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

                                    23403 E Mission Avenue, Suite 220F

                                    Liberty Lake, WA 99019

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.  The course will also explore the teaching methodology that supports learning mathematics standards, such as Common Core State Standards (CCSS).  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, Revised 2015, Revised 2017, Revised 2020


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.


Expected Learning Outcomes

As a result of this course, participants will demonstrate their ability to:


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 and supports learning mathematics standards, such as the Common Core State Standards (CCSS).  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:

·         Complete all four information sections showing a competent understanding of the material presented in each section.

·         Complete all four section examinations, showing a competent understanding of the material presented.  You must obtain an overall score of 70% or higher, with no individual exam score below 50%, and successfully complete ALL writing assignments to pass this course.  *Please note: Minimum exam score requirements may vary by college or university; therefore, you should refer to your course addendum to determine what your minimum exam score requirements are.

·         Complete a review of any section on which your examination score was below 50%.

·         Retake any examination, after completing an information review, to increase that examination score to a minimum of 50%, making sure to also be achieving an overall exam score of a minimum 70% (maximum of three attempts). *Please note: Minimum exam score requirements may vary by college or university; therefore, you should refer to your course addendum to determine what your minimum exam score requirements are.

·         Complete all course journal article and essay writing assignments with the minimum word count shown for each writing assignment.

·         Complete a course evaluation form at the end of the course.


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 conceptual teaching. The chapter also explores the methodology in relationship to the Common Core State Standards. 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

All assignments are reviewed and may impact your final grade.  Exceptionally or poorly written assignments, or violation of the Academic Integrity Policy (see course syllabus for policy), will affect your grade. Fifty percent of your grade is determined by your writing assignments, and your overall exam score determines the other fifty percent.  Refer to the Essay Grading Guidelines which were sent as an attachment with your original course link. You should also refer to the Course Syllabus Addendum which was sent as an attachment with your original course link, to determine if you have any writing assignments in addition to the Critical Thinking Questions (CTQ) and Journal Article Summations (JAS).  If you do, the Essay Grading Guidelines will also apply.


Your writing assignments must meet the minimum word count and are not to include the question or your final citations as part of your word count.  In other words, the question and citations are not to be used as a means to meet the minimum word count.


Critical Thinking Questions

There are four CTQs that you are required to complete. You  will need to write a minimum of 500 words (maximum 1,000) per essay. You  should explain how the information that you gained from the course will be applied and clearly convey a strong understanding of the course content as it relates to each CTQ.  To view the questions, click on REQUIRED ESSAY and choose the CTQ that you are ready to complete; this will bring up a screen where you may enter your essay.  Prior to course submission, you may go back at any point to edit your essay, but you must be certain to click SAVE once you are done with your edits.


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

Journal Article Summations

You are required to write, in your own words, a summary on a total of three peer-reviewed or scholarly journal articles (one article per JAS), written by an author with a Ph.D., Ed.D. or similar, on the topic outlined within each JAS section in the “Required Essays” portion of the course  (blogs, abstracts, news articles or similar are not acceptable). Your article choice must relate specifically to the discussion topic listed in each individual JAS. You will choose a total of three relevant articles (one article per JAS) and write a thorough summary of the information presented in each article (you must write a minimum of  200 words with a 400 word maximum per JAS). Be sure to provide the URL or the journal name, volume, date, and any other critical information to allow the facilitator to access and review each article. 


To write your summary, click on REQUIRED ESSAYS and choose the JAS that you would like to complete. A writing program will automatically launch where you can write your summary. When you are ready to stop, click SAVE.  Prior to course submission you may go back at any point to edit your summaries 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 click SAVE before you write another summary 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 Fort Hays State University in Kansas. Currently, she teaches graduate courses in the Advanced Education Programs Department. She supervises research projects, mentors students, and writes curriculum. Dr. Chappell has over 29 years of teaching experience and 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.

Boaler, J. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass.

Burns, M. (2013). Go figure: Math and the common core. Educational Leadership, 70(4), 42–46.

De Visscher, A., Noël, M-P., & De Smedt, B. (2016). The role of physical digit representation and numerical magnitude representation in children’s multiplication fact retrieval. Journal of Experimental Child Psychology, 152, 41–53. doi:10.1016/j.jecp.2016.06.014

Gardner, H. (2006). Multiple intelligences: New horizons in theory and practice. New York, NY: Basic Books.

Glatthorn, A., Boschee, F., Whitehead, B., & Boschee, B. (2018). Curriculum leadership: Strategies for development and implementation (5th ed.). Thousand Oaks, CA: Sage.

Humphrys, C., & Parker, R. (2018). Digging deeper: Making number talks matter even more. Portsmouth, NH: Stenhouse.

Kobett, B. M., & Karp, K. S. (2020). Strengths-Based teaching and learning in mathematics. Thousand Oaks, CA: Corwin Press.

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

Muschla, J. A., & Muschla, G. R. (2012). Teaching the common core math standards with hands-on activities. San Francisco, CA: Jossey-Bass.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.

NCTM [National Council of Teachers of Mathematics]. (2017). Compendium for research in mathematics education. Reston, VA: Author.

Peng, P., Namkung, J. M., Fuchs, D., Fuchs, L. S., Patton, S., Yen, L., Compton, D. L. Zhang, W. Miller, A., & Hamlett, C. (2016). A longitudinal study on predictors of early calculation development among young children at risk for learning difficulties. Journal of Experimental Child Psychology, 152, 221–241. doi:10.1016/j.jecp.2016.07.017

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

Singer-Dudek, J. & Greer, R. D. (2005). A long-term analysis of the relationship between fluency and the training and maintenance of complex math skills. Psychological Record, 55(3), 361–376. doi:10.1007/BF03395516

Swars, S. L., & Chestnutt, C. (2016). Transitioning to the Common Core State Standards for Mathematics: A Mixed Methods Study of Elementary Teachers' Experiences and Perspectives. School Science & Mathematics116(4), 212–224. doi:10.1111/ssm.12171

Van de Walle, J. A., Karp, K.S., Bay-Williams, J. M., Wray, J., & Brown, E. T. (2018). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Upper Saddle River, NJ: Pearson.

Van de Walle, J. A., Karp, K. S., Lovin, L. A., & Bay-Williams, J. M. (2013). Teaching student-centered mathematics: Developmentally appropriate instruction for grades pre-K–2. Boston, MA: Pearson Education.

Wilson, P. H., Downs, H. A. (2014). Supporting mathematics teachers in the common core implementation. AASA Journal of Scholarship & Practice, 11(1), 38–47. https://www.aasa.org/uploadedFiles/Publications/Journals/AASA_Journal_of_Scholarship_and_Practice/JPS-Spring2014-FINAL-v2.pdf


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.



Updated 4/7/20  JN