1 University of Texas Brownsville College of Education

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University of Texas Brownsville
College of Education
Syllabus
EDCI 6341: Teaching Algebraic Concept
Fall 2012
Conceptual Framework &
Knowledge Base
The conceptual framework contains four core
concepts that are themes through which we
organize and deliver our programs; hence they
are central to our vision of professional
educators and scholars. These include:
 Inter-culturalism
 Interrelatedness
 Inquiry
 Pedagogical Leadership
College of Education Theme
Teaching, learning and scholarly inquiry for
an intercultural world
College of Education (COE)
Mission Statement
 To prepare highly skilled
professionals to assume roles and
positions in teaching, research, educational leadership, and human development.
 To provide undergraduate and graduate programs based on proven best practice,
knowledge acquisition, reflective inquiry, critical thinking, and respect for the
cultural and linguistically diverse learner.
 To continuously develop a dynamic local, state, national, and international,
dimension that promotes innovations and contributes to scientific educational,
economic, and social change.
College of Education (COE) Vision Statement
The vision of the College of Education is to be consistently recognized as fullyaccredited and as a nationally and internationally respected college in the areas of
science, mathematics, educational technology and intercultural dimension (language,
literacy, culture and interdisciplinary studies in regard to preparing teachers,
counselors, administrators, educational researchers, and professional at all levels, not
only for the school system but for other economical and service areas which require
training, human resources, development and life-long learning.
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Teacher preparation programs of the College of Education will be central to the
mission of the University and will have national prominence. It will be at the
forefront in programs for English Language Learners and, through teacher
preparation, P-16 and life-long education initiatives will be a model for helping to
close the student achievement gap.
All of these will require the COE to be noted for the quality of its graduates, the
scholarship of its faculty, and the leadership and service they provide to the local,
regional, and national educational communities in the previously mentioned areas.
Note: Be advised that the College of Education conducts ongoing research
regarding the effectiveness of the programs. You will receive one survey in the final
semester prior to graduation regarding your program during your time here. A
second survey will occur within one year following graduation from or completion
of a program, and will be sent to your employer. This survey will focus on the
preparation received at UTB. Please remember that your response to these surveys
is critical to UTB excellence.
Department of Teaching, Learning & Innovation (TLI) Mission Statement
The mission of the Department of Teaching, Learning, and Innovation is to prepare and
develop highly skilled professionals for leadership roles in the educational practice and
service of our region, state and nation, accomplished through rigorous, comprehensive
and innovative curricula.
The undergraduate and post baccalaureate programs engage students in the acquisition of
knowledge, skills and disposition for entering the teaching profession, and in the use of
inquiry to improve pedagogy for diverse learners.
The graduate programs cultivate an active community of scholars who promote research
and develop educational leadership to serve as advocates for educational excellence and
lifetime learning.
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Department of Teaching, Learning, and Innovation
EDCI 6341 Teaching and Learning Algebraic Concepts
Fall 2012
Professor: Dr. James A. Telese, Professor of Mathematics Education
Telephone: 882-7669 (Office)
Email: [email protected]
Office Hours: Mon. - Thur. 2-3:30 PM, or by appointment
Class Time: Saturday 8:30 AM- 4:00 PM
Location: EDBC 1.220
Catalog Description
This course covers learning theories related to the teaching of school algebra, as well as
strategies for teaching algebraic concepts. Topics include best practices based on
research, development of materials for supporting the learning of foundational algebraic
concepts. Students will utilize technology and tools.
Course Objectives:
The course will provide activities, information, and instruction that will enable K-12
teachers to:
•
Compare and contrast current national and state curriculum standards (e.g., TEKS);
•
Use internet resources to identify current curriculum projects and other innovative
mathematics materials in algebra;
•
•
Apply learning theory to the teaching of algebraic concepts;
Design instructional approaches for the teaching algebra to all students;
•
Develop algebra lessons and activities for students of diverse cultural backgrounds;
•
Develop various strategies for evaluating higher-order algebraic thinking and
reasoning.
Textbooks are not required. Materials will be supplied by the instructor.
Suggested readings:
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French, D. (2002). Teaching and learning algebra. New York: Continuum.
Driscoll, M. (1999). Fostering algebraic thinking. Portsmouth, NH: Heinemann.
Wagner, S., & Kieran, C. (Eds.) (1989). Research issues in the learning and
teaching of algebra. Reston, VA: NCTM. (Red)
Mathematical Sciences Education Board (1998). The nature and role of algebra
in the K-14 Curriculum. Washington, D.C.: National Academy Press. (blue)
Coxford, A., & Shulte, A. (Eds.) (1988). The ideas of algebra, K-12, 1988
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Yearbook. Reston, VA: NCTM.
