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 430

Overview

Students' Mathematical Thinking (3 per semester, maximum of 6) Develop abilities in planning, conducting, and interpreting mathematics interviews to gain an understanding of students' thinking processes and current knowledge.

Course Objectives

At the end of this course, students will...

1. Be able to design, conduct, and interpret mathematics interviews with PreK-12 students,
2. Appropriate principles and practices of interview-based mathematics assessment into a range of professional activities, including everyday classroom teaching and formalized, academic research projects,
3. Understand current, research-based characterizations of mathematical thinking and their implications for assessment,
4. Understand at least one framework related to student thinking about a particular mathematical concept as found in research literature from the field of mathematics education, and
5. Apply principles of teacher learning and professional development in order to establish and maintain a productive professional learning community with a group of colleagues.

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.

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.

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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.

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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	Weight
Discussion Forum Reflection Posts (3)	30%
Blog Posts (4)	20%
Short Assignments (4)	20%
Interview Project	25%
"Stop and Think!" Questions	5%
Total	100%

Discussion Forums

You will actively participate in constructing our classroom community, in which we learn from and with one another. Our discussion forums will raise and answer questions for one another based on course content, such as assignments and readings. You will also draw upon your own experiences and challenges as a teacher and student of mathematics. It is important that we hold one another accountable for our collective growth as mathematics teaching professionals.

It is important to note that you will not be given a grade based on your instructor’s assessment of your participation in our discussion forums. Rather, your grade on this assignment will be based on the Discussion Reflection self-assessment you complete at the end of each module, in which you will evaluate yourself and provide evidence that you were an active, collegial, and professional member of our Discussion Forum community. More details about the Discussion Reflection self-assessment are provided below. If you are not an active, collegial, and professional member of our Discussion Forum community, you will not be able to provide sufficient evidence to receive full credit for your Discussion Forum participation.

We will be using the discussion forum located in our course community space, which is linked on the student menu. For each lesson, your instructor will post a topic prompt in each discussion forum.

First Week of Discussion Forum:

• Read the prompt and make your Initial Post by Tuesday at 11:59 PM (EST).
• This is a post-first forum which means you will not be able to see any other posts’ until you make your initial post.

Second Week of Discussion Forum…

• You are expected to read and respond to at least 2 of your classmates by Sunday at 11:59 PM (EST) of the second  week. Sometimes your instructor will allow you to choose which posts to respond to; other times your instructor will require you to respond to specific posts
• You may have an initial post for the next discussion forum due this week by Tuesday

Your initial reply is expected to be at least one paragraph (about 5 sentences), and your responses can be a little bit shorter (about 3 sentences). You should write professionally (e.g., complete sentences and standard spelling), but you can be conversational (i.e., you do not need to use a formal or academic stance, and you can certainly write from a  “first person” perspective!).

Your posts should reflect that you have read and thought about that lesson’s content and readings. You should be critical, raising questions about how the readings relate to your own experiences as an educator and a learner. Your posts should reflect a willingness to consider new ideas, and you should also help support your classmates’ learning by posing thoughtful questions or proposing interesting connections. At two points of the semester, you will be asked to identify to your instructor which of your classmates have been especially helpful and supportive to your professional growth through their comments on our Discussion Forum.

Discussion Forum Reflection

At the end of the each module you will self-assess your contributions to the Professional Learning Community (i.e., your class) through the discussion in the forums. This graded, private self-assessment will be your only grade for all of the forums in the module. Your discussion forum grade is based on how well you articulate and provide evidence of your contributions.

Provide your answers to the questions below by reflecting on your participation in the Discussion Forums this module. This is your chance to comment on your overall contributions to the Professional Learning Community. Your 2-3 paragraph reflection should address the following questions by providing SPECIFIC examples. Provide dates of posts, names of classmates, or direct quotes as helpful so that your instructor can evaluate your claim by easily finding the piece of evidence to which you are referring.

