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When I was taking courses in the engineering curriculum in the 50's, there was always one question asked in advance of every exam: "Do you accept slide-rule accuracy?"
Anybody here know what a slide rule is?
I know what one is but don't know how to use them. I remember when my mom went to nursing school after we were all in school and used one.
Just checked the kids' grades online. DS15 had a "Group Test" with and without a calculator. They got 15/15 withOUT the calculator and 13/15 WITH the calculator .
Cylindrical or circular? In a tiny bit of irony (to me anyway and if I recall correctly) it was developed shortly after Napier's logarithm. I don't have extensive experience with it, but I did have a friend in high school who was a whiz with it.
Fast-forward to today, and they teach "Lattice Multiplication" which is a spin-off of Napier's Bones. Therein lies my irony.
Either way, I'm pretty sure my kids will continue to have no clue (other than a vague reference to one that some nerdy cartoon character uses).
They'll have no interest either as it's not "electronic" enough.
Such is the generational shift - hard to accept I suppose, but the truth nonetheless.
I had a professor so good at using a slide rule that he didn't have to use it. He just had to look at it and he'd say "That's about 987.6543 J" before any of us could punch it in on a calculator and he'd be right every single time. He was a great professor.
I did learn how to use a slide rule in high school but calculators came out right after that and I've forgotten enough that I can't read one with any degree of accuracy. If you want a ballpark figure I can do it.
I applaud those schools that really use calculators as tools and not crutches but sadly it's not practiced nationwide. I also suspect it's misused more than used correctly.
When I was taking courses in the engineering curriculum in the 50's, there was always one question asked in advance of every exam: "Do you accept slide-rule accuracy?"
Anybody here know what a slide rule is?
I know, and I had one in college for chemistry class. What really is the difference between using a slide rule and using a calcualtor? You still have to know what numbers do put in.
I'm also familiar with the old time adding machines, also the abacus.
There is the key. Do you know that there are kids graduating HS that have never used graph paper and have no idea what it is for ?
They can show you the graph on a scientific calculator but cannot do the same "by hand". They do not know how to solve and graph an equation but they do know how to plug in numbers and hit a button.
Technology is improving grades which is not the same thing as improving education.
When was the last time someone needed to make a graph by hand for their job?
Excel is the tool most people turn to (or Sigmaplot for scientists). I teach my students both software applications but they make graphs by hand once just to be sure they know how. Than never again.
This is another reason that I became a math teacher. All through school, I couldn't explain that there just weren't any steps for many of my problems. I copied them neatly and then wrote the answer for most of the problems that I did. I understood what I was doing, but there weren't any "steps"--it was intuitive. It wasn't until I studied the calculus in college that anyone explained to me that there is a lot of math that is intuitive. Anyone who ever tried to follow an inductive proof past the point where it said, "It is obvious that..." knows that sometimes intuition saves you, and sometimes it doesn't.
I told my students that they had to show the work when the objective was to learn a new method. Otherwise, they were fine to just write the answer as long as they could explain it. I gave no partial credit if they got the answers wrong if I couldn't see where their error lay. Most students needed to show their work, but the option was there for those who could just look and know.
I think that teachers need to clarify what they want their students to achieve--a right answer, or the right answer according to a particular technique. When I came upon a teacher who was absolutely intractable, I would show my work using methods that they hadn't taught, just to entertain myself.
Although I use a lot of technology in my class, the time I spent in computer science taught me that it is very undependable. My father's math books from the 1950s had a lot of mental math that I wish were taught to students today. I find that I can usually do simple calculations more quickly by regrouping numbers in my head than trying to find a calculator.
That's what I did today when I was teaching binary notation--a little lagniappe that I threw in before we went to lunch. Is that even being taught anywhere? It's not at my school, nor has it been taught there for quite some time. It was a topic in my senior Advanced Math class. We had no AP or pre-cal or trig, just Algebra I, Geometry, Algebra II, and Advanced Math. I learned enough to go straight into Calculus I in college, and no, I didn't do my homework or show my work unless I needed to in order to solve the problems. (I did show my work in calculus just because it was so aesthetically appealing!)
Totally disagree.
Part of science is the ability to communicate your findings in a way that others can follow your work. If you do not show your work than it makes peer review that much harder.
Part of science is the ability to communicate your findings in a way that others can follow your work. If you do not show your work than it makes peer review that much harder.
Is it really that different in math?
I don't really know. When I left the science community back in the early 80s to go into education, I discovered that all the bemoaning of the quality of education majors was based in fact. There were only one or two teacher candidates in my classes who had a clue. My math methods professor often told us anecdotes about her elementary education majors that made me cringe.
In my thinking at the time, math was a tool and not the end in itself. As long as the work was accurate, and the student had mastered the technique that I was teaching, I saw no reason to write steps just for the sake of writing them. As far as communicating the findings to the teacher, that was based on the fact that I knew my students. They did have to show their work when they were learning a new technique. Very few of my students could work problems without going through steps, but I was teaching the students who had been expelled or who had failed all through school and been socially promoted. It wasn't really an issue. If I had ever taught any advanced classes, I may have rethought my practices.
As it was, the alternative grouped students by grade rather than subject, so it was more of a learning-center style tutorial group where each student had an individual plan of work. As there were usually only 4-8 students in a class, I had a good grasp of each one's strengths and weaknesses. I had some students who could go through two or three chapters of algebra in a week and make 100% on their tests. Others didn't even know their math facts, so I had to develop plans to help them master basic skills.
Once I began teaching pre-algebra at the regular high school, I was working with students who really didn't know how to do more than add whole numbers. Most of them were in the juvenile justice system and had little to no engagement in school, so the class was often their last stop before they dropped out or were sent on to aforementioned alternative school. I haven't taught math since then. In the intervening years, graphing calculators have become the basis for the courses that I taught, and I've never learned how to use one. If I had to teach math now, it's the first thing I would have to do. I don't even know if they show the work for you to write down.
Now that I'll be eligible to retire at the end of this year, I think the likelihood of my teaching math again is remote. But you never know!
I know what one is but don't know how to use them. I remember when my mom went to nursing school after we were all in school and used one.
For those of you who have never seen a slide rule.
A logarithm is a mathematical function such that you can multiply two numbers by adding their logarithms. So a slide rule is like two rulers, on which you can add the logarithmic values of two numbers, and where two numbers coincide, is the logarithmic value of the product of the two numbers.
Take two ordinary rulers, and place one so that the end of one is on the "2" of the other. Then, the 6 of one will be on the 8 of the other. So 8 is the sum of 2+6. But the graduated marks on the rulers progress according to the logarithms of the numbers, so the adding of 2 and the 6 will line up at the mark for 12, the product of 2x6.
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