Wednesday, November 30, 2011

Dangers Inherent in the Trivialization of Psychotherapy

!±8± Dangers Inherent in the Trivialization of Psychotherapy

DEFINITION OF PSYCHOTHERAPY

For the purposes of this essay, I will use the term "psychotherapy" to refer to a particular type of interpersonal process intended to facilitate conscious awareness of that which had previously been unconscious. It is not meant to include the direct attempt to modify behavior, whether overt as action or covert as thoughts and feelings, through medication or manipulation of the external consequences of behavior. Similarly, it does not include counseling, coaching, advising, or teaching as its primary goal.

THE RECENT HISTORY OF PSYCHOTHERAPY

In its current form psychotherapy has been popular for only about a century, although its roots are ancient. Freud called attention to the importance of the personal unconscious, repository of those thoughts and feelings which are unique to a particular individual and presumed to be a result of his or her personal life experiences and genetically transmitted instincts. Jung invited us to notice the collective unconscious, where we find ourselves connected to all of humanity through shared patterns of thoughts and feelings. Each of them found the contents of a person's dreams to be of particular value in accessing the unconscious, whether personal or collective. Many followers of these two pioneers have refined the methodology for accessing these two types of unconscious material and integrating it into one's conscious awareness, particularly with regard to the manifestation of unconscious material in the transference and countertransference. However, Freud and Jung deserve most of the credit for making popular in modern culture the idea that the exploration and integration of unconscious material is a very important task, perhaps even the most important task any person can undertake.

THE GOAL OF PSYCHOTHERAPY

Interestingly, both Freud and Jung became interested in the unconscious through their role as physicians, whose goals are healing and the alleviation of suffering. Each of them realized that these goals could be served through greater conscious awareness of the unconscious, although Freud's model implied somewhat more modest goals than Jung's. Freud held that greater awareness of the contents of the personal unconscious might help one to adjust more comfortably to the demands of civilization, but that a certain degree of discontent was unavoidable. Jung believed that the exploration of the collective unconscious could reveal the purpose of one's life and bring one closer to a state of union with God. It is important to note that, in spite of a difference in the ultimate goal of psychotherapy, the exploration of unconscious process, particularly as manifested in the contents of dreams and fantasies, were considered to be central in its achievement.

THE LARGER IMPORTANCE OF PSYCHOTHERAPY

As noted above, psychotherapy is a new name for an ancient practice. Introspection in the broadest sense has ancient roots in practices such as contemplation, meditation, dream incubation and interpretation, fasting and other ascetic practices, prayer, religious ritual, music, ingestion of psychedelic plants, vision questing, sleep deprivation and the like, to facilitate it. The intentional use of any technique which facilitates introspection implies that introspection is in some way of value. Whether one limits that value to the alleviation of some psychological suffering, as Freud would, or sees the value as ultimate spiritual realization, as Jung would, there is no disagreement that there is value in the facilitation or enhancement of introspection.

One way to examine the value of introspection is to think about one's source of authority. In particular, the external versus internal locus of the source of authority is important to consider. If an external authority, such as parents, culture, or church, leads me to believe that I should feel guilty or fearful, then the alleviation of such guilt or fear may come about as a result of discovering a more powerful internal source of authority which contradicts this belief. Of course there can be no guarantee that one can contact a more powerful internal source of authority. Similarly, there is not guarantee that, once contacted, it will indeed counteract a belief previously instilled from an external source of authority. However, many examples of such a counteraction are part of the experience most psychotherapists.

Here is a personal example of the shift from an external to an internal source of authority. I was born in Utah and raised a Mormon. I left Utah in the first year of my life, and left the Mormon church in the second decade. The final chapter took place in my fourth decade, after having cultivated my sense of inner authority in therapy for 8 or 10 years, when I managed to get myself officially excommunicated. During the course of the trial which resulted in my excommunication, I was sternly admonished by some of the members of the jury that the price I was going to pay in the hereafter for having been cast out of the Mormon brotherhood would be high indeed. This invocation of the external authority of the belief system of the church produced a brief surge of terror in me--what if they were right? Realizing after a few moments that my great fear was the result of my having been abusively conditioned as a child by such frightening stories, my terror quickly converted to rage. Now paying more attention to my inner authority, I managed to suppress expression of both of these strong emotions and to continue with a fairly interesting dialogue with my jurors, and even got invited to offer a closing prayer when the trial came to an end. The most powerful experience of my inner authority came after I walked out of the church. When I got to the parking lot, and was quite separate from those who represented external authority of the church, I spontaneous and exuberantly began to leap into the air and shout for joy.

