Posted in Humor

Things you learn in math education forums

You always get good ideas from forums (or fora), whatever form they are. If you want great insights about math and science education, try attending a PhD forum or seminar. I’ve just been to one. Following are some of the things I learned from the spirited discussion during the question and answer portion from these serious educators.

  1. We complain that our learners are not doing well in their Maths especially in secondary schools. These students are now engineers, doctors, lawyers, and politicians. We trust them anyway (except the politicians).
  2. It is only in math that 1+1 = 2. In real-life, it doesn’t work that way. For example, when two churches combine, you get 3 – the new one and the two old ones. This also applies to political parties.

    number theory
    number theory
  3. On the question of the relevance of your PhD to science education. Short answer by the speaker: I am now relevant to the science education. They now have one learned participant in the science education discourse.
  4. Why do we always expect the teachers to know all their Maths? Answer: It is probably because of our experience of our teachers in first grade as all-knowing. We believe everything teacher say and it was important for us then to have believe them. I think we need to grow up.
  5. Tell me, “Do you know of a mathematician who know all their mathematics?” Why should a math teacher know all their math? This is not fair to teachers. Do you complain in the media when a doctor misdiagnose your illness?math teachers
  6. “My conclusion in my review of literature why, despite the extent of research about teaching and learning algebra we still have not solved the difficulty of learning it, is that because algebra is a moving target.”
  7. “I initially thought to explore the reasons of students absenteeism in lectures. But then I thought, why should they when they can find great lectures in the net. Now I do not know how to proceed from here. Will anybody suggest a research question that’s not in the net?”
  8. “In my interview with teachers, most of them said that they don’t really know why students are not getting the test. When they teach them, they seem to understand everything they are discussing and solving. My interview with students confirms this. The students said that they understand everything during the lectures but they couldn’t answer the same questions and problems in the test.”
Posted in Humor

The Learning Pyramid

I attended a lecture today on how to help Year 12’s pass their examinations. One of the slides that captured my attention was the Learning Pyramid. It says that the information retained by our learners is a function of the kind of learning experiences we provide. The percentage shows what is left in the brain after 2-3 weeks. It is very important that teachers take these to heart especially when designing instruction. As you can see in the pyramid, lectures or teacher talk has the least retention rate. I don’t know why most teachers still prefer it, really.

I searched the net for source of this Learning Pyramid. Everyone seemed to be sourcing it to the National Training Laboratories, Bethel, Maine. However, I did make my own original contribution to the learning pyramid – a learning task that has 100% retention rate. Mine is not based on empirical research but from my own experience. This is the reason I blog. And I highly recommend this as a method of teaching and delaying the onset of dementia.

Why Blog

Learning experience vs retention rate

You may also want to know another pyramid – Bloom’s Taxonomy for iPads.

Posted in Humor

Christmas GeoGebra Applet

candlesHere’s wishing you the choicest blessings of the season. The applet was adapted from the work of Wengler published in GeoGebra Tube. Being an incurable math teacher and blogger I can’t help not to turn this unsuspecting christmas geogebra applet into a mathematical task.

Observe the candles.

1. When is the next candle lighted?

2. On the same coordinate axes, sketch the time vs height graph of each of the four candles?

3. What kind of function does each graph represents?  Write the equation of each function?

3. If the candles burns at the rate of 2 cm per second and all the candles are completely burned after 20 seconds, what is the height of each candle? (Note: These are fast burning candles 🙂 )

[iframe https://math4teaching.com/wp-content/uploads/2012/12/PEACE.html 650 700]

Posted in Humor

Definitions of Commonly Used Words in Math Lectures

It’s time to review some terms you hear in math lectures. If you are not doing well in math, it’s probably because of miscommunications and not for any other reason.

BRIEFLY: I’m running out of time, so I’ll just write and talk faster.

BRUTE FORCE: Four special cases, three counting arguments, two long inductions, and a partridge in a pair tree.

BY A PREVIOUS THEOREM: I don’t remember how it goes (come to think of it, I’m not really sure we did this at all), but if I stated it right, then the rest of this follows.

CANONICAL FORM: 4 out of 5 mathematicians surveyed recommended this as the final form for the answer.

CHECK FOR YOURSELF: This is the boring part of the proof, so you can do it on your own time.

CLEARLY: I don’t want to write down all the in-between steps.

ELEGANT PROOF: Requires no previous knowledge of the subject, and is less than ten lines long.

FINALLY: Only ten more steps to go…

HINT: The hardest of several possible ways to do a proof.

IT IS WELL KNOWN: See “Mathematische Zeitschrift”, vol XXXVI, 1892.

LET’S TALK THROUGH IT: I don’t want to write it on the board because I’ll make a mistake.

OBVIOUSLY: I hope you weren’t sleeping when we discussed this earlier, because I refuse to repeat it.

ONE MAY SHOW: One did, his name was Gauss.

PROCEED FORMALLY: Manipulate symbols by the rules without any hint of their true meaning.

PROOF OMITTED: Trust me, it’s true.

Q.E.D. : T.G.I.F.

QUANTIFY: I can’t find anything wrong with your proof except that it won’t work if x is 0.

RECALL: I shouldn’t have to tell you this, but for those of you who erase your memory after every test, here it is again.

SIMILARLY: At least one line of the proof of this case is the same as before.

SKETCH OF A PROOF: I couldn’t verify the details, so I’ll break it down into parts I couldn’t prove.

SOFT PROOF: One third less filling (of the page) than your regular proof, but it requires two extra years of course work just to understand the terms.

THE FOLLOWING ARE EQUIVALENT: If I say this it means that, and if I say that it means the other thing, and if I say the other thing…

TRIVIAL: If I have to show you how to do this, you’re in the wrong class.

TWO LINE PROOF: I’ll leave out everything but the conclusion.

WITHOUT LOSS OF GENERALITY (WLOG): I’m not about to do all the possible cases, so I’ll do one and let you figure out the rest.

Please use the comment form to share your own commonly used words in your math lectures.

Source: