Posts Tagged ‘STEM’

Why Study Math?

Dear Reader,

Do you ever notice that no one asks this? We might ask why about some of the higher maths like trig and calculus but we don’t ask why study math at all like we might for art or music or even history. It’s kind of a pet peeve of mine that the STEM subjects, as they call them, (STEM stands for Science, Technology, Engineering and Math) are so emphasized while others are neglected. But we never ask why we study math at all. It’s always good to consider these things though and in the section for this week’s Charlotte Mason Blog Carnival, Charlotte invites us to do just that.

Charlotte is arguing, as she often does, against certain ideas prevalent in her day. The big one here seems to be that studying math with train certain faculties in the child’s mind, will cause them to exist even. Charlotte, believing as she does in the personhood of each child, rejects the idea that we produce any such faculties in our students. She believes that the powers of logic and reasoning which they need are already in them. Nor does she seem to believe that these powers need to be trained particularly by us. She questions also whether the logical training of mathematics actually carries over to any other area of life (an idea which has also been floated in our own day).

So why study math? The answer, to Charlotte, is because of its own inherent beauty:

“We take strong ground when we appeal to the beauty and truth of Mathematics; that, as Ruskin points out, two and two make four and cannot conceivably make five, is an inevitable law. It is a great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence,––that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter, should give to children the sense of limitation which is wholesome for all of us, and inspire that sursum corda which we should hear in all natural law.” (pp. 230-31)

In our own day, I think we have lost this idea. We do really emphasize math (along with the other STEM subjects) but our goal is just to get ahead of other countries. We don’t study math for its own sake nor do we talk about its beauty or how it shows us the constancy and absoluteness of its laws. Charlotte discusses math under the heading “Knowledge of the Universe” which it is but knowledge of our universe has its greatest value in that it points us to the Creator of the Universe and tells us something of His character. This, then, is the true value of math and the best reason for studying it.

One final note, while math is important, Charlotte cautions us against letting it become too important. It is, she says, very easy to test and this fact tends to make it assume greater proportions than it should have:

“But education should be a science of proportion, and any one subject that assumes undue importance does so at the expense of other subjects which a child’s mind should deal with. Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.” (p. 231)

This again is a warning that we need to hear.

Charlotte sums it all up very well:

“To sum up, Mathematics are a necessary part of every man’s education; they must be taught by those who know; but they may not engross the time and attention of the scholar in such wise as to shut out any of the score of ‘subjects,’ a knowledge of which is his natural right.” (p. 233)


Fostering Creativity

Dear Reader,

Scott Kaufman’s book, Ungifted: Intelligence Redefined, which I finished reading recently has inspired me with a lot of new thoughts. I have already given my review of the book and talked about motivating learning. Now I want to talk about fostering creativity.

The first question we must ask is why? Why is creativity important? It is certainly not something most public schools manage very well. Of course, such things are not easy with so many children that one must move through the system. Being different or doing things differently is not very welcome when one must juggle the needs of 20 or more children. As Kaufman says:

“Everyone has unique needs and is worthy of encouragement. In the real world, people clearly  differ in their inclinations, passions, dreams and goals . . .

Not so in school. In this particular microcosm of reality, you aren’t supposed to be different.” (Kindle loc 218; no page number given)

But there has been some evidence that what we need is creativity. The emphasis lately seems to be on keeping ahead of the world in the sciences. While personally I am not sure this should be our sole aim, fostering creative thinking can also help us in this area. New discoveries and inventions happen when someone thinks in a way no one has before. We need what is called “divergent thinking” and to get produce it we need to encourage children to think of alternative ways of doing things. In his book Free to Learn, Peter Gray goes so far as to say that this sort of thought is not only not promoted in the schools but actually suppressed:

” . . . most students learn to avoid thinking critically about their schoolwork. They learn that their job in school it to get high marks on tests and that critical thinking interferes. To get a good grade, you need to figure out what the teacher wants you to say and then say it.” (Free to Learn, p. 79)

A different sort of environment is needed if we really want to maintain our edge. We need to stop focusing on standardized tests and on getting the information we choose into kids. Instead, we need to allow them time and space to play with ideas and to explore multiple ways of doing things. A creative, playful atmosphere leads naturally to a scientific mindset:

” . . . whenever children or adults bring imagination and creativity into their efforts toward discovery, they are combining play and exploration. In adults, we call that science.” (Free to Learn, p. 123)

There is apparently a kind of IQ test called the Torrance test which measures creativity and divergent thinking. It will, for example, give a picture and ask the test-taker to give as many possible explanations for the situation they see as possible or to ask as many questions about it as they can think of. What these tests show is that creativity has “significantly decreased, with the decline between kindergarten and third grade being the most significant” (Ungifted, p. 280). It seems notable to me that the time span when creativity declines is just that time when we begin to limit children’s play, when we begin to demand that they focus on what we care about and their free time becomes greatly reduced. Now I know that as people age they naturally play less, but I have also seen that homeschooled children seem to play more and to remain playful till much later ages than their traditionally schooled peers. So clearly if given the time and opportunity, children will remain children, with all their natural playfulness, for much longer.

And this play doesn’t just foster creativity; it also helps develop well-rounded individuals who can see beyond their own point of view (I know many adults who could really use this ability!):

“Psychologists have also become increasingly aware of the importance of pretend play as a vital component to the normal cognitive and social development of children . . . The important concept of ‘theory of mind,’ an awareness that one’s thoughts may differ from those of other persons and that there are a variety of perspectives of which each of us is capable, is also closely related to imaginative play.” (Ungifted, p. 138)

Play contributes to flexible thinking. It also is associated with flexibility in other areas. Torrance, the developer of the creativity test mentioned above, came up with a list of characteristics which he believes contribute to divergent thinking. They include: “love of work, sense of mission, deep thinking, tolerance of mistakes, well-roundedness, and feeling comfortable as a minority of one” (p. 282).

