Teaching Elementary
Math Conceptually:
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
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.
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.
As a result of this course, participants will demonstrate
their ability to:
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.
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.
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.
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.
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. (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.
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 & Mathematics, 116(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