Eastern Connecticut State University
Department of Education
Current Issues/Trends in Math Education (EDU 532)
Spring 2009 Course Outline
Instructor: Dr. Hari P. Koirala Class hours: 4:00–6:45 pm; M
Office: Webb 154 Classroom: Webb 213
Office hours: Tuesday 3–4 pm; Wednesday 9–11 am; Thursday 10–12 noon; or by an appointment
Phone: 465–4556 (W) 456–1657 (H) Email:
Web: http://www.easternct.edu/personal/faculty/koiralah/
______
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 elementary school mathematics lessons and units. This course is built around the content and process standards as outlined in the Principles and Standards for School Mathematics published by the National Council of Teachers of Mathematics (NCTM, 2000): Number & operations, algebra, geometry, measurement, data analysis & probability, problem solving, reasoning & proof, communication, connections, and representation. All course goals, objectives, and themes are interconnected with the ECSU Education Unit conceptual framework, Connecticut Common Core of Teaching (CCCT), and the standards of the Association for Childhood Education International (ACEI). The table below provides an outline of how the goals and objectives of this course align with the proficiencies from the conceptual framework and the ACEI standards. Also, each goal/objective is associated with a student product that would be completed during the course.
Course Goals/Objectives/ECSU Proficiencies/ACEI Standards
Course Goals/Objectives / Alignment /ECSU Proficiencies / ACEI Standards / Products /
By the end of the course students will:
1. 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. / 1.1 / 2.3 / Attendance, Participation, & Dispositions (APD)
Philosophy (PH)
Unit plan (UP)
Clinical Report (CR)
Portfolio (PO)
2. Formulate clear and meaningful questions about the content to motivate and engage students in learning. / 1.1 / 1.0 / UP, CR, PO
3. Use various mathematical processes such as problem solving, reasoning, communication, connections, and representation in designing mathematics lessons and units. / 1.1, 2.1, 2.2, 3.1 / 2.3 / PH, UP, CR, PO
4. Be aware of the availability, use, and limitations of a variety of resources and strategies to enhance student learning of mathematics. / 2.2, 2.3 / 1.0, 3.1 / PH, UP, CR, PO
5. Use technology such as computers, calculators, and other multi-media in the teaching of mathematics. / 4.1 / 1.0, 3.1 / APD, PH, UP, CR, PO
6. Plan, design, and implement curriculum lessons and units in mathematics which are consistent with the national and state standards. / 2.1-2.4 / 1.0, 2.3, 3.1-3.5, 4.0 / PH, UP, CR, PO
7. Use various assessment strategies such as questioning, journals, and portfolios to monitor student learning and improve instruction. / 2.4 / 4.0 / APD, PH, UP, CR, PO
8. Understand constructivist perspective on learning and how it can be applied to design and carry out activities for the growth of students’ mathematical understanding. / 2.1-2.4 / 1.0 / APD, PH, UP, CR, PO
9. Demonstrate their ability to support the diverse needs of students in terms of exceptionalities, race, ethnicity, gender, culture, and socioeconomic status. / 5.1, 6.1 / 3.2 / APD, PH, UP, CR, PO
Course Assignments[*]
Attendance, Participation, Dispositions, and Online Threaded Discussion [28%]
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 posted in the Blackboard Learning System. You are expected to participate in each of these discussions by posting your message and responding to at least two messages posted by class members. The postings in online discussion will weigh 19% of the course grade. Your postings will also affect your disposition grade, which carries 9% of the course grade. For details, please see the attached disposition rubric and the Blackboard Learning System.
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.
Overview and Design of a Unit [21%]
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 units
· an account of how this unit might fit with other subject areas
· Ways of assessing students’ understanding of mathematics
At least two of following mathematics topics should be covered in the unit:
· Number sense (Counting, Seriation and ordering, Classification, One-to-one correspondence)
· Number Operations (Addition, Subtraction, Multiplication, Division)
· Fractions (Basic concepts, Equivalent fractions, Operations)
· Decimal (Basic concepts, Operations)
· Money (Recognition, Operations, Problem solving)
· Measurement (Imperial/Metric, Operations, Perimeter, Area, Volume)
· Probability (Games, Basic concepts)
· Data Analysis (Data collection, Presentation, Analysis)
· Graphs (Pictograph, Histogram, Bar diagram, Line graph, Pie-chart)
· Geometry (Recognition and properties of shapes)
· Introducing variables and equations
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 work in small groups of 2-3 people to bounce off ideas. However, you have to submit your own individual unit. The unit plan will be evaluated based on the attached rubric.
Clinical Report and Presentation [18%]
This assignment is directly related to your clinical experience in an elementary classroom. While in school, you are expected to investigate students’ understanding of mathematics. You can accomplish this task by implementing the following steps:
a) Talk to your clinical experience teacher in advance and get his or her approval to teach a mathematics classroom or a small group of students. Design a lesson plan, find appropriate manipulatives or teaching aids, and teach a 15-45 minute lesson.
b) Give two students (one at a higher mathematical level and one at a lower mathematical level) a problem (related to lesson objectives) to solve. You may want to pick these students before the initial topic is taught (please coordinate this with your teacher.). Collect their work and also interview them to investigate their mathematical understanding. Make sure to take good interview notes. If it is hard to take notes during the interview you can record the interviews in a tape and transcribe them later in your convenience.
c) Analyze the student work and determine their understanding of mathematics. Do you think that these students achieved the lesson objectives? If so, what is the evidence? If not, what went wrong?
