Great question. I believe that successful understanding and implementation of Quantitative Reasoning and Mathematics in general requires imagination first and foremost. I have recently edited a book that partially addressees this. However, after serving as the senior efitor, I have been able to focus my own pedagogical beliefs that have always proven to be effective. Unfortunately, junior faculty, which I no longer consider myself a member of (I've paid my dues) aren't encouraged to challenge the accepted classic Methods, especially when it comes to math. Mathematics education in US needs to be severly dismantled, not all of it. There are many schools such a my home institution, joined by Columbia, Harvard, NYU, Yale, just to name a few. Give students context, and let them discuss any patterns, predictions, hypothesis, experimentation, all of which rely on the ability to imagine. This process is of course supervised. I am the facilitator of the learning process, not a rule generating machine.  This teaching method is harder for the instructor, because it requires imagination on our part. Quick example. In intro to math of finance, my students make up a client, or imagine themselves in the future, and use BLS, to describe the education, number of years to get to the salary point they are at, where does this person live, how much is their rent .... Eventual learning outcomes: constructing and interpreting pie charts, manipulating percents, understand inflation, examine cost of living, amortizing a loan, accruing money in a savings account, deal with big purchases, compounding and eventually exponential function, all in the context of the story of this imaginary/theoretical person. It's amazing how invested they become in this nonexisting figure. The math, excel exercises are seen as a means to an end as it should be. I have been able to develop quite a few of these approaches that the students enjoy, the underlying concepts are investment in learning and, of course, imagination.  I'll share a few more.  Knowledge is not proprietary, it's all of ours, and I will share as much as I can.

Dear Sir, the very development of brain from child hood listening and learning about all incidences is nurtured with imagination. the bed time stories from child hood heard and accepted with every individual imagination of their own. So  -  imagination is a humble but powerful tool to teach and can make the student imagine what you are trying to imagine is a great successful methodology of teaching which sustains to recall from memory. The most explicit attention I usually give to my students when I teach Human Anatomy in a classroom is to presume or imagine every organ as a part of a building block which in total configures structurally and functionally for the living body and many such varied imagination some times explained by students about the function of every muscle to nerves is so easy to pick up and expose the meaning of it. Thus imaginative initiation about any topic to teach with absolute meaning maintained for Good understanding remains success for any length of time with the students. Thanks. 

In preparing the teaching workforce for today's diverse classrooms, I invite ECCE undergraduates to imagine they were students of different cultures in class and ask them to think of how their teacher could make the lesson interesting for them. Usually, they are able to understand that as teachers they need to accommodate for the diverse backgrounds of students in their classes. I also use supporting articles like those attached that I have written to demonstrate that I am walking the talk. I hope that this is helpful to your question.

Best regards,

Debr

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Imagination is key to the development of alternative thinking aspect. New teaching methods indicate that thinking alternatively is essential. The school spent a lifetime teaching the same way. Saying that there is only one way to resolve things, I think this is the reason for the stagnation and even decline in the learning of children in school.

We must give the opportunity for children to think of an alternative way to promote and develop their creative abilities. This should be the objective of the school of the future

Many thanks for your considered responses thus far. I will certainly reflect on them further.  Einstein is quoted as saying "Imagination is everything. It is the preview for life's coming attractions.

Are there ways you are fostering imagination to teach to the unknown future?

Dear Madam, imagination is the very root source of every innovation we have today, nobody can deny it, but again to imagine at what depth and how much influence of strength does the imagination can be encouraged or enriched or extended is the challenge to express to any individual with regard to imagination. Thanks

Dr. Hameed,

I so agree. We may call on the imagination but how are we strengthening and deepening the imagination of ourselves and our students?

Perhaps the answer lies in the methodology we use. We must give a chance to answer without conditioning the response from students. Imagination has to boost encouraging to think differently and enhancing the search for solutions and alternative responses teacher.

Thank you

I am currently conducting a PhD in how teachers in non -arts based disciplines in higher education foster the imagination of their students. Just finishing off writing now actually. I did three ethnographic case studies - in fourth year quantum physics, first year Medieval European History and post-graduate Finance, which was run a s a simulation. Just thought you might be interested. 

I found the teachers had not thought about it much (except the physics educator) but that didn't mean they weren't cultivating students' imagination or creativity. So observation was a good method. 

Dear Gloria, I so agree with  imagination having a general trajectory towards the futute.it is our internal attempt to reconcile things and hypothesise and envision possibilities. It's very important not to confuse what we're talking about with the other use of the term, as in wow this book is so imaginative (referring to the authors ability to put them selves in a created world and imagine different characters etc.). That is certainly not what I'm talking about.  On the other hand, a child constructing a model in his mind of why and how the sun comes up IS imagination.  Putting on a different hat, as a doctoral student, all I had to rely on was imagination. My field was very narrow, not only did I read the major contributions, I've met the authors. And after you've gathered the available tools, now it's imaginations term. 

Joy,

I am very interested in your PhD study! It is fascinating to discover how important one's imagination is  ( when asked) yet how frequently it can be shut down (or ignored) in formal schooling. It is this wondering that interests me.

Loosening the imagination of the management research craft worker.