Apart from just allowing children more time to play, is there anything we can do to foster creativity? Kaufman says yes. Rather than moving them quickly from one task to another, we need to allow them time to process and reflect:

” . . . imposing high attention demands on children may rob them of the chance for important reflection that can allow them to make personal meaning out of the material and reflect upon the social and emotional implications of that knowledge.” (p. 254)

Even daydreaming, which on first glance seems to detract from the time spent learning, serves a purpose and can help children develop appropriately:

“… if we want to facilitate future compassion, future planning, self-regulation, and divergent thinking, we should set up conditions that allow for mind wandering.” (p. 256)

We tend to think, even as homeschoolers who have supposedly opted out of the system, that what we do as teachers is what matters most. But Kaufman spends some time talking about how much more we learn implicitly than we learn from explicit instruction. I think we tend to feel the pressing nature of our goal and the short time we have in which to accomplish it and so the tendency is to try to cram in as much as we can. But this can often be counterproductive. We need instead to make time for play, daydreaming, and allowing the child to follow their interests and to explore different ways of doing things. So I will end with one more quote from Ungifted:

“This is due in large part to the original purpose of intelligence testing: to develop a test that predicts the ability to learn from explicit instruction. But once we take into account personal goals in addition to the goals of others . . .we see the adaptive value of a wider range of spontaneous cognitive processes such as daydreaming, pretend play, spontaneous creative generation, implicit learning, and intuition.” (p. 304)


Learning History

Dear Reader,

The Charlotte Mason Blog Carnival is working its way through her sixth volume, Towards a Philosophy of Education. This coming week’s chapter is on history. It is significant that the title of this section is “The Knowledge of Man: History.” Even in the title we get a clue as to why Charlotte believes history is so important. When we study history, we study human beings. We learn (if we are doing it correctly) how they have acted and why. And through them we learn about ourselves. And hopefully this is knowledge that we can apply practically to the problems of our own day. Charlotte says,

“To us in particular who are living in one of the great epochs of history it is necessary to know something of what has gone before in order to think justly of what is occurring to-day.” (p. 169)

The how of history in Charlotte’s method is pretty simple, read living books and narrate. She says that her schools can cover much more ground in this way, doing away with time-consuming and dry lectures. Each reading is done only once; the student is required to pay attention the first time or he will miss it. Of course, if the material were very boring, the pupil would probably not mind this. But the idea is that history should be fascinating, if only the right books are chosen, and that the child will naturally pay attention:

“. . . . the concentration at which most teachers aim is an innate provision for education and is not the result of training or effort.” (p. 171)

The attitude of the teacher is important here. If we assume that the material will be boring or that the student is incapable of attending, then we will likely reap what we sow.

Following the reading, the child narrates. This is not memorization. We are not to require specific facts of them. If things are going as they ought, the child should have envisioned the story as they read or heard it:

“Trusting to mind memory we visualise the scene, are convinced by the arguments, take pleasure in the turn the sentences and frame our own upon them; in that particular passage or chapter has been received us and become a part of us just as literally as was yesterday’s dinner; nay, more so, for yesterday’s dinner is of little account tomorrow; but several months, perhaps hence, we shall be able to narrate the passage we had, so to say, consumed and grown upon with all the vividness, detail and accuracy of the first telling. All powers of the mind which we call faculties have brought into play in dealing with the intellectual matter thus afforded; so we may not ask questions to help the child to reason, paint fancy pictures to help him to imagine, draw out moral lessons to quicken his conscience. These things take place as involuntarily as processes of digestion.” (pp. 173-74)

We must really need quality books to produce such a reaction. A textbook is not going to cause children to see and feel what they read. Note that Charlotte says we are not to ask questions. The important thing is that the child takes away what they will; the details we deem vital may not be what catches their attention.

Charlotte also mentions the use of a Book of Centuries. This is a way for students to make some record of what they have learned, a kind of timeline and journal combined. For more on that, I recommend this excellent post from Higher Up and Further In.

It does not sound to me like the children in Charlotte’s school were reading a lot of history. She speaks of 50 pages a term which even in a fairly short-term does not sound like much to me. It also does not sound like they go over the same material multiple times. Instead, they progress through English history as they grow with sections on other times and cultures added in at various points. She does stress the need to study more than one’s own land. Since she was British, English history is the core of her students’ learning, but she mentions also French , ancient and Indian history.

It is an interesting question how we Americans should apply this. To study the history of our own country is, of course, necessary. But our history is so short. We have used Heritage History this year which approaches the Middle Ages by looking specifically at Britain. This has worked well and been interesting for our family. It has certainly helped me understand how some  ideas important to our own society came to be.

It is sad to me to think that the study of history is being undervalued today. There is a lot of emphasis on science and math with the assumption that these are what our country needs to stay ahead of the world. It is not that Charlotte did not teach science, but it seems to have played a back seat in her system to history. And I think it says something about what we value that we talk little about history and  a lot about science and technology (they even get a clever acronym: the STEM subjects). Our modern goal is to get or stay ahead. This is materialistic and competitive. It is also very much focused on tangible, mechanistic things. But in Charlotte’s conception, history is the focus because it tells us about who we are as people. It is not about getting ahead but about being better. And I tend to think that being ahead means nothing if we are not better.