Eastern Connecticut State University
Education Department
Principles and Practices of Teaching Mathematics (EDU 464)
Outline,Fall 2008
Instructor: Dr. Hari P. KoiralaClass hours:Wednesdays,5-6:45 pm & online
Office: Webb 154Classroom: Library 145
Office hours: Mondays 3–4 pm; Tuesdays & Thursdays 10–12 noon; or by an appointment
Phone: 465–4556 (W)456–1657 (H)Email:
Web:
Purpose of the course
The overall goal of this course is to encourage you to embrace the challenge of learning to teach mathematics through inquiry into students’ understanding of mathematics and the mathematics curriculum. Although there are no recipes and formulas for teaching mathematics, this course will provide you opportunities to explore how students learn mathematics and how you can use various teaching approaches to engage students into mathematical thinking. A significant portion of this course will be spent on designing and analyzing secondary school mathematics lessons and units. This course is built around five major themes of mathematics teaching standards: Problem solving, reasoning and proof, communication, connections, and representation as outlined in the Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics (NCTM, 2000). The table below provides an outline of how the goals and objectives of this course align with the performance expectations from the ECSU Conceptual Framework andthe NCTM program standards for beginning (and practicing) teachers. Also, each goal/objective is associated with a student product that would be completed during the course.
Course Goals/Objectives/Performance Expectations
Course Goals/Objectives / AlignmentECSU Candidate Proficiencies / NCTM Standards for Teachers / Products
By the end of the course students will:
- Demonstrate in-depth understanding of content knowledge including central concepts, principles, skills, tools of inquiry, and structure of mathematics by using various mathematical contents such as number and number operations, patterns and relationships, functions and algebra, measurement and geometry, and statistics and probability in designing mathematics lessons and units for students.
Philosophy (PH)
Unit plan (UP)
Clinical Report (CR)
Portfolio (PO)
Performance Assessment (PA)
- Be able to formulate clear and meaningful questions about the content to engage students in learning.
- Become enthusiastic about mathematics and appreciate the multiple ways mathematics can be interpreted and learned.
- Use various mathematical processes such as problem solving, reasoning, communication, connections, and representation in designing mathematics lessons and units.
- Be aware of the availability, use, and limitations of a variety of resources and strategies to enhance student learning of mathematics.
- Use technology such as computers, calculators, and other multi-media in the teaching of mathematics.
- Plan, design, and implement curriculum lessons and units in mathematics which are consistent with the national and state standards.
- Use various assessment strategies such as questioning, journals, and portfolios to monitor student learning and improve instruction.
- Understand constructivist perspective on learning and how it can be applied to design and carry out activities for the growth of students’ mathematical understanding.
- Demonstrate acceptance of, and respect for, individual differences and talents among students, including students from different gender, ethnic, racial, socioeconomic, language, and religious groups and create supportive learning environments for all students to maximize their learning and develop independence, social competence, and positive self-concept.
Course Grading
The assignments are intended to be creative (and not merely reproductive) undertakings. Simply completing all of the requirements for an assignment will not insure a top grade.
Method of Grading
A rangeAn insightful and challenging piece of work that goes beyond the requirement of the course. [90–100%]
B rangeAll of the elements have been completed and there is evidence of critical or creative thought that goes beyond what was discussed in class. [80–89%]
C rangeAll of the required elements of the assignments have been fulfilled but there is no evidence of critical or creative thought that goes beyond what was discussed in class. [70–79%]
D rangeSome elements of the assignment are missing. [60–69%]
If you are a student with a disability and believe you will need accommodations for this class, it is your responsibility to contact the Office of AccessAbility Services at 465-0189. To avoid any delay in the receipt of accommodations, you should contact the Office of AccessAbility Services as soon as possible. Please note that I cannot provide accommodations based upon disability until I have received an accommodation letter from the Office of AccessAbility Services. Your cooperation is appreciated.
Course Texts
Posamentier, A. S. (2003). Math wonders to inspire teachers and students. Alexandria, VA: Association for Supervision and Curriculum Development.