You may choose to locate the sources, but readings will be provided as necessary.
Rationale: Algebra is a gateway to other mathematics and science courses. Many
students who do not successfully complete Algebra I may decide not to continue their
study of mathematics. They tend to view algebra as totally unrelated to their daily life. It
has become imperative that students experience an algebra curriculum that is meaningful,
based on applications, and encourages the students to progress toward other mathematics
courses. The effective teaching of algebra has the potential to meet the goal of fostering
mathematical understanding for future success.
Objectives:
The course will provide activities, information, and instruction that will enable K-12
teachers to:
•
Compare and contrast current national and state curriculum standards (e.g., TEKS);
•
Use internet resources to identify current curriculum projects and other innovative
mathematics materials in algebra;
•
•
Apply learning theory to the teaching of algebraic concepts;
Design instructional approaches for the teaching algebra to all students;
•
Develop algebra lessons and activities for students of diverse cultural backgrounds;
•
Develop various strategies for evaluating higher-order algebraic thinking and
reasoning.
Course Calendar
Date(s)
September 1
Activity
Fostering Algebraic Thinking pretest
September 22
Fostering Algebraic Thinking
October 6
Fostering Algebraic Thinking
October 20
Children’s Thinking in Math K-5
November 3
Teaching Math TEKS with Technology
November 10
Assessments in Mathematical Knowledge
November 17
Teaching Algebraic Concepts
December 1
Teaching Algebraic Concepts
December 8
TAC-Final Exam/posttest
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Evaluation:
Mentoring Journal
25%
Projects, papers
50%
Participation
15%
( 0-absences 100; 1- absence 90; 2 or more 70 unless excused.)
Presentation
10%
A+
A
AB+
B
BC+
C
C-
98-100
93-97.9
90-92.9
88-89.9
83-86.9
80-82.9
77-79.9
73-76.9
70-72.9
Regular class attendance is essential; material discussed in class will go beyond and
enrich textbook readings and assignments. As a graduate level course, you will be
expected to participate in class seminars and conduct various types of research.
Policy notes:
 Grading: Assignments will be graded by the course professor. Students may not
request a final grade from the professor via the telephone to the office, e-mail or
snail mail. The student will have access to the grade over the university system.
A grade of an “I” can be negotiated if there is an emergency only.
 Students are bound by the catalog and the student handbook and the grant
requirements.
 Electronic Equipment: Cell phones, please set phones on vibrate.
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Class Assignments
National and State Standards Assignment
EDCI 6341
Professor Telese
Due Date: 9/29
1. Select a concept in Algebra or Number Concepts and trace its development over the
grades K-12. Record observations such as, objectives, or how the topic is being
addressed in the Texas Essential Knowledge and Skills (TEKS), which are accessible
through the TEA website, http://www.tea.state.tx.us/rules/tac/chapter111/index.html. In
addition, examine the Texas Response to the Focal points.
Write a 2-4 page analysis of how the concept should be taught. Also, note:
 How the concept is to be assessed, or can be assessed.
 Include a discussion of what you think students need to know to develop that
concept within a particular grade.
 How are the Focal Points arranged to develop algebraic thinking?
 Reflect on how the TEKS compare to the chapter by Thorpe, “What should we
teach and how should we teach it?” (to be provided)
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Research on an Algebra Topic
EDCI 6341
Professor Telese
Date Due: 10/20
Procedure:
1. Select an important concept, procedure, or idea in algebra (e.g., linear equations,
variables, expressions, negative numbers, functions, graphs, factoring, using technology
to teach algebra, language issues).
2. Read several research articles, reviews, chapters, or conference presentations, which
focus on the topic. Try to concentrate on more recent work (within the last 5-10 years).
The readings should be research studies, not teaching suggestions. The research may be
data-based, case studies, interviews, or other approaches to studying learning in students
K-12 (not their teachers). Journals such as Journal for research in Mathematics
Education, Journal of Educational Psychology, American Educational Research Journal
are examples. Papers presented at the NCTM research sessions, Psychology of
Mathematics Education meetings, and AERA meetings can be found in ERIC.
3. Write a 10-12 page paper that analyzes and summarizes what you have found and
reflects your analysis of the research and how it fits with your experience with students.
The paper should include:
Introduction
Briefly define the topic you have chosen, its place in the algebra curriculum, why
you chose it and, if appropriate, the particular age/grade/special population/other
demographic group you have chosen. The latter is not required; you may look at research
on the topic without regard to any particular special group. (However, you might
consider looking at research that deals with students who are similar to students in our
population.)