Part 1: The first part of the reflection asks you to reflect on your level of engagement with the prompts and your classmates. For part 1, address each of the following items.

• How did you contribute to the forums themselves?
  • Did you post enough times to be considered a contributing member of the discussion?
  • Does it seem like you double-check your postings for grammar, spelling, and so on? Are you making an effort to communicate clearly?
  • Did you post consistently, on a regular schedule, or did you just wait until the last minute?
• How did you contribute to the ideas of the course?
  • Did you contribute new ideas or content?
  • Did you connect specific ideas from our course to other course ideas or to your own experiences?
• How did you contribute to the community (the people in the course)?
  • Did you learn something from a classmate?
  • Did you contribute to others' learning?
  • Did you ask constructive and challenging questions of your peers?
  • Did you reply to questions and issues raised by your peers?
  • Did you engage in deep conversations with your peers (three or more threads deep)?

Part 2: Self-assessment summary

Examine your answers to the questions above and consider your participation in the Discussion Forums this module. Comment on your overall contributions to the Professional Learning Community. What were your strengths and weaknesses as a developing professional? What did you add? What is something you can work on in the next module? Write at least one paragraph assessing yourself in this component of our course.

Blog

Blogs are an increasingly popular venue for educators to engage in professional learning with one another. Blogs can be effective for promoting personal reflection about your own teaching practice, but through this assignment we also want to cast blogging as a format for making your professional growth more public. In other words: blogs can be a hybrid of personal, reflective journal space and collective, professional learning space. Throughout the semester, we will visit and critique existing teacher blogs, we will examine guidelines for creating and maintaining professional teacher blogs, and we will draw upon those experiences to construct our own virtual space. We will all share our posts with one another. At the conclusion of each Module, you will be asked to use our course blog space to articulate your reflections on your professional learning during that Module. Each blog post should be a text-based post in which you articulate a “wondering,” a “curiosity,” or a “tension” that the course material is raising for you.

Note: Your posts will only be visible to the members of this course. However, anytime you post something in an online environment it could always be copied and distributed. Please do not use any student or co-worker's full names. Also, think before posting anything that could perceived as negative towards your school or place of employment.

These blog posts are intended to be very open-ended, so there should be wide variety in topics and approaches. You will be encouraged but not required to read your classmates’ posts. The hope is that you will find this experience meaningful enough that at the end of this course, you will think about creating a teaching blog for your own professional development. Furthermore, articulating curiosities may help you identify possible topics for an inquiry project that you can pursue later in your program in CI 501 or for your master’s paper.

For the purpose of this course we will be using Sites@PSU for our blog.  Sites are free to Penn State students, faculty and staff. Sites are powered by Word Press. If you have any technical problems, please contact the World Campus Help Desk.

Short Assignments

Throughout the course you will complete four short assignments related to the course material. These assignments will vary in format, but they are different from the other course assignments and projects in two important ways.

• First: the only audience for these assignments is your instructor. Although you may refer to the assignment or what you learned from it in other assignments which are shared with others (such as the Discussion Forum or the Blog), your instructor is the only person who is officially the reader.
• Secondly, each of these assignments is bound in time. Unlike Discussion Forums and blogs, which we will visit repeatedly over the entire course, and unlike the interview project, which is sustained activities to which we will devote attention, the four short assignments are designed to be introduced and completed in the same lesson. Your instructor will spend a commensurate amount of time returning feedback.  The short assignments are…
  • SA #1: Concept map on mathematical thinking (Lessons #1 & 2): In this assignment you will create a one-page graphical representation synthesizing the readings about the nature of mathematical thinking. See this video for a quick introduction to concept maps from the PSU Library: Creating a Concept Map. You will submit this assignment in Lesson #1, and then you will revise this assignment in light of what you’ve learned in the course in Lesson #8.
  • SA #2: Assessment comparison table (Lessons #2 & 3): In this short assignment you will complete a table comparing the affordances and challenges of a variety of methods of classroom assessment. You will draw upon your own experiences in mathematics classrooms and you will also draw upon ideas from readings. Please use the assessment comparison table template to complete the file and submit it via the dropbox in lesson 3.
  • SA #3: Quiz. Applying a framework to student written work and interview data (Lessons #5): In this short assignment you will apply a framework that was presented in the lesson to assess and interpret student thinking as represented in written samples and in video clips from interviews. You will interpret student thinking by writing short answers to approximately 5 questions. This is an open-resource quiz, so you can refer to any content from the course or that you’ve created yourself, but you will be limited to one hour, so it will be important that you are somewhat familiar with relevant course material beforehand.  
  • SA #4: Revisiting and revising the concept map (Lesson #8) In this assignment you will annotate your original concept map. How has your understanding of mathematical thinking changed as a result of your experiences in this course? You will answer this question by creating a new concept map and then writing a paragraph comparing your first concept map with your revised concept map.

