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Archive for the ‘Maths’ Category

Fixing Math Education

August 25, 2011

I just read a brilliant article in the New York Times about a suggested overhaul to teaching math.  It argues that much of what is on the standard curriculum will never apply to the average adult.

THERE is widespread alarm in the United States about the state of our math education. The anxiety can be traced to the poor performance of American students on various international tests, and it is now embodied in George W. Bush’s No Child Left Behind law, which requires public school students to pass standardized math tests by the year 2014 and punishes their schools or their teachers if they do not.

All this worry, however, is based on the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong. The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.

Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a “reform” version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life.

For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a “group of transformations” or a “complex number”? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.

Whilst this is not news to us, the suggestions given for overcoming this problem are very simple yet quite brilliant all the same.

A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching “pure” math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations. The former is how algebra courses currently proceed — introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities — for instance, Einstein’s famous equation E=mc2, where E stands for energy, m for mass and c for the speed of light.

There’s not many common sense ideas in education at the moment.  It’s good to stumble upon one that is clearly steeped in common sense.

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Maths Lessons Should be “Toughened Up”: Gove

June 30, 2011

Michael Gove might think that rigorous daily and weekly testing in maths is the answer, but my experience tells me that testing doesn’t work for all types of students.  There are some students that lift their game when tested.  Their competitive juices get going, and their drive to get a good grade is palpable.  Then there are students who need to learn in a less pressurised and more r
elaxed setting.  They freeze during formal testing, but progress extremely well when the focus is on the skill or concept rather than the grade.

Michael Gove disagrees:

All primary school children should be given daily maths lessons and weekly tests to stop pupils falling behind those from the Far East, Michael Gove suggested today. 

Mr Gove said schools should also “bear in mind” a system used in Shanghai where pupils have daily maths lessons and regular tests to “make sure that all children are learning the basics”.

What disappoints me as a Primary Maths teacher, is that in the quest for better results the focus becomes testing instead of engagement.  I believe that Maths can be taught in a turgid and lifeless way.  Conversely, it can be taught in an interesting, engaging and creative way.  Whilst constant testing will make students resent the subject, there are ways of teaching maths which can engage and excite students.

The answer to improving our students’ maths skills should not result in them hating the subject.



The Obstacle Course that is Teaching Maths

February 9, 2011

Below is the second maths lesson in a series of original maths lessons I have devised over the years:

 

Maths Obstacle Course

I devise a simple obstacle course using whatever playground equipment the school has.  Slides, monkey bars, polls, ladders and bridges are all useful.  The obstacle course doesn’t need to be intricate, long or complex.  Students should be able to finish it within half a minute maximum.

I take the students out to the playground.  They have no idea what we are doing.  They may ask me, but my reply is “You’ll see.”  The reason why I don’t tell them it’s a maths lesson is because maths has a stigma, and just the mention of it will deflate some students’ expectations.

Usually outdoor lessons require pencils, worksheets and clipboards.  The students are relieved when they find out that none of these implements are required.

With the students congregating around the playground equipment, I tell them that they are going to be doing an obstacle course.  I show them the route they need to take and tell them that each individual will be timed while doing the course.  Each student gets one attempt only, with their personal time written down.  On completion, I order the times privately while the students get a drink of water.

Only the 5 quickest times are read out, so as not to upset or demoralise any of the slower performing students.  Of course, if other students request to know their time, I tell them.  At this point we walk back to the classroom.

On arrival, I write the times in random order on the board.  Using the times, students will take part in some of the activities below, depending on their age and maths proficiency:

Activity 1:  Order the times from quickest to slowest;

Activity 2:   Round the times to the nearest second, tenth of a second etc;

Activity 3:  Work out the total time taken cumulatively over the entire class;

Activity 4:  Work out the average time for the entire class;

Activity 5: Chart the times using Excel and create a chart such as a column graph which presents the data in graphical form; and

Activity 5: Students estimate what time they think they would get should they be given a second attempt.  They will also be asked to give reasons for their answer (e.g. it could be faster the second time around due to a greater awareness of the route, or an improved strategy, yet it could be slower due to fatigue or the pressure to perform).

Even though the main chunk of the lesson is spent doing something that can hardly be called maths, it serves as a basis for engaging the students.  The skills covered in the lesson include measuring time, adding decimals, ordering number, rounding, IT, graphing, averaging and predicting.

It’s a great feeling watching the students get a shock when they find out that the PE lesson they thought they were taking part in, ends up being referred to as a maths lesson.

And ultimately, that’s the point.  Maths is in everything – even the things that give the students pleasure.