Research Findings
Summarize the studies that you have read, organized in a logical and cohesive
format. Try not to simply go down the list giving results of each study. Identify two or
three key findings or ideas across the studies and provide information on each one,
making reference to the appropriate research studies. This section should be objective,
giving information about the findings, without your opinions and criticism.
Discussion
Present you discussion of the research studies. This section may include a
critique of methodologies used in the research, alternative interpretations of the results,
relating the findings to other research you have read previously, relating the research to
your own experience with students, implications for classroom practice, and
recommendations for further research.
Bibliography
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Research Paper Rubric
Introduction
3-the introduction clearly states how the algebraic topic fits within the curriculum,
includes background information about a particular group, but not necessary. The
introduction describes clearly the goal of the paper.
2- As above, but there is some indication that the author is unclear about the topic
and the goal of the paper.
1-a poorly written introduction that does not offer guidance for the writer as to
what the paper is about, the topic is not related to algebraic understanding, and the
author fails to describe a direction of the paper.
Research Findings
3-research findings are used more often than not, in comparison to teaching
strategies, which may be included. A balance is evident. The findings are tied
together in a coherent fashion. Personal opinion is omitted when presenting
findings, only the facts are described.
2-There is indication that the author relied too much on teaching strategies rather
than research, a balance between the two is not evident. There is a haphazard
approach to presenting the information without a clear, coherent organization of
the content. Opinions are evident but not overly done.
1-a poorly presentation of information that is too old, irrelevant, an over reliance
on teaching strategies, use of commercial sources rather than scholarly sources.
Opinions are used often to describe content.
Discussion
3-the discussion offers insight based on material in the above section. Critiques of
studies are included based on knowledge of what may work or not (not
necessarily based on research methodology, depending on background); the
critiques is reflective of authors sophistication with research studies. Comments
regarding why particular teaching strategies would be useful and helpful based on
knowledge from readings and class discussions. Related ideas to own
experiences. Offers implications for classroom practice. Offers clear
recommendations for future research.
2-The discussion is somewhat coherent; there is evidence that the author used
research findings and thought about the impact of the findings. A few comments
about particular teaching strategies but not related to own practice. Offers little
support from class readings or discussions. A tendency to rely on own
experiences and not how research and methods can be used to help teaching in the
classroom. The level of insight is superficial. Recommendations for future
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research are limited and illustrate a lack of understanding of the current state of
the topic.
1-the author rambles throughout the discussion. There is no evidence that the
author interpreted research findings, for practice and based on own experiences.
There is evidence of an over reliance on personal experience, rather than
supporting experience from research. No recommendations are made.
Bibliography
3-Written in APA style with no errors, provides primary sources and scholarly
secondary sources, a balance between the two, or a thorough use of primary
sources. Sources are current/recent, and/or included major documents such as
NCTM Standards and landmark studies, major researchers in the field.
2-Written in APA style with minor errors in format. There is a tendency to have
used more scholarly secondary sources rather than primary sources. Fails to
include at least NCTM standards, some sources are not recent or current, included
references that are not related to the topic.
1-citations are not in APA style or has many/major errors in formatting
references. Used commercial sources. An over reliance on secondary sources. No
inclusion of major documents, researchers in the field, many sources are not
current, relevant or recent.
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Classroom Algebra Case Study and (possible Presentation)
Professor Telese
Date Due: 11/10
1. Select an important concept, procedure, or idea in algebra (e.g., linear equations,
variables, expressions, negative numbers, functions, graphs, factoring).
2. Choose a focus for a research study on the topic. You may wish to discuss your idea
with me prior to beginning your research. Write a brief rationale for your choice of
focus; that is, what is it that interests you or makes you curious regarding the topic.
3. Develop and carry out a research study. The study should gather "real" data from
"real" people. The data need not be from a test or questionnaire. It can be oral or written
prose, or videotape of someone doing something, or pictures or drawings or computer
printout that some one produced. It is preferred that you conduct the study using your
students or student. You need not conduct a study on the whole class; you may choose to
conduct an in-depth and/or qualitative case study using one or two subjects.
Your report, written in APA Style 6th Edition, should generally follow this outline:
Introduction: A brief review of relevant research and experience, concluding with a
statement of the question(s) to be addressed by the study.
Design: A clear description of the subjects, the procedure, the data collected (a copy of
the instrument used to collect data should be attached), and how the data to be analyzed.
Include a provision for conducting a clinical interview. This means that you should
include as part of your data, a session where you observe your subject completing an
algebraic task, and noting how the subject is performing the task by asking the subject to
think out loud as the task is being performed. You may video record this or audio tape
the interview, which will then become part of your data through a transcription or
summary of the event.