A more interesting question about internal versus external authority comes up when there are major philosophical or moral questions in need of answers. Questions about the purpose of one's life, the ultimate nature of reality, or what is intrinsically moral in response to a given situation, are examples of such questions. These are the types of questions that come up repeatedly during the course of one's life, and one is therefore well advised to have some ongoing way of introspecting deeply enough to be able to find answers as they are needed.

As example of the need for such answers was presented a few years ago by the publication of the book, Hitler's Willing Executioners (Goldhagen, 1996). It told of the thousands of German citizens, seemingly normal and decent human beings, who willingly went along with one of the most ghastly examples of genocide the world has seen. It is interesting to speculate about the response of a German bureaucrat to the news that he will no longer be managing the logistics of railroad cars filled with merchandise bound for market. Starting tomorrow his job will be the same with the minor exception of the cargo, which will now be human beings bound for torture and death. He goes home, has dinner with his family, helps his children with their homework, makes love with his wife, and goes back to work the next day to carry out his slightly revised duties. What is missing from this picture? I would suggest that introspection is missing. If this man had a habit of introspection, whether through prayer, meditation, contemplation, or psychotherapy, it is hard to imagine that he would go to work the next morning believing that his participation in genocide would not be in violation of some intrinsic moral principle. (For research supporting this rather broad generalization, see May, [1987].) Without such introspection, he is at the mercy of external authority, in this case the German state, which clearly reports to him no moral conflict in his compliance. In fact, quite the opposite is the case.

I am not suggested that a brief course of psychotherapy or meditation instruction would have stopped a German bureaucrat in his or her tracks in the weeks before genocide became the assignment of the day. The development of moral awareness that I am suggesting such introspective practices might have fostered would have to begin much earlier. The popular TV show, "The Sopranos," makes an attempt to examine what might happen when a person whose moral development has arrested at an early age is exposed to psychotherapy as a adult. The result is certainly not a rapid compensation for earlier deficiencies in such development. What I am suggesting is that a habit of introspection over the course of one entire life, or at least one's entire adult life, can make a difference.

At the most generic level it would seem that the capacity for introspection may be something like a muscle. With regular use it becomes flexible and strong and can be very helpful to its owner. Without regular use it atrophies and becomes useless. In the most extreme case of neglect of the inner life, one not only loses the capacity to introspect deeply; one also can lose the awareness that there even exists any significant internal territory to explore through introspection. Such a loss makes one extremely vulnerable to the Hitlers of the world, which in turn makes all of us vulnerable. Just as there is increasing evidence that regular mental activity can counteract the loss of cognitive capacity that often accompanies aging, so regular introspective activity could be expected to sustain the capacity to introspect.

Although the Hitlers of the world give a dramatic lesson about our vulnerability as a species if we lose sight of our internal resources, more mundane examples abound. The young retail clerk who cannot make the simplest of change without using the calculator built into the cash register has lost sight of an internal ability to calculate. The weatherman who tells us that tomorrow will be a miserable day because rain is predicted invites us to forget that we can decide for ourselves whether we enjoy rainy weather. The increasingly bizarre warning labels that come with electronic appliances, telling us to refrain from all sorts of things that would only be done by a person too handicapped to live outside an institution or a person committed to a painful suicide, invite us to ignore our common sense.

However, it is the ignoring of our internal resources regarding how to live a meaningful and a moral life that presents the greatest possibilities for individual and mass misery. A life without a conscious sense of meaning or purpose will generate a certain desperation of its own, which is in some way the manifestation of the unconscious as it tries to get one's attention regarding the failure to heed one's calling. However, if one's habits and culture do not generally support introspection under such circumstances, one is likely to express one's desperation in harmful ways. The situation is made worse by the absence of internal awareness of morality, leaving even greater room for destructive acting out of such desperation.

The use of introspection to discern an inner moral awareness is particularly under assault in much of the world today. Laws, regulations, ethics codes, religious creeds, mandatory sentencing, and other external constraints on behavior, are displacing our internal awareness of what is moral and what is not. As such external rules proliferate, they invite us to forget that we ever had any internal way of knowing such things in the first place--like the young clerk who scarcely is aware of having the capacity to make change without a cash register. Psychotherapy is one way to facilitate a reconnection with our inner moral compass.

