Critical Thinking Mathematics Classroom

April 28, 2015, Volume 2, Issue 6, Number 1


Driving Question: How Do Educators Design Classrooms Designed to Pull Learning, Not Push Information?


Creativity, innovation, critical thinking, problem solving, communication, and collaboration are all a part of a 21st century math learning experience. 21st century math classrooms are not defined with program adoptions, learning resources and online tools, but rather are defined by how the learning experience is brought to life. Understanding how instruction can be designed to develop 21st century knowledge and skills requires an understanding of the differences between "push and pull" learning.

Is your math classroom "designed to pull learning"?
Too often our system is designed for instructional efficiency that pushes information, and not to pull authentic learning. Authentic learning experiences provide students' ownership of their learning path with choice, application, discovery, struggle, success, and feedback. Practices that center on an inquiry based, real world problem approach provide a frame of authentic learning. The 21st century classroom is one that has expectations for all math learners to achieve at high levels, a place where "pulled learning" is the classroom's primary function.


"Every function has an optimal design", a quote that if we take time to understand it, can become pivot point for designing a new pulled learning educational system. In previous generations, the primary function of schools was to provide instruction and as a result our entire system designed schools, contracts, schedules, curriculum, and instructional approaches that helped our system to match this function. 21st century schools and math classrooms have a different function: ensure high levels of learning for all. As a result we are faced with a need to redesign our instructional approach across classrooms, schools, and the entire system from push to pull.

What happens when educators allow the math learner to pull themselves through the learning experience." Math instruction that matches the primary function, student learning, are designed to do more than push' information. When the classroom is focused on the learner, these designs include aspects which challenge the learner to go beyond understanding knowledge and/or skills to where they must apply their thinking. The designs must also allow the learner to become an expert beyond the content area that include their ability to self asses their present level of performance as well as how to advocate for their next step in the learning journey.

Taking Flight with Pull
F.L.I.G.H.T. " where learning takes flight!"
is a Waukesha public school that worked through the complexities of creating a 21st century learning experience. At F.L.I.G.H.T. Academy learning is driven by three pull questions:

  • What are you going to learn?
  • How are you going to learn it?
  • How are you going to show what you learned?

These questions are the driving force behind how learners are engaged in defining their daily learning experiences. The three questions are also the starting point for the teachers as they design an instructional/learning framework.

At the Academy, all learners are in constant technological contact with what they know and where they are going next, their performance data is in their hands. The data informs the learners not only of their performance levels, but also creates an ownership of learning. Each learner is now better prepared to plan for the next target, as well as to tailor the instructional style to how they learn best. Instructional experiences can be direct instruction, research, group learning, technology-supported learning, or any means that the learner sees as a pathway to performance. Here, as Richart and Morrison have noted, "understanding is not a precursor to application, analysis, evaluating, and creating, but a result of it."

The final phase in the learning process at F.L.I.G.H.T starts when students think about
how they are going to show they have learned. At this point the cycle is complete and the learners have allowed the learning experiences to unfold where knowledge and skill acquisition occurred with student ownership. At F.L.I.G.H.T, students truly have a math classroom with facilitated learning through independence guidance, high-expectations and technology.

The School District of is seeing accelerated achievement results in math classrooms that are based on an instructional model centered on pulling knowledge, skills, and dispositions. While many classrooms are 'pushing' knowledge towards the learners, our 21st century classrooms are shaping the disposition of the learner first, then designing learning experiences where application and discovery build 21st century skills as a means to knowledge acquisition.

The result is a pull-based classroom designed for learning. In the math classroom as in all others, the instructor 'pulls' the experience into the hands of the learner. Learners learn how 
they must 'pull' their way through the learning experience. The difference in math classrooms of the past as compared to the 20th Century models still prevalent today is as simple as the differences between push and pull.


