals and
selecting tasks; Equity
▪ NCTM membership
▪ R 1: The Case of Marie Hansen
▪ MP: The Patio Problem
Week 3
Sept. 7
Standards for mathematical
practice; Curriculum
▪ R: Orchestrating Discussions
▪ MP: The Chicken Problem
▪ Questioning Strategies (part of the
Interview Assignment)
Week 4
Sept. 14
Standards for mathematical
practice; Tasks – Launching and
exploring
▪ R: The Power of Incorrect Answers
▪ MP: Building with Toothpicks
Week 5
Sept. 21
Standards for mathematical
practice; Tasks – Summarizing and
discussing
▪ R: Representations as a Vehicle…
▪ MP: Lucky Draw Fundraiser
▪ Interview Protocol (part of the
interview assignment)
Week 6
Sept. 28
Questioning; Writing lesson plans
▪ R: Never Say Anything a Kid Can
Say
▪ MP: Making the Data
▪ Find an open ended task on nctm.org
and bring 5 copies to class
Week 7
Oct. 5
Questioning; Writing lesson plans
▪ R: The Truth About PEMDAS
▪ MP: Bar Average Problem
Week 8
Oct. 12
Midterm – Online, no class meeting
Week 9
Oct. 19
Assessment in mathematics
1
Assignments Due
▪ R: Modifying Our Questions…
▪ MP: Brenda’s Blocks
R denotes Reading and MP denotes Math Problem
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Week
Date
Topics
Week 10
Oct. 26
Case stories
▪ R: Ideas about Symbolism…
▪ MP: The Rabbit Pen Problem
▪ Bring an artifact of your PTR to class
(the task you will use, the lesson plan
you have written, student work
collected, etc.)
Week 11
Nov. 2
Learning trajectories
▪ R: van Hiele revisited
▪ MP: How Much Area Does a
Trapezoid Trap?
Week 12
Nov. 9
Manipulatives
▪ R: Dividing Fractions and Problem
Solving
▪ MP: Fractions of a Square
Week 13
Nov. 16
Technology
▪ R: Radical Equations
▪ MP: Greatest Area Problem
▪ Plan-Teach-Reflect Due
Week 14
Nov. 23
Week 15
Nov. 30
Expert Presentations
Week 16
Dec. 7
Expert Presentations
Finals
Dec. 14
FINAL EXAM 4:30 – 6:30 p.m.
EDMT 544, Fall 2011
Assignments Due
No Class – Thanksgiving Break
▪ Threading a Process Standard Due
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Course Assignments
* This section provides a summary of the major assignments for this course. You will receive a detailed
assignment sheet and rubric for each assignment (with the exception of the weekly journal and math
problem).
Weekly Journal and Math Problem
Each week for class you will be expected to read an article and complete a math problem. After reading
the article you will respond in your Blackboard journal to the prompt provided. Do this by class time to
earn 5 points. Your weekly math problems will be due by Monday at noon (unless otherwise noted in
class). This due date accommodates your fellow students so that they can prepare a discussion of the math
problem for class. You may turn your math problems in to the folder outside my office door by this time
or on Blackboard under the ‘Math Problem Turn In’ button. Substantive solutions with explanations
(more than a single calculation with an answer) will earn 5 points. Answers only will not earn any credit.
Interview Assignment
The goal of a diagnostic interview is to find out what a child is thinking at a particular time in terms of
concepts and procedures. The idea behind this project is to make you more familiar with an increasingly
popular alternative assessment technique and help you develop your understanding of how students think
about and communicate their mathematical understanding. In addition, you will look for the Standards of
Mathematical practice in your students thinking so that you can reflect on how to help your future
students develop these skills.
Plan-Teach-Reflect Assignment (PTR)
Two major components of teaching are planning and reflecting. The Plan-Teach-Reflect assignment is
designed to help you develop habits of mind around these practices that have proven to produce more
effective teaching and learning. This assignment contains five components: (1) Open ended task chosen
for the lesson and discussion of the task, (2) Thinking Through a Lesson (TTL) protocol, (3) Lesson plan
associated with the task, (4) Reflection on student learning and teaching of the task, (5) Revised lesson
plan with annotations.
Leading a Reading Discussion
Graduate work implies a level of leadership beyond what is expected at the undergraduate level. By
preparing a leading a discussion of one of the class readings you are demonstrating your ability to
understand and synthesize the material from the reading as well as your ability to be a leader by engaging
your peers in meaningful discussion.
Threading a Process Standard
The NCTM process standards articulate the ways that students should learn and do mathematics, and they
provide substantial information about how to make this happen. In this assignment you will find/create
three tasks that exemplify one of the process standards that would be taught in different content units in a
single grade. You will teach one of these tasks and reflect on the success of the task in supporting your
chosen process standard.
Expert Presentation
It is impossible to discuss all of the interesting topics and student thinking possible in the span of one
semester. This project allows you to become an expert in an area of interest to you and to share your
findings with our class. Together you and a partner will research something (student understanding, the
use of technology or a manipulative, etc.) around a particular mathematical topic (i.e. slope) using articles
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from Mathematics teaching in the Middle School. Using information from at least three articles you will
summarize what you have found. During the last two weeks of class you and your partner will give a 5 –
7 minute presentation describing your findings with a one-page handout for your peers.
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Bibliography
Boaler, J., & Humphreys, C. (2005). Connecting mathematical ideas: Middle school video cases
to support teaching and learning. Portsmouth, NH: Heinemann.
Ellis, M. W., & Malloy, C. E. (2008). Mathematics for every student: Responding to diversity
grades 6 - 8. Reston, VA: National Council of Teachers of Mathematics.
Lawrence, A., & Hennessy, C. (2002). Lessons for algebraic thinking: Grades 6-8. Sausalito,
CA: Math Solutions.
National Council of Teacher of Mathematics. (2000). Principles and standards for school
mathematics. Reston, VA: Author.
Smith, M. S., Stein, M. K. (2011). Five practices for orchestrating productive mathematics
discussions. Reston, VA: National Council of Teachers of Mathematics.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standardsbased mathematics instruction: A casebook for professional development (Second ed.).
New York: Teachers College Press.
Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learner generating
examples. Lawrence Erlbaum: Mahwah, NJ.
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