Course syllabus

Instructor: Dr. Sergei Abramovich

Office: Satterlee 210

Phone: (315) 267-2541 (office)

E-mail: abramovs@potsdam.edu

**Course rationale**

This course is designed as an introduction to computational methods for concept development in school mathematics by using an electronic spreadsheet program. It demystifies the stereotype of using this commonly available software as a pure computation oriented program. Students will explore various pedagogical strategies and alternative computational ideas aimed at the design of spreadsheet-enabled lessons relevant to K-12 mathematics curriculum. Developed in accord with the NCTM Standards, the course activities will be oriented towards fostering one's ability to take intellectual risk in making pedagogical and/or curricula decisions in a technological paradigm.

In 1997 the President's Committee of Advisors on Science and Technology, Panel on Educational Technology prepared a number of high level strategic recommendations related to the effective use of technology within America's schools. In particular, the Panel emphasized the importance of technology-oriented pedagogy that promotes learning with technology vs. learning about technology. This implies that the focus of computer-enhanced teacher education courses should be the application of a computer as a cognitive tool and not the acquisition of skills in operating a computer by using a specific programming language. Latest developments in educational uses of generic software Microsoft Excel (electronic spreadsheet) may reduce the need for programming to minimum and thus can significantly affect school mathematics instruction. Furthermore, spreadsheets as one of the components of computer literacy, may be construed as a new generation of school based educational software appropriation of which by teachers is not limited by financial constraints and commercial availability. A proficiency of teachers in the use of a spreadsheet as a tool for conceptual development and educative growth becomes a crucial factor in advancing such use with children.

The course is designed as a graduate level course with the goal to address the above issues. It emphasizes a disciplined approach to the design of computational procedures involving data structures and logical constructs that are common in many application programs and programming languages. The course is intended to provide prospective teachers with experience of how mathematical concepts evolve from a familiar quantitative situation if one is allowed to problematize the familiar in a purposeful way. In particular, the proposed course demonstrates how the use of a spreadsheet can mediate the development of mathematical concepts and their subsequent use as problem solving tools. Such approach enables teachers in training to experience the exploration, discovery, and re-invention of mathematical ideas through spreadsheet-mediated activities, to appreciate meaningful links among different concepts through exploiting their multiple representations in a spreadsheet environment.

**SUNY Potsdam Education Unit Conceptual Framework**

**A Tradition of Excellence: Preparing Creative and Reflective
Practitioners**

GRED 504 course supports the SUNY Potsdam Education Conceptual Framework in several ways. First, through experiences provided in this course students will continue to develop as "well educated citizens" by modeling the skills, attitudes, and values of inquiry relevant for mathematics content and by appropriately using technology such as the Internet, word processing, spreadsheets, and other electronic information technologies. They will continue to develop as 'reflective practitioners" by modeling inquiry, practice, and reflection in their field experiences and journals. They will effectively use research-based models of curriculum, instruction, and assessment as they plan for instruction, design, and teach lessons meeting the diverse learning needs of students, promoting reflective inquiry, critical thinking, and problem solving, incorporating appropriate technology. They will identify national and state learning standards that are related to their lessons. They will develop as "principled educators" by demonstrating

(a) appropriate integrity and competence for beginning level pre-service teachers,

(b) professional behavior in their classes and in the field,

(c) ability to work with pre-K-6 students and teachers, and

(d) disposition to see the elementary classroom as a site for inquiry.

**Course outline**

Students will be engaged in the creation of a variety of spreadsheet-based interactive environments, among them

- numeric tables which mediate the discovery of number patterns;
- prime number generators;
- interactive environments which support NYS curriculum materials;
- simple melodies like "Happy Birthday to You" (computer generated music);
- manipulative environments for hands-on mathematical explorations.

In addition, students will be introduced to "ready-to-use" spreadsheet-based computational environments and will be asked to design and present spreadsheet-enabled mathematics (mini) lessons relevant to K-12 core curriculum as suggested by the NY State Education Department. Through these presentations various pedagogical strategies and alternative computational ideas will be discussed.

