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**Raissa Octaviani Gunawan (2nd Winner)**

Now this is Albert Einstein’s quote, “Try not to become a man of success. Rather become a man of value.”

What do you think his quote trying to tell us?

From my point of view,.. For example: “A wealthiest man with higher education in mathematics, or better yet to become a man of heart and a true hero.”

Share your opinion…

]]> Bud Blake’s **Tiger** (September 11, rerun) mentions Tiger as studying the times tables and points out the difference between studying a thing and learning it.

Marc Anderson’s **Andertoons** (September 12) belongs to that vein of humor about using technology words to explain stuff to kids. I admit I’m vague enough on the concept of mashups that I can accept that it might be a way of explaining addition, but it feels like it might also be a way of describing multiplication or for that matter the composition of functions. I suppose the kids would be drawn as older in those cases, though.

Bill Amend’s **FoxTrot** (September 13, rerun) does a word problem joke, but it does have the nice beat in the penultimate panel of Paige running a sanity check and telling at a glance that “two dollars” can’t possibly be the right answer. Sanity checks are nice things to have; they don’t guarantee against making mistakes, but they at least provide some protection against the easiest mistakes, and having some idea of what an answer could plausibly be might help in working out the answer. For example, if Paige had absolutely no idea how to set up equations for this problem, she could reason that the apple and the orange have to cost something from 1 to 29 cents, and could try out prices until finding something that satisfies both requirements. This is an exhausting method, but it would eventually work, too, and sometimes “working eventually” is better than “working cleverly”.

Bill Schorr’s **The Grizzwells** (September 13) starts out by playing on the fact that “yard” has multiple meanings; it also circles around one of those things that distinguishes word problems from normal mathematics. A word problem, by convention, normally contains exactly the information needed to solve what’s being asked — there’s neither useless information included nor necessary information omitted, except if the question-writer has made a mistake. In a real world application, figuring out what you need, and what you don’t need, is part of the work, possibly the most important part of the work. So to answer how many feet are in a yard, Gunther (the bear) is right to ask more questions about how big the yard is, as a start.

Steve Kelley and Jeff Parker’s **Dustin** (September 14) is about one of the applications for mental arithmetic that people find awfully practical: counting the number of food calories that you eat. Ed’s point about it being convenient to have food servings be nice round numbers, as they’re easier to work with, is a pretty good one, and it’s already kind of accounted for in food labelling: it’s permitted (in the United States) to round off calorie counts to the nearest ten or so, on the rather sure grounds that if you are counting calories you’d rather add 70 to the daily total than 68 or 73. Don’t read the comments thread, which includes the usual whining about the Common Core and the wild idea that mental arithmetic might be well done by working out a calculation that’s close to the one you want but easier to do and then refining it to get the accuracy you need.

Mac and Bill King’s **Magic In A Minute** kids activity panel (September 14) presents a magic trick that depends on a bit of mental arithmetic. It’s a nice stunt, although it is certainly going to require kids to practice things because, besides dividing numbers by 4, it also requires adding 6, and that’s an annoying number to deal with. There’s also a nice little high school algebra problem to be done in explaining why the trick works.

Bill Watterson’s **Calvin and Hobbes** (September 15, rerun) includes one of Hobbes’s brilliant explanations of how arithmetic works, and if I haven’t wasted the time spent memorizing the strips where Calvin tries to do arithmetic homework then Hobbes follows up tomorrow with imaginary numbers. Can’t wait.

Jef Mallet’s **Frazz** (September 15) expresses skepticism about a projection being made for the year 2040. Extrapolations and interpolations are a big part of numerical mathematics and there’s fair grounds to be skeptical: even having a model of whatever your phenomenon is that accurately matches past data isn’t a guarantee that there isn’t some important factor that’s been trivial so far but will become important and will make the reality very different from the calculations. But that hardly makes extrapolations useless: for one, the fact that there might be something unknown which becomes important is hardly a guarantee that there is. If the modelling is good and the reasoning sound, what *else* are you supposed to use for a plan? And of course you should watch for evidence that the model and the reality aren’t too very different as time goes on.

Gary Wise and Lance Aldrich’s **Real Life Adventures** (September 15) describes mathematics as “insufferable and enigmatic”, which is a shame, as mathematics hasn’t said anything nasty about *them,* now has it?

As I mentioned in that post, we were going to switch math curriculum to what I consider a softer math that involves story telling (my daughter loves to read).

Here is what I’m noticing since the switch:

1. When asked what subject she wants to do next, my daughter will often say math as her choice. Previously, math was always the last subject mentioned.

2. My daughter shows me (proudly) that she knows how to solve the problems. Prior to the switch, she would whine or cry and tell me she didn’t know what to do.

3. She is learning about other subjects, in addition to math. For example, in her math book the other day she learned the difference between evergreen and deciduous trees and the difference between herbivores and carnivores.

4. She is getting practice reading. Since this math book is story based, she enjoys reading out loud (and laughing at the storyline).

