Welcome to the GRED 565 web site.

The protected part of the course (where the Course Materials Booklet and presentation summaries written by the students (Potsdam campus) are located) can be entered by using the user name and the password only (provided in hard copy of the course syllabus).

Syllabus and schedule of presentations and topics exams. (Potsdam Campus).

Materials for WATERTOWN sections of GRED 565/EDUC 310 (SECTION 1 and SECTION 2): Class Files , Excel file Document 1. The links to SECTION 1 and SECTION 2 lead to presenation summaries written by the students in the corresponding sections.

Homework (Potsdam campus).

Virtual Manupulatives

New York State Next Generation Mathematics Learning Standards

Common Core meeting on 11/11/13

New York State Testing Program Grade 4 Common Core Mathematics Test

Computational environments.

Curriculum Module Updates (Engage NY)

Annotated 2013 Mathematics NY State Test Questions for Grades 3-8

Printable math worksheets.

Rubrics web site.

Helping your child learn mathematics web site (U.S. Department of Education).

Cool-Math Games web site

NCATE (National Council for Accreditation of Teacher Education).

Principles and Standards for School Mathematics (NCTM).

Show-Me Center (information and resources needed to support selection and implementation of standards-based middle grades mathematics curricula).

The Eisenhower National Clearinghouse

School Jobs Bulletin Board. See also http://www.teachmath.org/

Digits of PI.

Tutor Bot (interactive arithmetic game)



GRED 565 (Potsdam Campus)

Elementary Mathematics: Content & Methods

Spring 2021


Instructor: Dr. Sergei Abramovich

Office: Satterlee 210

Office Hours: by Email and via Zoom.

Phone: (315) 267-2541 (office n/a during remote teaching)

E-mail: abramovs@potsdam.edu


Background and Rationale


Contemporary mathematics pedagogy measures an educative growth of a student not in terms of the production of correct answers but in terms of the quality and diversity of thinking. Nowadays, a competence in elementary mathematics teaching means much more than the ability to get a right answer to a standard, procedure-bounded problem. The competence includes an in-depth understanding of the concepts behind procedures being taught and awareness of various tools conducive to mediate conceptual development. This course will reflect change and growth in mathematics education set by the Common Core State Standards Initiative [1] adopted by New York State in 2010 toward the goal of having greater focus and coherence in teaching school mathematics. The course will attempt to increase the confidence level of a future teacher in creating learning situations at the elementary level in which simply stated questions about familiar concepts can generate a considerable amount of inquiry. In that way, the course instructor “ensures that candidates develop a deep understanding of the critical concepts and principles” [2, p. 2] of mathematics.  

To this end, mathematics currently involved in K-6 program as recommended by the New York State Education Department as well as by the Ontario Ministry of Education will be highlighted as a dynamic discipline, built on progressively connected ideas and mutually related concepts. Students will be introduced to current issues and trends in mathematics education such as the use of concrete embodiments (physical manipulatives) and computing technology (including electronic manipulatives), revision of curriculum and professional standards, assessment of authentic performance, and social constructivism.

 SUNY Potsdam Education Unit Conceptual Framework

A Tradition of Excellence: Preparing Creative and Reflective Practitioners


GRED 565 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


Course Content and Pedagogy


The course content will revolve around the following eight Standards for Mathematical Practice set by the Common Core [1]: (1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct valuable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look and make use of structure; (8) Look and express regularity in repeated reasoning. The course pedagogy will be aligned with the following Instructional Shifts that are of critical importance for implementing the above eight standards for Mathematical Practice: Focus, Coherence, and Rigor. The demonstration of these shifts will be supported by a variety of mathematics education materials. In that way, teacher candidates would be able to “understand that learning and developmental patterns vary among individuals, that learners bring unique individual differences to the learning process, and that learners need supportive and safe learning environments to thrive” [3, p. 8]. Furthermore, in accord with the National Council of Teachers of Mathematics Professional Standards for Teaching Mathematics [4], the course pedagogy will also focus on developing proficiency in:



To this end, student-centered discussions of selected mathematics education research publications and Common Core State Standards for Mathematics will be a part of the course activities. Students will be expected to read these publications by using the campus (Crumb) library and the Internet resources. Fostering the ability to use such resources is one of educational objectives of this (graduate level) course.


Text book and other required materials


Students are expected to attend, be prepared for, and participate professionally in each class. This includes the ability to support classroom activities by participating in discussions of homework and readings. Professionalism also includes the ability to keep notes of all class discussions and home assignments, using library and the Internet resources to access information, using e-mail and word processing programs as educational tools.

Special note regarding the weekend offering of the course. Because of intensive nature of studies in such a format, students who miss any weekend (or the time-equivalent combination of classes) will be asked to drop the course and take it at a different time.Those students who miss one full day (either Friday or Saturday) due to a family emergency (which must be documented) may be allowed to make up work in some form (TBA) at the discretion of instructor.



Students are expected to read the text book, course materials, and selected mathematics education publications as assigned by the instructor. Throughout the semester, please plan to watch carefully for assignments given. Some assignments may involve the use of a computer and students must plan for time to work in a Mac computer lab on such assignments. Students are expected to have (or acquire) a minimum knowledge of Microsoft Word, Microsoft Excel, and Dynamic Geometry programs. Note that these high expectations on the use of digital technology are set for students (and their teachers alike) as early as in elementary grades. The goal of this kind of teaching and learning is to “model best practices in digital learning and technology applications that EPP [education preparation provider] expects candidates to acquire” [2, p. 30].


