Patterns of Problem Solving

Professor Hlas
hlascs (@)
Student drop-ins / Zoom appointments

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

That's all it is. You just begin. You do the math. You solve one problem…and you solve the next one…and then the next. And If you solve enough problems, you get to come home.
Mark Watney, space pirate

Sometimes the best way to solve your own problems is to help someone else.
Uncle Iroh in Avatar: The Last Airbender

The problem is not the problem. The problem is your attitude about the problem.
Captain Jack Sparrow

Course Information

This course is designed to explicitly identify heuristic strategies that may be helpful in solving non-routine mathematical problems. 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 we cannot convince others of our solution. Everyone will be expected to share strategies and explain solutions.

Course learning outcomes include: identify appropriate heuristic strategies for non-routine mathematics problems, execute heuristic strategies to arrive at a possible solution, check that the strategy lead to a correct solution.

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

Course structure

Course materials

  1. Crossing the river with dogs: Problem solving for college students (Johnson, Herr, & Kysh, 2004). ISBN: 1-931914-14-1.
    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

Important dates


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

Class presentations 10 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, third is 3 MP, fourth is 4 MP. Presentations past this are worth +1 MP bonus.

Homework 7 × 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.

Problem-posing project 🤔 22 MP

Groups of students will create a "new" problem and present it to their peers. Details regarding this presentation will be discussed after the first exam.

Exams 3 × 20 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 the ability to apply class material to new situations.

Exams are in-person and individually completed. Each exam focuses on more recent material, but mathematics is cumulative so expect to see previous material again. Exams allow for a note sheet (1 page, 1-sided, handwritten), approved calculators and other class manipulatives.

Exams will be scored using the same scoring for homework assignments.

Exam bonus +10% MP

The highest exam score (including the final exam) will be given +10% MP bonus to allow for individual differences between students. This will be computed at the end of the semester.

Tips for a successful semester

The course schedule is your friend. I continually update it to make sure it is always as current as possible. All class activities, handouts, and daily recommendations should be listed. If something is missing or unclear, please let me know so I can make improvements for the benefit of everyone in the class. Speaking of calendars, the one thing I wish I knew as a college student is to schedule study time for each class. This strategy ensures time is spent on each classes in productive ways.

Mathematics is a form of abstract thinking that is better learned through active participation. In one study (Deslauriers et al., 2019), students were either taught via lecture or through active learning. Students in the lecture class felt like they learned more, but they actually scored lower than the active learning group. Active learning means that class will often begin with a challenging problem. During class the students and the instructor will work together to solve the problem(s) and learn some mathematics along the way (Liljedahl, 2017; Brown et al., 2014; Ericsson, 2006).

One way to actively engage with mathematics is to try homework or Webwork before class discussion on the topic. This strategy helps inform your learning during class time because you will have an idea of what you know and what you still need to learn (Pan & Sana, 2021; Brown et al., 2014).

When solving problems do not expect perfection. Problems are designed to be challenging to encourage learning. Little, if anything, is learned from "easy" tasks. Speaking of learning, we will try to avoid tricks/shortcuts as these often distract us from the mathematics and create extra work to unlearn bad habits.

After each class, educational research recommends we reflect on what was learned. One way to review is to rewrite class notes. For a specific note-taking suggestion, please see the Feyneman's Notebook Method that encourages rewriting a day's lesson with a one-page restriction. Hand-written notes also lead to more brain activity than other methods (Umejima et al., 2021; Askvik et al., 2020; ScienceDaily, 2011).

Another method for review is to focus on activities with immediate feedback. For example, WeBWorK, flash cards, study groups and practice testing all have elements of formative feedback that is immediate (Weimer, 2017; Dunlosky, 2013; ScienceDaily, 2013; Butler et al., 2008; Ericsson, 2006).

Frequently Asked Questions (FAQ)

When/how is the professor available outside of class?

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

My student drop-in schedule and sign-up for Zoom appointments are posted at

What is the attendance policy?

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 (e.g., taking a group quiz individually).

If you are absent, please check the course schedule then meet with the instructor via drop-in hours, Zoom, or email to make sure you are caught up. Graded work that occurs during an authorized absence (school functions, emergencies or illness) may be made up for full credit. Other absences may complete graded assignments late for 90% credit or these assignments may be completed early for full credit.

Late work is expected to be completed within two weeks of the due date or by the last day of classes, whichever occurs first. In situations where a makeup cannot occur, the final exam score may be used as a proxy for a missing assignment. Students missing a week or more of class should contact the Dean of Students Office to get extra support.

What if I am stressed out?

College can be difficult. After all, if it wasn't then you likely are not learning very much. Everyone can benefit from placing their personal well-being as a top priority throughout the semester. Should you want some emotional support for any reason, you can access free counseling services (even one short session to problem solve solutions) from the UWEC Counseling Services on campus. They provide a variety of online and in-person services, including some virtual wellness workshops. Call them at 836-5521, stop by Old Library room 2122, or check out the website to make an appointment:

Students also have FREE access to UW System Mental Health Support through Mantra health – a telehealth service available 24/7 days a week (call or text: 888-531-2142 or go online at:; sign up using your UWEC email address). You can also reach out to the WI-branch of the national crisis/emotional support text line by texting "HOPELINE" to 741 741 or use the national suicide prevention lifeline: 988 Please use these resources to support your mental well-being and success as a Blugold!

What if the math class is too easy or too difficult?

The Department of Mathematics also 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 or for other solutions.

How does grading work?

Final scores (rounded up to the nearest whole number) are compared to the grading scale given in the syllabus to determine a final grade. Individual scores or grades will not be modified because they represent a student's progress in the class throughout the semester. If there is a mistake in scoring, please contact the instructor as soon as possible to get the error fixed.

Midterm grades do not have a score table so are based on the percentage of points completed at the time of midterm submission.

Note: I dislike the University's scale of "F" because I have never once felt that a student has "failed" a class. Instead, I prefer to think of this as a "not pass" where insufficient evidence has been demonstrated by a student to move on to the next level.

What if I need accommodations (like extra time on tests)?

Please let me of know ways that I might be helpful when you notice possible suggestions. For individual accommodations, please contact the Services for Students with Disabilities Office in Centennial Hall 2106 at the beginning of the semester.

What else do I need to know?