Teaching Elementary Math Conceptually:

A New Paradigm


Instructor Name:          Kim Chappell, Ed.D.

Phone:                          509-891-7219

Office Hours:                8 a.m. to 5 p.m. PST Monday - Friday

Email:                          kim_chappell@virtualeduc.com

Address:                       Virtual Education Software

                                    16201 E Indiana Ave, Suite 1450

                                    Spokane, WA 99216

Technical Support:        support@virtualeduc.com



Welcome to Teaching Elementary Math Conceptually, an interactive computer-based instruction course designed to expand your methodology for teaching Mathematics. The course will explore an innovative teaching model that incorporates strategies for teaching concepts constructively and contextually. The goal is for you to gain a deeper understanding of the underlying concepts of various math topics and to explore the principles of teaching those concepts to learners. This course will focus on the topics of number sense, basic operations, and fractions.


This computer-based instruction course is a self-supporting program that provides instruction, structured practice, and evaluation all on your home or school computer.  Technical support information can be found in the Help section of your course.


Course Materials (Online)

      Title:          Teaching Elementary Math Conceptually: A New Paradigm

      Instructor: Kim Chappell, Ed.D.

      Publisher:   Virtual Education Software, inc. 2010


Academic Integrity Statement

The structure and format of most distance learning courses presume a high level of personal and academic integrity in completion and submission of coursework. Individuals enrolled in a distance-learning course are expected to adhere to the following standards of academic conduct.


Academic Work

Academic work submitted by the individual (such as papers, assignments, reports, tests) shall be the student’s own work or appropriately attributed, in part or in whole, to its correct source. Submission of commercially prepared (or group prepared) materials as if they are one’s own work is unacceptable.


Aiding Honesty in Others

 The individual will encourage honesty in others by refraining from providing materials or information to another person with knowledge that these materials or information will be used improperly.


Violations of these academic standards will result in the assignment of a failing grade and subsequent loss of credit for the course.


Level of Application

This course is designed to be an informational course with application to work or work-related settings. The intervention strategies are designed to be used primarily with elementary students, or any students who struggle with understanding mathematics.



Course Objectives

·        Expand conceptual understanding of number sense, basic operations, and fractions

·        Explore a conceptual model of teaching math            

·        Develop skill in designing constructive learning experiences 

·        Explore foundational mathematical principles

·        Investigate integrating conceptual teaching into curriculum


Course Description

The course Teaching Elementary Math Conceptually: A New Paradigm is designed to explain and connect the major concepts, procedures, and reasoning processes of mathematics. Current research and trends in math education will be discussed to outline a teaching methodology that is conceptual, contextual, and constructive. Activities are presented to explain underlying concepts and illustrate constructive teaching. The course has been divided into four chapters covering four math topics: number sense, addition and subtraction, multiplication and division, and fractions. Emphasis is on exploring how to develop mathematical understanding in learners.


Student Expectations  

As a student, you will be expected to:


Course Overview

Chapter 1 – Number Sense

The first chapter outlines the teaching model, including a discussion of the conceptual, contextual, and constructive teaching of math. Comparisons are drawn between traditional math education and current trends in math education. The chapter also explores how to develop conceptual understanding of number sense, counting principles, and place value. Example activities are presented, both to explain mathematical concepts and to illustrate teaching strategies.


Chapter 2 – Addition & Subtraction

The second chapter covers concepts in addition, subtraction, and estimation. This chapter explores foundational concepts to develop computational fluency without memorization. Strategies represent conceptual and constructive teaching. A unique manipulative tool is introduced that is used extensively to develop operational concepts and expand place value principles.


Chapter 3 – Multiplication & Division

The third chapter develops concepts in multiplication, division, and prime numbers. In this chapter, designing contextual problems is discussed. Strategies presented are designed to construct operational concepts that are foundational to fractions. Place value concepts are expanded, and prime number concepts are developed.


Chapter 4 – Fractions

The final chapter explores fractional understandings. Alternative manipulatives are used to develop essential concepts as well as computational principles. In addition, a unique strategy is presented to find common denominators, equivalent fractions, and reduced fractions. All operations, including division, are presented using manipulatives to teach for understanding.



At the end of each course section, you will be expected to complete an examination designed to assess your knowledge. You may take these exams a total of three times. Your last score will save, not the highest score.  After your third attempt, each examination will lock and not allow further access.  The average from your exam scores will be printed on your certificate.  However, this is not your final grade since your required writing assignments have not been reviewed.  Exceptionally written or poorly written required writing assignments, or violation of the academic integrity policy in the course syllabus, will affect your grade.  As this is a self-paced computerized instruction program, you may review course information as often as necessary. You will not be able to exit any examinations until you have answered all questions. If you try to exit the exam before you complete all questions, your information will be lost. You are expected to complete the entire exam in one sitting.


Writing Assignments

This course has two required writing components.  ALL ASSIGNMENTS ARE REVIEWED. Exceptionally or poorly written assignments, or violation of the academic integrity policy noted in the course syllabus, will affect your grade. Be sure to refer to the Grading Guidelines for Writing Assignments, sent as an attachment with your original course link.

It is highly recommended that you write and save all writing assignments in an external word processing program (such as Word or Notepad), and then copy and paste these into the course program so that you will have backup copies.

