Math 149: Explorations in Modern Math

Course Information

  • Institution: Dordt University
  • Course: Math 149-01 (3 cr.)
  • Term: Spring 2022
  • Instructor: Dr. Mike Janssen, Associate Professor of Mathematics
  • Classroom: CL 2246
  • Class time: 1:00-1:50pm MWF
  • Office: SB 1612
  • Student Hours: Make an appointment or drop by
  • Course textbook: Explorations in Modern Math, Spring 2022 edition (in progress)
  • Catalog Course Description: This course is focused on exploring college-level mathematics relevant for all students, regardless of discipline. We will investigate modern mathematical topics including number theory, modeling, fractals, infinity, probability, making meaning from data, and decision-making. Mathematical thinking, reasoning, and pattern discovery will be particularly emphasized. A guided discovery approach will be utilized, and we will discuss how a Reformed perspective impacts our view of the quantitative world. Prerequisite: an ACT mathematics score of 22 or higher or satisfactory completion of one course from Mathematics 100, 108, 115.

Required resources

Learning Objectives

In this course, students will

  • be communicators by working together in groups on mathematical puzzles and sharing their thinking with the class. (CD)
  • be explorers by playing with God’s mathematical creation, explicitly with the Rubik’s cube, and implicitly with other puzzles and questions. (CS)
  • be connectors by exploring the power and limitations of mathematics for modeling the physical creation, and applying mathematical thinking to articulate a vision for a more just society. Students will also explore the notion of mathematical truth, and assess its place in understanding God’s creation. (RO, CS, CR)
  • be ambassadors by identifying, analyzing, and presenting on an aspect of beauty in mathematics. (RO, CS)

Assignments

The best way to learn mathematics is to do mathematics, and so we will regularly engage in the following items of work to strengthen our mathematical muscles.

In-Class Explorations

The heart of this course is the in-class work. Our class meetings will typically start with a short (5-10 minutes) introduction to the main questions under consideration. You’ll then work in assigned groups of approximately 3 to explore the activities from the textbook for the day. We’ll wrap up with discussions of whatever you found the most interesting, as well as some big-picture takeaways.

This mode of instruction is highly interactive; it is therefore essential that you participate in class each day. Group participation will be monitored, and groups will regularly share their thinking with the class. Additionally, you will be asked to write clean, correct versions of some of your solutions in the Weekly Work, and, depending on the grade you are aiming for, you may request to present 2-3 solutions to the activities to the class.

Presentations

Each class will conclude with a discussion of the big ideas and takeaways from the day’s work. Throughout each class meeting, we’ll also occasionally (as a class) discuss solutions to the activities. Depending on the grade you are aiming for, you may volunteer to present your group’s thinking and lead the discussion on an activity. You will be assessed primarily on the clarity of your explanation and your ability to satisfactorily answer relevant questions.

Weekly Work

On most Wednesdays, a Weekly Work assignment will be due on Canvas. Specifics will vary from week to week, but they will typically include (but are not limited to): exercises from the textbook; a short essay/reflection question; an activity from our class explorations to which you’ll write up clean, clear solutions. These will be submitted in PDF form, which may include smartphone scans of written work (though unreadable work may result in you work assessed as a non-passing designation). Your work will be assessed Pass/No Pass on good-faith effort to be complete and correct.

Checkpoints

Over the course of the semester, we will have eight Checkpoints; seven of them will be worth five points, while one (the Cube checkpoint) will be worth 10 points, for a total of 45 points possible. With the exception of the Cube checkpoint, these will typically take the shape of short quizzes. The number of points you earn will play a major factor in your final grade. Revisions may be allowed based on feedback. Checkpoints will be given on the following days.

  1. Checkpoint 1: Jan. 21
  2. Checkpoint 2: Feb. 4 (Cube solve)
  3. Checkpoint 3: Feb. 18
  4. Checkpoint 4: Mar. 4
  5. Checkpoint 5: Mar. 25
  6. Checkpoint 6: Apr. 8
  7. Checkpoint 7: Apr. 22
  8. Checkpoint 8: May 6

Reading Reflections/Discussions

Along the way, we’ll read Francis Su’s Mathematics for Human Flourishing, and consider the ways in which the practice of mathematics can help us lead lives of shalom. After reading a set of chapters, you’ll write a short (less than 3 pages) response to the ideas therein. A few days later, we’ll have an in-class discussion in small groups. Due dates are:

  • Chapters 1-5: reflection due February 2, class discussion on February 4
  • Chapters 6-7: reflection due February 21, class discussion on February 23
  • Chapters 8-11: reflection due March 23, class discussion on March 25
  • Chapters 12-13, Epilogue: reflection due April 22, class discussion on April 25

Final Project

The final project will highlight some aspect of beauty in mathematics. You may choose to work with others. There are several steps to completing the project:

