Extracted from the book: Habits of Mind across the Curriculum (edited by Arthur L Costa and Bena Kallick)
Click HERE for the description of each of the Habit of Mind
We have identified 10 habits, that we think are relevant to our Maths classroom...
Here are some notes extracted from the book cited above
(1) Persisting
If the only tool you have is a hammer, you will treat the whole world as if it wre a nail
~ Edward de Bono
When we approach a problem, we often have the misconception that there is "one best strategy". If that strategy does not work, we give up in frustration.
People persist because they can draw on multiple ways to solve problems. If Plan A doesn't work, they back up and try Plan B. Therefore, we must celebrate multiple ways of finding solutions.
Good questions to ask ourselves:
- Who has another way to solve the problem?
- What is another approach to solving this problem?
- What are some other strategies?
The secret of getting ahead is getting started. The secret of getting started is breaking your complex overwhelming tasks into smaller manageable tasks, then starting on the first one.
~ Mark Twain
Before a learning activity, time is usually taken to develop and discuss the strategies to attack the problems. Such work include rules, directions, time constraints, and purpose. We would use this guidance during our work and to evaluate our performance afterward.
During the activity, it is useful for us to be able to describe the strategy, why we choose to use it and reflect on how well that strategy is working. It is also helpful if we can describe the path we intend to pursue next to solve the problem.
(3) Think Flexibly
We enhance the habit of thinking flexibly when we must alter our perspective and see things from other points of view. Let's try to solve a problem "outside" our best learning style.
Let us describe how we could look at a problem differently.
For example, can we find the pattern in this string of letters? AEFHIKLMNTVWXYZ
(4) Thinking about Thinking (Metacognition)
Thinking aloud... allowed!
Describing our thinking while we solve a problem seems to beget even more thinking. We must do mre than learn how to find answers. we must become aware of the cognitive processes that produced answers.
When reflecting on our learning, it is useful to ask ourselves these questions...
- What did I do first?
- What steps did I take when I was uncertain about my work?
- How did I change my course of action? Was it profitable?
- If I were to do this work again, is there anything that I would do differently? If so, describe what that might be and why I would do it.
When we check for accuracy, we should ask questions like...
- How do we know we are right?
- What other ways can we prove that we are correct?
- What did we do first?
- What clues did we have that we were on the right track?
- How did we know where to begin?
- What led us to make that decision?
- When we said we started at the beginning, how did we know where to begin?
Astronauts use [the Habit of Mind] checking for accuracy before each space mission!
Striving for accuracy is of great value not only in classroom but in the wider world as well. Pharmaceutical research, surgery, piloting, bookkeeping - all require a commitment to accuracy.
Some skills and strategies that we could apply when striving for accuracy and precision:
- Always check the working and presentation
- Show your work to a friend for feedback
- Review the rubric to see if we have met the criteria before turning in our work
- Don't just write the answer. Show the work so that we can go back and find errors
- Learn from our mistakes so we won't make them again
- Know the rules and apply them
- Use a different strategy than the first one to see if we get the same answer
- Make sure we know what the instructions mean before we begin
It is in the formulation of the problem that individuality is expressed, that creativity is stimulated, that nuances and subtleties are discovered
~ Herbert Thelen
It is helpful for us to pose study questions for ourselves before and during our reading of textual material. Self generating questions facilitate comprehension. We know that reading with a purpose stimulates a more focused mind. Questioning while reading provides an opportunity for us to predict what is coming next in the story.
(7) Applying Past Knowledge to New Situation
The main fuel to speed the world's progress is our stock of knowledge and the brake is our lack of imagination.
~ Julian Simon
Whenever we begin a new learning, pose questions that will get us to search our memories to brainstorm and generate past knowledge:
- What do we remember about...?
- When have we ever seen anything like this?
- As we recall...
- Tell what I already know about...
- If you were to design a new...?
- What would it be like if...?
- Where else would you use this information?
- In what other situations could we apply this?
- In what careers and jobs would this Habit of Mind be needed?
This report, by its very length, defends itself against the risk of being read.
~ Winston Churchill
Our oral language is often filled with omissions, generalisations and vagueness. Our language is value laden, sometimes deceiving, and conceptual rather than operational.
Being alert to this vagueness and then clarifying or probing for specificity causes others to define our terms, become more specific about our actions, make precise comparisons and use accurate descriptors. Clarifying language also clarifies thoughts.
The vague terms we use fall into several categories:
- Universals: always, never, all, everybody
- Vague action verbs: know about, understand, appreciate
- Comparators: better, newer, cheaper, more
- Unreferenced pronouns: they, them, we
- Unspecific groups: teachers, parents, things
- Assumed rules or traditions: ought, should, must
- When you hear: He NEVER listens to me
- Clarify by probing for specificity: "Never" or "Never ever?"
- When you hear: EVERYBODY has one
- Clarify by probing for specificity: "Everybody?" or "Who, exactly?"
- When you hear: THINGS go better with...
- Clarify by probing for specificity: "Which things, specifically?"
- When you hear: Things go BETTER with...
- Clarify by probing for specificity: "Better than what?"
When our senses are dull and sluggish, our thinking is dull and sluggish. All information gets into the head through our sensory pathways. Sensory exercises therefore hone our powers of perception:
- Sight
- Touch
- Sound
- Smell
- Taste
It is good to rub and polish our brain against that of others.
~ Michael De Montaigne
After each cooperative task is completed, take time to reflect on how well individuals and groups worked together:
- What contribute to the group's success?
- How did each group member contribute to and learn from the experience?
