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Syllabus

The information contained on this page is designed to give students a representative example of material covered in the course. Any information related to course assignments, dates, or course materials is illustrative only. For a definitive list of materials, please check the online catalog 3-4 weeks before the course start date.


MTHED 520: Analysis of Research in Mathematics Education


Overview

Analysis of Research in Mathematics Education (3) Survey of the status of knowledge about mathematics learning and instruction, K-12; analysis of research procedures; instruments for evaluating research.
Prerequisite: MTHED 412W or MTHED 420;  3 credits in statistics; teaching experience.


Course Objectives

At the end of this course, students will be able to:

  1. Understand contemporary reserch on the teaching and learning of mathematics with respect to specific foci within understanding of mathematics, artifacts used in mathematics instruction, the teaching of mathematics, and affective issues in the teaching and learning of mathematics.
  2. Apply mathematics education research to mathematics education of students in grades K through 12.
  3. Understand major constructs used in research on the teaching and learning of mathematics.

Topics

  • MODULE 1: MATHEMATICS
    • Lesson 1: What is mathematics?
  • MODULE 2: UNDERSTANDING MATHEMATICS
    • Lesson 2: What does it mean to understand mathematics?
    • Lesson 3: Understanding mathematical understanding
    • Lesson 4: Understanding the mathematics in students' explanations
    • Lesson 5: Representations
  • MODULE 3: UNDERSTANDING GROWTH IN MATHEMATICAL UNDERSTANDING: LEVELS OF UNDERSTANDING
    • Lesson 6: Van Hiele Levels
    • Lesson 7: Transition from arithmetic to algebra
    • Lesson 8: Process-object perspectives and the case of function
  • MODULE 4: ARTIFACTS FOR LEARNING MATHEMATICS
    • Class #9: Enacting a mathematics curriculum: Process and curriculum tasks
    • Class #10: Roles of examples in mathematics instruction
    • Class #11: The teaching and learning of mathematics in the context of mathematics-specific technology
  • MODULE 5: MATHEMATICS TEACHING
    • Class #12: Constructs that describe mathematics teaching: Hypothetical learning trajectories
    • Class #13: Mathematics teaching noticing
    • Class #14: Understanding mathematics teaching
  • MODULE 6: AFFECTIVE FACTORS IN MATHEMATICS LEARNING
    • Class #15: Mathematical identity and success in mathematics learning

Required Course Materials

Most World Campus courses require that students purchase materials (e.g., textbooks, specific software, etc.). To learn about how to order materials, please see the Course Materials page. You should check LionPATH approximately 3–4 weeks before the course begins for a list of required materials.

MTHED 520 has no required textbook. You will be expected to complete readings that will available within the course (embedded) or on library reserve.


Library Resources

Many of the University Libraries resources can be utilized from a distance. Through the Libraries website, you can

  • access magazine, journal, and newspaper articles online using library databases;
  • borrow materials and have them delivered to your doorstep—or even your desktop;
  • get research help via email, chat, or phone using the Ask a Librarian service; and
  • much more. 

You must have an active Penn State Access Account to take full advantage of the Libraries' resources and service.  The Off-Campus Users page has additional information about these free services.


Technical Requirements

Technical Requirements
Operating System

Canvas, Penn State's Learning Management System (LMS), supports most recent versions of Microsoft Windows and Apple Mac operating systems. 

To determine if your operating system is supported, please review Canvas' computer specifications.

Browser

Canvas supports the last two versions of every major browser release. It is highly recommended that you update to the newest version of whatever browser you are using.

Please note that Canvas does not support the use of Internet Explorer. Students and instructors should choose a different browser to use.   

To determine if your browser is supported, please review the list of Canvas Supported Browsers.


Note: Cookies must be enabled, and pop-up blockers should be configured to permit new windows from Penn State websites.
Additional Canvas Requirements For a list of software, hardware, and computer settings specifically required by the Canvas LMS, please review Canvas' computer specifications.
Additional Software

All Penn State students have access to Microsoft Office 365, including Microsoft Office applications such as Word, Excel, and PowerPoint.

Students will need a PDF reader, such as Adobe Reader.

Hardware

Monitor: Monitor capable of at least 1024 x 768 resolution
Audio: Microphone, Speakers
Camera (optional, recommended): Standard webcam - many courses may require a webcam for assignments or exam proctoring software.

Mobile Device (optional) The Canvas mobile app is available for versions of iOS and Android. To determine if your device is capable of using the Canvas Mobile App, please review the Canvas Mobile App Requirements.


Student Education Experience Questionnaire (SEEQ)

During the semester you will receive information for completing the Student Education Experience Questionnaire (SEEQ). Your participation is an opportunity to provide anonymous feedback on your learning experience. Your feedback is important because it allows us to understand your experience in this course and make changes to improve the learning experiences of future students. Please monitor email and course communications for links and availability dates.


If you need technical assistance at any point during the course, please contact the Service Desk.