Results: A summary of the results of the study, including any tables, analyses, graphs, or
descriptions of the data. This section reports only results, it does not discuss or give
reasons for why the results are the way they are.
Discussion: Interpret and explain the results. How do they provide information about the
question(s) asked in the introduction? How do they fit with the research cited in the
introduction? Is there other research not mentioned earlier that might help explain the
results. What implications (taking into account any limitations of the study) do the
results have for practice?
References: This section contains an alphabetical listing by author in APA style format
of the sources cited in the text of your introduction or reference to any study cited
elsewhere in your report.
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Appendix: Instrument(s)-this may include any student work sample, tests,
questionnaires, interview transcripts, etc. that were used for data collection.
The case study presentation should be a semi, to formal presentation. The presentation
should be developed as if you were going to present at a conference, using overhead
slides, or a projection device. You are to highlight during the presentation the major
details of your case study, i.e., rationale, methodology, results, and discussion.
Case Study Evaluation
Introduction
Rationale provided that
clearly describes the topic’s
importance.
3
2
1
Rationale not clear
Literature Review
Review presents recent
research.
3
2
1
References outdated.
Review presents brief
account of students’
misconceptions.
3
2
1
Presents how students
best learn topic.
3
2
1
Poor or lacks discussion.
Procedures
Lesson presentation in
detail.
3
2
1
Poor or sketchy description.
Student reaction(s)
clearly presented.
3
2
1
Poor or sketchy description.
What was taught
and how taught are
clearly presented.
3
2
1
Poor or sketchy description.
3
2
1
Shallow reflective comments.
Reflection/Conclusion
Evidence of deep reflection of
teaching event presenting
positives and negatives.
Poor review of
misconceptions.
Description of changes
to lesson based on evidence
provided.
3
2
1
Superficial changes or lack of
or inappropriate modification
of lesson.
Student’s strengths and
weaknesses based on
presented discussion.
3
2
1
Indications that s&w not
grounded in teaching episode.
2
1
0
not presented
Van Hiele level presented
with rationale.
Student interview reflects
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insightful questions and
processes geared to obtaining
students’ understanding. 4
3
2
1
0
no interview.
Mentoring Log/Journal
Due Date 12/4
The granting agency requires that MTMs establish a cadre of teachers at each
participant’s school within the same grade level. Each participant is to have at least 5
other teachers in the cadre, who are referred to as Cadre Members (CMs). You are to
conduct 12 hours of training, and or mentoring, with your cadre through out the semester.
You may consider this do this at planning sessions, after school for an hour each week, or
some other strategy.
This contact is to be documented by a mentoring journal and a summary reflection of
your activities whether training, mentoring or both. The documentation training includes
a sign-in sheet, date, times, and topic along with an agenda. For mentoring, keep a
journal that documents your interaction with the teachers, which describes your efforts to
help a fellow teacher(s) improve their teaching of mathematics, their reactions, and your
thoughts and reflections of the process. If you do both, then both items are required.
Your sign in sheets and agendas need to be submitted following each session via
email you may bring them with you to the next class meeting.
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Departmental policies
1. Academic honesty and integrity is expected of all students. This course demands a high level
of scholarly behavior and academic honesty on the part of all students. Examples of academic
dishonesty include but are not limited to: (1) turning in work as original that was used in whole
or part for another course and/or instructor without obtaining permission from this instructor in
advance; (2) turning in another person’s work, in part or in whole, as your own; (3) copying from
professional works without citing them; and (4) any form of cheating on exams. Violations of
academic integrity/honesty while carrying out academic assignments may, at the discretion of the
instructor, receive a zero on the particular work in question, receive an “F” in the course, and/or
be brought before a higher level of governance for possible dismissal from the university.
Discipline may include suspension or expulsion from the University. This is a matter of
professional ethics for anyone involved in the field of education.
According to the UT System Regents' Rules and Regulations, Part One, Chapter VI, Section 3,
Subsection 3.2, Subdivision 3.22: "Scholastic dishonesty includes but is not limited to cheating,
plagiarism, collusion, the submission for credit of any work or materials that are attributable in
whole or in part to another person, taking an examination for another person, any act designed to
give unfair advantage to a student or the attempt to commit such acts."
2. Americans with Disabilities Act:
• Americans with Disabilities Act: Students with disabilities may request
assistance through Disability Services, an office of the Counseling Center.
