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IntMath Newsletter: Good math teachers, writeLaTeX, TIMSS

By Murray Bourne, 30 Jul 2013

30 Jul 2013

In this Newsletter:

1. What makes a good math teacher?
2. Resource: WriteLaTeX
3. TIMSS summary
4. Math puzzles
5. Friday math movies
6. Final thought: Procrastination

1. What makes a good math teacher?

As part of my job as a teacher trainer, I observe a lot of classes. Some teachers have obviously got what it takes, and some have a way to go in honing their skills.

In Defining Teaching Effectiveness, Maryellen Weimar lists several qualities a teacher should develop in order to be effective. She consolidates research findings from several studies, and concludes a good teacher is one who:

  • Motivates students to learn by making the subject interesting;
  • Is knowledgeable;
  • Presents the material clearly;
  • Is approachable and helpful;
  • Is available to students;
  • Is intellectually challenging;
  • Cultivates thinking skills;
  • Sets high standards; and 
  • Encourages self-initiated learning. 

It's a good list, but I feel it is missing a few crucial elements.

  1. While the list includes "approachable", that's not the same as the rapport a good teacher needs to have with students. Rapport is the 2-way relationship that ensures students and teachers feel connected to each other and to the learning task. The social context in which learning takes place has a big impact on learning effectiveness. I've walked into too many classrooms where the teacher doesn't even greet the students as they arrive, or even make eye contact.
  2. Good observation skills are vital for good teaching. A teacher needs to be able to spot body language (confusion, tiredness, boredom) and make appropriate adjustments to the lesson.

What are your thoughts, either as a student or a math teacher? What do you think makes a good math teacher? Please leave your responses here.

2. Review: writeLaTeX

writeLaTeX collaborative online math editor

writeLaTeX is an online tool which allows you to create math documents collaboratively. But it's best if you know LaTeX syntax first.

Review: write LaTeX

3. TIMSS summary

writeLaTeX collaborative online math editor

TIMSS is the Trends in International Mathematics and Science Study that is conducted every 4 years, and involves 4th and 8th grade students.

The 2011 Mathematics Report (free PDFs) makes for interesting reading. Sixty three countries took part in the TIMSS in 2011, and as usual, East Asia scored well:

Singapore, Korea, and Hong Kong SAR, followed by Chinese Taipei and Japan, were the top-performing countries in TIMSS 2011 at the fourth grade. Similarly, at the eighth grade, Korea, Singapore, and Chinese Taipei outperformed all countries, followed by Hong Kong SAR and Japan. [Source]

(Mainland China and India do not, as yet, participate in TIMSS.)

Governments are more likely to enter their country in these international comparisons if they believe their students will go well (or they are trying to spur their country on to greater heights), and this study does not cover all countries, so the comparisons may not be all that meaningful.

Also, it is well known that the Confucian approach to education as adopted in Asian countries (learn for the exam - don't worry too much about meaning or application) means they tend to be very skilled in exam technique.

The report has chapters comparing the key matters influencing success in math, under the headings:

  • Home Environment
  • Support for Mathematics Achievement
  • School Resources for Teaching Mathematics
  • School Climate
  • Teacher Preparation
  • Classroom Instruction

In Singapore, for example, each of the above 6 aspects is in a healthy state. Parents here worry endlessly about how well their children are performing (even taking time off near major exams to give extra tuition to their kids), and there is considerable investment by the government in education (14% of expenditure is on education).

TIMSS gives us some good insights into possible ways of improving mathematics education outcomes.

normal curve

Related reading:

You may be interested in my Math Tests and Rice Paddies which talks about some of the possible reasons why Asians tend to do well in math.

4. Math puzzles

The puzzle in the 4 July IntMath Newsletter challenged you to find a particular integer involving squares.

The correct answer with explanation was given by: Infinity, Alan, Devanie, Francis & Sai Krishna.

New math puzzle

A design team is testing a new car for its fuel efficiency at different speeds. They start at 40 km/h and reduce the speed by 2 km/h every hour for an integral number of hours. If they had maintained the original rate, the journey would have taken 2 h 45 min less. What was the distance travelled?

Leave your responses here.

5. Friday math movies

Fermat's Last Theorem

(a) Fermat's Last Theorem

Here's a great story involving an intriguing proof that spans 350 years. It's a PBS documentary.

Friday math movie: Fermat's Last Theorem

How math guides ships at sea

(b) How does math guide our ships at sea?

Here's an important use of mathematics in the real world - navigation at sea. We learn about dead reckoning, sextants, clocks and new mathematics.

Friday math movie: How does math guide our ships at sea?

7. Final thought: Procrastination

Now that I'm a freelance consultant, I have more control over how I use my time. I get to the end of the day and think about what I've achieved (usually the interesting stuff), and notice the large pile of things (the tedious or otherwise boring stuff) that will have to wait until tomorrow. I then remember these immortal words:

The next time you feel the urge to procrastinate - just put it off. [John D. Rockefeller]

Until next time, enjoy whatever you learn.

See the 12 Comments below.

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


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