Tuesday, September 26, 2006

Helping girls learn Mathematics

Lately, I came across a few commentaries on this important topic in the popular media. I have also received a summary of a research project through my thesis supervisor. Naturally, as a teacher at a girls' school, I am very interested.

Just slug it out like the boys: The first serious attempt at tackling the issue brings us to an excellent Simpsons episode - girls just want to have sums! I always take the Simpsons seriously, and they seem to really care about education. If you know the episode, you can skip the next two paragraphs.

In this episode, Principal Skinner lets fly that he thinks girls are more likely to struggle with maths and science. He gets booed and, eventually, fired. The new principal, a feminist, divides the campus into two, so the boys do not drown out the girls with their loud voices.

In the girls' half of the campus, a different sort of maths is taught. One which is unlike that of men - something to be worked out and attacked. Instead, maths becomes something that engages the senses. Lisa gets fed up and disguises herself as a boy so she can learn "real math" . When she wins the school award for maths, she reveals herself to prove that girls are just as good as boys, but Bart declares: "The only reason Lisa won is because she learned to think like a boy! I turned her into a burping, farting, bullying math machine!"

The episode seems to ridicule the view that maths is defined in a way that has suited males over the ages. Maths is what it is, and everyone needs to learn it in the same way. I am very interested in your reading of this episode, as mine is not particularly thought out!

Encourage the parents to enrol them in British single-sex schools! An article in Melbourne's Herald Sun reports that girls who graduate from British single-sex schools earn 10% more than those who graduate from mixed schools. This was put down to the fact that they were more likely to take subjects such as Physics. I am really skeptical about such research as it compares means and masks a lot of important data such as whether the comparison was made between equally endowed schools.

Teachers should vary their instruction and assessment methods: The Australian Association of Mathematics Teachers put out a "national statement on girls and mathematics" in 1990. In it, they suggest that teachers value certain modes of learning which appeal more to girls. Teachers should "make more extensive use of discussion methods, small group collaborative work and open-ended investigations". Assessment should "include projects, presentations, essays" etc...

I use these things (apart from essays) in my practice, however I have observed that boys tended to dominate group work and presentations when on a teaching round at a mixed school. There is no denying that I have seen my students' eyes light up whenever we have done something creative, involving the use of colours and patterns.

Teachers should use cues which make students concentrate on their strengths rather than gender: My thesis supervisor sent an email to his research group with a blurb from an American dude called "Richard Morin [Pew Research Center]". In it, he points out that research has shown that "women score much lower on math tests if they are first asked unrelated questions about gender issues. The phenomenon is known as 'stereotype threat'". This has led two other dudes, Matthew S. McGlone of Texas Uni and Joshua Aronson of New York University to conduct an interesting experiment.

They surveyed 90 college students, half of each gender. A third of them were asked why they chose to study at a private liberal arts college. "The goal was [to] nudge these young women and men into thinking how smart and accomplished they were." This group exhibited the least variance on a visual-spatial ability test which they took immediately after the survey.

You make up your mind. I will appreciate any input from readers on this topic.


Technorati tags: Teaching Mathematics

Thursday, September 21, 2006

This rectangle is a square

Earlier this year, my nephew visited from overseas with his Maths holiday homework. He was on summer holidays between years 8 and 9. This is one of the questions I can translate:

Show that a rectangle ABCD, such that AB=√125 and BC=3√45 - 2√20 is a square.

You could post your answer in the comments field or try it with your students and post their answers instead.


Technorati tags:

Solution to the make up four puzzle

A virtual star to Mr. B. on solving the puzzle. Remember, the idea is to move only one stick to make the equation correct:

Starting postions: | + || + ||| = 4
Solution: | + | + | + | = 4
(move one of || to make a "+" with the middle stick in |||)

I have made a little Flash animation to demonstrate it, but I can't figure out how to upload this to Blogger. If you know, please advise.