This is not to say that external constraints on behavior are always negative. I am quite pleased to have external constraints when needed in the short to prevent injury and death to humans as well as other species. They may also raise awareness by calling to the public's attention certain problems that need to be addressed. However, in the long run such external constraints run the risk of displacing and weakening our internal constraints. These internal constraints seem to me to be our only long term hope. If we rely on some of us to wield the power to constrain others of us, who will constrain the some of us who are constraining the others? If power corrupts, where will those in power turn for the moral awareness that could prevent them from being corrupted? If I take a maintenance antibiotic to combat any infection that I might get, having the antibiotic doing the work my immune system should and could, how can I expect my immune system to remain robust or even reasonable competent?

ON THE TRIVIALIZATION OF PSYCHOTHERAPY

Given the significance noted above of reclaiming deep introspection through psychotherapy, it is noteworthy that psychotherapy itself is in some ways under attack at the present time. At the most superficial level this attack has to do with funding--i.e. payment for psychotherapy by private health insurance and public agencies. Although a statistical case can be made for the proposition that good psychotherapy pays for itself in increased productivity and reduced utilization of other general medical resources, there seems to be a trend toward the restriction of third party funding for psychotherapy. One theory frequently put forward to explain this strange trend is that it is simply a result of the greed and shortsightedness of the CEOs of managed care organizations. No doubt these factors play a role.

At a deeper level a more pernicious trend is emerging--the trivialization of psychotherapy. Those who find deep introspection to be personally threatening have always expressed their anxiety through deprecating references to psychotherapy as involving self-absorption, navel gazing, and mental masturbation. More recently the ways in which psychotherapy is trivialized have become more subtle and perhaps even auto-immune in nature. That is, even among those who describe themselves as psychotherapists there seem to be increasing numbers who see their work as little more than providing a mental tune-up so that the client can function more efficiently in his or her already prescribed role in society. At the core those who dismiss all introspection as nonsense, and those who see psychotherapy as merely intended to relieve symptoms, both seem to share a disregard for the importance of deep introspection and the human relationship in the conduct of psychotherapy.

If one assumes that the human relationship is important in psychotherapy, then the selection of a good psychotherapist for a particular person involves much more than finding one with certain academic or professional credentials. It involves some exploration of the inherent compatibility, or fit, between the two persons involved before a prediction can be made of the probable outcome of the psychotherapy. Such exploration is all but prohibited by most managed care arrangements. First the psychotherapist is usually referred to as a "provider of services," a term which seems to connote that the function is more important than the person. That might be true for a person who delivers a pizza to one's home, but it is most certainly not true for a person with whom one contemplates entering into a most intimate relationship. After getting past the insult of thinking of one's psychotherapist is a provider of services, one is told that it is necessary to select a psychotherapist from a preselected panel of candidates, a very small fraction of those who might otherwise be available. The members of this panel have usually been chosen on the basis of some minimal academic requirements and the willingness to work under adverse conditions. These adverse conditions include low pay and frequent violation of the privacy necessary for effective psychotherapy.

The trivialization of psychotherapy as a result of the conditions imposed by managed care is increasingly being matched by conditions imposed by the professional disciplines which provide formal training and credentials for most psychotherapists. Psychology is probably the discipline with the most noteworthy case of identification with the aggressor. It has actively promoted the "manualization" of psychotherapy. This term does not refer to conducting psychotherapy without the use of machinery; it refers to the notion that for any given condition, like depression, there is a single correct therapeutic approach to be taken. This approach can be described in a manual, and then any person who can read the manual and follow its instructions can perform the psychotherapy. While it may be true that anyone who can read a map and drive a car can deliver a pizza, it is certainly not that simple with psychotherapy. For psychology as a profession to pretend otherwise trivializes and demeans psychotherapy.

I was recently involved in an informal supervision session, in which a very mature and sophisticated psychotherapist presented a complicated clinical dilemma which had arisen in one of her psychotherapy groups. Several respected colleagues, all working within essentially the same theoretical framework, offered feedback. Although the underlying premises about the importance of such things as authenticity, integrity, and respect were the shared by all, the actual recommended actions to be taken diverged greatly. The woman presenting the case thoughtfully took in all these recommendations, asked for clarification or elaboration regarding some of them, and then formulated her next intervention for her group. She also commented that the diversity of opinion from highly respected colleagues was both disturbing and relieving, since it made clear that there is no single correct approach to any given clinical situation. Clearly this woman is not a candidate for getting involved in anything the looks like "manualization." On the other hand, she is someone to whom I would refer, without hesitation, a person I love.

