Patterns of Problem Solving

Professor Hlas
hlascs (@)
Drop-in times

It is a mistake to think you can solve any major problems just with potatoes. (Douglas Adams)

Course Information

This course is designed to provide the strategies needed to approach any problem in a variety of disciplines and contexts. This goal will be achieved by:

  1. Strategy focus – Implicit strategies and representations for solving mathematics problems will be made explicit.
  2. Group work – Working in groups provides insight into different ways of thinking than your own. This will be beneficial for discovering multiple solutions to any problem.
  3. Communication – The ability to solve a problem is largely meaningless if you cannot convince another person of the solution. Everyone will be expected to share strategies and clearly explain solutions.

This course helps students meet the following Liberal Education Learning Outcome(s):

More course information is available on Canvas.



  1. Crossing the river with dogs: Problem solving for college students (Johnson, Herr, & Kysh, 2004). ISBN: 1-931914-14-1.
    Important: the book is used almost daily so please bring to class!
  2. A calculator is recommended, but not required. Calculators with internet connections (e.g. cell phones) will not be allowed on exams.

Course references



Some problems will be difficult and solutions may be illusive. The only way to fail such a problem is to not attempt it. Students earn "math points" (MP) for demonstration of mathematical thinking in their solutions.

Daily presentations (15 MP)

At the beginning of most classes, students will be expected to present solutions at the board. Opportunities to present will be given for in-class problems, alternate solutions to board problems, and ungraded homework.

Individual presentations are scored based on completion. The first presentation is worth 1 MP, the second worth 2 MP, and so on. Presentations past the fifth are worth +1 MP bonus.

Homework (6 × 10 MP)

Homework assignments will generally be five questions, two of which will be randomly selected for grading. See homework scoring for more information regarding homework expectations.

Math Retreat presentation (30 MP)

Groups of 1-4 students will select and present a "new" problem during Math Retreat. Details regarding this presentation will be discussed after the first exam.

Exams (3 × 25 MP)

"To assess conceptual knowledge, researchers often use novel tasks … Because children do not already know a procedure for solving the task, they must rely on their knowledge of relevant concepts to generate methods for solving the problems." (Rittle-Johnson, Seigler, Alibali, 2001, p. 347). Assessments are a part of the learning experience so will require mastery of class material and will require the ability to apply class material to new situations.

There will be two in-class exams and a final exam. Each exam focuses on more recent material, but mathematics is comprehensive so expect to see material from previous exams again.

One page of notes is allowed for each exam. Approved calculators will be allowed on all exams.

Exam bonus (+20% MP)

The highest exam score will be given +20% MP to allow for individual differences between students. This will be computed at the end of the semester.

Fine print

Email is the best way to reach me. I typically respond within 24 hours, but do not check email in the evenings or on Saturdays due to family commitments.

Attendance A record of attendance is required by the University to maintain accurate class rosters. Attendance is not graded but poor attendance may impact participation in group activities.

Absences If you are absent, please check the course schedule then meet with me (drop-in hours, Zoom, or email) so I can make sure you are caught up. Authorized absences (school functions, emergencies or illness) may be made up for full credit. Other absences may be completed early for full credit, or late for 90% credit. Late work is expected to be completed within two weeks of the original due date or by the last day of classes, whichever occurs first.

Entry-level switching The Department of Mathematics allows students within entry-level mathematics courses (i.e., 010, 020, 104, 109, 112, 114, or 246) to move up to a higher numbered course during the first two weeks of a semester or move down during the first three weeks. Please contact the instructor for more details.


Student Accommodations Any student who has a disability and is in need of classroom accommodations should contact the instructor and the Services for Students with Disabilities Office in Centennial Hall 2106 at the beginning of the semester.

Academic Integrity Any academic misconduct in this course will be submitted to the Dean of Students.

Mandatory Reporter As a Wisconsin State employee, the instructor is obligated to report any crimes to the Dean of Students, including claims of sexual harassment or sexual assault. The Dean of Students office may reach out to you to offer resources and support.

Community As members of this class we are members of a learning community that values all people with all backgrounds. Please remember that our words and actions affect everyone within our community and remember a little positivity can go a long way.