The other day while my children were playing with their cousins, I decided to watch some TV while I folded mountains of laundry. When I clicked the remote, Who Wants To Be a Millionaire—Whiz Kid came on and I was instantly intrigued. A young adult contestant was in the midst of making his thinking visible as he worked to answer the question. He was running through the calculations and connections (the process) he used to solve the problem, and then, with great confidence, he declared that “A” was his final answer. Impressed by the student’s work, I smiled and waited for the host to exclaim,“That is correct!” Ah, but here is where dreams get dashed, because the host replied, “I’m so sorry, although your calculations were correct, the question asks which is not correct.”
I paused the TV and grabbed my sister, who is also an educator. I replayed those seconds of the show knowing she would empathize with what I was feeling, because this contestant’s misstep is all too familiar. And she did, remarking, “Well, now isn’t that the hardest thing to teach!”
The “that” my sister referred to is teaching students to revere the process - getting them to slow down and enjoy the ride in a sense, as they draft a story or work through a math problem. So, just how do we cultivate this tough-to-teach mindset and skill? The first step is to identify goals for our math students. We want math students to be flexible thinkers, because flexible thinkers are complex problem solvers. We want them to analyze and make sense of the problem before rushing to get to the answer. (Let’s call the rush the game show syndrome, right? In the rush for a million dollars, that poor whiz kid forgot to analyze the question and check his work.) Ultimately, when students view a problem as something they have to make meaning with—rather than as something merely to solve, they are better able to visualize multiple ways to solve it (the process), and more likely to check themselves and shift their thinking throughout the process (flexibility).
Strategies for Process Approach Teaching
What follows are some moves we can make to shift students from answer-oriented learners to process-oriented learners.
Help learners embrace flexible thinking. Let your students know that it is more fruitful to think of processes, plural, rather than a single process or single way to approach a complex problem. A problem requires us to perform many different skills at once and shift our thinking as needed. So, make sure you walk the talk of modeling flexible thinking. Ask yourself, “Do I teach to a single process, focusing on one algorithm or one step-by-step strategy?” If you tend to, instead, explore the many processes out there; share them, have students share theirs, set up opportunities to debate processes and prove them; even pose problems with multiple solutions. Creating a mathematical community that looks beyond the answer will make math more enjoyable and meaningful.
Check the messages you send about speed. Often, students begin to hate math because they feel math is all about getting the correct answer, fast. Ask yourself whether you unwittingly fall into “right” and “wrong” approaches to problems, seem rushed, cut corners on wait time, or have little collaborative activities that promote flexible thinking. Remember, we must go slow to go fast. We can devote class time to explore the math in order to create a deep meaning for the math.
Promote process-oriented feedback. During whole group and small group lessons, name and notice aloud exactly what students are doing. Help make their thinking visible so they can see their current thinking and possible next steps. Instead of praising the answer or the speed (which we often inadvertently do), praise specific parts of the process and the effort. Also, spend time discussing graded assessments - confer with each student after assessments, allowing him or her to explain their thinking and processes—this will help you determine the types of errors so that you can give specific feedback. All of this time spent on process conveys the message that learning from mistakes is more important than the letter grade.
Don’t rescue—help them swim to shore. When you see students struggling, give them some wait time. Let them embrace the struggle. If you do need to jump in, start by asking questions to support their thinking or, if needed, maybe throw out a “If I was doing the problem, I often…” and highlight a part of your thinking process that they could borrow. Also, set up routines that take you out of the “rescue” equation. If you sense students wait for help from you, co-create with the class a list of “What to do when stuck” routines, that remove you as a line of support. For example students could: look for a similar problem in their notebooks; slow it down and take out the number; phone a friend; consult with your math buddy. All of these routines foster independence and take away the stigma of stumbles and struggles.
Life Skills for Every Kind of Whiz Kid
This blog has focused on math, but every idea here can be applied in any content area. After all, these are life skills, not just math skills. In fact, according to the World Economic Forum, complex problem solving and critical thinking are the number 1 and 2 (respectively) most valued skills in the workforce. So, let’s prepare all students for whatever life they choose by recognizing the time involved in productive thinking and by valuing individual meaning-making processes. As for that whiz kid on Who Wants to be a Millionaire, he showed attention to many parts of the process, had the confidence to take the risk of doing math on national TV, and will no doubt learn from his mistake. Or maybe it’s more apt to say, we all learn from our mistakes.
Shanna Anderson studied at Seton Hall University and The University of Virginia. Certified in Mathematics, Elementary Education, and Special Education, Shanna brings her love of learning, the power of “...yet”, and the need for reflection into her work as an Educator and Instructional Coach.