Research Guides: Professional Development: Making Thinking Visible: Scholarly Journals and Authoritative Websites

EBSCO Host: Making Mathematical Thinking Visible

Making Mathematical Thinking Visible
Mathematics can be viewed as complex structures comprising intricate and profoundly useful webs of relationships. Students can experience mathematics in this way when working on mathematical tasks such as problem-solving, modelling, investigations or problem posing. Yet these kinds of tasks are seldom implemented in many upper-secondary and tertiary mathematics classrooms, and are sometimes dismissed by students and educators with the remark, "These are fun problems, but where's the maths?" The goal of this report was to develop ways of reporting to students, teachers and other stakeholders, the complex mathematical activity students engage in while exploring mathematical structures. The authors focused on a specific class of mathematical tasks that they call risky mathematising tasks, in which students are required to create an original (to them) mathematical product through mathematising a challenging, complex and novel situation. The authors aimed to develop forms of reporting that highlighted the complex mathematising students engaged in during these tasks, while retaining and respecting the holistic (structural) nature of such mathematical activity.

Making Thinking Visible
The article discusses the significance of visible thinking on students in the U.S. Thinking routines are one element of visible thinking, which help learners to ponder on topics that might not seem to invite intricate thinking. Visible thinking has six key principles which include learning as a consequence of thinking, good thinking is not only a matter of skills but also a matter of dispositions, the development of thinking is a social endeavor and fostering thinking requires making thinking visible. Moreover, its goal is to deepen learning in the content areas and fostering thinking skills and dispositions in schools which creates a chemistry that can be truly transformative for learners and teachers.

Visible Thinking Routines to Engage Students and Check for Understanding
The following teaching and learning activities are modified from a session presented at the SEV VCE Teachers’ Conference in 2016. The activities were framed around the key knowledge from the Units 1 and 2 Study Design for Australian and Global Politics, however, the routines can be adapted for any topic, at any level.

Project Zero
Visible Thinking: At the core of Visible Thinking are practices that help make thinking visible: Thinking Routines loosely guide learners' thought processes and encourage active processing.

Making Thinking Audible and Visible via Cooperative Learning
This chapter begins with a section that describes cooperative learning and explains eight cooperative learning principles. The second section looks briefly at why making thinking audible and visible enriches students' thinking. Making thinking audible means that teachers and students speak out what is going through their minds as they do a task, while making thinking visible means that teachers and students show what is going on in their minds as they go about a task.

Cultures of Thinking: Modelling Leads to Student Success
The article reports on several factors that helps in the improvement of teaching effectiveness in classroom including the model of learning and thinking, visible thinking, and learning from examples. Topics mentioned include the views of author Ron Ritchhart on the importance of model for thinking to students, the promotion of learning to students, and the importance of educational quality.

Enhanced Critical Thinking Skills Through Problem-Solving Games in Secondary Schools
This paper considers one method of enhancing critical thinking through a problem-solving game called the Coffee Shop. Problem-solving is a key component to critical thinking, and game-playing is one method of enhancing this through an interactive teaching method.

The Modeling Toolkit: Making Student Thinking Visible with Public Representations
Modeling is one of the scientific practices featured in the Next Generation Science Standards (NGSS) (Achieve Inc. 2013). This practice is central to the work of science because modeling activities can prompt new questions for investigation, which, in turn, can lead to evidence and information that can be incorporated into a revised model. Models can also support explanations of natural events and processes.

Making Critical Thinking Visible for Student Analysis and Reflection: Using Structured Documentation to Enhance Effective Reasoning and Communication
Today's workforce is in need of workers who are capable of strategic information gathering, flexible thinking, and adaptive approaches to problem-solving (Partnership for 21st Century Skills 2009)--all hallmark aspects of critical thinking. But how can we effectively target and build these complex thinking and reasoning skills in the classroom? Moreover, how can we help students recognize, document, and use processes of critical thinking as they solve authentic scientific problems?