To save your essays:


When you select the question or article you wish to respond to, ‘Simple Text’ or ‘Text Edit’ will launch automatically. When you are finished entering your response, simply click SAVE. 

You must SAVE before you write another essay or move on to another part of the course.


1)      Essay Requirement: Critical Thinking Questions

There are four Critical Thinking Questions that you must complete. You will do research on the questions and write brief essay responses relating it to the course content (and your personal experiences, when possible).  To view the questions, click on REQUIRED ESSAY and choose the Critical Thinking Question that you are ready to complete; this will bring up a screen where you may enter your essay.  You must write a minimum of 500 words (maximum 1,000) per essay.  You may go back at any point to edit your essays, but you must be certain to click SAVE once you have completed your edits.

You must SAVE before you write another essay or move on to another part of the course.


2)   Essay Requirement: Journal Articles

This task requires you to write a review of three peer-reviewed or scholarly journal articles, preferably written by an author with a Ph.D. (blogs and news articles are not acceptable) of your choice on a topic related to this course.  You may choose your topic by entering the Key Words (click on the Key Words button) into a search engine of your choice (Bing, Google, Yahoo, etc.).  Choose three relevant articles and write a critical summary of the information given in each article, explaining how the information relates to, supports, or refutes information given in this course. Conclude your review with your thoughts and impressions (200 words per journal article minimum, 400 words maximum). Be sure to provide the journal name, volume, date, and any other critical information to allow the instructor to access and review that article.


To write your essays, click on REQUIRED ESSAY and choose the Journal Article that you would like to complete; this will bring up a screen where you can write your review. When you are ready to stop, click SAVE.  You may go back at any point to edit your essays, but you must be certain to click SAVE once you are done with your edits. For more information on the features of this assignment, please consult the HELP menu.

You must SAVE before you write another essay or move on to another part of the course.



Instructor Description

Teaching Elementary Math Conceptually: A New Paradigm was developed by Kim Chappell. Kim Chappell is an Assistant Professor of Education at Crown College in Minnesota. Currently, she teaches undergraduate courses in the Teacher Education Department. She supervises student teachers, mentors students, and writes curriculum. Professor Chappell has over 19 years of teaching experience, 14 of those years in grades 1 through 8. She spent 9 years teaching middle school mathematics. She holds two master’s degrees, a Master of Education in Curriculum and Instruction, and a Master of Science in Mathematics Education. She also holds an Ed.D. degree in Instructional Leadership.


Contacting the Instructor

You may contact the instructor by emailing Professor Chappell at kim_chappell@virtualeduc.comor calling her at

509-891-7219, Monday through Friday, 8:00 a.m. - 5:00 p.m. PST.  Phone messages will be answered within 24 hours.  Phone conferences will be limited to ten minutes per student, per day, given that this is a self-paced instructional program. Please do not contact the instructor about technical problems, course glitches, or other issues that involve the operation of the course.


Technical Questions

If you have questions or problems related to the operation of this course, please try everything twice. If the problem persists please check our support pages for FAQs and known issues at www.virtualeduc.com and also the Help section of your course.


If you need personal assistance then email support@virtualeduc.com or call (509) 891-7219.  When contacting technical support, please know your course version number (it is located at the bottom left side of the Welcome Screen) and your operating system, and be seated in front of the computer at the time of your call. 


Minimum Computer Requirements

Please refer to VESi’s website: www.virtualeduc.com or contact VESi if you have further questions about the compatibility of your operating system.


Refer to the addendum regarding Grading Criteria, Course Completion Information, Items to be Submitted and how to submit your completed information. The addendum will also note any additional course assignments that you may be required to complete that are not listed in this syllabus.




Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 27–44). Reston, VA: National Council of Teachers of Mathematics.


Burns, M. (1998). Math: Facing an American phobia. Sausalito, CA: Math Solutions Publications.

Fix, A. (2009, January 16). Personal communication. Crown College: St. Bonifacius, MN.


Gardner, H. (1993). Frames of mind: The theory of multiple intelligences. New York: Basic Books.


Glatthorn, A., Boschee, F., & Whitehead, B. (2005). Curriculum leadership: Development and implementation. Thousand Oaks, CA: Sage.


Kalman, R. (2004, November). The value of multiple solutions. Mathematics Teaching in the Middle School, 10(4).

Laureate Education, Inc. (Executive Producer). (2005). Fractions, grades 6–8. Baltimore: Author.


Maier, G. (2006). The algebra blues. Connect Magazine, 19(3), 24-25.

McClain, K., & Schmitt, P. (2004, January). Teachers grow mathematically together: A case study from data analysis. Mathematics Teaching in the Middle School, 9(5), 274-279.


National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.


National Council of Teachers of Mathematics. (2004). Developing number sense. Retrieved October 21, 2004, from http://illuminations.nctm.org/index_d.aspx?id=252


Seeber, F. (1984). Patent No. 4560354. USA.


Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Upper Saddle River, NJ: Pearson.

Course content is updated every three years. Due to this update timeline, some URL links may no longer be active or may have changed. Please type the title of the organization into the command line of any Internet browser search window and you will be able to find whether the URL link is still active or any new link to the corresponding organization's web home page.


9/2/14 JN