The most recent example of the trivialization of psychotherapy in our culture has come in the form of legislatively mandated keeping of "Medical Records." In some instances legislation has been written in such a way as to include psychotherapists in general, and psychologists in particular, within its requirements. For psychotherapists to keep such records has at least two trivializing implications for psychotherapy. First is the implication that there would be some genuine utility in the keeping of such records. This assumes that a person could move from one psychotherapist to another, have his or her "Medical Records" transferred to the new psychotherapist, and pick up where he or she left off with the previous psychotherapist. This is a preposterous assumption when applied to as personal a relationship as is involved in psychotherapy. The second, and perhaps more chilling, implication of such record keeping is contained in the actual act of writing down for possible future disclosure to others, as yet unnamed, any meaningful part of what transpires in psychotherapy. It would be hard to imagine a mechanism more antithetical to the creation of the kind of trust and safety required for meaningful psychotherapy to take place.

WHAT IS TO BE DONE?

The problems arising from the trivialization of psychotherapy are the tip of the iceberg. The trivialization of introspection lies below it, with grave consequences for the Titanic of humanity if ignored. No amount of enforcement of current or future environmental laws have a chance of saving the earth in the long run unless a significant percentage of humans have a more immediate and personal experience of a deep connection to other humans in particular and to All Things in general. A similar statement could be made about the possibility that international treaties, tribunals, and organizations will save us from future wars or nuclear holocaust through their ability to impose external constraints on our behavior. As mentioned above, they may heighten our awareness of the problems we face, and they may helpful by starting meaningful dialogue between people who would otherwise be killing each other. However, if such dialogue does not ultimately lead to a greater appreciation of The Other, genocide will merely be postponed. Dialogue combined with introspection can provide the opportunity to genuinely experience "walking a mile in your enemy's moccasins," and this experience can in turn open us up to non-violent options for dealing with old hatreds and fears. Anything that facilitates the kind of introspection which can lead to such deeply meaningful experiences increases our chances of survival, not to mention peace of mind. Anything one can do to support the profound significance, as opposed to trivialization, of such a process should help. The first step probably has to be a reaffirmation of the importance of deep introspection in one's own life. Clearly psychotherapy is not the only way to do this, but it is a very good place to start.

References
Goldhagen, Daniel Jonah, Hitler's Willing Executioners: Ordinary Germans and The Holocaust, 1996, Alfred A. Knopf, New York, 640 pages.

May, Gerald G. Will and Spirit, 1987, Harper, San Francisco, 368 pages.

ADDENDUM
Since this paper was originally drafted, two things have occurred which call for additional comments. The first of these is the series of tragic events which took place on 9-11-01. The second is the response of the editor to the first draft. Among other things she notes that deep introspection might lead to the desire for violence, rather than the opposite, and that many good and moral people do not introspect and have never experienced psychotherapy.

In the weeks after September 11, like many others, I found myself very curious about the motivational dynamics of those who had been willing to kill so many others. What began to emerge for me was a picture of young men who had been completely cut off from meaningful interpersonal support for introspection since they were very young. This means not only the deprivation of anything as structured and formal as psychotherapy, but also the absence of any opportunity for more informal interpersonal exchanges having to do with introspection or subjective experiences other than those prescribed by family, friends, religion, and one's entire social milieu. In the extreme I imagined what it would have been like for one of those young men, in the months before September 11, to have raised doubts or misgivings about the plans they were making. A dream, a fantasy, or an emotion that had such implications would have to have been suppressed or repressed almost immediately. Certainly to allow oneself such experiences, and to open discussion about them with one's fellows, would have been to risk complete rejection as a minimum, and immediate death as a high probability.

At the opposite extreme would be the ancient mystical and meditative traditions of the world. What little I know of Buddhist and other such practices is that an enormous variety of powerful subjective experiences are expected when the seeker enters into the particular form of deep introspection associated with a given tradition. Vivid fantasies of unbridled sexuality and violence are common, but in the end give way to--or perhaps are part of-- experiences which ultimately develop deep compassion and equanimity in the seeker. Psychologically this process may be seen at least in part as a withdrawal of the projection of evil which, when projected, leads to the perception of "evil-doers" in external reality and the conviction that one's holy task is to slay them. The Vietnamese Buddhist monk Thich Nhat Hanh reports having been able to view the corpses of six young men he regarded as his sons, brutally murdered because of their opposition to the war in Vietnam, and still feel compassion for their killers.