Write a report. In your report you must cite at least three course readings, including both the Connecticut and NCTM standards. You also need to provide a reference page using the APA formatting. Your report must include the following:
i) Describe the context and mathematical levels of students that you taught, including the two students you selected. Describe the lesson (content and standards).
ii) Discuss the problem and interview questions that you asked the two students.
iii) Analyze your teaching, student work, and interviews. Discuss with evidence whether or not the lesson objectives were met.
iv) Finally provide your reflection on how you would change the lesson to better suit the students’ needs.
In your report, you need to attach the lesson plan and some work samples from the two students you selected. Your report should be no more than 5 pages in length (double-spaced), excluding the attachments.
You will also need to give a 10 minute presentation to the EDU 532 class about your lesson. Your oral presentation in class should include the following steps:
a) Bring the manipulatives/resources used in the school classroom. If no resources were used, you must prepare similar manipulatives/resources to demonstrate to the class during your presentation.
b) Describe the lesson (content and standards) you observed and the mathematical levels of students (1-2 minutes).
c) Carry out a portion of the lesson in EDU 532 class, including an activity with the manipulatives/resources that you bring to the class (5-6 minutes). During your activity make sure that EDU 532 class is engaged. Your job is not to lecture what you did but to engage the class in a meaningful way.
d) Ask a question and lead the discussion (1-2 minutes). Make sure that the question is related to the topic of your presentation.
Portfolio Development [24%]
This is the final assignment for the course. The purpose of this assignment is to help you further in becoming a reflective practitioner. In your portfolio, include the activities, lessons, and units you have developed in this course, which may be useful for you in teaching your future elementary school mathematics classes. However you need to consider so many other options that are available to you through reading materials, and various resources from the Internet. In addition, your portfolio must reflect how you plan to implement the NCTM Standards in your future teaching (See attached rubric for more details).
The portfolio contains the following sections:
1. A cover page and table of contents
2. A philosophy statement.
3. A collection of six artifacts--samples of professional work, drawn from classes and teaching experiences, which demonstrate specific competencies as outlined in the NCTM standards and the CCCT.
The documents comprise the largest section of the portfolio and will include such items as lesson and unit plans, clinical report, samples of students’ work, constructed learning materials, software and website reviews. In particular, your portfolio must have artifacts to demonstrate your mathematical teaching ability.
In order to demonstrate your mathematical content knowledge and mathematical processes, you can include varieties of projects completed in EDU532. In addition, you can use activities from mathematics courses such as MAT 139, MAT 140, and elementary school textbooks. The portfolio must contain a total six artifacts directly related to the rubric. Each artifact included in the portfolio must follow a page of overview. It will identify the importance of the artifact including, what the entry is, what it demonstrates, and how it benefits students at the elementary school level.
Grading
Final grades in this course will be determined on total points earned out of 100 in the following way:
95–100 A 90–94 A- 87–89 B+ 84–86 B 80–83 B-
77–79 C+ 74–76 C 70–73 C- 65–69 D+ 60–64 D Below 60 F
Please pick up your final paper in my office, Webb 154, within two weeks of its submission. The paper not picked up will be discarded by the third week. If you cannot pick up your paper within the time frame, please include a self addressed stamped envelope for mailing.
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 (860) 465-5573. To avoid any delay in the receipt of accommodations, you should contact the Office of AccessAbility Services as soon as possible. Please understand 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 Materials
Connecticut State Department of Education (2005). 2005 Connecticut mathematics curriculum framework. Hartford, CT: Author. Available at http://www.state.ct.us/sde/dtl/curriculum/currmath.htm
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author. Available at http://www.nctm.org/standards/
National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: Reston, VA: Author. Available at http://www.nctm.org/standards/default.aspx?id=58
Please note that these materials would be integrated throughout this course.
Readings
Beckmann, C. E., Thompson, D. R., & Austin, R. A. (2004). Exploring proportional reasoning through movies and literature. Mathematics Teaching in the Middle School, 9(5), 256-262.
Behrend, J. L., & Mohs, L. C. (2006). From simple questions to powerful connections: A two-year conversation about negative numbers. Teaching Children Mathematics, 12(5), 260-264.
Brown, A. S., & Brown, L. L. (2007, Winter). What are math and science test scores really telling U.S.? The Bent of Tau Beta Pi, 13-17.
Burns, M. (2002). Algebra in the elementary grades? Absolutely! Scholastic Instructor, 112(3), 24-28.
Burns, M. (2007). Nine ways to catch kids up. How do we help floundering students who lack basic math concepts. Educational Leadership, 65(3), 16-21.
Clements, D. H., & Battista, M. T. (1990). Constructivist learning and teaching. Arithmetic Teacher, 38(1), 34-35.