math success skills

There never seems to be enough time, right?

It is rare for me to have a conversation with teachers and we don’t talk about how little time we have to teach. I find myself complaining just as much as everyone else. It’s so easy, given the amount of things teachers are required to do.

Consequently, it becomes easy to say “I don’t have time to teach success skills” such as critical thinking, communication, collaboration, and project management. For years, it was the reason why I didn’t teach it. However, I now see that it cost me time and robbed my students of the skills that are the heart of the successful use of mathematics. 

The strategies I use to teach critical thinking, communication, collaboration and project management are connected to the mathematical practices identified in the Common Core State Standards. This is important because exercising mathematical practices is how students are supposed to learn mathematics. As the Common Core states, the practices are “ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter.”

The eight CC mathematical practices lead back to the success skills emphasized by PBLWorks.

Here is a table that shows how the practices and four key success skills connect.

Critical Thinking

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively

Use appropriate tools strategically

Look for and make use of structure

Look for and express regularity in repeated reasoning


Construct viable arguments and critique the reasoning of others

Model with mathematics

Attend to precision


Construct viable arguments and critique the reasoning of others

Model with mathematics

Project Management Make sense of problems and persevere in solving them


Critical Thinking 

I admit this has been the most challenging of all the success skills to teach. It happens quickly, and mostly inside our minds. One of my favorite ways to teach it is by using the Question Formulation Technique (QFT) as the entry event in a project. It is a simple process of students generating questions and organizing those questions. The ability to question is the heart of critical thinking and how to make sense of math problems. Here is a PowerPoint example of the QFT used to launch a pre-calculus project about analyzing cellular signals. 


This skill is often the most difficult for students in math. The opportunity to explain a mathematical concept is not common in a math classroom. Set a goal for students to spend at least half of the class period communicating, rather than you doing most of it. One of the greatest resources I have found that has helped me up the communication in my class is a book from NCTM called Five Practices for Orchestrating Productive Mathematical Discussion. It lays out how to structure a lesson to promote student discourse. I love this structure because it aligns perfectly with sustained inquiry and supports all of the mathematical practices. Here is a video that explains the process. 


Of all the skills, this is one where it is really helpful to have frequent direct teaching moments. The best way I have found to teach and develop collaboration is through icebreakers and team builders, where students get to know each other while practicing a specific collaboration skill. To open the class, my students begin with sharing their "roses and thorns." At least once a week, we do a team builder. I love one called "Superheroes" created by my friend and former National Faculty member Andrew Miller. Students work in teams where each person is a superhero. They must use their powers to solve a problem. Teams act out the solution to another team, which must guess their different characters. After the activity, we debrief to talk about the collaboration skills used and how they transfer over into other work.

Project Management

This success skill has a lot of moving parts. It requires direct teaching, consistent practice, and constant feedback on the process. As the High Quality Project-Based Learning Framework explains, it means “students use a project management process that enables them to proceed effectively from project initiation to completion.” I am so grateful that I found out several years ago about KWHLAQ from Silvia Rosenthal Tolisano, which is an update to the “Know-Want to Learn-Learned” chart. I loved how it is a visible tool that shows the cycle of project management. I created a paper version of the cycle that students use with all projects. 

All of the above strategies are easy and take little class time, but makes the time so much more rich and engaging for students.

And for remote learning, they are easily transferable to an online environment. It is imperative that we move from simply showing how to do a process to helping our students be the process. 

Telannia Norfar, National Faculty
Telannia Norfar is a mathematics teacher at a public high school in Oklahoma City, OK. She has taught all high school courses including AP Calculus. She is co-author of Project-Based Learning in the Math Classroom by Prufrock Press.