Interview Project

This assignment is the culminating project for our course and is an opportunity for you to design, conduct, and interpret a mathematics interview with a PreK-12 grade student. Additionally, you will demonstrate your ability to share findings from your interview in a variety of formats so that other educators can learn from your interview. Some parts of this assignment will be completed with groupmates and other parts of the assignment will be completed individually. At the beginning of the assignment, you will be assigned to a group (2-3 other classmates) based on the mathematical topic  and grade band that you are interested in and have access to. You and your groupmates will use question banks that will be provided to design a shared interview protocol. Once your protocol has been reviewed and approved by your instructor, you will each conduct at least one interview with a student at the appropriate grade level. You will video record the interview and will share parts of it with our class. Before the interview both you and the student’s parents/guardians will sign appropriate permission documents.You will analyze your video by transcribing selections of dialogue. There will be 2 products from this project:

Your grade for this assignment will be based on:

1. The individual report. You will write a 500 word report in Microsoft Word and submit it via dropbox. This report will conform to the published guidelines of the Call for Manuscripts to the Back Talk department of the journal Teaching Children Mathematics. Note: This is no longer an active call for manuscripts, but editors of the NCTM teacher journals may still consider a manuscript following these guidelines to be eligible for publication. As such, your instructor may encourage you to submit your report to Teaching Children Mathematics, Mathematics Teaching in the Middle School, or Mathematics Teacher. (20 points)
2. The group presentation. You and your 2-3 groupmates will compose a 15-minute presentation in YouSeeU for viewing by some of your classmates. Your presentation should include the following elements:
   1. Provide some background information about the students (age, why you chose them, what conditions you interviewed them in, etc.)
   2. Include at least 1 video clip from each of you and 2 images of student work, along with your interpretations of each.
   3. Include at least 1 finding about each individual student and at least 1 finding about the group of students.
   4. Your voices should all be heard during the presentation, for approximately equal amounts of time.
   The presentation will be worth 20 points, and part of your grade on this component is based on your groupmates’ evaluations of your contributions as a group member. The quality and quantity of feedback that you provide about your groupmates’ contributions and two other groups’ presentations. You will be assigned 2 other groups’ whose presentations you must view and evaluate. Some of your feedback will be shared and some parts of your evaluation will be kept confidential. Your grade on this component is based on how insightful, constructive, and thorough your feedback is 10 points

Category 5: "Stop and Think!"

Throughout the course content you will be prompted to respond to thought-provoking questions--called "Stop and Think!"--that will only be seen by your instructor. Those questions will help you pause and think about the content, and they also provide feedback to your instructor. Individually you will not receive feedback on these, and these will not be read by your peers, but your instructor may comment on patterns of student responses, may adjust instruction in light of these patterns, and will also assess your level of engagement with these questions over the entirety of the course.