Perhaps most people navigate a middle course, being somewhat introspective in a random or unconscious sort of way. Thanks to sleep researchers we know that everyone dreams, whether or not the dreams are available for conscious recall upon awakening. Similarly, everyone daydreams, although there appear to be enormous differences in the degree to which this experience is invited or suppressed. In any case, a certain degree of introspection seems to be inherent in the human condition. It is up to us to decide how much to nurture this tendency, as individuals and as a culture or society.


Dangers Inherent in the Trivialization of Psychotherapy

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Monday, November 28, 2011

The Top 6 Calculator Apps For the iPhone

!±8± The Top 6 Calculator Apps For the iPhone

Our recent article on the top 6 calculator apps for Android was a big hit, and since then we've been getting search inquiries about iOS. You asked for it, and we are delivering. We've searched out Apple's app store for our favorite 6 calculator apps for the iPhone and iPod touch. Since there was a wide disparity in cost of apps, we set the ground rule that we were searching for apps that cost less than . In fact, this list turned out to be our favorite 6 iPhone calculator apps for under .

#1 Graphing Calculator+ by xNeat.com

Graphing Calculator+ is our pick for the best all around iPhone calculator app. It greatest strength is that it does so many different things well. A switch button takes you easily between the calculators different modes. Those modes are graphing, scientific, handwriting, a polynomial calculator, and linear equations calculator. There's still room for improvement. In particular, we wish the scientific calculator had fractions, and that the grapher had trace. But the app is simple and powerful, and the fact that it automatically finds max, min, intercepts, and intersection points pretty much makes up for the lack of trace.

Pros: Handwriting support, graphing scientific, quadratic and cubic solver, systems of linear equations

Cons: Handwriting mode not always accurate, decimals only

Cost: .99

#2 Graphicus by Serafim Chekalkin

We are huge fans of Graphicus. If only every graphing calculator were this easy to use. No need to read the user manual here, just jump right in. Graphicus brings you almost all the information you could want about Cartesian, polar, and parametrics graphs in an incredibly elegant interface. Trace, extrema, inflection points, tangent lines are all readily available with a few taps of your finger. On the downside, there is no simple scientific calculator. It's also a minor bummer that there's no 3D in an app that's 100% focused on graphing, but there's only one app on this list that has 3D.

Pros: Offers everything graphical, intercepts, trace, inflection points, max/min, complete

Cons: Just a grapher

Cost: .99

#3 Symbolic Calculator by Janos Barkai

If you need a CAS for your iPhone, this is the app for you. For those who have used a TI-89, you'll feel right at home with with Symbolic Calculator. The focus of this app is it's computer algebra system, and the interface is pretty easy to use for those familiar with Texas Instrument's CAS calculators. If you're new to CAS's, just tap the question mark next to a given command, and an example will pop up demonstrating how to use the syntax appropriately. You can also use this app to graph, although it feels a little counter-intuitive until you get the hang of it, and the graphing features are simplistic compared to some of the other apps on this list.

Pros: For a CAS, simple to use, offers example input for each

Cons: Graphing could be nicer, mathprint only after inputting

Cost: $.99

#4 Graph It by Tezmo

Another excellent grapher is Graph It. This is also full featured grapher, which offers the ability to trace, find intercepts, and roots, as well as graph derivatives and integrals. It also offers a full scientific calculator with two-line display. The user interface is ok, but might take some getting used to for some users, particularly for the scientific calculator mode.

Pros: Full featured grapher, also a full scientific calculator

Cons: UI takes a little getting used to

Cost: $.99

#5 Quick graph by Columbiamug

For those in need of a 3D graphing app, Quick Graph is the way to go. There are other positives here too such as a strong user interface, simple to use polar coordinates,and a good 2D graphing interface. Screen caps are another built in feature. The real selling point, though, is the 3D, which is well rendered and even accepts cylindrical and spherical coordinates. It is possible to use this app as a scientific calculator, but the interface feels a little strange.

Pros: Polar and 3D, screen caps of graphs

Cons: No trace features, don't feel designed for non-graphing calculation

Cost: Free

#6 Powerone LE by Infinity Softworks

Not everyone is looking for a fancy grapher. For those looking for a more standard scientific calculator, Powerone LE fits the bill. It's got a very intuitive interface that you'll pick up right away. Powereone also features unit conversion and a currency converter that stays current to international currency exchange rates. Additionally, its got a simple statistics calculator that finds the mean of a series of numbers. It could be better if the scientific features used a two-line interface.

