**Habits & Mindsets:**

Thinking Flexibly

Thinking Flexibly

**Introduction**

Why is Thinking Flexibly important?

Vision For Excellence:

Students

Vision For Excellence:

Teachers

Resource 1:

RAFT Activity

**Tiffany Chui, Destiny Dike, Kelly Kimpton, & Isaac Yoon**

Resource 2:

Fostering Mathematical thinking &

Problem Solving

(Math Specific)

Resource 4:

Number Talks

(Math Specific)

Resource 5:

HOM Assessment Rubric

(General Resource)

Resource 6:

Riddle Activity

(General Resource)

Resource 8:

Socratic Seminar Implementation Guide

(General Resource)

Resource 10:

Implementation Calender

Resource 7:

Group Reflection Handout

(General Resource)

Resource 3:

Incorporating Worthwhile Real-World Tasks

(Math Specific)

Resource 9:

Flexible Object Activity

Resources

Socratic Seminar discussions are “collaborative, intellectual dialogue facilitated with open-ended questions about a text” (Socratic, p.1). Such discussions promote deeper thinking and creates a space for students to examine various issues, reflect on different ideas, and articulate various points-of-view. “Students are encouraged to think out loud and to exchange ideas openly while examining ideas in a rigorous, thoughtful, manner” (Socratic, p.1). Grappling with the indefinite answers to open-ended questions and considering the perspectives of others encourages the plasticity of the mind. This develops the ability to rewire the mind and the thought processes within. With consistent and intentional incorporation of this resource students will gain the ability to “approach a problem from a new angle using a novel approach” (Costa & Kallick, 2000, p.4).

The attached media resource provides an example of an activity that teachers can use in order to actively promote flexibly thinking in the classroom, at home, and in their communities. Teachers can use any classroom object, or have students bring in individually selected objects, and engage in an interactive activity in which students identify various uses of common objects. Structuring such an activity will help students “change their perspective” (Habits, p.4) concerning the world around them and “reform [their] thoughts based on new information” (Socratic, p.4). This ability to “shift, at will, through multiple perceptual positions” (Costa & Kallick, 2000, p.4) establishes a strong foundation upon which students can build the habit of Thinking Flexibly and fluently.

We need people who can read and write. But what we really need is people who cannot only read the instructions but change them. They need to be able to think outside the lines.

- Richard Gurin

(Costa & Kallick, 2009, p. 45)

As schools embody the transformations of our 21st century society, there has been a change in what drives our students’ educational journeys. Whereas content was once the primary priority in the classroom, it is becoming more critical to integrate habits of mind into everyday instruction. Incorporating habits of mind into academic curriculum postures students to hone the skills necessary to remain globally competitive in an ever-changing modern society.

Our group focused on the habit of mindset, Thinking Flexibly. Costa & Kallick (2009), in Habits of Mind Across the Curriculum: Practical and Creative Strategies for Teachers, define flexible thinking as “altering our perspective and seeing things from other points of view” (p. 45). In a classroom environment, students must be given opportunities to transition between macrocentric thinking (seeing the big picture), microcentric thinking (finding the details), and retrocentric thinking (working with the end goal in mind) (Costa & Kallick, 2009, p. 45).

Our goal is to create a classroom where the teacher provides meaningful opportunities for students to understand and appreciate various perspectives. With this in mind, we designed a toolkit for teachers who want to integrate flexible thinking more successfully in their day-to-day instruction. It provides strategies for all ranges of teachers. There are resources for those just beginning the habits of mind journey with their students and there are also resources for teachers who want to enhance their current habits of mind instruction. There are four resources for the secondary mathematics teacher and five resources for the secondary general education teacher. From assignments to rubrics, we hope our toolkit encourages teachers to lead a more flexible classroom.

In a flexible classroom, there are distinct roles for students.

Flexibly Thinking Students are...

Eager to find and share different ways to problem solve.

Grappling with content in collaborative groups.

Appreciative of different strategies and listening to others with an intent to understand.

Creating their own unique strategies on a consistent basis.

Navigating between the problem’s bigger picture and details (Johnson et al, 2005) without teacher scaffolding.

Operating with an internalized a growth mindset (believe intelligence is a developed trait).

Presenting their individual methods to the class and engaging in whole class discussions comparing the multiple approaches.

In a flexible classroom, there are distinct roles for teachers.

Flexibly Thinking Teachers are...

Producing classroom environments where students feel comfortable sharing their creativity.

Demonstrating bendable and changeable methods of teaching students the same concept.

Encouraging students to create their own ways to approach a problem.

Planning exploratory tasks where students make sense of the new material on their own.

Presenting multiple solutions and perspectives with which to view a problem.

Asking questions to students in order to solicit their opinions.

Modeling "the capacity to change their mind as they receive additional data” (Costa & Kallick, 2000, p.4)

Holding students accountable in finding their own alternatives.

Carrying an overall belief that all students can learn.

