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

 

 

Int Welcome to Teaching Elementary Math Conceptually, an interactive computer-based instruction course designed to expand your methodology for teaching Mathematics. The course explores 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 concepts underlying various math topics and to explore the principles of teaching those concepts to learners. You will also explore how to develop computational thinking, which is foundational to learning computer science. The course expands the teaching methodology that supports learning mathematics standards, such as Common Core State Standards (CCSS) and STEM concepts related to technology. This course will focus on the mathematics topics of number sense, basic operations, and fractions, along with the key strategies that connect mathematics and technology.

 

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

Publisher:

Virtual Education Software, inc. 2010, Revised 2015, Revised 2017, Revised 2020, Revised 2024

Instructor:

Kim Chappell, Ed.D.

 

 

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) and STEM concepts related to technology. 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. The emphasis is on exploring how to develop mathematical understanding and computational thinking in learners to support achievement in mathematics and technology.

 

 

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%, 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 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 and STEM concepts, including computational thinking. The chapter also explores the four key strategies for connecting technology and mathematics (decomposition, abstraction, pattern recognition, and algorithm design) and how to develop a 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. The computational thinking strategies of decomposition, pattern recognition, and algorithm design are expanded.

 

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. Technology concepts are connected using the strategies of abstraction and algorithm design.

 

Chapter 4 – Fractions

The final chapter explores fractional understandings. Alternative manipulatives are used to develop essential concepts and computational principles. In addition, a unique strategy is presented for finding common denominators, equivalent fractions, and reduced fractions. All operations, including division, are presented using manipulatives to teach for understanding. The computational thinking strategies of decomposition and algorithm design are expanded.

 

 

Examinations

At the end of each chapter, 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.  Your final grade for the course will be determined by calculating an average score of all exams.  This score will be printed on your final certificate.  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.

 

 

Instructor Description

Teaching Elementary Math Conceptually: A New Paradigm was developed by Dr. Kim Chappell. Dr. Chappell is an associate 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 34 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 Dr. Chappell at kim_chappell@virtualeduc.com or 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.

 

 

References

Aho, A. V. (2011). Ubiquity symposium: Computation and computational thinking. Ubiquity. https://ubiquity.acm.org/article.cfm?id=1922682

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). National Council of Teachers of Mathematics.

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

Burns, M. (2013). Go figure: Math and the common core. Educational Leadership, 70(4), 42–46. https://ascd.org/el/articles/go-figure-math-and-the-common-core

Chappell, K. (2023). Number nudget: Developing number concepts. Pressbooks. https://fhsu.pressbooks.pub/numbernudget/

Cuny, J., Snyder, L., & Wing, J.M. (2010). Demystifying computational thinking for non-computer scientists. Unpublished manuscript in progress, referenced in http://www.cs.cmu.edu/~CompThink/resources/TheLinkWing.pdf

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. https://doi.org/10.1016/j.jecp.2016.06.014

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

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

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

K–12 Computer Science Framework. (2016). http://www.k12cs.org

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

Lee, I. (2016). Reclaiming the roots of CT. CSTA: The voice of K–12 computer science education and its educators. http://www.witty.ca/uploads/4/7/6/4/4764474/csta_voice_magazine__march_2016-pp3-5-compthinking.pdf

Liljedahl, P., & May, Marlin. (2023). Building thinking classrooms in mathematics, grades K–12: 14 teaching practices for enhancing learning. Corwin.

MacDonald, B. L., & Thomas, J. N. (2023). Teaching mathematics conceptually: Guiding instructional principles for 5–10 year olds (1st ed.). Corwin.

Muschla, E., Muschla, J. A., & Muschla, G. R. (2014). Teaching the Common Core math standards with hands-on activities, K–2. Jossey-Bass.

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

National Council of Teachers of Mathematics. (2017). Compendium for research in mathematics education. 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. https://doi.org/10.1016/j.jecp.2016.07.017

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

Sheldon, E. (2017, March 30). STEM: Computational thinking across the curriculum. Edutopia. https://www.edutopia.org/blog/computational-thinking-across-the-curriculum-eli-sheldon

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. https://doi.org/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. https://doi.org/10.1111/ssm.12171

Thornson, K. (2018). Early learning strategies for developing computational thinking skills. Getting Smart. https://www.gettingsmart.com/2018/03/18/early-learning-strategies-for-developing-computational-thinking-skills/

Van de Walle, J. A., Karp, K.S., Bay-Williams, J. M., Wray, J., & Brown, E. T. (2022). Elementary and middle school mathematics: Teaching developmentally (11th ed.). 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. 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://eric.ed.gov/?id=EJ1023730

 

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 12/12/24  JN