  1. Rank the topics: You will be presented with a list of possible topics (including space to propose your own) and asked to rank them in order from most to least interesting. Your topic will be assigned based on your rankings in such a way that no one gets the same project topic. Due March 18.
  2. Preliminary Report: By April 1, you will submit a 1-2 page description of what you have learned about your topic, what questions you still have, and what artifact you are planning to create. Due April 1.
  3. Artifact: By May 6 (last day of class), you will create something that communicates or otherwise explores meaningful mathematics related your topic. That is, you should go deeper than just a surface-level understanding. You have freedom in what, exactly, you create. Here are some preapproved artifacts:
  • A work of fine, visual, or literary art, with a 300-450 word interpretive guide. You can make or write something that explores the mathematical idea. Much of the work of your interpretive guide is in helping your audience understand the significant mathematics that is being explored so that we can better grasp your work.
    • A research paper and slide deck. If you are not so keen to create a work of art, perhaps you’d rather write an 1800-2400 word research paper describing the mathematics you explored, as well as its history and why it is thought to be beautiful. You will cite at least five (5) reputable edited sources and format your paper using MLA guidelines. You should also prepare a short (3-5 minute) slide deck for the presentation (see below).
    • A lesson plan and activity. If education is your thing, maybe you’d like to create a lesson plan using the full Dordt Education Department lesson plan template that introduces the students you hope to teach to your particular topic (e.g., if you are hoping to teach middle-level students, aim it at 6-8th graders). You should also create the activity that you would use to help these students explore the topic, as well as a short slide deck to help our class understand your topic and what you’ll ask the students to do.
    • Other. In your topic rankings, you may propose to do something not on this list. You should carefully describe what you will do so that I have a clear sense that it will be roughly equivalent in depth and workload to the preapproved options. If I don’t think it is, I will either ask for clarification, suggest an alternative based on your idea and topic, or assign you to one of the preapproved options.
  1. Presentation: By the last day of class (May 6), you will submit plans for a short (less than 5 minutes) presentation. We will give our final presentations in person during our assigned final exam slot, 10:30am-12:30pm, Thursday, May 12.

Grading

In general, your final grade will be the highest fully completed row in the following table.

Weekly Work Presentations Checkpoint Total Reflections Project
A 13 3 40 4 E
A- 12 2 38 4 E
B+ 11 2 36 4 E
B 10 1 34 4 M
B- 9 1 32 3 M
C+ 8 - 30 3 M
C 7 - 26 2 M
C- 6 - 22 2 M
D 4 - 18 1 M

Other Polices and Advice

  • I am generally fairly accepting of late work, with a built-in 24-hour grace period for any non-classroom activities. Additional time beyond the 24-hour grace period must be approved ahead of time.
  • Student hours are your time to ask questions about all aspects of the class and college life. If you can’t find an appointment, send me an email! I will do my very best to accommodate your schedule.
  • Email Policy: I check my email twice per school day: once in the morning, where I’ll deal with any emergencies, and once in the afternoon, when I’ll respond to other emails (including any that have come in since the morning). If you require a more immediate response, you’re welcome to come find me in my office.

Additional Information

Dordt University Student’s Right to Accommodations Policy

Dordt University is committed to providing reasonable accommodations for students with documented qualifying disabilities in accordance with federal laws and university policy. Any student who needs access to accommodations based on the impact of a documented disability should contact the Academic Enrichment Director: Sharon Rosenboom, Academic Enrichment Center, Office: L166, (712) 722-6488, Email: Sharon.Rosenboom@dordt.edu.

Dordt University Academic Dishonesty Policy

Dordt University is committed to developing a community of Christian scholars where all members accept the responsibility of practicing personal and academic integrity in obedience to biblical teaching. For students, this means not lying, cheating, or stealing others’ work to gain academic advantage; it also means opposing academic dishonesty. Students found to be academically dishonest will receive academic sanctions from their professor (from a failing grade on the particular academic task to a failing grade in the course) and will be reported to the Student Life Committee for possible institutional sanctions (from a warning to dismissal from the university). Appeals in such matters will be handled by the student disciplinary process. For more information, see the Student Handbook.

Classroom Attendance Protocol

As we begin the Spring 2022 semester, class attendance policies and procedures as outlined in the Student Handbook are in place. To paraphrase the Student Handbook, Dordt University as an institution remains committed to in person instruction for face-to-face courses. As a result, you are expected to be present for every class period and laboratory period. Should you need to miss class for any reason, contact your instructor as soon as possible (either prior to the absence or immediately following). Absences for Dordt-sponsored curricular or co-curricular activities will be communicated by the activity sponsor and are considered excused.

Methods of making arrangements for missed work are back to normal (pre-COVID). You are responsible to contact your instructor. Your instructor is not required to provide real time (synchronous) learning for you should you be absent for class for any reason (ex. Zooming into your real time class). Your instructor is also not required to provide asynchronous virtual learning materials for you (ex. recordings of missed classes, slide decks, other materials on Canvas). While some instructors might utilize some of the synchronous/asynchronous methods of making up work on occasion, you should not expect all instructors to provide these experiences automatically. Methods of making up missed work might include: contacting a fellow student to get notes from class, extensions on assignments or labs, or other methods as determined by your instructor. Making arrangements for missed class work is your responsibility!

Please see your instructor’s specific attendance policy.

Tentative Schedule

  • January 14-Feb. 4: Rubik’s Cube
  • Feb. 7-Feb. 25: Truth and Reasoning
  • Feb. 28-Mar. 30: Math and Democracy
  • Apr. 1-13: Modeling Creation with Math
  • Apr. 15-29: Math of Networks
  • May 2-6: Catch up/TBD