University of Texas Brownsville
College of Education
Syllabus
EDCI 5340: Teaching Mathematics for Understanding
Fall 2013
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:
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Inter-culturalism
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Interrelatedness
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Inquiry
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Pedagogical Leadership
Teaching, learning and scholarly inquiry for an intercultural world
College of Education (COE)
Mission Statement
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To prepare highly skilled professionals to assume roles and positions in teaching, research, educational leadership, and human development.
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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.
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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.

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.

Department of Teaching, Learning, and Innovation
EDCI 5340 Teaching Mathematics for Understanding
Fall 2013
Professor: Dr. James A. Telese, Professor of Mathematics Education
Telephone: 882-7669 (Office)
Email: james.telese@utb.edu
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:
• Explain the components that promote the development of mathematics understandings.
• Identify factors in the classroom that foster deep learning.
• Describe characteristics of effective mathematics teaching.
• Design instructional approaches for the teaching of mathematics to all students.
• Develop an observation tool for teaching mathematics for understanding.
• Develop various strategies for evaluating higher-order mathematics thinking and reasoning.
Textbooks are not required. Materials will be supplied by the instructor.
Suggested readings:
 Fennema, E., & Romberg, T. (Eds.) (1999). Mathematics Classrooms that
Promote Understanding . Mahwah, NJ: Lawrence Erlbaum and Associates.
 The Effective Mathematics Classrooms, White Paper . Available at: http://www.ipsi.utexas.edu/docs/alg_readiness_toolkit/Admin%20white%20paper
_NL_2-1-10.pdf
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 Making Sense:
 Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H.,
 Olivier, A., & Human, P. (2000). Teaching and learning mathematics with understanding . Portsmouth, NH: Hienemann.
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National Research Council. (2001). Adding It Up: Helping Children Learn
Mathematics . Washington, DC: The National Academies Press. Available at: http://www.nap.edu/catalog.php?record_id=9822
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National Research Council. (2002). Helping Children Learn Mathematics .
Washington, DC: The National Academies Press. Available at: http://www.nap.edu/catalog.php?record_id=10434
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Suh, J. (2007). Tying it all together: Classroom practices that promote mathematical proficiency for all students. Teaching Children Mathematics,
October, 163-169.
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DOI: 10.3102/00028312033002455
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The Effect of Meaningful Tasks on Secondary One Students’ Mathematics
Examination Performance and Engagement, available at http://www.iaea.info/documents/paper_4d529ec3.pdf
http://pasdtechtraining.wikispaces.com/Math+%26+Technology+in+the+Classroom http://people.exeter.ac.uk/PErnest/pome16/discussion.htm
You may choose to locate the sources, but readings will be provided as necessary.
Rationale : “In order to prepare mathematically literate citizens for the 21 st century, classrooms need to be restructured so that mathematics can be learned with understanding” (Fennema & Romberg, 1999, p. 19). Mathematics teachers must be adept at providing instructional strategies that foster deep learning rather than superficial content knowledge. Deep learning is necessary for the transfer of knowledge and skills to new situations.
Course Calendar
Introduction/Worthwhile Mathematics Tasks 8/28
9/4 Teaching and Learning with Understanding

9/11
9/18
9/25
10/2
10/9
10/16
10/23
Equity
Case Study Research
Teaching Basic Number Concepts and Skills as Problem solving
Using students’ intuitions to develop understanding of space
Promoting understanding in middle grades
Developing understanding of Statistics
Teaching and learning algebra
10/30
11/6
11/13
11/20
Math Tools as learning Support
Social Culture of the classroom
Assessment in Classrooms that promote understanding
Assessment in classrooms that promote understanding
12/4
12/11
Presentations
Final Exam
Evaluation:
Classroom observation
Case Study
Observation Tool
Assessment Design
15
25
15
25
Research Paper 20
A+ 98-100 4.00
A 93-97.9 4.00
A- 90-92.9 3.67
B+ 87-89.9 3.33
B 83-86.9 3.00
B- 80-82.9 2.67
C+ 77-79.9 2.33
C 70-76.9 2.00
D 60-69.9 1.00
F 59 and Under 0.00
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.