Ryan Krohn is Assistant Superintendent, School District of Waukesha, Wisconsin. Ryan's work is centered on redesigning aspects of the current instruction-based system into a system that is designed for learning. Twitter: @pullED_learning
email: This e-mail address is being protected from spambots. You need JavaScript enabled to view it School District of Waukesha website: FLIGHT Academy website:


For years creativity was discouraged in schools. Teachers were imposing strict guidelines kids should follow when doing their assignments. There was only one correct answer and one accurate process, while everything else was wrong. In that old-fashioned setup, following rules and standards was the best way to become a successful A grade student. Luckily, things started to change lately. Teachers slowly started to recognize the huge importance of fostering creative thinking in the classroom. Math class teachers are surely one of the pioneers of creativity – inspired teaching.

Creative Thinking = Divergent thinking

When thinking about the word divergent, I’m sure you had negative connotations coming to your mind. Now, let’s stop for a moment and see what the word divergent really means. Scholars describe divergent as tending to be different or develop in different directions. Divergent thinking refers to the way the mind generates ideas beyond prescribed expectations and rote thinking. Is being different really that bad? Although we can all agree it’s not, it’s been rooted deeply in our minds that different means wrong. Why is that so?

As children, our divergent capability operates at a genius level. Starting with our education, the system teaches us that doing things differently is wrong. Due to the system suppression, the ability to think divergently decreases drastically as we grow.

What exactly the divergent thinking has to do with creativity? The definition of creativity is the ability to come up with original, unique solutions to problems or ideas. In other words, creating something new, a new value. That being said, thinking differently than others is actually required if you want to come up with something different, something unique. So, basically, thinking divergently is a key to creativity.

Fostering Critical Thinking Inside Classroom

The world we have known is changing rapidly. Set of skills we have now, might not be valid in few years. The ability to adapt to new conditions and situations is a crucial skill. Employers want you to look beyond the answers. Creativity is valued as the most important business skill, while creative thinking is one of the keys to economic prosperity in the 21st century. So, how can we prepare our children for this fast changing, hectic environment?

By allowing students to nourish their creative thinking in the classroom you are preparing them for the world outside of it. Turn your classroom into an open space of free thinkers and wonderers. Allow your students to use new thinking tools, to tweak solution paths and facilitate new processes. The best way for students to learn how to think creatively is to let them think creatively. Let them test, revise and draw conclusions from their own judgments. With time, they will become more and more confident in their thinking.

Creative Thinking in Math Classroom

Lack of creative thinking in math classroom results in memorizing techniques, without imagining how, where or why to use them in real life. Setting up an environment in which mistakes are allowed, and making sure that your students know there is more than one solution to a problem will go in favor of creativity. Math is as much about posing problems as problem-solving, and at that point, the creativity is in noticing there is something to investigate. Another powerful tool in supporting students as independent, creative thinkers is the use of questioning. In this environment, classroom needs to value difference and learn from that diversity and creativity. I have listed few techniques that will help you out in boosting creative thinking in math classroom.

Number Talks

Number talks are sessions where students present various solutions to math problems. They are not using pencil, pen, calculator or algorithm, but only their mental process often referred to as mental math. Students solve problems by breaking and decomposing numbers. Once they solve the problem, they need to explain the logic of their solutions to the entire class. It is a great way of both facilitating students’ creative thinking and practicing their argumentation. 

Teachers usually structure number talks in a way that students sit on their seats, while a teacher writes down their solutions on a board. It sometimes may be hard for all the solutions to fit a board, causing that some of them have to be erased. Further on, students might not be able to see all the writings on a board from their seats. AWW has a simple solution to these problems. Use AWW as an online smartboard and let your students solve problems from their seats. Solutions will display both on a smartboard or a projections screen and their own devices. You can manage students’ participating rights, as you don’t want them all to be able to draw at the same time.

Writing Their Own Problems

One of the ways to spark creative thinking inside the classroom is by letting your students write their own math problems. Benefits of this practice are various. You can assess whether your students can apply higher-level thinking skills. Students can improve their argumentation skills while they practice explaining the logic behind their problems. You will also get a feedback at which level of understanding are they, as they will come up only with the problems they can personally solve. Students will include their personal stories and experiences into their explanations. Thanks to that, you will learn a great deal about your students’ interests and life outside of a classroom.



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