National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.Reston, VA: Author.Available from
Connecticut State Department of Education. (2005). 2005 Connecticut Mathematics Curriculum Framework: A guide for the development of PreK-12mathematics understanding. Hartford, CT: Author. Available from
Reading List
Blake, R. & Verhille, C. (1985). The story of zero. For the Learning of Mathematics, 5(3), 35–47.
Brinkmann, A. (2003). Mind mapping as a tool in mathematics education. Mathematics Teacher, 96(2), 96-101.
Britton, K. L., & Johannes, J. L. (2003). Portfolios and a backward approach to assessment. Mathematics Teaching in the Middle School, 9(2), 70-76.
Breyfogle, M. L., & Herbel-Eisenmann, B. A. (2004). Focusing on students’ mathematical thinking. Mathematics Teacher, 97(4), 244-47.
Chappell, M. F., & Strutchens, M. E. (2001). Creating connections: Promoting algebraic thinking with concrete models. Mathematics Teaching in the Middle School, 7(1), 20-25.
Davis, B. (1997). Listening to differences: An evolving conception of mathematics teaching. Journal for Research in Mathematics Education, 28(3), 355-76.
Donovan II, J. E. (2006). Using the dynamic power of Microsoft Excel to stand on the shoulders of giants. Mathematics Teacher, 99(5), 334-339.
Edwards, B. (2005). Have you lost your marbles? Three creative problem-solving approaches. Mathematics Teaching in the Middle School, 11(1), 18-21.
Edwards, M. T. (2004). Fostering mathematical inquiry with explorations of facial symmetry.Mathematics Teacher, 97(4), 234-41.
Hackmann, D. G. (2004). Constructivism and block scheduling: Making the connection. Phi Delta Kappan, 85(9), 697-702.
Halpern, C. M., & Halpern, P. A. (2006). Using creative writing and literature in mathematics classes. Mathematics Teaching in the Middle School, 11(5), 226-230.
Horak, V. M. (2005). Biology as a source for algebra equations: Insects. Mathematics Teacher, 99(1), 55-57.
Hrabowski, F. A. (2003). Raising minority achievement in science and math. Educational Leadership, 60(4), 44-48.
Johnson, J. M. (1997). The birthday problem explained. Mathematics Teacher, 90(1), 20-22.
Ketterlin-Geller, L. R., Jungjohann, K., Chard, D. J., & Baker, S. (2007). From arithmetic to algebra. Educational Leadership, 65(3), 66-71.
Kieren, T. E., Davis, B. A., & Mason, R. T. (1996). Fraction flags: Learning from children to help children learn. Mathematics Teaching in the Middle Grades, 2(1), 14–19.
Kramer, S. L. (1996). Block scheduling and high school mathematics instruction. The Mathematics Teacher, 89(9), 758–768.
Lufkin, D. (1996). The incredible three-by-five card! Mathematics Teacher, 89(2), 96-98.
Mikusa, M. G., & Lewellen, H. (1999). Now here is that authority on mathematics reform, Dr. Constructivist! The Mathematics Teacher, 92(2), 158-163.
Mvududu, N. (2005). Constructivism in the statistics classroom: From theory to practice. Teaching Statistics, 27(2), 49-54.
Reeder, S. L. (2007). Are we golden? Investigations with the golden ratio. Mathematics Teaching in the Middle School, 13(3), 150-55.
Reeves, A. (1996). Mathematics investigator: You hit the jackpot. Mathematics Teaching in the Middle School, 1(9), 736-737.
Roberts, S., & Tayeh, C. (2007). It’s the thoughts that counts: Reflecting on problem solving. Mathematics Teaching in the Middle School, 12(5), 232-237.
Scher, D. (2003). Technology tips: The parallelogram theorem revisited. Mathematics Teacher, 96(2), 148-149.
Shultz, H. S. (2005). Internal rate of return. Mathematics Teacher, 98(8), 531-33.
Shultz, H. S., Shultz, J. W., & Brown, R. G. (2003). Unexpected answers. Mathematics Teacher, 96(5), 310-313.
