Category: Uncategorized

Is it OK for our children to use textbooks with a copyright of 1999?

Written Nov 18


I agree with John Taylor Gatto (A Different Kind of Teacher, 2001), that textbooks are generally not very effective:

I came to see that the school edition wasn’t a real book at all but a disguised indoctrination. The book had been rendered teacher-proof and student-proof.


However, there are cases (such as Mathematics) where a textbook is important. I homeschool our daughter, and I purchased Mathematics; A Human Endeavor, by Harold Jacobs. I have the second edition, copyrighted 1982. I have reviewed many textbooks and options for studying math, and believe this provides an outstanding overview. Since the fundamental ideas of math do not change (at least at this level), there is no need for constant updates. In some cases, the classic is the best.

In other cases, particularly when information is changing rapidly (such as the sciences and technology), recent updates are important. However, don’t get carried away with the idea that newest is best. Often the better idea is to read some of the source documentation, and also to explore alternate viewpoints.


How can I learn mathematics in YouTube?

Written Oct 12, 2016

YouTube is only a medium. Other media include lectures (oral/visual), books, etc.

If you want to learn math on YouTube, you would need to find videos that convey the information you are trying to learn, in the format that makes it easy for you to understand.

There are many videos about math on YouTube. However (just like with any way of teaching, including books), there are good and bad ones. How can you decide which videos are the right ones for you? For example, Vi Hart has a lot of great videos about math, but I don’t think you would learn math from her videos.

If you want to learn basic math (through high school), I believe Khan Academy is a good place to start. After that, I would look at some university level courses such as Math and Logic Courses | Coursera, or MIT Free Online Course Materials.

p.s. Thinking about this further, I realized that Jo Boaler (Stanford University) has a great TED Talk on YouTube. Jo has some great ideas about learning math which you can review at her website: Inspiring Students to Math Success and a Growth Mindset


What is the right way to study History?

Written Oct 5, 2016

Well … that depends on what you are really asking.

If you are asking how to study History for a test, then the answer is to find out what you are expected to know; what you are expected to understand; and what are the criteria for passing. Therefore, you should ensure that you have a clear understanding of what the teacher expects. Once you know that, you can formulate a study plan – take notes, answer practice questions, etc.

If you are asking the more general question about studying History as a means of understanding our past, then there are various approaches:

  • Start with an overview of world history
    • Textbook
    • Videos on Youtube
    • Coursera (or other MOOC)
  • Focus on a large theme, or civilization. For example:
    • Greek or Roman Civilization
    • China
    • Ottoman Empire
    • US History

As you learn more about aspects of history, you can continue your studies. You can read, or watch videos or lectures. You can also start studying original sources. For example, you could read books written in the period of interest. Perhaps you could visit areas of interest (such as the Roman Forum, or Herculaneum).

How would you design an “ideal” school?

Written Oct 2, 2016

Perhaps the ideal school is … not a school!

What is the purpose of a school? If it is to teach the skills required to survive in society, most kids seem to be able to learn much of that themselves. (This is the approach advocated by John Holt (educator), proponent of unschooling).

Perhaps the ideal school is … a tutor

Benjamin Bloom wrote a paper about different types of learning and their efficacy . In this paper, he was exploring methods which approached the effectiveness of one-to-one tutoring. In other words, the gold standard of teaching is .. tutoring.

Or perhaps the ideal school is … a mix of options

Benjamin Bloom was searching for an alternative to tutoring because he believed that one-to-one tutoring was too expensive for society to implement. However, the internet has given us the means to cheaply implement tutoring – every student can watch videos or participate in online learning (think Khan Academy) at any time. The teacher can then become a mentor, coach, guide, or even a tutor. (Flipped classroom)

Or perhaps the ideal school is … the Sudbury school

In the Sudbury School model, the students are basically in charge of their education. They get to deliberate on the curriculum and administration of the school. They are active participants in their own education. Essentially, this model is “unschooling” in a school setting.

My ideal school is … the freedom to choose my ideal school!

Does time slow down during math class?

Written Sep 30, 2016

Humans are not aware (by design) of the dark planet which occupies an eccentric orbit between Earth and Mars.


We have followed your development for many of your years, particularly in the field of mathematics (the language of our universe), and also the other sciences – especially physics.

We were pleased to note the progress in Mathematics made by the Babylonians, Greeks, Egyptians and others. Our discussions with al-Khwarizmi helped speed the development and understanding of algebra. However, we were somewhat disturbed by the tendencies shown by Newton and Liebniz, as the capabilities they developed indicated the likelihood of our discovery. And that rascal Einstein was particularly troublesome. Fortunately, our introduction of discussions regarding string theory (and particularly multiple dimensions) has served to obfuscate your understanding.

Our leaders therefore determined to further confuse and hinder our earthly brothers and sisters efforts to use mathematics to understand the universe around them. Our weapon, which has been extremely successful, we referred to as “New Math”.


Unfortunately, the portal we chose, a blue box (within what you refer to as “Great Britain”), was detected. Fortunately, the public relations campaign we initiated to mask the real intentions of the portal was successful beyond our wildest dreams – the Tardis is now regarded as a fictional prop.

The concept behind New Math was simple – a virus was implanted in the minds of mathematics teachers. When New Math is taught to students, the virus is replicated within the students. An unanticipated side effect of the New Math virus is that, while attempting to learn the principles of mathematics, the perception of time is retarded.

As a result of the overwhelming success of the New Math virus, our leaders have authorized the deployment of a new weapon – “Common Core Standards”.

What are the pros and cons of project based learning?

Written Sep 22, 2016

Learning RetentionPBL employs Active Teaming Strategies


  • Project-Based Learning involves “discussion”, “doing” , and “Immediate Use”, all of which have demonstrated high rates of retention.
  • PBL has a significant body of research demonstrating its effectiveness as a learning method. (See Jo Boaler’s work at Inspiring Students to Math Success and a Growth Mindset as an example).


  • Takes more effort to properly set up PBL lessons.

Why do parents decide not to send their children to pre-school?

Written Sep 15, 2016

I recently recommended to close friends that they only send their child to pre-school (or kindergarten) if they are sure that no attempts will be made to formally educate their child. I also suggested that if they decide to send their daughter, they should select one that emphasizes play, and hands-on activities (such as Montessori).


Why did I do this?


This is a brief review of the relevant research evidence which overwhelmingly supports a later start to formal education. This evidence relates to the contribution of playful experiences to children’s development as learners, and the consequences of starting formal learning at the age of four to five years of age

There are several strands of evidence which all point towards the importance of play in young children’s development, and the value of an extended period of playful learning before the start of formal schooling. School starting age: the evidence

It is unusual for any researcher to describe research results as overwhelming.

Therefore, the first (recommended) decision is to delay formal learning. The second (recommended) decision is maximize opportunities for playful learning.