Published Thursday, Dec. 15, 2011 2:00AM EST

http://www.theglobeandmail.com/news/opinions/margaret-wente/why-alex-cant-add-or-subtract-multiply-or-divide/article2271359/

http://www.theglobeandmail.com/news/opinions/opinion/too-many-teachers-cant-do-math-let-alone-teach-it/article2183700/

Amazed  at the number  of  comments this story generated.

MARGARET WENTE

Is your kid struggling with math? Is she flustered by fractions and laid low by long division? Here’s a secret: Her teacher may be struggling, too.

An alarming number of elementary-school teachers are so uncomfortable with math, they can’t teach it properly. This means that more and more students are arriving at university without having grasped the basics.

Across the country, university math professors report that the math skills of students who are studying to become teachers are generally abysmal. Basic skills such as adding fractions or calculating percentages are frequently beyond them. “If you don’t know math, you can’t teach math,” says Anne Stokke, a math professor at the University of Winnipeg who has launched a petition to raise the standards.

In Manitoba, education students often arrive at university with no more than what’s called “consumer math,” which is what you take in high school if you can’t do real math. To qualify as teachers, they need only one university-level math course – not nearly enough to make up for years of neglect. Even teachers who aim to specialize in high-school math only need to take a few basic courses. “As it stands, I don’t think they come out of university with the proper background to teach mathematics to kids either in elementary school or in high school,” Fernando Szechtman, a math professor at the University of Regina, told the CBC.

You might think that the nation’s faculties of education – the institutions that teach the teachers – would be concerned about this problem. After all, their job is to ensure that teachers know their stuff by the time they’re unleashed on the classroom.

But this concept of teacher training is pathetically behind the times. Today’s faculties of education have much loftier goals in mind. According to them, their main job is to sensitize our future teachers to issues of social justice and global inequality.

“Classes in elementary schools have complex human interactions that involve political, racial, economic and gender issues,” writes Cecilia Reynolds, the dean of education at the University of Saskatchewan. Her faculty is now considering whether to make the math course an elective – meaning that future teachers wouldn’t have to demonstrate any proficiency at all. She thinks math training should be more child-focused, “taking into consideration if that child is aboriginal, if that child has autism, whether that child ate a breakfast that morning.” Her own professional interests are in gender relations, equity and social justice.

Dr. Reynolds is a product of the OISE school of pedagogy, by far the most influential in Canada. And improving student achievement through effective teaching methods is not a priority for the Ontario Institute for Studies in Education. It has a research and advocacy arm, the Centre for Urban Schooling, that’s designed to connect it with schools in inner cities. As part of its commitment to “social justice and equity for all students,” the centre “works collaboratively on education projects that challenge power relations based on class, race, gender language, sexuality, religion, ethnicity and ability in all aspects of education both formal and informal.” If only it were interested in math.

Unfortunately, the people who educate the educators sound like the wacky wing of the NDP. Here’s Fern Snart, the dean of education at the University of Alberta: “To educate students beyond the superficial,” she writes, “we must engage them in transformational processes and deep thinking such that they understand the Western position of privilege that is often reflected in issues of diversity, power, and justice, and that they move to an internalization of responsibility related to this privilege.”

No wonder little Emma doesn’t know her times tables. She’s way too busy learning how her Western position of privilege entrenches gender relations. Or something like that.

Of course, the current math curriculum is no help, either. It’s long on “discovery” and short on practice and problem-solving. “They don’t seem to want the kids to practise any more,” says Prof. Stokke, who runs an after-school math club for 12-year-olds. But the biggest problem is that too many teachers simply don’t know the subject. “You wouldn’t send your child for piano lessons to somebody who can’t play the piano,” she says. It’s so obvious – to everyone but the people who educate the educators.

In Brief:

http://www.fcpp.org/publication.php/3905

Media Release – Something is Wrong With the State of Math Education in Canada

Frontier Centre study defends traditional math education

Winnipeg, MB: The Frontier Centre for Public Policy is proud to release a groundbreaking study authored by Frontier’s education research fellow Michael Zwaagstra. The study, entitled Math Instruction that Makes Sense, demonstrates conclusively that traditional math education methods are superior to the highly ineffective, discovery-based instructional techniques that are in vogue now in educational curricula. Zwaagstra shows why these techniques do not allow students to master basic math skills.

Zwaagstra draws on a wealth of relevant studies to argue that, “ in order for students to receive a strong grounding in math, they need to spend more time practicing math skills such as basic addition and subtraction along with the standard multiplication tables.” “There is ample research evidence showing that deliberate practice is the best way to gain mastery over a particular subject or skill,” said study author Michael Zwaagstra.