Making Maths Fun is Not Mission Impossible

February 2, 2011


I’m no teaching guru – just an ordinary teacher that loves his job. I am a primary level generalist teacher, which means I teach all major subjects such as Maths, English, Social Studies and Science. As much as I love teaching all subjects, I find Maths most exciting.

Is it because I have a background in Maths? Absolutely not. I have an Arts degree.

Is it because I am good at Maths? On the contrary. As a student I would frustrate my teachers no end. As a kid, I had as much chance of passing a maths test as Homer Simpson has of suffering from dandruff!

The reason I love teaching maths is that I find it an untapped and underrated subject for injecting creativity and role-play. Last week I wrote about how primary teachers often struggle to teach maths, as they mostly come from a humanities background.

Commenting on that post, loyal reader and frequent contributor Margaret Reyes Dempsey, wrote, “I’d love to read a post about some of the ways you approach math in the classroom.”

Every week I will endeavour to describe an innovative Maths lesson I have concocted.

 

Lesson 1: Mission Impossible Maths (Place Value)

I get the students to bring a pair of sunglasses to school for homework. The students invariably ask me what the glasses are for. I tell them it’s a surprise. They automatically think science, perhaps an activity out in the sun. The truth is, the sunglasses are nearly irrelevant, only there to raise curiosity and engagement.

On the day of the lesson I take the kids to our small but homely hall. I carry a briefcase and have on my own pair of “spy” glasses. The kids have no idea what is in the briefcase, and have no clue what is happening. I sit them down on the floor and tell them that there is a problem. There is a mansion close by. In that mansion there is a suitcase. In the suitcase there is a key. The key, in the hands of evil would change the world as we know it. It would give them the power to ban all music except for the golden oldies and make sure that nothing but news is on TV. The kids groan at the prospect. Lucky you are here, I tell them. You are the best spies in the world, and your mission is to break in to the mansion and get the key before they do. I call their names out, adding their secret spy name e.g. Sammy “The Drummer” Smith. The spy name is just another opportunity for me to connect with the interests and skills of my students. I split them into groups based on ability, as the lesson will involve maths problems ranging from basic to more complex.
I take them outside and show what they have to do to break into the mansion. I show them the slide which I call “The Tunnel of Terror.” Getting through the tunnel will be tricky, as a wrong turn would send out the crocodiles. To get through the tunnel without being eaten, group 1 has to work together to order a sheet of 5 digit numbers from lowest to highest number.

I then take the class to the school door, or “Dynamite Door”. To gain access to the mansion, Group 2 has to order a sheet of 5-digit numbers, this time from highest to lowest, otherwise the door will explode.

I show the class the door that leads to the hall, or as I call it “The DNA door.” To gain access to the room in which the suitcase is kept, Group 3 has to bypass the special DNA sensitive handle. To do that, they are given 6-digit numbers to order.

Group 4 has to get past the infra red sensors to get to the suitcase. This involves making as many 4-digit numbers from, for example, 4, 3, 1, 8. Once they have gotten past all 4 obstacles they will face one more test (to be revealed at the time) before being able to open the briefcase. They are told they have 45 minutes and the time starts now …
I distribute the sheets to each group, watching them feverishly try to solve the problems without making a mistake. Each group appoints a checker, to check for a careless error that would complicate this dangerous mission. If a group finishes early, they are quiet, because they rely on the proficiency of the other groups. When all groups are done we go back to the slide. The clock is still running.

The first member of group 1 reads the first part of the answer and when I confirm that it’s right goes down the slide. The other members do the same until they have all slid down the slide. Members of group 2 read out their answers. On getting the right answer each member is allowed access through the door until they are all inside the building. The same for Group 3 with their door and Group 4 with the sensors.

The final challenge involves a representative from each group stepping forward to help break the suitcase code. I tell the 4 representatives that the code number is between 3,500 and 3,600, and they have to guess it right. All I can tell them is whether their guess is higher, lower or spot on.

Once the final code has been broken, the person that correctly broke it gets to open the case and take out the key. They usually get the key with only a few minutes left to spare. You should see the cheers and hugs that come about from unearthing the key. It is such a great bonding experience.

I do this lesson in the second week of the school year. At that stage my students almost uniformly claim they hate maths with a passion. It is only after the lesson that I spill the beans that they had just taken part in a maths activity. In reality, it was nothing more than a set of dry worksheets with a bit of imagination and wackiness added on.

If you feel that this lesson would be suitable for your kids, I’d love to know how it goes.

