I don’t think it’s that people can’t get that without pencil and paper; it’s that they can’t get it without doing what Daniel Kahneman called “System 2 Thinking,” as explained in his book Thinking, Fast and Slow.
That was a great book, by the way, and I highly recommend it.
Perhaps. Now we are getting into pedagogy, but having read Kahneman I wonder if that isn’t the result of abandoning math drills in education. It’s repetition that moves thinking from system 2 to system 1.
My memory of grade school math was that we did a LOT of drills. We had to memorize multiplication tables up to 12 X 12, and we did that by getting thousands of drill questions. It was really common to go into math class and fjnd out that we were getting a snap drill and had to answer 100 simple math problems. If we were getting drilled on the multiplication tables, the test had a time scale that prevented you from actually calculating the result on paper. “There are 100 simple multiplication problems to answer. You have ten minutes”
We also had basic addition and subtraction drills, long after kids could do it on paper. The purpose was simply to make such simple arithmetic automatic.
I imagine kids still get tests on these subjects, but nothing like,the constant drills we used to get. As I recall we also,had flash card tests where we would be flashed an equation and had to write down the answer. The cards came fast and furious, and if you couldn’t do the problem quickly in your head you had to abandon it when the next card came up.
These constant drills were a big part of elementary arithmetic back in the day. By grade four almost every kid could answer instantly if you asked, “What’s 12 X 7?” or almost instantly answer, “what’s 172 - 36?”. And I’ll bet you those people could still do it today.
Having a basic table like that committed to system 1 makes further math easier and faster, and allows your brain to think about the new concepts without having to waste brain power with basic multiplication. I feel sorry for kids who weren’t taught that way and can’t do basic arithmetic without a pencil and paper, or at all.
Absolutely. He has a lot of other great books as well.
I tend to think you need both, when it comes to mental math. Up to some amount of digits you should be able to do fairly basic mental arithmetic and even have some results just memorized. The rest is understanding how to set up the equation, and if you’ve done that right then let the calculator do the hard work. If I know that the concentration of something is x/y, and I have y amount, there’s no value in trying to mentally calculate the product of 3.27 and 1473 or whatever. What matters is that if that’s in mg/mL, I don’t then report that my 1.473 L of solution contains 4,816 grams of material or something.
Well, you are both right. If you make that error in a casual read, that is normal, and not a issue. But if you make that error after studying it closely, that’s pretty bad.
Heh, the other week, a carpenter mentioned to me that he heard about slide rules, thought they sounded cool, and wanted to learn more about them. (btw I have no idea where you would go today to buy a slide rule that is 1. new 2. good)
Don’t know about “new,” but eBay is full of pretty good looking used slide rules, of all types.
Amazon has quite a few slide rules for sale:
I don’t know if you’d consider this “good” due to legibility, but wristwatches designed for pilots often have a circular slide rule built into the bezel.
Franklin Reck’s book The Dilworth Story mentions a BIG slide rule Mr. Dilworth had : “A fabulous spiral 105-inch job that carried logarithms to seven decimal places.”
You don’t, if you mean the classic ‘slipsticks’. There are “new”, good slide rules that are basically unused ones that have been in boxes for decades, though.
There are hardly any actual slide rules there. Most are rules (or ‘rulers’). The actual slide rules listed are the circular ones for navigation.
Oh yeah? What about these slide rules?
https://www.amazon.com/Complies-Reflective-Resistant-Sigo-Signs/dp/B093TS3SMP/ref=sr_1_15?dchild=1&keywords=slide+rule&qid=1627419155&sr=8-15
I sit corrected
Apparently it is both an entrance and an exit exam…
Truly weird if that is what it is.
From:
In California, you must take the CBEST if :
• You are applying for a CTC approved teacher preparation/credential program
• You are applying to be a day to day substitute
• You are applying for a first teaching credential
As I understand it,
bullet one is to enter a training program for teachers (presumably a 4 year program).
bullet 3 is for applying for a credential to be a teacher.
Being required to pass the same test before and after a 4 year college program doesn’t say much for the college…
Or am I missing something?
It sounds to me like it’s technically a requirement to become a teacher, but programs use it as a “filter” instead: since the skills on it aren’t really taught by the program, there’s no reason to let someone into the program who can’t pass it, only to have them fail it at the end.
So the failure rate doesn’t tell you much about those who actually become teachers, any more than the LSAT tells you about lawyers.
That makes sense to me, and is the impression I get, too.
Calling it a “certification exam” may give the impression that passing the exam certifies you to be a teacher, which (IIUC) is not how it works: passing the exam is just one of the requirements for being certified as a teacher.
It sounds like it does certify you to be a sub.
Honestly, as a teacher, I wish subs didn’t have to have college degrees. I’d love a test like this instead. I need a sub to be reliable and conscientious, not a content expert. The college degree requirements means we get people with college degrees willing to work part time erratic jobs with no benefits for less than $100/day. This is not a great pool!
Without the specifics of your post, in many countries teacher unions are politically powerful. There are often strong efforts not to measure teaching performance. Which is silly since good teachers require a certain level of competence, which should not be overwhelmingly difficult to achieve in most cases. Of course, the best teachers have a lot more skills than competence.
Thanks.
This makes a lot of sense.
The issue isn’t the quality of the teacher or the education of the teacher, it is simply poor labeling.
CBEST is a basic test anyone in the education field, or anyone interested in the education field should be able to pass. It isn’t the certification test tp be a teacher. I don’t know what testing is required to become a teacher in California, but hopefully it is more than CBEST. Talking about CBEST as a certification test (as my quoted description did), is a disservice to the public and to the education field.
Frankly, after all these years, I wonder if this mistake is deliberate. Throw up a straw man like this so that everyone can focus on this issue to complain about and then at the critical moment of the debate explain that there is a simple misunderstanding and lets move on. The tactic isn’t unheard of in many fields.
There is a separate problem, I which I mentioned above, that tests of this nature are known to be racially and culturally biased. Some people, even though they can do the arithmetic (and understand the words), are going to be effectively just giving random answers to some of the questions.
I think that there is broad agreement in the industry that such people are failed by the education system, but the solutions aren’t ‘sustained practice and study’.