Suarez, D. (2007). When students choose the challenge. Educational Leadership, 65(3), 60-65.
Wade, W. R. (2006). A dialogue between calculator and algebra. Mathematics Teacher, 99(6), 391-393.
Walker, E. N. (2007). Why aren’t more minorities taking advanced math? Educational Leadership, 65(3), 48-53.
Walmsley, A. L. E, & Muniz, J. (2003). Cooperative learning and its effects in a high school geometry classroom. Mathematics Teacher, 96(2), 112-116.
Watson, J. M. (1988). Three hungry men and strategies for problem solving. For the Learning of Mathematics, 8(3), 20–26.
Tentative Weekly Calendar
Session / Course readings/AssignmentsWeek 1
September 3 / Course introduction
CT and NCTM Standards and focal points, Professional journals
Week 2
September 10 / Current issues in mathematics education
Constructivist view of learning
Hackmann (2004); Kramer (1996); Mikusa, & Lewellen, (1999)
Read CT and NCTM Standards and focal points
Draft philosophy of mathematics education due
Week 3
September 17 / What do the Standards really intend?
Planning lessons and units
Brinkmann (2003)
Complete reading CT and NCTM Standards and focal points
Week 4
September 24 / Assessing math learning
Performance and portfolio assessment
Connecticut Academic Performance Test (CAPT)
Britton & Johannes (2003); Breyfogle & Herbel-Eisenmann (2004)
Final philosophy of mathematics education due
Week 5
October 1 / Problem solving
Edwards (2005); Roberts & Tayeh (2007); Suarez (2007); Watson (1988)
Text chapters 1, 2, and 3, pp. 1-98, 198-214, 229-270
Week 6
October 8 / Teaching of numbers and their relationships
Number systems, Number theory, Number patterns
Blake & Verhille (1985), Text chapters 1 & 2, pp. 1-98 Continued
Draft unit plan due
Week 7
October 15 / Teaching of fractions, decimals, percent, ratio, and proportion
Kieren, Davis, & Mason (1996); Davis (1997)
Week 8
October 22 / Teaching of probability and statistics
Johnson (1997); Mvududu (2005); Reeder (2007); Reeves (1996); Text chapter 7, pp. 215-228
Final unit plan due
Week 9
October 29 / Teaching of algebra
Integers, equation balance, algebra tiles, algeblocks etc.
Chappell & Strutchens (2001); Horak (2005); Ketterlin-Geller et al. (2007); Shultz, Shultz, & Brown (2003); Text chapter 4, pp. 98-122
Week 10
November 5 / Teaching of algebra continued
Performance Assessment Due
Week 11
November 12 / Teaching of geometry and measurement
Shapes, symmetry, tessellation, proofs
Halpern & Halpern (2006); Lufkin (1996); Walmsley & Muniz (2003)
Text chapter 5, pp. 123-197
Week 12
November 19 / Teaching with technology
Donovan II (2006); Edwards (2004); Scher (2003); Shultz (2005); Wade (2006)
Week 13
November 26 / Thanksgiving Holiday
Week 14
December 3 / Student presentations
Clinical report due
Week 15
December 10 / Course Wrap up
Hrabrowski (2003); Walker (2007)
Portfolio Due
Disposition Reflection due
Course Assignments
Attendance, Participation, Dispositions, and Online Threaded Discussion [24%]
One of the purposes of this course is develop a community that is concerned about the teaching and learning of mathematics. Each member of the class is essential to the development of a learning community and, as such, regular attendance and participation is expected of all students in classroom and online.
Each student must participate in an online threaded discussion, every two weeks. For each thread, students are required to choose one article from the course readings, summarize it, and then relate it to a math article that the students find on their own through an online database or library search. The articles that you searched must have been published within the last 3 years, unless the article has a historical significance in the topic chosen. Students must provide a full reference of the searched article using the APA format and provide a summary of the article. If the article is available online, a link to the website or a PDF file must be provided. A posting should not be more than one page long. In addition to your posting, you must respond to at least one discussion posted by class members. The postings in online discussion will weigh 15% of the course grade. Your postings will also affect your disposition grade.
