Diagnosis and Remediation in Elementary Mathematics (K-6)
ELE 643
Syllabus
Course Description
The purpose of this course is to address the cognitive needs of first through sixth grade students who underachieve when learning mathematics. The reasons for the inability of some students to grasp mathematics vary from child to child. It is for this reason that teachers must teach mathematics concepts and skills so they are understood and remembered by all students. The course will prepare teachers to diagnosis and remediate a population of students, known as dissimilar learners.
The goal of this course is to provide teachers with the skills to assess and adapt instruction. The lessons and remediation must be designed in terms of developmental instructional strategies that promote thoughtful, active learning, and connections to earlier concepts. The use of functional assessments of students' strengths and areas of concern will determine the intervention strategies needed to increase achievement.
For learners to be successful, teachers must assess students' individual abilities and characteristics. The selection of appropriate and effective instructional strategies based on these assessments is the key to developing a solid foundation for struggling students to be successful.
The most effective approach that benefits the dissimilar learner is one that is multidimensional and systemic. The course will provide teachers with the skills needed to understand this approach by planning for maximum flexibility, manageable units of classroom time periods, and incorporating all teaching and behavioral methods.
Objectives
Upon completion of this course the teacher will be able to:
- Recognize reasons why students struggle with mathematics and identify the needs of dissimilar learners.
- Learn how to diagnosis, prescribe, and remediate students who struggle with mathematics.
- Assess performance in mathematics.
- Understand the impact of place value on mathematics, common errors associated with place value, and instructional strategies needed to remediate
- Identify what students should know about addition and subtraction and recognize error patterns to determine instructional strategies.
- Comprehend the errors associated with multiplication and division to determine instructional strategies.
- Understand why students struggle with rational numbers and determine instructional strategies to correct common errors.
- Identify common errors associated with fractions and determine instructional strategies to correct these errors.
- Gain knowledge of instructional strategies to remediate common errors in problem-solving.
- Design instructional activities to remediate students who struggle with mathematics.
Curriculum Design
Diagnosis & Remediation in Elementary Math (K-6) is a forty five-hour, 3 graduate credit course taught online. There are thirteen modules which require the students to participate in reading assignments (text and web), reflective practices, assessing, prescribing, and understanding remediation practices, analysis of information, research, and the development of instructional activities for remediation.
Time Requirements
This course is offered over a period of 15 weeks. Modules are completed over the 15-week period pending length of assignments per week.
Skill and Hardware Requirements
Students may use either a Macintosh computer or a PC with Windows 2000 or higher. Students should possess basic word processing skills and have Internet access as well as an active email account. Students also are expected to have a basic knowledge of how to use a Web browser, such as Internet Explorer, Mozilla Firefox, Safari, etc.
Course Materials
The required textbooks for this course are:
Richardson, Lloyd, Sherman, Helene, and Yard, George. Teaching Children Who Struggle with Mathematics: A Systematic Approach to Analysis and Correction. 1st edition. New Jersey: Pearson Education, Inc., 2005. 1-229. ISBN: 0-13-098463-9
Guillaume, Andrea. Classroom Mathematics Inventory for Grades K-6. 1st edition. Boston: Pearson Education, Inc., 2005. 1-291. ISBN: 0-205-40264-X
"Recommended Reading List" provided and updated for each term. The course content includes many online readings, website reviews, research reading assignments, forum postings and other written projects.
Course Outline
Introduction: Introduction & Overview
Objectives: In this beginning exercise, the instructor will confirm the accuracy of e-mail addresses for all students. The instructor will then send a welcome message to the class. The students have this first week to acquaint themselves with the format of the course, the textbook, and the methods of communication.
Contents:
- Introduction to the online class environment
- Meet the classmates
- Meet the instructor
- Become familiar with the online course content
- Review the course outline
- Review the course syllabus and relevant information
- Become familiar with the text structure
- Review Chapter Overviews
- Review Project Information
Module One: The Dissimilar Learner and Mathematics Instruction
Objectives:
- Students will gain knowledge of the Learner-Centered Approach.
- Students will develop an understanding of why students struggle with mathematics.
- Students will understand how to teach mathematics effectively.
Contents:
- Problem and Solution
- Learner-Centered Approach
- Why do Students Struggle with Mathematics
- How is Mathematics Taught Effectively
- Discussion Questions
Module Two: Assessing Performance in Mathematics
Objectives:
- Students will understand the kinds of outcomes in mathematical education.
- Students will study the different assessments to determine outcomes in mathematical education.
- Students will gain knowledge of principles of assessment.
- Students will learn how to assess learners with diverse needs in mathematics.
Contents:
- Outcomes in Mathematical Education
- Different assessments for Different kinds of Outcomes
- Principles of Assessment
- Assessment and the Diverse Learner
Module Three: Assessing Understanding and Performance in Mathematical Processes
Objectives:
- Students will gain knowledge of the mathematical processes protocol and how to administer it.
- Students will understand how to assess computation with whole numbers.
- Students will understand how to assess extended work with number and operations.
- Students will understand how to assess performance in algebra and functions.
