As reported in Education Week (April 25, 2012), "big shifts are afoot as 45 states and thousands of school districts gear up to implement the Common Core State Standards in mathematics. The standards will change the grade levels at which some content is introduced, push aside other topics altogether to achieve greater depth, and ask students to engage in eight 'mathematical practices' to show their understanding, from making sense of problems to reasoning abstractly and constructing viable arguments."
Making sense of problems and reasoning about them -- in other words, making students' thinking "visible" as they grapple with mathematics -- is at the heart of the new book by Don S. Balka and Ted H. Hull, Visible Thinking Activities: 23 Lessons for Problem Solving (Didax, 2012). This month we're pleased to bring you an exclusive interview with Don and Ted as well as downloadable activity pages from their book and Internet links for more in-depth exploration of the research-based approach called "visible thinking." We hope this issue of Class Ideas will deepen your understanding of visible thinking and how it can support your efforts to implement the eight Mathematical Practices outlined in the Common Core.
Co-authors Don Balka and Ted Hull define visible thinking as "the overt, conscious process of being aware of one's thinking, the teacher's thinking, and the thinking of other students in the classroom." Recently the authors answered our questions about visible thinking, the approach it lays out for teachers, and the implications for student success in our highly technological world.
Q: In your book, you say that the "visible thinking" approach to problem solving consists of "high-interest problems that serve to promote students' active engagement." How does this approach differ from/improve upon traditional approaches to teaching problem solving in mathematics?
A: In many classrooms, problem solving means finding the answer to "word problems" by following a list of steps identified by a heuristic. Students are taught to locate the numerals, identify key words, and then perform the required operation. Although these steps are important as students learn mathematics, conceptual understanding is often missing. When students are asked to explain their thinking, they merely repeat the procedural steps.
Problem solving through the lens of visible thinking requires students to struggle with challenging but engaging problems. The process routinely requires students to work with partners or in small groups. Different students may have different solution paths. Rather than extract key words, students working together must think and reason. They must also communicate their thinking and reasoning to other students as well as justify their solution and solution path.
Q: Is it fair to say that the visible thinking approach asks more from teachers in the way they prepare for and orchestrate their math lessons? And if so, are teachers able to adapt their teaching fairly easily to incorporate visible thinking, or is it something that requires targeted training?
A: Many teachers have already received training on strategies that support visible thinking. Unfortunately, they were not introduced to the rationale for using such strategies. Yes, visible thinking requires more intention in planning and presenting lessons, but teachers should not be overwhelmed by the transition. Planned, targeted training expedites the transition process. Teachers need to experience a variety of mathematics problems that incorporate visible thinking.
Q: What research is the visible thinking approach based on?
A: Making student thinking visible is referenced in the National Research Council's book Adding It Up. While no explicit definition is provided, the inference is fairly easy to understand. Translating the implications for visible thinking into actions does require some intentional thinking. The National Research Council further identifies research on effective strategies such as engaging tasks, student involvement, collaboration, ongoing formative assessment, and timely feedback. The relationship between these strategies and visible thinking is straightforward. In our work and writings, we have used the following definition: "Visible thinking is a conscious, deliberate set of actions that provides clear evidence of the current level of student knowledge and understanding. It is the overt, conscious process of being aware of one's thinking and the thinking of other students in the mathematics classroom."
Q: Group work plays an important role in the activities outlined in your book. Can you say more about the importance of group work in making mathematics thinking "visible"?
A: In order to truly learn mathematics, students need time to process and clarify their understanding as well as connect the new understanding to previous content. In traditional learning such as lecture, too much information is provided without sufficient breaks for processing the information. Furthermore, process time is not independent seatwork time.
Working in groups or pairs requires students to communicate their thinking and understanding. Group work time provides opportunities for self-check. Does my understanding match the understanding of others in my group? Also, students are far more willing to discuss and ask questions within small groups. Finally, students are willing to exert more time and energy in solving a problem when they are in a group. Effective effort is a critical element in learning.
Q: The lessons in Visible Thinking Activities address the Common Core Standards for Mathematics, with specific focus on helping teachers incorporate the five process standards into their mathematics teaching. Why is this so important?
A: NCTM identifies five process standards that heavily influence the eight CCSM Standards for Mathematical Practice. These process standards guide how teachers should teach, and students should learn, mathematics. As important as these standards are, to date they have not been effectively translated to classroom instructional actions. These process standards serve as a guide for the transformation of classrooms. If these standards are not implemented, instructional change, and therefore student learning, will not improve.
Q: The book includes traditional and "transformed" problems. What is the importance of presenting students with more open-ended ways of thinking about math?
A: In our technological world, the demand for more mathematically competent employees is enormous. Many businesses and industries cannot find employees who are competent. As a result, positions go unfilled or a shuffled off to foreign destinations. Mathematical literacy is as important as reading literacy. Historically, this has not been the case. Our educational system was designed to gradually screen out students so only a few actually moved to college and obtained advanced degrees beyond high school. Career and college readiness means far more than just "going to college." Students exiting public schools must be prepared to handle a lifetime of learning. Mathematics must be seen and used as an efficient problem-solving tool. Problem solving now requires insight, innovation, and interaction. Businesses need employees who can effectively work together for a common goal to meet immediate challenges. Employees are actively seeking solutions to problems that literally did not exist a decade or even, perhaps, a year ago.
Q: Why should busy teachers care about visible thinking?
A: Our experience is that teachers care deeply about their students. In this age of testing and teacher accountability, teachers are rapidly burning out. They are often struggling to remember why they became teachers. Due to this intense pressure, teacher workloads have dramatically increased, yet student workloads apparently have not. What are teachers supposed to do, just talk faster? Assign more homework? Give more multiple-choice tests? These methods are not going to achieve the desired results.
Teachers must become facilitators and guides. Activities that promote visible thinking revive the art and science of teaching. The focus is on students -- what students have learned, and how students have learned. When students have engaging tasks, and can actually begin thinking, effort increases and learning increases. Furthermore, retention and connections increase. With increased retention and conceptual understanding, the need to constantly revisit and reteach the same mathematics content day after day, and year after year, is greatly diminished. Visible thinking activities provide opportunities for immediate intervention to correct misconceptions. As a result of incorporating visible thinking activities into instruction, students are more receptive when teachers need to teach concepts or skills directly. Also, teachers better understand the current brain research on process time, have instructional strategies that quickly and efficiently enhance learning, and have an increased "tool kit" of effective strategies to make thinking visible.
Our back-to-school issue will be brimming with ideas for ways to get the new school year off to a great start. In the meantime, watch your inbox for fantastic summer specials on a range of great Didax products, and don't forget to follow us on Facebook. See you in August!