Disposition Rubric
At the end of this course, you must submit a 1-2 page reflection describing your strengths and challenges with respect to target or acceptable dispositions as explained in the rubric. Grades will be determined by carefully comparing your reflection with my notes. Although you will write your disposition reflection at the end of the course, you will have opportunities to demonstrate required dispositions throughout this course. If needed, meetings will be conducted with individual student(s) to discuss how dispositions can be improved.
Target (3) / Acceptable (2) / Unacceptable (0-1)Class participation / Attended every class or missed one, always came on time, submitted all assignments by their due dates, was not distracted, and was actively engaged in group and whole class activities. / Missed two or three classes, almost always came on time, submitted all assignments by their due dates, was not distracted, and was actively engaged in group and whole class activities. / Missed more than 3 classes, often came late, and/or was inactive or distracted in group/whole class activities.
Professionalism / Read professional and research journal(s) in their discipline(s) to improve their own personal and professional growth, sought membership of professional organization(s) to become involved in the professional community of educators, and demonstrated passion and enthusiasm for their discipline(s) and methods of teaching. / Read professional and research journal(s) in their discipline(s) and demonstrated some passion and enthusiasm for their discipline(s) and methods of teaching. / Did not read professional and research journal(s) in their discipline(s) and/or did not demonstrate passion and enthusiasm for their discipline(s) and methods of teaching.
Respect / Displayed professional and ethical behavior in the class, always paid attention and listened to peers and the instructor of the class with respect, and often responded thoughtfully and appropriately to the ideas of peers and the instructor. / Displayed professional and ethical behavior in the class, and always paid attention and listened to peers and the instructor of the class with respect. / Did not display professional and ethical behavior in the class and/or did not pay attention to the ideas of peers and the instructor of the class.
Philosophy of Mathematics Education [9%]
Write a two-page statement of your philosophy of mathematics education. Specifically write your goals of mathematics teaching and the roles of students and teachers in the learning of mathematics. You have to first submit a draft of your philosophy for the instructor's feedback. In the final version of your philosophy, you must include the first draft as an appendix.
Philosophy Rubric
Target (3) / Acceptable (2) / Unacceptable (1)Logic and clarity / The philosophy statements are direct, straightforward, and unambiguous. The paper consists of well defined and clearly developed paragraphs which are consistent and logically connected to each other maintaining the flow of the paper. It is well focused. / The philosophy statements are generally clear but sometimes ambiguous. The paper consists of clearly developed paragraphs which are logically connected to each other maintaining the flow of the paper. It is focused. / The philosophy statements are unclear and ambiguous. The paper does not consist of well defined and clearly developed paragraphs. It does not maintain the flow of the paper. It is not focused.
Connections to classrooms / The statements are supported by meaningful examples and illustrations from classroom and/or personal experiences. / The statements are supported by examples from classroom and/or personal experiences. / The statements are not supported by examples from classroom and/or personal experiences.
Readings, citations, and formatting / The philosophy statements are based on critical reflection of course readings. The paper follows proper APA formatting consistently. / The philosophy statements are based on reflection of course readings. The paper follows APA formatting. / The philosophy statements are not based on reflection of course readings. The paper does not follow proper APA formatting.
Overview and Design of a Unit [18%]
This is a very important assignment that students must complete in this course. This assignment will consist of several elements. Its main purpose is to help students develop a non-traditional unit of mathematics that could be used in their teaching. The unit will include:
- A concept map;
- A unifying theme and assumptions for the unit;
- A list of the resources that might be used;
- Statements of how the unit aligns with some of the state and national standards;
- Objectives of the unit;
- A sample lesson plan;
- A tentative timeline, showing a possible sequence of unit topics and the amount of time allotted to each topic;
- An account of how and where this unit might fit with other mathematical units;
- An account of how this unit might fit with other subject areas;
- A description of how the unit will provide students with problem solving opportunity and enhance their problem solving skills;
- A description of how the unit helps students to develop their mathematical reasoning and proofs;
- A description of how the unit encourages students communication skills;
- Ways of assessing students’ understanding of mathematics.