The course includes students' work on a project aimed at the development of a topic relevant to school mathematics instruction from a computational perspective. Students will be expected to chose a topic for such a project, formulate questions to be explored, and decide on directions in which the ideas can be extended. In such a way, an assessment will be oriented toward developing ones ability to take intellectual risk in making pedagogical and/or curricula decisions. Work on the project will end up with participation in the procedure of computer-mediated reciprocal teaching &emdash; a spreadsheet-based presentation to the whole class.

There is no textbook for the course. However, the following web sites may be useful for your work:

1) Lesson plans in mathematics (http://ericir.syr.edu/Virtual/Lessons/Mathematics/index.html)

2) NCTM Principles and Standards 2000 (http://standards.nctm.org/)

3) New York State Education Department

4) Spreadsheets in education (http://sunsite.univie.ac.at/Spreadsite/spreaded.html)

5) The Tower of Hanoi web sites

(http://www.cs.wm.edu/~pkstoc/toh.html)

(http://www.lhs.berkeley.edu/Java/Tower/towerhistory.html)

7) E-Tutorial for Microsoft Excel 97

8) A Brief History of Spreadsheets

9) e-Journal of Spreasheets in Education

Also, some course materials will be put on a local server
(ClassFiles volume of the Zeus Server, folder **GRED 504** within
the folder **abramovs**). Everything placed in ClassFiles is
automatically "published" on the Web at http://zeus.potsdam.edu. This
option is convenient for those students who will be using non-campus
(home) computers. To access ClassFiles on the Internet, make your
way, via your browser, to the folder GRED 504 and see a list of
files; holding down the OPTION (Mac) or SHIFT (Windows) key while
clicking on the document will cause the document to be downloaded to
your computer. You can then double-click on the document and open it
on your own computer, assuming that you have the same program that
was used to create it.

**Evaluation Criteria**

Students are expected to attend, be prepared for, and participate in each class. Students must also plan for time to work with others in a computer lab on spreadsheet-based assignments. More specifically, the following criteria will be used to calculate the final grade:

Class participation and attendance 20%;

Assignments 50%;

Final Project (including its presentation) 30%.

Grades will be assigned according to the following scale:

100%-94% - 4.0; range 87%-93% - 3.7; range 80%-86% - 3.3; range

73%-79% - 3.0; range 66%-72% -2.7; range 59%-65% - 2.3; range 52%-58% - 2.0; below 52% - 0.0.

It is expected that all work will be the students own otherwise documented. Failure to credit others for direct quotations and ideas will be considered plagiarism and will result in the student receiving a grade of 0.0 for that assignment.

Conceptual Framework Alignment: Professional behavior, works well with others, effectively uses instructional technology, critically analyzes and solves problems, demonstrates knowledge of state standards.

Course assignmnets

Five course assignments can be found in the following password required domain of the course.

Computational environments for elementary mathematics.

Pet Store problem (NYS Core Curriculum, Classroom Idea for grades 1-2, # 1D).

Multiplication facts using color tiles (NYS Core Curriculum, Classroom Idea for grades 1-2, # 3C).

Census taker and farmer's daughters (Course Materials, Core Curriculum, Classroom Idea for grades 5-6, # 1A).

Money sharing (NYS Testing Program, # 19).

Mr. Ruiz (NYS Testing Program, # 15).

Abundant numbers (NYS Core Curriculum, Classroom Idea for grades 5-6, # 7A).

Multiplication with Fraction Tiles (NYS Core Curriculum, Classroom Idea for grades 5-6, #3C)

Stem-and-leaf plot and averages (NYSCore Curriculum, Classroom Idea for grades 5-6, #4D).

Is the game fair? (NYS Core Curriculum, Classroom Idea for grades 5-6, # 1B).

Computational environments for middle and secondary mathematics.

Patterns in the multiplication table.

Discount (NYS Core Curriculum, Math A, example 1B, p. 127).

Prime factorization (NYS Core Curriculum, Grades 7-8, assessment example 1B, p. 104).

Mean as a balance point (NYS Core Curriculum, Grades 7-8, assessment example 5D, p. 109).

Clock arithmetic (NYS Core Curriculum, Math A, example 2C, p. 135)

Tessellations (NYS Core Curriculum, Math B, example 7M, p. 165).

Two video rental clubs (NYS Core Curriculum, Math A, example 7C, p. 133).

Bernoulli experiment (NYS Core Curriculum, Math B, example 6D, p. 160).