Welcome to the GRED 565 web site.
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
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).
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
Curriculum Module Updates (Engage NY)
Annotated 2013 Mathematics NY State Test Questions for Grades 3-8
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).
(information and resources needed to support selection and
implementation of standards-based middle grades mathematics
The Eisenhower National Clearinghouse
School Jobs Bulletin
Board. See also http://www.teachmath.org/
Digits of PI.
Tutor Bot (interactive arithmetic game)
Elementary Mathematics: Content & Methods
Instructor: Dr. Sergei Abramovich
Office: Satterlee 210
Office Hours: by Email and via Zoom.
Phone: (315) 267-2541 (office n/a during remote teaching)
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  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
SUNY Potsdam Education Unit Conceptual Framework
A Tradition of Excellence: Preparing Creative and Reflective
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
- appropriate integrity and competence for beginning level
- professional behavior in their classes and in the field,
- ability to work with pre-K-6 students and teachers, and
- disposition to see the elementary classroom as a site for
Course Content and Pedagogy
The course content will revolve around the following eight Standards for Mathematical Practice set by the Common Core : (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 , the course pedagogy will also focus on developing proficiency in:
- selecting mathematical tasks to engage children's interests
- orchestrating classroom discourse in ways that promote
- seeking, and helping children seek, connections to previous
and developing knowledge;
- using, and helping children use, technology to pursue
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
- EDUC 310/GRED 565 Course Materials Booklet written by Sergei Abramovich.
(Available in pdf on the proteched part of the course website).
- A pen/jump drive (512 MB), compass, ruler,
color pencils/markers, scissors.
- SUNY Potsdam e-mail account is required.
- Several materials for the course will be put on the Internet (and/or Moodle)
regularly. To access the course web site, go to
computer that has the Internet connection will be OK). In order to
access a protected part of the site, click at the hyperlink "A
protected part of the GRED 565 course" (on the top of the page).
Upon clicking, a computer will require entering User Name and
Password. The User Name and the
Password are given in my email sent on Jan 23, 2021. This would make specific course materials
available to the GRED 565 students only.
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:
- the preparation of not fewer than a 600-word summary of a
publication (a write-up) which must be submitted as an MS Word document to the course instructor
electronically following the schedule published on-line;
- the preparation of not fewer than a 300-word reflection on the
publication (a write-up) which must be
submitted as an MS Word document to the course instructor electronically by the day and time of the presentation;
- conducting a 35-minute discussion of an assigned
publication (longer presentations would not be appreciated).
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 -
Individual reflection of not less than 300 words submitted by email on time
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:
- conceptual development (emphasis on conceptual understanding
versus operational understanding),
- reflective inquiry (creating a learning environment in which
students feel comfortable to ask "what if" and "why" questions and
reflect on their work),
- search of connections between different concepts (e.g.,
addition and subtraction, multiplication and division, etc.),
- the use of technology (e.g., physical manipulatives,
computers, the Internet, computer-generated worksheets, overheads,
and so on).
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.
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
Home assignments 20%
The use of technology 10%
Topic exams 30%
Final Project 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
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.
 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.
 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.
 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.
 National Council of Teachers of Mathematics. (1996). Professional Standards for Teaching Mathematics. Reston, VA: Author.
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