For registration, advising, disability services, help with materials, exams, general problem solving, visit World Campus Student Services!


Course Requirements and Grading

Assignment Summary
Assignment TypesWeight (%)
Ungraded Quizzes5%
Ungraded Posts10%
Responses to Posts5%
Linking Research and Practice Notes10%
Graded Posts25%
End-of-Module Papers15%
Major Paper30%
 100%
Grading Scale
Grading Scale
Letter GradeRange (%)
A93 to 100
A-90 to < 93
B+87 to < 90
B83 to < 87
B-80 to < 83
C+77 to < 80
C70 to < 77
D60 to < 70
F0  to < 60
 
Please refer to the University Grading Policy for Undergraduate Courses for additional information about University grading policies. Course Schedule
The schedule below provides the topics we will be covering in this course, along with the associated time frames and assignments. Due dates vary in the lesson; check individual assignments and your course calendar in Canvas for the specific due dates. Note: All lessons run from Wednesday to Tuesday.
  • Course length: 15 weeks
Getting Started
Getting Started
Activities and Assignments:
  1. Read the full syllabus and post any questions in the Syllabus Questions discussion forum
  2. Configure your Zoom room
  3. Submit your Elevator Pitch video
 
MODULE 1: MATHEMATICS
Lesson 1: What is Mathematics?
Lesson 1
Activities and Assignments:
  1. Post in the L1.1: Definition of Mathematics discussion forum
  2. Post in the L1.2: Compare Your View of Mathematics discussion forum
  3. Complete the L1.3 Research in Mathematics Education Self-Check
  4. Complete the L1.4: Research Questions: Combination of Conditions Self-Check
  5. Participate in the L1.5: End of Lesson 1 Reflection discussion forum
 
MODULE 2: UNDERSTANDING MATHEMATICS
Lesson 2: What Does It Mean to Understand Mathematics?
Lesson 2
Activities and Assignments:
  1. Post in the L2.1: What Does It Mean to Understand Mathematics discussion forum
  2. Participate in the L2.2: Conceptual and Procedural Knowledge discussion forum
  3. Complete the L2.3: Application of Strands of Mathematical Proficiency activity
  4. Participate in the L2.4: Mathematical Understanding in "Little Big League" discussion forum
  5. Participate in the L2.5: End of Lesson 2 Reflection discussion forum
Lesson 3: Understanding Mathematical Understanding
Lesson 3
Activities and Assignments:
  1. Complete the L3.1: Understanding Students' Through Task-Based Interviews activity
  2. Complete the L3.2: Understanding Students' Solving of Word Problems activity
  3. Complete the L3.3: Inquiring Into Student Understanding Through Task-based Interviews activity
  4. Complete the L3.4: Inquiring Into Student Understanding Through Task-Based Interviews activity
  5. Complete the L3.5: Understanding Mathematical Understanding in Informal Setting activity
  6. Participate in the L3.6: End of Lesson 3 Reflection discussion forum
  7. Obtain approval for your Master Paper: Research Investigation topic from your instructor by the end of Lesson 8 at the latest for the question you have generated. The instructor can give you advice on whether your question is a viable one to pursue.
 
Lesson 4: Understanding the Mathematics in Students' Explanations
Lesson 4
Activities and Assignments:
  1. Submit Linking Research and Practice Notes 1
  2. Participate in the L4.1: Understanding the Mathematics in Students' Explanations discussion forum
  3. Participate in the L4.2: Role of the Teacher in Encouraging Mathematical Thinking discussion forum
  4. Participate in the L4.3: Role of the Teachers in Encouraging Mathematical Thinking discussion forum
  5. Obtain approval for your Master Paper: Research Investigation topic from your instructor by the end of Lesson 8 at the latest for the question you have generated. The instructor can give you advice on whether your question is a viable one to pursue.
 
Lesson 5: Representations
Lesson 5
Activities and Assignments:
  1. Complete the L5.1: Using Representations in Problem Solving activity
  2. Participate in the L5.2: Graphs as Representation discussion forum
  3. Participate in the L5.3: Children's Representations discussion forum
  4. Participate in the L5.4: Overall Perspective on Representation in Mathematics Learning discussion forum
  5. Complete the L5.5: Representing Relationships Among Variables, Part 1 activity
  6. Participate the L5.6: Representing Relationships Among Variables, Part 2 discussion forum
  7. Participate in the L5.7: Role of Internal and External Representation discussion forum
  8. Submit Modules 1 and 2 Paper
  9. Obtain approval for your Master Paper: Research Investigation topic from your instructor by the end of Lesson 8 at the latest for the question you have generated. The instructor can give you advice on whether your question is a viable one to pursue.
 
