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 Math videos

A 21st century skill: reading and writing codes

In Should We Do Away with Calculation, Conrad Wolfram says that if you want to know if students understands a computational procedure, ask them to do a program, let them code it.Here is another video which calls students to learn coding. The video titled What Schools Don’t Teach featuring Bill Gates, Mark Zuckerburg, and other software developer giants speaking, urges kids to learn how to write codes. Reading and writing codes should now indeed be part of our curriculum. And for the arts inclined? Well to borrow from WordPress: ‘Code is poetry’.

What schools don’t teach video promotes code.org, a nonprofit foundation created to help computer programming education grow.

To drive the point, see the graph below from code.org.

computer programming

Posted in Algebra

Math knowledge for teaching fractions and decimals

No one can teach mathematics without knowing mathematics but not everyone who knows mathematics can teach it well. Below are two tasks about teaching fractions and decimals that would give us a sense of the kind of mathematical knowledge we teachers need to know apart from knowledge of the content of mathematics. As teachers it is expected of us to have knowledge of students difficulties and misconceptions in specific domains of mathematics. We are also expected to know the different representations or models of concepts to design an effective instruction. The two tasks were used in a study about mathematical knowledge for teaching of pre-service teachers.

Task 1

You are teaching in 7th grade. You want to work on multiplication of fractions, using the following numbers:

a) 10 x 3        b) 10 x 3/4          c. 10 x 1 1/5         d. 10/11 x 1 1/5

  • Create a problem using an everyday context, accessible to students and easily visualized, that uses the repeated addition sense for multiplication;
  • Prepare an illustration that works and that you could use for all numbers to help students visualize the operation;
  • Show, for each case, with the illustration and specific explanations, how one can make sense of c) from the answer obtained in a).
Task 2
Arrange the following numbers from the least to the greatest:
           2.46        2.254        2.3       2.052          2.32
Many of your students have written:
2.052     2.3         2.32        2.46     2.254
An others have written:                    
2.052     2.254     2.32        2.46        2.3
Complete the following steps:
  1. Describe and make sense of the error(s) committed by students;
  2. Find a similar task in which the students’ reasoning would lead to the same error, confirming their strategy;
  3. Find a similar task in which the students’ reasoning would lead to a right answer;
  4. How would you intervene in these difficulties
This is the third in the series of posts on mathematical knowledge for teaching. The first is about Tangents to Curves and the second one is about Counting Cubes.
You may use the comment section below to answer the questions or share your thoughts about mathematics teaching.  I hope you find time to discuss this with your co-teachers.