The course activities will include (depending on a final enrollment) up to seven student-centered discussions of research publications relevant to elementary mathematics curriculum. (These publications will be available online). To this end, teams of students will be created. Each team (or an individual) will be responsible for doing one such discussion. More specifically, this will include the following collaborative activities:



Each such summary will be put on the course web site on a week preceding a discussion with understanding that the whole class can be prepared for discussion by reading this summary via the Internet. (In order to count the number of words in a typed document, one can use "Word Count" feature from Tools menu of MS Word program). One copy of each document is required for a team. In evaluating a presentation, the following rubric will be applied:

Group e-summary of not less than 600 words submitted by email  on time - 20%

Individual reflection of not less than 300 words submitted by email on time - 20%

The use of a computer during the presentation - 20%

The use of (virtual) manipultives during the presentation - 20%

Conducting whole class discussion during the presentation - 20%

Submitted individual reflections will be graded and emailed back to each student (with my evaluation of the whole presentation)


Two topic exams will be given during the semester. These topic exams (to be arranged) will be based on readings, homework, and activities presented in the class. A reading list will be given a week before a topic exam. There will be no make-up topic exams given unless illness or family emergency occur (these must be documented).


A final exam for the course will be replaced by work on a final project. A final project may take different directions. One such direction is to develop a lesson based on one of the key idea/strands from mathematics core curriculum as recommended by New York State Department of Education/Ontario Ministry of Education (see mentioned above GRED 565 Course Materials) and/or Common Core State Standards for Mathematics. The second direction is to structure a project as a journal that reflects on one's experience in observing an elementary mathematics classroom in the field. Reflections should describe one's observations in terms of their connection to ideas studied in the course. Finally, the third direction is to reflect on a possible involvement in teaching mathematics during a field experience. Regardless of a direction chosen, an underlying philosophy of a final project should be structured by the following basic assumptions of contemporary classroom discourse:


The length of a final project is expected to be three to five pages (not fewer than a 1000-word document typed on a computer). Team projects (not more than three students in a team) are welcome, but collaboration on a project is not required. On the cover sheet of the project please type your e-mail address (it should include e-mail addresses of all team members if it's a collaborative project).


If your final project is an observation journal, please follow guidelines provided in the document Field Experience Guidelines." Of particular interest is any information related to students' asking questions during a lesson, the discussion of more than one way to solve a problem, the availability of manipulatives and computers in the elementary classroom and their use by a host teacher. If the use of these tools was never observed, please write about that including grade level(s) observed. Information submitted in your final project based on classroom observations will be considered strictly confidential.

If you are involved in student teaching during your practicum, please write in your final project about topic taught and instructional materials used; describe most interesting episodes from your teaching experience.

If your final project is a lesson plan, it should be relevant to the elementary classroom. Your lesson plan may be based on one of the Common Core State Standards for Mathematical Content or on one of the strands in the Ontario Mathematics Curriculum. In your lesson plan please address such issues as the use of manipulatives and information technology, conceptual development, the promotion of reflective inquiry and diversity of thinking among students.



Home assignments 20%

The use of technology 10%

Topic exams 30%

Final Project 20%

Presentation 20%


An interactive chart titled Calculation of Grade is attached to the password-required domain of the course web site. Note: Blue numbers related to exams are subject to change.

According to the chart: range 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 . 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.


[1] Common Core State Standards. (2010). Common Core Standards Initiative: Preparing America’s Students for College and Career [On-line materials]. Available at: http://www.corestandards.org.

[2] Council for the Accreditation of Educator Preparation. (2013). CAEP Accreditation Standards and Evidence: Aspirations for Educator Preparation. Recommendations from the CAEP Commission on Standards and Performance Reporting to the CAEP Board of Directors. Washington, DC: Author.

[3] Council of Chief State School Officers. (2011, April). Interstate Teacher Assessment and Support Consortium (InTASC) Model Core Teaching Standards: A Resource for State Dialogue. Washington, DC: Author.

[4] National Council of Teachers of Mathematics. (1996). Professional Standards for Teaching Mathematics. Reston, VA: Author.


List of publications put on reserve at Crumb Library (n/a during remote teaching)

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics, Chapter 4: Standards for Grades Pre-K-2. Reston, VA: NCTM.

Conference Board of the Mathematical Sciences. (2012). The Mathematical Education of Teachers II, Chapters 2-4. Washington, D.C.: Mathematical Association of America.

Common Core State Standards Initiative (2011). Common Core Standards for Mathematics. http://www.p12.nysed.gov/ciai/common_core_standards/.

Schifter, D. (1998). Learning Mathematics for Teaching: From a Teacher's Seminar to the Classroom. Journal of Mathematics Teacher Education, 1, pp. 55-87.

Anderson, A., Anderson, J., and Shapiro, J. (2004). Mathematical Discourse in Shared Storybook Reading. Journal for Research in Mathematics Education, 35(1), pp. 5-33.

Fuys, D.J., and Liebov, A.K. (1993). Geometry and Spatial Sense. In R. Jensen (ed.), Research ideas for the classroom: Early childhood mathematics. NCTM: Reston, VA.

Nunes, T. (1992). Ethnomathematics and everyday cognition. In D. A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning . New York: MacMillan.

Schedule of presentations and topic exams (Spring 2021)

Monday 9:00 a.m. section

Monday 7:10 p.m. section

Tuesday 4:30 p.m. section