Saturday, September 16, 2006

Make up four: a puzzle

A colleague gave me this puzzle yesterday. It is very cool.

Rearrange the sticks on the left hand side of the equal sign, so the sum does equal 4.

| + || + ||| = 4

Note: The plus signs are also made up of sticks.

Post your answers in the comments field.

Technorati tags: Technorati tags:

Merit-based pay and formative assessment

Several reports have been released of late telling the government to lift the financial status of teachers if the shortage -both current and looming- of Maths, Science, and LOTE teachers is to be solved. The past two federal ministers of education, Brendan Nelson and Julie Bishop, have responded to such reports by asking their state counterparts to implement a merit-based pay scale for teachers.

Teacher unions are usually opposed to such ideas. They argue that good measures for teacher effectiveness are lacking and that such moves would be divisive as they would promote competition in the staff room.

The Education Wonks have an editorial (or wonkitorial as they call it) commenting on a scheme in Iowa which links teachers' pay to the grades achieved by their students in standardised tests. They point out that some research studies have shown that students do not take these tests seriously enough, and teachers would end up being penalised for their students' carelessness. In another wonkitorial they point out that the No Child Left Behind program would turn teaching into the only profession where 100% effectiveness is not only expected, but required.

What is of interest to me is how results on standardised tests are used to improve student learning. To my knowledge, the student learns his/her grade, the parents see their child's rank in the state, and the teacher feels baffled or justified depending on whether the grade confirms or disproves school-based assessment.

Responding to the push for such high-stakes assessment, Professors Paul Black and Dylan Wiliam, of King's College in London, wrote a fabulous paper entitled Inside the Black Box: Raising Standards Through Classroom Assessment. This and other such papers brought the idea of formative assessment (aka assessment for learning) to the fore.

One thing that Black and Wiliam argue is that teachers are well trained in grading assessment tasks, but are usually unsure about how to use their findings to support student learning. This might seem to be a criticism of teachers, but these scholars then proceded to working with teachers in the UK to look at ways in which formative assessment could be implemented. In their work, they did not condescend to teachers. Instead, they presented general ideas and allowed the teachers to lead the way in discovering effective ways to implement formative assessment. I highly recommend the book: Assessment for Learning: Putting it into practice, by P. Black, C. Harrison, C. Lee, B. Marshall and D. Wilima.

An example I read in a recent paper is that of a preservice teacher who pretested primary (elementary) school children on their knowledge of the moon. He concluded that they knew "very little" and proceeded to teach his unit assuming nothing. This was because, while they knew that the moon was not a source of light like the sun, only two could explain their thinking . The author of this paper suggested that the next lesson should have been based on the question: if the moon is not a source of light, how do you think it glows? This would have been an example of using one's assessment of what students knew to guide further learning.

So, what does all this have with teachers' pay? There is a two part answer:
1- Raising the stakes even higher will make standardised tests an even greater source of anxiety and even less useful for learning; and
2- This could lead to schools in "rough" suburbs finding it even harder to recruit good teachers, as these would leave to work with kids who are more likely to get higher grades.

Black and Wiliam suggest a value-added assessment of teachers' performance, where a teacher is rewarded for the improvement his/her students have made between standardised tests.


Technorati tags: Teaching Formative Assessment

Thursday, September 14, 2006

Have an inspirational (or hopeful) story? Submit them here

Over at rickety contrivances of doing good, Susan is planning on starting a carnival of hope. Why not contribute a post to such a great idea. Unfortunately, time is running out for the first issue. Come on bloggers, we are interesting people to whom many good things happen. Let's share them with the world!

Also, at spunky homeschool, they are running a contest for inspirational educational stories. You could win yourself a digital camera.


Sunday, September 10, 2006

Answer to PQR puzzle

Yeo Hui gets the -virtual- cake for solving the problem first. Mr. Person has again provided the most publishable solution:

It was easy enough to test the cases here. There are only 4 possibilities--444, 555, 777, and 888--that could possibly give three-digit quotients with all digits being different. Looks like it's 444: 148 x 3 = 444.