MODULE 3: UNDERSTANDING GROWTH IN MATHEMATICAL UNDERSTANDING: LEVELS OF UNDERSTANDING
Lesson 6: Van Hiele Levels
Lesson 6
Activities and Assignments:
  1. Complete the introduction to Van Hiele levels activities
  2. Complete the 6.1: Van Hiele Levels Test Self-Check
  3. Participate in the 6.2: Van Hiele Phases of Instruction discussion forum
  4. Obtain approval for your Master Paper: Research Investigation topic from your instructor by the end of Lesson 8 at the latest for the question you have generated. The instructor can give you advice on whether your question is a viable one to pursue.
 
Lesson 7: Transition from Arithmetic to Algebra
Lesson 7
Activities and Assignments:
  1. Complete the 7.1: Perspectives on Algebra Self-Check
  2. Participate in the 7.2: Difficulties With Beginning Algebra discussion forum
  3. Complete L7.3: Complexities of School Algebra Self-Check
  4. Participate in the 7.4: Addressing Difficulties With Understanding Algebra discussion forum
  5. Submit 7.5: Addressing Difficulties With Understanding Algebra revision
  6. Obtain approval for your Master Paper: Research Investigation topic from your instructor by the end of Lesson 8 at the latest for the question you have generated. The instructor can give you advice on whether your question is a viable one to pursue.
 
Lesson 8: Process-object Perspectives and the Case of Function
Lesson 8
Activities and Assignments:
  1. Complete L8.1: Operational/Structural Conception Self-Check
  2. Complete L8.2: APOS Theory Self-Check
  3. Participate in the L8.3 Process Object Perspectives discussion forum
  4. Submit Module 3 Paper
  5. Obtain approval for your Master Paper: Research Investigation topic from your instructor by the end of Lesson 8 at the latest for the question you have generated. The instructor can give you advice on whether your question is a viable one to pursue.
 
MODULE 4: ARTIFACTS FOR LEARNING MATHEMATICS
Lesson 9: Enacting a Mathematics Curriculum: Process and Curriculum Tasks
Lesson 9
Activities and Assignments:
  1. Participate in the 9.1: Enacted Curriculum discussion forum
  2. Submit 9.1: Enacted Curriculum revision
  3. Participate in the 9.3: Standards Tasks discussion forum
  4. Submit 9.4: Standards Tasks revision
  5. Submit 9.5: Level of Cognitive Demand assignment
  6. Continue working on your Major Paper: Research Investigation
 
Lesson 10: Roles of Examples in Mathematics Instruction
Lesson 10
Activities and Assignments:
  1. Submit Linking Research and Practice Notes 2
  2. Complete the 10.1: Abstract and Concrete Examples activity
  3. Complete the 10.2: Variance in Mathematical Structure activity
  4. Participate in the 10.3: Examples, Nonexamples, and Counterexamples discussion forum
  5. Complete 10.4: Examples Self-Check
  6. Participate in the 10.5: Experience with Examples discussion forum
  7. Solve the Just for Fun activity
  8. Continue working on your Major Paper: Research Investigation
 
Lesson 11: The Teaching and Learning of Mathematics in the Context of Mathematics-Specific Technology
Lesson 11
Activities and Assignments:
  1. Complete the Technology Explorations activity
  2. Participate in the L11.1: Technology in Mathematics Education discussion forum
  3. Participate in the L11.2: Technology in Mathematics Explorations discussion forum
  4. Participate in the L11.3: Technology Effects on Mathematics Education discussion forum
  5. Submit L11.4: Technology Effects on Mathematics Education revisions
  6. Submit Module 4 Paper
  7. Continue working on your Major Paper: Research Investigation
 
MODULE 5: MATHEMATICAL TEACHING
Lesson 12: Constructs that Describe Mathematics Teaching: Hypothetical Learning Trajectories
Lesson 12
Activities and Assignments:
  1. Complete L12.1: Learning Progressions - Ratio and Proportion Self-Check
  2. Participate in the L12.2: Mathematical Idea Essential to Understanding Ratio and Proportion discussion forum
  3. Continue working on your Major Paper: Research Investigation
 
Lesson 13: Mathematics Teacher Noticing
Lesson 13
Activities and Assignments:
  1. Complete L13.1: Propositions About Teacher Noticing Self-Check
  2. Participate in the L13.2: Teaching Noticing and MOST discussion forum
  3. Submit 13.3: Teaching Noticing and MOST revision
  4. Continue working on your Major Paper: Research Investigation
 
Lesson 14: Understanding Mathematics Teaching
Lesson 14
Activities and Assignments:
  1. Submit Linking Research and Practice Notes 3
  2. Participate in the 14.1: Classroom Mathematics and Personal Mathematics discussion forum
  3. Submit Module 5 Paper
  4. Continue working on your Major Paper: Research Investigation
 
MODULE 6: AFFECTIVE FACTORS IN MATHEMATICS LEARNING
Lesson 15: Mathematical Identify and Success in Mathematics Learning
Course Wrap-up and Reflection
Activities and Assignments:
  1. Participate in the 15.1: Mathematical Identity and Success in Mathematics Learning discussion forum
  2. Submit Major Paper
 

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