At least two of following mathematics topics should be covered in the unit:
- Number and Number Operations (integers, rational, real, sequences, etc.)
- Algebra (equations, inequalities, algebraic equivalence, functions, etc.)
- Geometry (Shapes/properties and proofs)
- Measurement (Imperial/Metric, Operations, Perimeter, Area, Volume etc.)
- Data Analysis (Data collection, Presentation, graphs, Analysis, etc.)
- Probability (Games, concepts, rules, combinatorics etc.)
- Trigonometry and calculus
The design of a unit should be based on the principle that “the whole is more than the sum of its parts.” That is to say a unit plan is more than a collection of lesson plans. You are encouraged to workin small groupsof 2-3 peopleto bounce off ideas. However, you have to submit your own individual unit. The unit plan is evaluated based on the attached rubric.
Unit Plan Rubric
Target (3) / Acceptable (2) / Unacceptable (1)Themes, timelines, assumptions, concept map, and objectives / The unit contains a clear description of unified theme, the grade level, topic, a tentative timeline, entry-level characteristics, features, resources to be used, concept map, and objectives that are clear and adequate. / The unit contains a clear description of unified theme, the grade level, topic, a tentative timeline, entry-level characteristics, features, resources to be used, concept map, and objectives, some of which may not be clear and adequate. / The unit lacks a clear description of unified theme, the grade level, topic, a tentative timeline, entry-level characteristics, features, resources to be used, and objectives, many of which are not clear and adequate.
Quality of sample lesson plan / The lesson plan includes all the components: topics, grade level, connection to the standards, objectives, procedures, assessment strategies, and accommodation plan. The lesson plan focuses on student engagement and mathematical understanding. / The lesson plan includes at least six components: topics, grade level, connection to the standards, objectives, procedures, assessment strategies, and accommodation plan. The lesson plan focuses on student mathematical understanding. / The lesson misses two or more components or does not focus on student mathematical understanding.
Assessment strategies / The unit contains sufficientnumber of assessment strategies and some sample quizzes, exams, projects, and alternative assessment techniques. Each assessment includes a rubric or grading criteria. / The unit contains adequatenumber of assessment strategies and some sample quizzes, exams, projects, and alternative assessment techniques. Some assessments include rubric or grading criteria. / The unit does not contain adequatenumber of assessment strategies or norubric or grading criteria is provided.
Mathematical content knowledge and processes / Shows understanding of content, by providing appropriate examples from at least two content areas, number and operations, algebra, geometry, measurement, data analysis and probability. The unit is fully supported by specific mathematics concepts and questions. Errors are not made.
Also demonstrates full understanding of mathematical processes, such as problem solving, reasoning and proof, communications, connections, and representations described in the NCTM Standards. / Shows understanding of content, by providing appropriate examples from at least two content areas, number and operations, algebra, geometry, measurement, data analysis and probability. The unit is supported by specific math concepts and questions. Errors are rarely made.
Also demonstrates understanding of mathematical processes, such as problem solving, reasoning and proof, communications, connections and representations described in the NCTM Standards. / Lacks understanding of mathematical content. Examples are not provided or they lack comprehension. Errors are made.
Does not demonstrate understanding of mathematical processes, described in the NCTM Standards.
Lessons connection / Fully demonstrates how the lessons in the unit are interconnected and how the unit is connected to other mathematics units in the curriculum and also other subject areas. / Demonstrates how the lessons in the unit are interconnected and how the unit is connected to other subject areas. / Does not demonstrate how the lessons in the unit are interconnected and how the unit is connected to other subject areas.
Dealing with diverse learners / The unit provides a clear description of how it can be extended to serve high or low ability students. Some activities are modified for this purpose. Uses technology as a tool for modification. / The unit provides a reasonably adequate description of how it can be extended to serve high or low ability students. Some activities are modified for this purpose. Uses technology as a tool for modification. / No clear description of how the unit can be extended to serve high or low ability students. Does not use technology as a tool for modification.
Note: Incomprehensible and missing responses will result in a score of 0.