Introduction

Welcome to Teaching Secondary Math Conceptually: Meeting Mathematics Standards, an interactive computer-based instruction course designed to expand your methodology for teaching Mathematics. The course will explore an instructional methodology 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 explore the principles of teaching those concepts to learners. The course will also explore teaching methodologies that support many federal and state standards. This course will focus on the topics of integers, fractions, factoring, and functions.

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 Secondary Math Conceptually: Meeting Mathematics Standards

Instructor: Kim Chappell, Ed.D.

Publisher: Virtual Education Software, inc. 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 classroom or academic-related settings. The teaching strategies are designed to be used primarily with middle and high school students, or any students who struggle with understanding mathematics.

Expected Learning Outcomes

· Expand conceptual understanding of integers, fractions, factoring, and functions

· Explore a conceptual methodology of teaching math

· Develop skill in designing constructive learning experiences

· Explore strategies to support learning the skills outlined in mathematics federal legislation

· Investigate integrating concrete modeling to support conceptual teaching

Course Description

The course Teaching Secondary Math Conceptually: Meeting Mathematics Standards is designed to explain and connect the major concepts, procedures, and reasoning processes of mathematics. Current standards and practices 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 to illustrate constructive teaching. The course has been divided into four chapters covering four math topics, i.e. integers, fractions, factoring and functions. 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%, 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 – Integers

The first chapter outlines the teaching methodology, 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 mathematics federal legislation. The chapter concludes with strategies for developing conceptual understanding of integers. Example activities are presented to both explain mathematical concepts and illustrate teaching strategies.

Chapter 2 – Fractions

The second chapter explores fractional understandings. Geometric and newly produced manipulatives are used to develop essential concepts and computational principles. All operations are presented using manipulatives to teach for fractional understanding. In addition, a unique strategy is presented to find common denominators, equivalent and reduced fractions. Example activities are presented to both explain mathematical concepts and illustrate teaching strategies.

Chapter 3 – Factoring

The third chapter develops concepts of prime numbers and factoring. Foundational principles for factoring are developed and applied to a variety of complex operations. Conceptual understandings are expanded to construct knowledge of exponents. Example activities are presented to both explain mathematical concepts and illustrate teaching strategies.

Chapter 4 – Functions

The final chapter explores the principles of functions. Strategies presented are designed to construct foundational understanding of functions. Example activities are presented to both explain mathematical concepts and illustrate teaching strategies. The chapter concludes with a discussion of standards for practice and integrating modeling into middle and high school math.

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 Secondary Math Conceptually: Meeting Mathematics Standards was developed by Dr. Kim Chappell. Dr. 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. Dr. Chappell has a Doctorate of Education degree in Instructional Leadership

Contacting the Instructor

You may contact the instructor by emailing Professor 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

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

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

Gardner, H. (1993). Frames of Mind: The Theory of Multiple Intelligences. New York: 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.

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

Langer-Osuna, J. M. (2017). Authority, identity, and collaborative mathematics. Journal for Research in Mathematics Education, 48(3). doi:10.5951/jresematheduc.48.3.0237

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

Maier, G. (2006). The algebra blues. Connect Magazine, 19(3), 24–25. https://www-mlc.stage.ciservers.net/resources/lessons/archive/gene/the_algebra_blues

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.

Muschla, J. A., Muschla, G. R., & Muschla-Berry, E. (2015). Teaching the common core math standards with hands-on activities: Grades 9–12. 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.

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

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.

Wills, J. (2010). Learning to love math: Teaching strategies that change student attitudes and get results. Alexandria, VA: ASCD.

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.

4/7/20 JN