Pros: Easy to use, nice UI, currency/unit converter, stays current, simple statistical analysis

Cons: One line calculation, no graphing

Cost: Free with option to upgrade to more powerful version for .99


The Top 6 Calculator Apps For the iPhone

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Monday, November 21, 2011

Using a Scientific Calculator In Mathematics Exams

!±8± Using a Scientific Calculator In Mathematics Exams

With exams approaching this is a short article with reminders and advice for anyone about to take a mathematics exam and who will need to use a scientific calculator.The most common calculator problems are:

- setting up the calculator in the right mode

- not being able to find the calculator manual!

- remembering to change calculator modes

- rounding and inaccurate answers

Why Use a Scientific Calculator?

Scientific calculators all use the same order for carrying out mathematical operations. This order is not necessarily the same as just reading a calculation from left to right. The rules for carrying out mathematical calculations specify the priority and so the order in which a calculation should be done - scientific calculators follow the same order. This order is sometimes abbreviated by terms such as BODMAS and BIDMAS to help students remember the order of doing calculations.

1st. Brackets (all calculations within a bracket are done first)

2nd. Operations (eg squaring, cubing, square rooting, sin, cos, tan )

3rd. Division and Multiplication

4th. Addition and Subtraction

Being aware of this order is necessary in order to use a scientific calculator properly. This order should always be used in all mathematical calculations whether using a calculator or not.

Scientific Calculator Check

There are two types of scientific calculator, the most recent type being algebraic scientific calculators. Algebraic scientific calculators allow users to type in calculations in the order in which they have been written down. Older scientific calculators need users to press the mathematical operation key after they have entered the number.

For example to find the square root of nine (with an answer of three) press: [button]

Algebraic scientific calculator: [SQUARE ROOT] [9] [=]

Non algebraic scientific calculator: [9] [SQUARE ROOT] [=]

Both these types of scientific calculator are fine for exams, but make sure you know how to use your own type.

If you are not sure whether you have a scientific calculator or not, type in:

[4] [+] [3] [x] [2] [=]

If you get an answer of 14, then you have a left to right non-scientific calculator.

If you get an answer of 10, then you have a scientific calculator as it has worked out the multiplication part first.

Lost Calculator Manuals

Calculator manuals tend to get lost very easily or you can never find them as an exam is approaching. A frequent request is what can you do if you have lost your calculator's manual? If it is a relatively new model then you can download a copy from the manufacturer's web site. If it is an old Sharp or old Casio calculator manual then you can still find these on the internet. Even with search engines, finding these manuals can take some time - the following link has information about new and old calculator manuals for Casio, Sharp, Hewlett-Packard and Texas Instruments: here.

Calculator Mode

Now that you have your calculator manual you can set your calculator to the correct settings. The standard settings are usually:

COMPUTATIONAL:

(use MODE button - choose normal not stat) NOT: SD or REG

DEGREES:

(use MODE or DRG button) NOT: RAD OR GRAD

NORMAL:

(use MODE or SETUP and arrow keys) NOT: FIX, SCI, ENG

Many calculators have a reset button on the back that can be pressed in using a pen or paper clip if you want the original factory settings.

The most common mistake is to leave your calculator in a previous mode and FORGETTING TO CHANGE IT BACK AGAIN ! (We've all done it, just try to avoid doing it in the exam !)

Common Calculator Mistakes

(a) Pressing the DRG button by mistake and not doing trigonometry questions in DEGREES mode. (If you are doing more advanced work then forgetting to change out of DEGREES mode !).

(b) Borrowing an unfamiliar calculator or getting a new calculator too close to the exam and not being familiar with the keys and how to change modes.

(c) Forgetting to write down and check work. Any exam with a calculator should have a warning on it! It is essential to write down the calculations that you're doing so that you can get method marks. You should also try and double check all calculations in case of pressing a wrong button.

(d) Rounding before the end of a calculation. Store calculations in the memory and use all the decimal places during calculations. If you use a rounded value too soon then you will lose accuracy.

(e) Forgetting to use brackets on division calculations (e.g. when dividing by ALL the bottom part of fraction).

Many calculators are now very powerful and have amazing computational power. Some of the programmable calculators are mini computers. Although they will all calculate 100% accurately every time, unfortunately they are only as good and as accurate as their operator!

It is often the case that candidates perform better without a calculator as it is very easy to make simple mistakes when using one. If you can do so, it certainly helps to have an idea of the rough size of the answer, so that you can see if an answer is sensible or not. It is also a good idea to repeat all calculations just in case you have made a key press error.


Using a Scientific Calculator In Mathematics Exams

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