The researcher should work within a concept of craft which involves producing useful and aesthetically pleasing work which is identifiable as coming from the hand of the individual craft worker. The research should be crafted in a reflexive style which reveals the researcher's own hand in ‘shaping’ the reality which it presents.

http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8551.1994.tb00132.x/abstract

I think Ross and David bring up some critical points.  Ross says he is a

"facilitator of the learning process" which is what all good teachers become (but not through any overt education).  Unfortunately, that is not what pre-service teachers are prepared to be as they get their undergraduate degrees.  Instead, each state has a list of specific behaviors they have to be able to perform (course objectives) which do not train them to facilitate learning, but only to deliver information.  I believe this is where David's comment that lack of imagination in classrooms is the cause of stagnation and decline in our schools is proven true.  I think it is no coincidence that those of you in the hard sciences see imagination as  so necessary when the general public sees the hard sciences as fixed and unalterable.  This is evidence that so many public education graduates have no imagination and that is why so many of them are not in STEM fields. 

I offer Joy a reason why only her Physics educator had thought about using imagination in the classroom.  How accurate do you think the following assessement is?  Could this be why David finds our classrooms so stagnant with students unable to grasp abstract concepts or to develop their own abstractions?

Typical American education system:

1.  The majority of high school students who make good grades learn well by reading, asking questions, and listening to teachers talk or for answers.

2.  The students who do well at university are typically students who do well by reading, asking questions about specific points they do not understand, and listening to teachers talk and for answers.

3.  The students who love school and want to become teachers typically learn by reading, asking questions about understanding of content, and listening to teachers talk and for answers.

4.  The people who really love school and go on to become professors typically learn by reading, asking questions, and listening.

5.  These professors teach the way they themselves learn best (if it worked for t hem it should work for others) by having students read, talking to them, and answering their questions.  

What happens to students who need more than this (understanding of what they heard the teacher say and what they read--Not what to do with that information). What happen when students need different input and interactions to learn more thoroughly over the long-term such as through the addition of demonstrations, solving problems with guided help, using the knowledge of others to help solve problems, or experimentation to see what works best?  Those people, if they are also good at reading, asking questions, and listening, become our STEM professionals.  The rest quit long before they finish school.  

Those who are uncomfortable learning through demonstrations, problem solving, and experimentation become teachers and all the other professionals of our world who often feel that STEM people are from another planet.  I believe it is our chickens producing eggs producing chickens producing eggs...ad infinitum... educational cycle which is crushing the imagination of the American people by the time they are in the 3rd grade.  If kids don't conform to the learning norms of the schools, they seldom become model students.  The conundrum is that most education professors do not know how to teach teachers how to facilitate learning because they themselves have never been taught to facilitate learning and they are skeptical of those methods anyway because they themselves find those other methods less useful than traditional ones.  As I said before, most teachers teach they way they themselves learn best.

Of course professors teach that that their students  must differentiate learning, but how many teach our new teachers  how to actually differentiate that learning to meet the needs of non-traditional learners and manage their classroom at the same time?  Typically, little other than an overview of understanding what non-traditional learners are and how not to insult them is even covered in the one required class of most education curricula.  Few if any of these courses actually tell pre-service teachers how to deal with 30 students who all read at vastly different levels and have substantially different sophisticated vocabularies necessary for understanding texts and teacher explanations.  

A case in point: In May 2014, the Nation's Report card reported that in reading, just 38 percent of seniors scored at or above grade level. And one-quarter of high school seniors are reading below grade level.  This means they do not understand much of what they read and hear at school, but there are few other means of input in most schools, and so the cycle continues.  Those who read and listen accurately, succeed and those who don't, get by.

 Until education professors learn how to teach pre-service teachers how to facilitate learning through imaginative, constructivist techniques, the cycle will continue and our STEM fields will continue to suffer.  And as Tajudeen says, young people's brains will cease to develop. 

Imagination has to bexplicitly valued in the teaching process, in words, actions, strategies and systems. It is no good asking for imaginative effort if as an example, assessment, was aimed at low order or declarative knowledge. If you want something valued in education, the whole system needs to be designed to value it. Many of my colleagues tell students that they value mistakes, and wonder why they don't respond positively. If students do not clearly recognise that mistakes (specifically mistakes as part of a process of discovery) are not valued they make a reasoned decision to avoid them.

I've been asking people of all ages about imagination.

Here's one from a boy of 6.  I wonder if teachers will take his relationship to imagination away?

Ben

It’s something in your head. It’s actually your brain. You get dreams and in your dreams you can solve problems with your imagination.

I work on the concepts to be joined in inductive or deductive form and try to observe what works best for them for each individual subject. There are many methods of scaffolding to nurture creativities in the forms of learning like outcome-based approach to student learning (OBASL), experiential learning, problem-based learning, co-curricular learning and I think adoption of ways of disseminating imagination or creativity depends on the forms of learning you adopt.

Just today, in teaching physics to 15 year olds, I asked them to imagine themselves in several scenarios and describe their physical sensations - in a car taking off at the lights etc. In another class talking about ethics and gene technologies, i asked them to imagibe a world where blond people were relegated to menial jobs and darker haired people got the cushy jobs. The look of horror on their faces was wonderful. Imagination is a wonderful tool in learning

Nice Dear Dayna Ford