Class Assignments
EDCI 5340
Classroom Observation
Due Date: 9/11
Select two colleagues to observe. Conduct at least three observations for each colleague.
During the observations, note events such as, the strategies they are using, tools, the level of discourse, types of questions, and the level of cognitive demand of the tasks and types of tasks used by the teacher.
Write a three to five page paper:
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Introduction-background knowledge of the school, teacher and students, and community, and rationale for the observation.
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Commentary-provide examples of the interactions of the teacher and student; the type of mathematics tasks used and instructional strategies.
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Critique-describe as best you can the strengths and weaknesses of the teachers observed, compare and contrast their instructional methods and classroom environment.
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Reflection-describe recommendations that would you offer to the teachers. Why were their similarities and differences in their approaches? How did their characteristics impact how they taught and what they taught?

EDCI 5340
Research Paper
Due Date 10/9
Write a 10-page research paper excluding references in APA style 6 th edition. The topic of the paper can be on anything related to developing deep understanding in mathematics classrooms, including assessment of such learning. You may choose to a topic around a mathematics content area like algebra, geometry, etc., professional development, use of technology, or equity issues.
Introduction
Briefly define the issue you have selected and a rationale for selecting the topic of interest. Describe the importance for teaching mathematics for understanding relative to your topic.
Research Findings
Summarize the studies and/or information that you have read, organized in a logical and cohesive format. Try not to simply go down the list giving results of each study. Rather express an argument for doing one thing or another. 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-include all material you looked at whether cited or not in APA style 6 th edition.
Research Paper Rubric
Introduction
3-the introduction clearly states how the topic fits within the curriculum, includes background information. 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 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.

Design Teaching Mathematics for Understanding Observation Tool
Due Date: 10/23
Simply design an observation tool using the principles of teaching mathematics for understanding. Observe colleagues upon completion. Make any changes that are necessary based on its initial use, and conduct additional observations and make any necessary changes. Write a 3 – 5 page paper reflecting on the quality of your tool.

EDCI 5340
Teaching Mathematics for Understanding Case Study
Due Date 12/4
1.
During a two-week period of your teaching, select an important concept, or idea in mathematics that you would strive to teach for deeper understanding.
2.
Implement strategies for teaching mathematics for understanding. You may wish to discuss your idea with me prior to beginning your study. Write a brief rational for you choice of focus.
3.
Develop and carry out a case study. This is to be akin to action research. 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 video tape of someone doing something, or pictures or drawings or computer printout that someone produce.
The focus should be placed on how you may have changed once you began to teach mathematics for understanding and the impact of that change on students’ mathematics understandings.
Your report written in APA Style 6 th Edition should generally follow this outline:
Introduction: A brief overview of relevant research, your background, and beliefs about teaching mathematics, any bias you may have, and what you intend to change in your teaching during the unit.
Design: Provide a clear description of your background and experiences, reflect on your past practices and describe your goals for the case study. Describe the students, the procedures you used and data you collected. If you keep a journal during, then it is part of your data collection, if you have a colleague observe you and note how you are teaching for understanding also becomes data; if you reflect with your colleague after the observation that do becomes data. Describe how you implemented any changes to your teaching in relation to teaching for understanding or using meaningful mathematics and assessment tasks. Assessment is critical; you may use formative assessment tasks that focus on getting at students understanding and how the results informed your teaching.
Results: A summary of what occurred. Include 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: How you changed, and evidence for that change. What insights did you obtain? What impact did it have on students? What would you do differently? How would you change to improve what you did?
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.
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.
Literature Review
Review presents recent research.
Review presents brief account of students’ misconceptions.
Presents how students best learn topic.
Procedures
Lesson presentation in detail.
Student reaction(s) clearly presented.
What was taught and how taught are clearly presented.
Reflection/Conclusion
Evidence of deep reflection of teaching event presenting positives and negatives.
Description of changes to lesson based on evidence provided.
Student’s strengths and weaknesses based on presented discussion.
Van Hiele level presented with rationale.
3
3
3
3
3
3
3
3
3
3
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
Rationale not clear
References outdated.
Poor review of misconceptions.
Poor or lacks discussion.
Poor or sketchy description.
Poor or sketchy description.
Poor or sketchy description.
Shallow reflective comments.
Superficial changes or lack of or inappropriate modification of lesson.
Indications that s&w not grounded in teaching episode.
0 not presented

Student interview reflects insightful questions and processes geared to obtaining students’ understanding. 4 3 2 1 0 no interview.

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.
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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

students, and the integrity of the university, policies on scholastic dishonesty will be strictly enforced. (refer to Student Handbook for more information).
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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.
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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.
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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.
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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.
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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.

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 6 th
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.