Students who need help with registration should contact the office several days
before registration. Those who need special services throughout the semester
should inform Disability Services several weeks before the semester. Some of the
services available include volunteer note takers, taped notebooks, memos to
faculty, special test conditions, sign language interpreting and registration
assistance. An Adaptive Technology Lab and Testing Service is available for
student use. To request services, students must register with the
Counselor/Coordinator of Disability Services. All services are elective and must
be requested each semester, as needed. Permits for parking in spaces designated
for the handicapped may be obtained at Campus Police, located at Cavalry Hall.
Proof of disability is required. TDD users who wish to contact the University by
phone may call through Relay Texas at 1-800-735-2989. For more information,
contact Disability Services, located at Tandy Hall 205 (956) 544-8292.

Academic Integrity/Honesty Statement: Students are expected to be above
reproach in all scholastic activities. Students who engage in scholastic dishonesty
are subject to disciplinary penalties, including the possibility of failure in the
course and dismissal from the university. "Scholastic dishonesty includes but is
not limited to cheating, plagiarism, collusion, the submission for credit of any
work or materials that are attributable in whole or in part to another person, taking
an examination for another person, any act designed to give unfair advantage to a
student or the attempt to commit such acts." Regents' Rules and Regulations,
Series 50101, Section 2.2. Since scholastic dishonesty harms the individual, all
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students, and the integrity of the university, policies on scholastic dishonesty will
be strictly enforced. (refer to Student Handbook for more information).
Emergencies (Weather Phenomenon): In the event of an emergency or should the
classroom become unavailable for class., quizzes, and /or exams, another location
will be made available through Blackboard. Please contact the departmental
secretary for the new location. In compliance with the Emergency UTB/TSC
Academic Continuity Program, academic courses, partially or entirely, will be
made available on the MyUTBTSC Blackboard course management system. This
allows faculty members and students to continue their teaching and learning via
MyUTBTSC Blackboard http://myutbtsc.blackboard.com, in case the university
shuts down as a result of a hurricane or any other natural disaster. The university
will use Blackboard to post announcements notifying faculty members and
students of their responsibilities as a hurricane approaches our region. If the
university is forced to shut down, faculty will notify their students using
Blackboard on how to proceed with their course(s). To receive credit for a course,
it is the student’s responsibility to complete all the requirements for that course.
Failure to access course materials once reasonably possible can result in a
reduction of your overall grade in the class.
To facilitate the completion of classes, most or all of the communication between
students and the institution, the instructor, and fellow classmates will take place
using the features in your MyUTBTSC Blackboard and UTB email system.
Therefore, all students must use Scorpion Online to provide a current email
address. Students may update their email address by following the link titled
“Validate your e-Mail Account” in MyUTBTSC Blackboard Portal. In the event
of a disaster that disrupts normal operations, all students and faculty must make
every effort to access an internet-enabled computer as often as possible to
continue the learning process.
Grade Appeals: If you (the student) do not agree with a grade on an assignment,
quiz, etc…it is your (the student) responsibility to appeal the grade to the
instructor within two days after the assignment was returned.
Copyright Infringement: Unauthorized duplication of copyrighted material are subject
to appropriate disciplinary actions as well as those civil remedies and criminal penalties
provided by federal law.
Syllabus Disclaimer: While the provisions of this syllabus are as accurate and
complete as possible, the instructor reserves the right to change any provisions
herein, not covered by UTB/TSC Handbook of Operating Procedures or UT
Regent Rule, with notice if circumstances so warrant. Every effort will be made
to keep students advised of such changes and information about such changes will
be available at all times from the instructor. It is the responsibility of each student
to know what changes if any, have been made to the provisions of this syllabus
and to successfully complete the requirements of this course. Questions regarding
information on the syllabus and course requirements need to be addressed by the
students when the syllabus is received.
3. Should our classroom meeting site become unavailable for any reason, another location has
been provided in order to take exams or make presentations that might have been interrupted.
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4. Grade grievance: The student has one calendar year from the date the grade is assigned to
initiate the grievance. The student must first meet with the professor. The normal channels then
are department chair or program director, and then dean.
Course policies (Including attendance and drop policy)
For example:
1. Attendance is important; as professionals and teachers, there are times when your other
profession duties may require your absence from class. This is understandable. Please clear your
absences with the professor.
2. Complete all assignments by the due date listed on the syllabus or announced in class.
Assignment grades will be lowered one point for each academic day that the assignment is late.
3. Please type all assignments, unless otherwise specified. Use double spacing for all
assignments and follow APA style 6th Editions when appropriate. It is recommended that
students keep photocopies of work turned in.
4. The instructor reserves the right to make changes in the syllabus, as deemed necessary in
cooperation with students. Students will be notified of any changes.