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 Teaching mathematics

George Polya’s Ten Commandments for Teachers

 

1. Be interested in your subject.

2. Know your subject.

3. Know about the ways of learning: The best way to learn anything is to discover it by yourself.

4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place.

5. Give them not only information, but “know-how”, attitudes of mind, the habit of methodical work.

teaching math

Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving

6. Let them learn guessing.

7. Let them learn proving.

8. Look out for such features of the problem at hand as may be useful in solving the problems to come – try to disclose the general pattern that lies behind the present concrete situation.

9. Do not give away your whole secret at once—let the students guess before you tell it—let them find out by themselves as much as feasible.

10. Suggest it, do not force it down your throats.

I got this from the plenary talk of Bernard Hodgson titled Whither the mathematics/didactics interconnection? at ICME 12, Korea, where he highlighted the important contribution of George Polya in making stronger the interconnection between mathematics and didactics and between mathematicians and mathematics educators.

If it’s too hard to commit the 10 commandments to memory then just remember the two rules below which is also from Polya. Combine it with Four Freedoms in the Classroom and you are all set.

George Polya on teaching math

How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)

Posted in Math blogs

Math Teachers at Play blog carnival #50 – submission

Hello  bloggers and teachers. This blog is hosting the 50th edition of Math Teachers at Play (MTAP) blog carnival this 18th of May 2012. Promote your favorite posts/articles by submitting the links using the MATP submission form before the 18th.

  1. Do you have a game, activity, or anecdote about teaching math to young students? Please share!
  2. What is your favorite math club games, numerical investigations, or contest-preparation tips?
  3. Have you found a clever explanation for math concepts and procedures? E.g. how to teach bisecting an angle, or what is wrong with distributing the square in the expression (a + b)^2.
  4. How do you make an upper-level (high school) math topics come alive?
  5. What is your favorite problem? (I hope not the students:-))
  6. What kind of math do you do, just for the fun of it?

Click here to see past editions of MTAP Carnivals.

Don’t be shy — share your insights! If you do not have a blog, just send your ideas and short articles at mathforteaching@gmail.com. I’ll find a way to publish it in the carnival.

The last math blog carnival I hosted was Math and Multimedia Carnival #17.

Posted in Curriculum Reform

Enduring understanding

To know the big picture ideas, to know the enduring understanding students are supposed to learn are indeed very important in planning and teaching a lesson. However, for teachers to be able to identify and articulate the enduring understanding for a particular content topic requires knowledge of the following:

  1. knowledge of the nature of the discipline;
  2. a deep content knowledge;
  3. knowledge of the connections among the different content topics
  4. some knowledge about the connection of your discipline with other discipline or subject area;
  5. knowledge of the relevance of your discipline to real-life

All these should already be partly articulated and reflected in the standards or curriculum framework to serve as guide to teachers when they design their lesson plans. If the curriculum framework is just a list of topics or some general statements then that’s bad news.

One can argue of course that teachers are expected to already know all these (the 5 items I listed above) and hence know the enduring understanding in their discipline. But the reality in this part of the world is that majority of our teachers still need more help in these aspects. This is my reason why we have to have a curriculum framework or Standards that supports the demands of articulating the enduring understanding expected in each unit before asking teachers to plan their “ubdized” (got this term from one reader of this blog) lesson.

Textbooks, which market themselves as “UbD-based”, or “UbD-compliant” should also be required to state the big ideas for the entire course and for each chapter or unit. Statements of enduring understanding and essential questions can also precede each chapter. Teachers can just add their own or state it in their own way when they make the lesson plans. It is not spoon-feeding the teachers. We just want them to have something to start with especially if the textbooks are their only resource.

Textbooks authors are supposed to have a clear big picture idea of what they are trying to teach in the textbooks and so why not require them to put it there. They have no business writing one if they don’t know the enduring understanding that students are supposed to learn. With all these in place, teachers will have more time to plan and design the lessons targeting these big picture ideas. They will also have more time to study their students’ difficulties and misconceptions about the topic and think of ways of addressing them. Most importantly, teachers will have more time to study the topic they are going to teach and how this content topic relates with previously learned concepts and future concept so they can find the right activity/ task and use appropriate assessment process. These are what can make or unmake a lesson, not whether or not the teachers use the backward or forward design in lesson planning.

This is my fifth post about this topic. Click here to link you to my other posts on UbD and backward design.

PS1. Having identified the enduring/essential understanding does not guarantee you’re going to have a good lesson plan or a good lesson implementation.

PS2. In one of the centennial lectures, part of the activities of the University of the Philippines centennial celebration, the speaker for education-related issues said that no one in this country is paying attention to learning. Indeed. We talk about lesson planning, we talk about curriculum frameworks and syllabus, we talk about multiple intelligences, …. we talk about essential understanding … we talk about everything except how pupils learn specific content topics.