The answer is therefore C. 13

Wednesday, September 06, 2006

Students' response to the death of Steve Irwin

After school on Tuesday, I went to the room where I normally teach my Year 9s to leave a message on the whiteboard. I saw a cross with the words: R. I. P. Steve Irwin. I imagined that it was a joke or something left from a drama presentation. I then learned that it was true when I turned on the radio in my car.

The reaction to Steve's death has been phenomenal in Australia. It is being compared with the reaction to the death of Lady Di. This is surprising to me as Australians are normally very harsh on their celebrities. Steve himself had remarked how he was not as appreciated in his own country as in the US. He referred to the "cultural cringe" that we often talk about.

What really surprised me was the amount of grief of my year 7 students. In the morning, during the 10 minute "homeroom" assembly, we say a prayer and the students get to pray for special intentions. The last two days have been dominated by prayers for Steve and his family. The girls seem to identify a lot with his daughter despite the difference in age.

The crocodile hunter was undone by one of the least vicious of the animals he had worked with. When men are interviewed they uniformly refer to his apparent invincibility. I guess most men of his age feel themselves invincible and are reacting to his death with a sense of shock.

I read today that the reaction in the US has also been great. People there loved him. Reportedly, they could not get enough of his landmark "Crikey!"

In the words of my students, "I pray for Steve Irwin, his family, and especially his daughter who was very close to him. Lord, hear us".


The latest in education carnivals

For those who want to keep their finger on the pulse (Ok, I am running out of intro lines!):

Monday, September 04, 2006

Puzzle: here's the product, what is the sum

The following is a question from the 2005 Australian Mathematics Competition - Junior Division (years 7 & 8):

In the multiplication

x 3

each of P, Q and R represents a different digit. The sum of P, Q and R is
(A) 16 (B) 14 (C) 13 (D) 12 (E) 10

If you know the answer, send it with an explanation to eliasblog@yahoo.com.au

Technorati tags: Puzzle

Saturday, September 02, 2006

It's a tough world out there!

Lately, I came across a chain letter purporting to report a speech given by Bill Gates at a high school. It lists the things that school does NOT teach (we are apparently meant to shout the "NOT") and how "politically correct teachings created a generation of kids with no concept of reality". At the same time, a blogger on The Age website also posted on the things we didn't learn at school.

Schools must tell kids to expect a harsh boss. "Rule 4: If you think your teacher is tough, wait till you get a boss." "... very few employers are interested in helping you FIND YOURSELF. Do that on your own time." I must say that all my employers, both in industry and in teaching, have been very accommodating. I would have been badly prepared by my school if they had planted suspicion of employers in my mind.

Schools must teach kids everything they will ever need in the world of work. "... how to survive a poorly run meeting ... how to prepare a powerpoint presentation ... how to write a 5 line email." I thought schools have been administring death by powerpoint for quite a while. I surely prepare my students for all those poorly run meetings they will have to endure: I get them in groups of 12 and give one of student a boring script to read. Yes, sir, I teach for the real world.

In all of these posts there are two themes in common: that school is not the real world and that school should be a reproduction of that world. Together with these themes, come two assumptions I used to make in my pre-education life: if people have not learnt something, it is because they were not taught it, and we know what people will need in the world of work, we just need the schools to get on with teaching it.

If the world is a place where everyone has to compete for the few places on the winning podium and if employers are harsh and uninterested in your wellbeing, then it is even more important for schools to be different. Employers will surely be grateful for people who have "found themselves" before they begin work. This way, they don't need to engage in such useless activities on the boss' time. I am sure no one at my school knew I would end up in an English-speaking country when they decided to teach me this otherwise irrelevant skill.

I'll get off my soap box and go play with my daughter. She'll teach me what is real and what is academic.

Technorati tags: Teaching School