Contents:
- Processes Protocol
- Computation with Whole Numbers
- Extended Work with Number and Operations
- Algebra and Functions
Module Four: Assessing Understanding and Performance in Mathematical Processes
Objectives:
- Students will understand the concept of place value and common errors associated with place value.
- Students will diagnosis place value errors.
- Students will develop a prescription for place value errors.
- Students will develop remediation strategies for place value errors.
- Students will develop instructional strategies and activities.
Contents:
- Geometry
- Measurement
- Data Analysis, Statistics, and Probability
- Interpreting data
- Planning Instruction
Module Five: Place Value
Objectives:
- Students will understand how to assess geometry.
- Students will understand how to assess measurement.
- Students will understand how to assess data analysis, statistics, and probability.
- Interpreting Evidence and Planning Instruction
Contents:
- Impact of Place Value
- Why do students struggle with place value?
- Error Patterns: Diagnosis, prescription, Remediation
- Instructional Strategies and Activities
- Discussion Questions
Module Six: Addition of Whole Numbers
Objectives:
- Students will understand the concept of addition of whole numbers and common errors associated with addition of whole numbers.
- Students will diagnosis addition errors.
- Students will develop a prescription for addition errors.
- Students will develop remediation strategies for addition errors.
- Students will develop instructional strategies and activities.
Contents:
- What is Addition?
- What should students understand about addition?
- Error Patterns: Diagnosis, prescription, Remediation
- Instructional Strategies and Activities
- Discussion Questions
Module Seven: Subtraction of Whole Numbers
Objectives:
- Students will understand the concept of subtraction of whole numbers and common errors associated with subtraction of whole numbers.
- Students will diagnosis subtraction errors.
- Students will develop a prescription for subtraction errors.
- Students will develop remediation strategies for subtraction errors.
- Students will develop instructional strategies and activities.
Contents:
- What is Subtraction?
- What should students understand about subtraction?
- Error Patterns: Diagnosis, Prescription, Remediation
- Instructional Strategies and Activities
- Discussion Questions
Module Eight: Division
Objectives:
- Students will understand the concept of division and common errors associated with division.
- Students will diagnosis division errors.
- Students will develop a prescription for division errors.
- Students will develop remediation strategies for division errors.
- Students will develop instructional strategies and activities
Contents:
- What is Division?
- What should students understand about division?
- Error Patterns: Diagnosis, prescription, Remediation
- Instructional Strategies and Activities
- Discussion Questions
Module Nine: Rational Numbers
Objectives:
- Students will understand the concept of rational numbers and common errors associated with rational numbers.
- Students will diagnosis rational number errors.
- Students will develop a prescription for rational number errors.
- Students will develop remediation strategies for rational number errors.
- Students will develop instructional strategies and activities.
Contents:
- What are rational numbers?
- What should students understand about rational numbers?
- Error Patterns: Diagnosis, prescription, Remediation
- Instructional Strategies and Activities
- Discussion Questions
Module Ten: Decimals
Objectives:
- Students will understand the concept of decimals and common errors associated with decimals.
- Students will diagnosis decimal errors.
- Students will develop a prescription for decimal errors.
- Students will develop remediation strategies for decimals errors.
- Students will develop instructional strategies and activities.
Contents:
- What are decimals?
- What should students understand about decimals?
- Error Patterns: Diagnosis, prescription, Remediation
- Instructional Strategies and Activities
- Discussion Questions
Module Eleven: Problem Solving
Objectives:
- Students will understand problem solving and common errors associated with problem.
- Students will diagnosis problem solving errors.
- Students will develop a prescription for problem solving errors.
- Students will develop remediation strategies for problem solving errors.
- Students will develop instructional strategies and activities.
Contents:
- What is problem solving?
- What should students understand about problem solving?
- Error Patterns: Diagnosis, prescription, Remediation
- Instructional Strategies and Activities
- Discussion Questions
Module Twelve: Planning Academic Content Lessons
Objectives:
- Students will examine guidelines for planning academic content lessons.
- Students will recognize processes for dealing with student lessons.
Contents:
- Academic Content
- Alternative Curricular Approaches
- Process
- Behavior
Module Thirteen: Analysis, Diagnosis, and Remediation of Mathematical Errors
Objectives:
- Students will analyze mathematical errors in student responses.
- Students will diagnosis the mathematical error in student responses.
- Students will develop remediation activities for student responses.
Contents:
- Complete a final project.
- Final Examination
Course Requirements:
| Requirements |
Points |
| Reflection Responses |
66 |
| Forum Postings |
28 |
| Discussion Questions |
36 |
| Remediation Activities |
36 |
| Final Project |
20 |
| Final Exam |
20 |
| Total |
206 |
Grades
206-192 - A
191-175 - B
174-155 - C
Student Academic Integrity
Participants guarantee that all academic class work is original. Any academic dishonesty or plagiarism (to take ideas, writings,
etc. from another and offer them as one's own), is a violation of student academic behavior standards as outlined by the
Teacher Education University catalog and is subject to academic disciplinary action.
Bibliography
Teacher Education University reserves the right to adjust and adapt this syllabus as necessary.