5. She is being shown how kindergarten math concepts are related to algebra.

6. There are significantly less tears and whining, in general, throughout the school day.

Please note this is not a knock against the previous curriculum. I still believe it is an excellent curriculum and will probably revisit it with my daughter at a later time. However, what I’m learning on this homeschooling journey is that it is not one curriculum fits all. Just because your child doesn’t do well with a particular curriculum, but others rave about, doesn’t mean that your child is less intelligent than theirs. It just means that that curriculum doesn’t work for *you*, and you have to find out what does work.

YES to no more tears (…at least math tears)!!!

]]>

In light of my last post (‘On the Nature of Morality’) I thought it fitting to present an alternative argument for the origin of our morality, this one with a very different approach to goodness than the first.

We need to establish what goodness is in order to create any reasonable system of morality, if we cannot do this then the system is not based on reason as such. We can begin with the observation that some acts are seen as intuitively wrong (e.g. murder, theft, lying), not always for the sake of anything else, simply because we see these things as wrong.

But what is wrong? And for that matter what is good? A satisfactory substitution for the idea of goodness is *something that stimulates positive sensations upon the moral faculties*. This is how we know that some acts are inherently wrong or right. Some acts are moral, some are not. So some acts stimulate the moral faculties, some do not. There must be a distinction between these, some quality that some acts possess but others do not.

All things appear to have a cause even if this is not strictly speaking the right way to look at the world. So all things in reality can be related to a cause even if it is not a *true cause*. We can postulate goodness and badness as real entities in themselves that lie within some actions. This is what causes the stimulation of the moral faculties (the stimulation *must *have what can be identifiable as a ‘cause’). These are known as *Moral Carriers*.

It makes more sense for all these Moral Carriers to have the same origin since they cause similar stimulation of the moral faculties. Whatever is the source of goodness is which has infinite potential (if all morals acts contain good then we could in theory have an unlimited number of them – hence we need a large source of goodness). It is therefore reasonable to postulate the existence of infinite goodness.

Such a source of goodness cannot have a spatial existence since it lies outside of the sensual realm. We could never hope to place infinite goodness somewhere since this would be completely illogical. Therefore the nature of this goodness must also be divinely simple hence goodness cannot consist of quanta. Therefore the only way goodness can be present in the sensual reality is if infinite goodness is reflected dimly in certain acts in our realm. There are certain intensities of this reflection and this is why some acts are more moral than others and some are more striking to us.

The reason goodness must be innate therefore is that we cannot comprehend that which has achieved infinite extension. Moral goodness is a reflection of infinite goodness. This has achieved infinite extension. Just as we cannot explain the infinite, we cannot explain a reflection of it. We must just *know* what moral acts are.

We discussed that the radius of the spool would decrease every time a layer of wire was used. They began calculating the resulting wire as layers were removed. This served as an excellent opportunity to introduce summation notation and a great practical use for the mathematics behind it. It seemed like a much better option than to add up dozens of calculations anyway.

When we arrived at our correct answer (with the desired units) of 1.98 miles, the questions and estimating didn’t end. They wanted to know how far they could stretch such a wire. Would it go to the edge of our campus and back? Would it go from here to the middle school? Could you go all the way to the grocery store?

They settled on taking the wire, running it out to the edge of the soccer practice fields and then running it all the way to the middle school sign. It ended up being, to the hundredth, the exact amount of wire we had, provided that someone would stand and hold the wire at the edge of the soccer field. I loved the attention to precision. I also loved that they were so savvy with Google Earth.

]]>

One statement I have been hearing lately is along these lines, “Austrians are not against all math, just SOME math” or, “Austrians are not against math, just mathematical predictions” etc etc. I find these claims to be rather telling of the person arguing on behalf of the Austrian position. These statements tell me right away they do not even know or understand the methodological position of their own school of thought. On their view, these 5 quotes need to be interpreted as only being against some math and/or mathematical predictions. Here are the relevant quotations:

“The only economic problems that matter, defy any mathematical approach” – Ludwig Von Mises

“Now, the mathematical economist does not contribute anything to the elucidation of the market process” – Ludwig Von Mises

“The equations formulated by mathematical economics remain a useless piece of mental gymnastics and would remain so even if they were to express much more than they really do” – Ludwig Von Mises

(These next two are my favorite)

“The mathematical method must be rejected not only on the account of its bareness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile: they divert the mind from the study of real problems and distort the relations between various phenomena” – Ludwig Von Mises

“Mathematics cannot and does not enter into measuring ideas or values that determine human action. There are no constants in these. There is no equality in market transactions. Therefore, mathematics does not apply. The use of mathematics requires constants. Mathematics cannot be used in economic theory” – Percy L. Greaves.

All of these quotes can be found in various articles on mises.org.