 

Please refer to the University Grading Policy for Graduate Courses for additional information about University grading policies. If, for reasons beyond the student's control, a student is prevented from completing a course within the prescribed time, the grade in that course may be deferred with the concurrence of the instructor. The symbol DF appears on the student's transcript until the course has been completed. Non-emergency permission for filing a deferred grade must be requested by the student before the beginning of the final examination period. In an emergency situation, an instructor can approve a deferred grade after the final exam period has started. Under emergency conditions during which the instructor is unavailable, authorization is required from one of the following: the dean of the college in which the candidate is enrolled; the executive director of the Division of Undergraduate Studies if the student is enrolled in that division or is a provisional student; or the campus chancellor of the student's associated Penn State campus.

For additional information please refer to the Deferring a Grade page.

Note: If you are planning to graduate this semester, please communicate your intent to graduate to your instructor. This will alert your instructor to the need to submit your final grade in time to meet the published graduation deadlines. For more information about graduation policies and deadlines, please go to the Graduation Information on the My Penn State Online Student Portal.

Formal instruction will end on the last day of class. Provided that you have an active Penn State Access Account user ID and password, you will continue to be able to access the course materials for one year, starting from the end date of the academic semester in which the course was offered (with the exception of library reserves and other external resources that may have a shorter archival period). After one year, you might be able to access the course based on the policies of the program or department offering the course material, up to a maximum of three years from the end date of the academic semester in which the course was offered. For more information, please review the University Course Archival Policy.

Academic Integrity

According to Penn State policy G-9: Academic Integrity , an academic integrity violation is “an intentional, unintentional, or attempted violation of course or assessment policies to gain an academic advantage or to advantage or disadvantage another student academically.” Unless your instructor tells you otherwise, you must complete all course work entirely on your own, using only sources that have been permitted by your instructor, and you may not assist other students with papers, quizzes, exams, or other assessments. If your instructor allows you to use ideas, images, or word phrases created by another person (e.g., from Course Hero or Chegg) or by generative technology, such as ChatGPT, you must identify their source. You may not submit false or fabricated information, use the same academic work for credit in multiple courses, or share instructional content. Students with questions about academic integrity should ask their instructor before submitting work.

Students facing allegations of academic misconduct may not drop/withdraw from the affected course unless they are cleared of wrongdoing (see G-9: Academic Integrity ). Attempted drops will be prevented or reversed, and students will be expected to complete course work and meet course deadlines. Students who are found responsible for academic integrity violations face academic outcomes, which can be severe, and put themselves at jeopardy for other outcomes which may include ineligibility for Dean’s List, pass/fail elections, and grade forgiveness. Students may also face consequences from their home/major program and/or The Schreyer Honors College.

How Academic Integrity Violations Are Handled
World Campus students are expected to act with civility and personal integrity; respect other students' dignity, rights, and property; and help create and maintain an environment in which all can succeed through the fruits of their own efforts. An environment of academic integrity is requisite to respect for oneself and others, as well as a civil community.

In cases where academic integrity is questioned, the Policy on Academic Integrity indicates that procedure requires an instructor to inform the student of the allegation. Procedures allow a student to accept or contest a charge. If a student chooses to contest a charge, the case will then be managed by the respective college or campus Academic Integrity Committee. If that committee recommends an administrative sanction (Formal Warning, Conduct Probation, Suspension, Expulsion), the claim will be referred to the Office of Student Accountability and Conflict Response.

All Penn State colleges abide by this Penn State policy, but review procedures may vary by college when academic dishonesty is suspected. Information about Penn State's academic integrity policy and college review procedures is included in the information that students receive upon enrolling in a course. To obtain that information in advance of enrolling in a course, please contact us by going to the Contacts & Help page .

Accommodating Disabilities

Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has resources for students with disabilities. The Student Disability Resources (SDR) website provides contacts for disability services at every Penn State campus. For further information, please visit the SDR website.

In order to apply for reasonable accommodations, you must contact the appropriate disability resources office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation based on the documentation guidelines. If the documentation supports your request for reasonable accommodations, your campus's disability resources office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.

Additional Policies

For information about additional policies regarding Penn State Access Accounts; credit by examination; course tuition, fees, and refund schedules; and drops and withdrawals, please see the World Campus Student Center website.