Maths and Primary Teachers Don’t Always Go Together

January 25, 2011

A school principal once said something to me which really stuck.  He said that if you look at a primary teacher’s academic background, you see a clear trend.  Most teachers come from a humanities background.  They studied Arts, Literature, Politics, History etc.  He said, only rarely do you find a primary school teacher with a maths background.  The unfortunate truth of the matter, he concluded, is that many primary school teachers are uncomfortable with teaching maths.  Many have limited skills and are simply not adept at effectively explaining maths concepts to their students.

I think there is a lot in what he said.  Whilst spending a year as a substitute teacher, I witnessed many schools and observed many teachers.  It is very rare to find a primary teacher that doesn’t possess an interest in literature and social studies.  It isn’t rare however, to find a teacher who groans at the prospect of teaching fractions or who becomes impatient when a student doesn’t seem to be taking in the method for solving an equation.

Early last year an article was printed in The Australian about the deficiencies of Australia’s education system to deliver acceptable maths outcomes. Even though it was written about Australia, I think it may well apply to many other countries as well.

A groundbreaking review of the mathematics and statistics disciplines at school and university by the Go8 found “the state of the mathematical sciences and related quantitative disciplines in Australia has deteriorated to a dangerous level, and continues to deteriorate.”

The review was compiled by a committee of the nation’s senior mathematicians headed by former University of Sydney vice-chancellor Gavin Brown.

It found that in 2003 the percentage of Australian students graduating with a major in mathematics or statistics was 0.4 per cent, compared with an OECD average of 1 per cent.

Between 2001-2007 the number of mathematics major enrolments in Australian universities fell by approximately 15 per cent.

I also came from a humanities background.  Before completing my degree in teaching, I studies Arts, majoring in English Literature and History.  I, like other teachers was terrible at maths during school.  Our school used to give high pressured maths tests all throughout the year.  I studied for them long and hard, yet managed to fail just about every single one of them.  One day I was so distraught at not being able to work out the answers, I secretly threw my test in the rubbish bin.  A week later my teacher approached me apologetically to tell me she somehow misplaced my test.

The interesting part of it was I actually liked maths.  Whilst it never came easy to me and was taught in a pressurised and negative way, I still managed to enjoy the subject.  In Year 12, I decided I wanted to do maths as one of my final year subjects.  The teacher, Principal and Vice-Principal thought I was crazy and tried to talk me out of it.  They were worried that my inevitably poor results on the three major assessment tasks would drag the class’ score down and tried to persuade me to take up economics instead.  I stubbornly refused.

As it turns out, I did quite well in the end, including earning an A on one of the assessments.  The same Maths teacher that didn’t want me in her class later told me I was her favourite student.  Not because I was the best behaved or the smartest, but because I was determined.  She was impressed that I chose to fight my maths demons rather than take the better grades on offer from doing economics.

Now as a maths teacher (I teach all general subjects), I can relate to the student that doesn’t get it.  I enjoy teaching maths in a style that I would have profited from as a child.  The creative scope for teaching elementary maths is almost limitless.  I like to set up maths role-plays in my class.  In teaching place value I set up a situation where the students are spies trying to break codes in order to thwart an evil plan.  For measurement I get the students to build towers and design tracksuits for Australia’s National sporting teams.

It’s always going to be hard for primary teachers to excel in teaching something they may have never excelled at when they were students.  But that can be a blessing in disguise.  Sometimes a rustiness in the subject helps you relate to the struggles of some of your students and encourages you to be more creative in the way you teach.

Girls and Maths

November 15, 2010

At a time when so much time and effort is exerted into getting better academic results from the boys, I wonder if we’re doing enough, if anything at all, to make maths more appealing to girls.

A study to be presented at an education conference in Melbourne this month shows girls performing poorly compared with boys in areas of high achievement and enrolment trends in year 12 maths subjects.

Its findings show a clear pattern of male dominance among the Victorian students who achieved the top 2 per cent of the study score results in each of the maths subjects between 2007 and 2009. //

Boys were heavily over-represented among the top scorers, relative to their enrolment proportions in each maths subject.

Sure, boys may be wired to excel in maths, but should that stop us from rethinking the way we teach it to girls?

I love teaching maths.  As a Grade 4 teacher, I teach all general subjects, yet maths is my favourite.  I find that there is so much scope for teaching the subject in a creative fashion rather than rote memory skills and algorithms, which can be boring and off-putting to many.  In class we become top-secret spies, prisoners, fashion designers and architects.  Sometimes the class don’t even realise it’s a maths lesson!

A creative approach to maths, especially in the early years, is just the tonic to make the subject more exciting and accessible – especially to girls.


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