Thinking Flexibly is an essential element in a students' education for several reasons:

Flexible thinking helps students recognize that learning is not “black and white.” Especially in the mathematics classroom, “teachers are notorious for inflexibility because of their own learning styles and their belief that mathematics is an “exact” science” (Costa & Kallick, 2009, p. 96). Flexible thinking encourages students to approach learning experiences with an open and adaptable mindset.

Students often have difficulties envisioning alternatives. Without alternative points of view, they become rigid in their thinking. “Rigid thinking prevents students from generating open-minded responses to various social situations. Therefore, teachers must help students to have three perceptual positions: 1) Macrocentric - allowing students to see the big and holistic picture, 2) Microcentric - giving students critical eyes for logical and analytical details, and finally, 3) Retrocentric - helping students to work from the end point and work backwards towards the beginning (Costa & Kallick, 2009, p. 45).

Flexible thinking encourages creativity and allows students to exercise lateral thinking. Students who think flexibly consider other points of view and are open to additional information. Flexible thinkers are not afraid of changing their minds and are receptive to others’ ideas. Creativity and the ability to consider alternate points of view are important 21st century skills that students need to be competitive in today’s growing society and marketplace.

Students are able to enhance the habits of thinking flexibly when they alter their perspective and “see things from other points of view" (Costa & Kallick, 2009, p. 45). RAFT tasks (Role, Audience, Format, Topic) allows students to consider other perspectives other than their own. This will develop their ability to generate open-ended responses to various social and academic situations. This resource provides assignment templates, rubrics, and student samples for all content areas.

URL link:

http://daretodifferentiate.wikispaces.com/R.A.F.T.+Assignments

“The dilemma is that the instructional approaches advocated by many commercially available problem-solving resources and curricula encourage teachers to train their students with “how to” approaches to problem solving.” This approach develops students as “problem performers” (students who excel in solving problems without much cognitive effort through specific heuristic strategy) rather than “problem solvers.” The worksheet that complements this resource is best suited for the beginning of a lesson. Its structure allows students to explore the problem and write down their thoughts prior to the teacher's introduction to the material. This encourages students to leverage previously learned knowledge, a general understanding of the content, while giving them an opportunity to collaborate with others. By emphasizing the process rather than the solution, students can focus on their reasoning and their approach instead of focusing on obtaining the correct answer. The worksheet also promotes collaboration, in which students critically examine each other's ideas and build upon each other’s processes. The final component of this worksheet allows students to reflect and make sense of the problem once the teacher provides opportunities for students to make necessary connections.

Costa, A. L., & Kallick, B. (2000). Describing 16 Habits of Mind. Retrieved from http://www.habitsofmind.org/sites/default/files/16HOM2.pdf

Costa, A. L., & Kallick, B. (2013). Habits of mind: Across the curriculum. Virginia: ASCD.

Costa, A. L, & Kallick, B. (2009). Habits of mind across the curriculum: Practical and creative strategies for teachers. Alexandria, Va.: Association for Supervision and Curriculum Development.

"HABITS OF MIND CONTINUOUS GROWTH PLAN OF ACTION ." COMMUNITY HIGH SCHOOL OF VERMONT, n.d. Web. 22 Feb. 2015. <http://danalesperance.weebly.com/uploads/1/4/7/2/14727510/habits_of_mind_continous_growth_plan.pdf>.

"Habits of Mind: Thinking Flexibly Teachers' Resource ." Student Web 2. Reinhardt, n.d. Web. 15 Feb. 2015. <http://studentweb2.reinhardt.edu/faculty-save/dpnichols/HabitsofMind/flex_thinking.pdf>.

"Socratic Seminar ." Northwest Association For Biomedical Research , n.d. Web. 22 Feb. 2015. <https://www.nwabr.org/sites/default/files/SocSem.pdf>.

In order to promote students' flexible thinking, it is vital for educators to think differently about the problems they present. In typical math classes, sets of problems are given to students that are rote, procedural, and repetitive. To capture students’ interests and engage them in more meaningful mathematics, it is beneficial to present problems that are relatable, interesting, and do not have an obvious solution. Using resources such as Mathalicious, math teachers can find lessons that promote problem solving and critical thinking. In Mathalicious lessons, students are challenged to construct their own unique arguments and justify their reasoning. Students who think flexibly must "consider alternative points of view or deal with several sources of information simultaneously" (Costa & Kalick, 2009, p.8). This is particularly necessary in Mathalicious problems since they apply to real life situations. An important component of facilitating these lessons include the facilitation of student discussion throughout the problem solving process. Multiple approaches to problem solving are shared, appreciated, and celebrated.

URL Link: http://www.mathalicious.com/

Students who are not accustomed to thinking flexibly often have very "ego-centered points of views" when it comes to problem solving. They have "difficulty in considering alternative points of view" and believe "THEIR way to solve a problem seems to be the ONLY way" (Costa & Kallick, 2009, p. 5) To combat these views and to ease students into thinking flexibly, teachers can incorporate quick number talks daily in class.

