Problem Solving Maps self-directed course

Become a master math coach to help your students and children be better math problem solvers

Course Summary

The need for a better math education is clear. With the ever-increasing advancement in technology and the tighter integration of the global economy, relevant social and business problems are more complex. Industries which require technology and science-based solutions are becoming the engine fueling countries’ growth. Math offers a rigorous and systematic process to improve problem-solving skills, which are useful not only for the highly complex but also for many daily life decisions. However, in spite of an abundance of teaching and learning resources, success in learning mathematics is still minimal.  We need something different!

Several years ago, Dr. Danilo Sirias started working on a set of tools to improve math education. Building on the knowledge from his classes and through trial and error with his two daughters, who at that time were in elementary school, he developed a system that is referred to as  Problem Solving Maps (PSM).

Problem Solving Maps (PSM) are graphic representations of three fundamental thinking processes--inductive thinking, deductive thinking, and analysis--which are relevant to solve math problems. The generic structure of PSM ensures that they can be used to learn math across multiple topics and grade levels (4-12 grades and beyond).  Whether you are a teacher, homeschooling, or just trying to help your children, the methodology covered in this course will dramatically improve your ability to help struggling math students.

White Pine Middle School
Michigan, USA

Problem Solving Maps have made complex ratio word problems accessible for all students. The difficult ratio word problems used to be something that only my strongest math students could handle, but with the Problem Solving Maps all kids can work their way through the problems."

Jennifer Gronski, 6th Grade teacher

The Problem Solving Maps are helping our students make concrete their thinking about abstract concepts. This process also allows teachers to clearly see where students are struggling so they can address these concerns easily and directly."

Vikki Wandmacher, Principal

What do you get in this course


Lectures explain each one of the three Maps, their logic ,and how to use them to coach students

Downloadable teaching materials
    • Access to download and modify over a 100 examples worksheets created and tested by teachers for different grades
Blank Templates
    • Ready-to-use blank PSM templates
A workbook
  • A downloadable 100+ page workbook that you can use as a reference
Academic paper
    Read a paper explaining some of the expected results from using PSM
  • Optional self-graded quizzes to test your knowledge

Felesia Harrel

I attribute much of the success of my Math students to the use of the Problem Solving Maps (PSM). One particular group that has maintained an “A” average in Math are my 7th grade students. My 7th graders started attending my center in the 6th grade and during that time, I introduced them to the PSM. This mathematical tool helped my students understand different concepts in Math, which are crucial to their success not only in school, but in preparation for the Math portion of the ACT and SAT Test as well.

I have also had much success using PSM on my developmental students at a local community college. I used PSM to teach my students, among other things, how to understand positive and negative integers. A great majority of them maintained a “B” or better in the class throughout the semester, which is a great accomplishment for those students that struggled with Math prior to taking that class.

Felesia Harrel, owner of College Bound Academic Learning Center in Saginaw, Michigan, offers all subject tutoring with main focus in Math and ACT and SAT Prep

Danilo Sirias

Dr. Sirias has a Master’s degree in Industrial and Systems Engineering and a Ph.D. in Business Administration. He is also a certified Critical Chain Project Manager and a certified TOCICO thinking process implementer. Dr. Sirias created the Problem Solving Maps methodology to teach mathematics which is currently being used in several countries to improve student's performance.  He is also the co-author of the book "Smash the Bottleneck: Fixing Patient Flow for Better Care."  This book lays out a concrete methodology for getting to the root of patient-flow problems and addressing them—quickly using the principles of the Theory of Constraints.

Course Curriculum

Course Pricing

Free module


  • Preview a couple of modules for free!

    • Include lectures about the Example-Conclusion Map (modules 0 and 1)

Lectures and quizzes

$39 USD

  • View all the lectures!

    • You can view all the lectures (modules 0 to 5)
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Complete Course

$49 USD

  • Access everything in the course!

    • Include all lectures and downloadable material (modules 0 to 7)
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