I am truly baffled as to how someone claiming to be an adherent of the Austrian School could read these, or any Austrian literature, and conclude that Austrians are only against the use of ** some** math. I have read a lot of Austrian literature, and I personally have never read anything that would support that claim. Of course, quotations cannot be “proof” of anything, but I do think they provide rather strong evidence in favor of my argument. Moreover, the Percy Greaves quotation is in response to the question, “is economics completely divorced from mathematics?” Clearly, from his response he thinks it is.

Another statement I hear from Austrians is that Neo-Classicals do not give them any mathematical propositions they should accept. This seems to be a rather silly statement, and in many ways, entirely meaningless. Austrians should accept all mathematical propositions that are true, from 1 + 1 = 2 to the propositions in set theory or algebraic topology etc.

However, to get specific I would like to point out two mathematical fields that have vast applications in economics. First is game theory. Game theory is a branch of mathematics first developed by Emile Borel, and then popularized by the works of Von Neumann, Morgenstern, Nash etc. There is a plethora of economic questions game theory answers. One example of such a question is – how do oligopolies decide on how much to produce given the production of the other firms? Game theory provides the answer to this question.

Second, is functional analysis. In general, functional analysis is the study of infinite dimensional vector spaces. This field answers the question – how can a copper mining company extract Q tons of copper from a mine over T years and maximize its profit? To find this function is one thing, and to prove it is the maximum of all functions is another. I would like to ask an Austrian how to solve this problem without the use of mathematics? In my view, it simply cannot be done.

Mathematics is vitally important to the study of economics, and to denounce it the way influential Austrian scholars have is exactly why I am not an Austrian economist.

- Jacob Westman

AUGUSTA – Maine’s Education Commissioner is asking the public and a panel of parents, educators and business leaders to inform improvements his Department plans to make to the state’s learning standards for mathematics and English language arts.

Maine Department of Education Commissioner Jim Rier announced today that a 24-member panel will begin work this week to assess the rigor and clarity of the standards.

Learning standards set what students should know and be able to do at each grade level.

In Maine, standards in eight content areas make up the Maine Learning Results, adopted in 1997. While the standards are established for all public schools by the Maine DOE with approval by the Legislature and the Governor, how educators support students in achieving them is a local decision.

Since 1997, there have been four updates to the Maine Learning Results, most recently in 2011 to the standards for math and English language arts.

Commissioner Rier hopes the Department’s review will focus attention on the specific standards and how to improve them, drawing on the experience of their implementation in Maine’s classrooms over the past three years.

“All Mainers want high standards for our students and know they are capable of meeting them,” Rier explained. “There is now greater awareness about our standards than ever before. This transparent review and eventual rulemaking process provides an opportunity to leverage that interest and bring Maine people together to ensure our state’s standards are the best they can be at preparing all of our students for college and career success.”

The panel will be comprised of parents, teachers, principals, superintendents, school board members, college professors and business leaders. Its work is public and members of the public are also invited to submit input to improve specific standards through an online comment form on the Maine DOE’s website.

The Maine Learning Standards Review Panel will hold its first meeting on Tuesday, Sept. 16 from 9 a.m. to 2:30 p.m. That meeting will largely focus on defining the review process.

Content-specific subgroups will then each hold four subsequent weekly meetings before a meeting of the full panel on Oct. 24. to finalize their recommendations. All meetings will be held at the Cross Office Building at 111 Sewall St. in Augusta.

The Commissioner will consider the input of the panel and public and plans to initiate a formal rulemaking process that would additionally allow for public comment. The changes would also require public hearings before the Department and the Legislature, which would have final approval authority.

Maine students would still be assessed on the current standards this spring for State and federal school accountability.

To submit public input or for more information about the Maine Learning Standards Review Panel including its members, meeting schedule and the standards it will review, visit www.maine.gov/doe/standardsreview.

-END-

]]>It is easy to recognize literacy activities happening throughout a young child’s day. We see them looking at books, drawing pictures, and using “kid writing” to write menus and stories. Yet, math concepts are sometimes not as easy to discern. The children are, in fact, practicing and experimenting with mathematical ideas and processes all of the time. Seeing patterns and connections are two of the most important supporting skills in math. Luckily, children naturally sort, classify, and connect everything in their world.

In basic terms, a pattern is a predictable, repetitive occurrence. We usually think of patterns in very concrete terms, such as in a repeating color set. Red, blue, red, blue is a basic pattern structure. However, the term pattern can be more broadly applied when we think of the patterns of less traditional things. A daily schedule that is typically similar is a pattern. Our diurnal lifestyle is a pattern. The types of food our families eat at different times of day can also be a pattern. When you decide to have pancakes for dinner, an American child can quickly pick up that it is a “special” or unusual choice. Our species thrives and operates on patterns. Though we will spend time on the more traditional ABA and ABBA patterns in our classroom, every moment of their lives our children are practicing the concept.

]]>We need PROPER vocational skills taught in schools alongside core subjects. Help the less academic gain vocational skills whilst still having the opportunity to study mainstream academic subjects.

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