Number talks begin with the teacher presenting a short math problem. Students must solve this problem mentally and are not allowed to use pen/pencil, paper, or a calculator. (An example of this is shown in the video resource as 18*5.) Once all students have solved the problem, the teacher facilitates a discussion on the different methods to solve the problem. The focus is not on the correct answer, but on the different ways to find the answer. These talks help students develop their number sense and their ability to think flexibly and manipulate numbers. Building number sense helps students grow confidence in dealing with numbers and provides a foundation for success in Algebra. Furthermore, number talks are quick ways that students can learn from others’ thinking.

“In developing the Habits of Mind of any other skill, it is helpful to have a sense of where you are currently and what the next steps are to achieve the ultimate goal of mastery” (Costa & Kallick, 2009, p. 29). Giving students a rubric helps gauge their progress in incorporating flexible thinking during tasks and assignments.

This rubric (Thinking Flexibly-Teacher’s Resource) is composed of four student-driven dimensions: has a wide variety of perspectives, evaluate usefulness of alternate ways, show appreciation for alternative points of view, and embody an adaptable mindset toward changes. For each dimension, there are three ratings: unsatisfactory, proficient, and exceeds. Prior its implementation, the teacher will take time to review the rubric with students to explain the ultimate target as well as steps students can take to reach it (Costa & Kallick, 2009, p. 29). It is recommended the teacher provide students with pieces of student work that exhibit flexible thinking and pieces of work that do not. This sets the expectation of what students need to achieve in order to exceed. It is also recommended that the teacher use this rubric consistently to encourage students’ use of flexible thinking. During implementation, the teacher should not only circle the rating the student received in each dimension, but also provide feedback as to how the student can better integrate flexible thinking.

URL Link:

http://studentweb2.reinhardt.edu/faculty-save/dpnichols/HabitsofMind/flex_thinking.pdf

The purpose of this activity is to get students developing multiple points of views while considering alternatives from their peers. This task is best suited for middle to high school students (Thinking Flexibly-Teacher’s Resource).

Prior to the activity, the teacher will “deliberately place students in heterogeneous groups based on their different learning styles, which will help them understand and appreciate varying points of view” (Costa & Kallick, 2009, p. 45). The teacher will initiate a class discussion to get students talking about characteristics of flexible thinking. What does it look like? What does it sound like? In what real world situations do we have to think flexibly? The teacher will make a list of student responses in the front of the classroom.

The teacher will pass out copies of seven riddles to each group. These riddles are design to elicit various answers. It is important to tell students there is no right or wrong answer. Give students 15 minutes to solve as many riddles they can and write down their solutions. During this time, the teacher will walk around and monitor student progress.. At the end of the 15 minutes, groups will present their solutions and a whole class discussion will be conducted on the importance of thinking differently to solve problems. At the end of the activity, the teacher should make connections between the flexible thinking required in this activity and the flexible thinking required in the classroom.

When implementing a new initiative, there must be clear goals, specific activities, a general timeline, and benchmarks indicating success. The following calender provides an outline for implementing habits of mind in the classroom generally, as well as the HOM: Thinking Flexibly specifically. The subject, grade-level, and school culture specific to each teacher will better inform the implementation process.

(Continuous, p.15-16)

Riddle #1

Put a coin in a bottle and then stop the opening with a cork. How can you get the coin out of the bottle without pulling out of cork or breaking the bottle?

Riddle #2

A student who was just learning to drive went down a one-way street in the wrong direction, but did not break the law. Why?

Riddle #3

Two students are sitting on opposite sides of the same desk. There is nothing in between them but the desk. Why can’t they see each other?

Riddle #4

Train A and Train B are crossing the country, from coast to coast, over 3,000 km. Train A is going East to West at 80 km per hour, and Train B is going West to East at 90 km per hour. Which train will be closer to the west coast when they meet?

Riddle #5

How can you throw a ball as hard as you can and have it come back to you, even if it does not hit anything, there is nothing attached to it, and no one else catches or throws it?

Riddle #6

All of Jenny’s pets are dogs except one. All of her pets are cats expect one. How many cats and dogs does Jenny have?

Riddle #7

(For use with Secondary students)

Three people check in a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers that the room rate is $25 and gives $5 to the bellboy to return to the people. The bellboy reasons that $5 is difficult to share among 3 people so he pocket $2 and gives $1 to each person. Now, each person paid $10 and got back $1. So they paid $9 each, totaling $27. The bellboy has $2, totaling $29. Where is the missing $1?

Group tasks that are meaningful and purposeful provide students with opportunities consider alternative perspectives. In order to encourage the use of flexible thinking in group tasks, “teachers and administrators need to provide students opportunities for practicing and demonstrating flexible thinking, which fosters a tolerance for others” (Thinking Flexibly-Teacher’s Resource, p. 4). The “Flexible Thinking: Group Reflection” is a resource students can engage in after group tasks to help them reflect on their use of flexible thinking. It asks questions that include, “Did any group members suggest new ideas when the original idea did not work? Were new ideas listened to and welcomed by all group members? Were new ideas flexible?” These questions make flexible thinking more apparent to students and can be effective when students have not yet internalized this habit of mindset.