Critical thinking skills are essential across all subjects and content areas. As we learn additional information, our brains find a way to create a new schema or adapt prior knowledge. When reading a novel, I have a vision in my head of the main character that evolves as I delve further into the chapters and enrich the picture with new details. In science, we create a hypothesis that is tested and confirmed or adjusted each time we see the results of our experiment. Although some may consider mathematics a “clear answer” subject, there are many opportunities for students to ponder and wonder as they refine their conceptual understanding.
The Standards for Mathematical Practice (SMPs) are at the heart of the work of mathematicians. In fact, these standards are so important that they are the same across grades K–12. As teachers, we encourage students to “make sense of problems and persevere in solving them” (SMP #1) and “construct viable arguments and critique the reasoning of others” (SMP #3). Building the mindset needed for both of these practices goes beyond the mathematics classroom; these practices illuminate critical thinking skills that are necessary across all content areas. The key word here is thinking. It is a given expectation that students are actively giving consideration to the idea rather than waiting for a classmate or teacher to provide the answer.
A Time and Place for Still Thinking
Our classroom first started using Still Thinking during math debates. Students were asked to stand near the answer that best fit their thinking in the moment, but I quickly realized that some of them were merely following others based on who they thought might have the correct answer. Following others is the exact opposite of what is intended by the Standards for Mathematical Practice, so it was time for another approach!
Using Still Thinking is a way to encourage students who are working to make sense of information in a way that is meaningful to them. Students find that a problem might require multiple reads to fully understand it. In How to Solve It, George Polya describes several strategies that can be used to check comprehension of the problem:
- Draw a quick sketch to represent the problem. In creating the sketch, consider key details of the story.
- Build a model. Using physical tools such as cubes, pattern blocks, or counters helps students visualize the situation.
- Act out the problem. Similar to drawing a sketch, acting out the problem helps students bring the story to life.
- Talk through a problem or retell it to a partner as a way to clarify details.
- Look for patterns. Students consider whether they have seen a similar problem before or recognize parts of the problem.
- Eliminate possibilities. Thinking about answers that are not reasonable is another way to refine important details.
Additionally, students might identify unknown vocabulary that requires definition to understand the problem. These strategies are a way for students to start on the problem, and provide a helpful tool for reflection. In every attempt, something is learned. If their chosen path does not lead to a solution, what did they learn from the attempt? How will the new information influence their next attempt?
Getting Started
Although math debates were a natural fit for our classroom to develop a mindset of Still Thinking, there are many ways you could accomplish this in your classroom. Modeling for students that you are “still thinking” as you think through a problem aloud is one way to demonstrate that problem-solving is not fast or easy. Students are not able to see the multiple questions we ask ourselves, our inferences, or the decisions we make, because these happen within our minds. Demonstrating the importance of thinking aloud helps students see the need to make space for Still Thinking opportunities.
Another important place to implement the language of Still Thinking is when you confer with students. Opening the conversation by asking, “What are you still thinking about?” is a way to help students clarify what they know and what they are wondering about a particular problem.
The Power of Still Thinking
Still Thinking empowers kids with an asset-based approach to learning. The teacher is trusting students to be thinking—which is empowering for kids! When we remove the pressure of arriving at a quick solution, students have the opportunity to ask questions and clarify their thinking.
For example, there have been times that students have remained at Still Thinking through an entire math debate while the majority of the class has identified the correct solution. Having the teacher reveal the correct answer at the end of the debate would rob students of the rich thinking they have been doing by Still Thinking.
Rather than pushing students toward the correct answer, I end the debate. Given the gift of time, students continue to think about the problem, gain additional perspective, consult resources (such as friends, parents, or books), and engage in further conversation. Typically, the students return later with the correct answer.
Still Thinking provides a framework for students to engage in critical thinking skills and learn to trust their own mathematical reasoning.