In order to improve our system of math instruction, schools must place a much stronger emphasis on mastering basic math skills and standard algorithms. Math curriculum guides must require the learning of standard algorithms, and textbooks must contain clear, systematic instructions as to their use.

Numeracy, a solid understanding of mathematics, is an important part of a well-rounded education but it is also essential for people to function competently in industrial and post-industrial economies, and in societies that rely on copious scientific and technological information to make decisions about our future. The proper school teaching of the discipline is paramount.

Zwaagstra points to the importance of a solid foundation in math skills as crucial for success in many college and university programs. He points out that these ineffective, yet commonly used techniques are leaving a whole generation of high school students unprepared for many of their academic or vocational programs.

A Copy of Math Instruction that Makes Sense can be downloaded HERE.

ABOUT THE AUTHOR:

Michael Zwaagstra is a research fellow at the Frontier Centre for Public Policy and specializes in education policy. He has extensive teaching experience at a variety of grade levels and currently teaches high school social studies in Manitoba. He received his B.Ed., Post- Baccalaureate Diploma in Education and M.Ed. from the University of Manitoba where he won several academic awards including the A. W. Hogg Undergraduate Scholarship, the Klieforth Prize in American History and the Schoolmasters’ Wives Association Scholarship. His columns promoting common-sense education reform have been published in major daily newspapers including the National Post, The Globe and Mail, the Winnipeg Free Press and the Calgary Herald. He is also a frequent guest on radio stations across the country. His best-selling ?rst book, What’s Wrong with Our Schools and How We Can Fix Them?, was released in 2010.

http://life.nationalpost.com/2011/09/09/math-is-tougher-than-reading-study-finds/

By Joannie Laucicus

Why is it that for some children reading is a snap, but math is daunting?

About six years ago, Jo-Anne LeFevre, director of the Institute of Cognitive Science at Carleton University, and her colleagues studied elementary students in Winnipeg, Ottawa and Peterborough.

One of the things they learned was that children need a more complex set of skills to master math than reading. These skills include the ability to process language, identify quantities and pay attention to the task. Children with attention deficit disorder, for example, often have difficulty with math. “It’s more complicated than reading,” says LeFevre.

Researchers are learning more and more about what works and what doesn’t when it comes to learning math.

Most parents, for example, have long grasped the idea that reading to children helps them acquire literacy skills. But preliminary research also suggests that playing simple number-based games, such as Snakes and Ladders, helps develop math skills.

“It’s independent of parents who read to kids,” says LeFevre, who points to a U.S. study of low-income preschoolers published in 2008 in Child Development.

The study found that children who played a game using numbers for about an hour scored higher on four numerical tasks than children who played the game using colours. The gains remained nine weeks later.

Previous research shows that proficiency in math at the beginning of kindergarten is strongly predictive of math achievement test scores later — in elementary school, in middle school and even in high school.

The same researchers also found that playing board and card games such as checkers and Go Fish at home meshed with numerical knowledge. At the same time, it’s not so clear whether children’s literature used to teach math is all that powerful, says LeFevre.

“I suspect that some aspects of math — like vocabulary, as well as number system knowledge — could come through nicely in this format, whereas other things need to be done using real objects and manipulatives (beads and blocks, for example) rather than words,” she says.

“And given our other research, some children will probably not benefit if their linguistic skills are relatively weak. In contrast, for children with good linguistic but weaker quantitative skills, perhaps learning about math concepts through literature would be ideal. As far as I know, no one has tried to find out.”

There are also cultural differences in the way math is taught. In China and other countries that produce successful math students, elementary school math is taught by math specialists rather than by generalist teachers, as in Canada. This probably makes a difference, she says.

Even a student’s mother tongue may play a role and researchers are probing this possibility. Cantonese, for example, has words for numbers based on units of 10. It’s relatively easy to grasp, even for very young children. It may set the stage for being comfortable with math.

The debate remains on whether today’s students have lost something because they didn’t learn math the way their parents did.

LeFevre believes there has been a decline in some kinds of math proficiency because children no longer do drills in school. She teaches a first-year statistics course at Carleton and notes that students have more difficulty doing pen-and-paper calculations. LeFevre, who is 50, says she can probably do three times as many problems in the same time as a 20-year-old student.

“It’s a huge change,” she says. “I teach skills. I see this.”

Are some people just genetically programmed to be better at math? Lynda Colgan, an education professor at Queen’s University, says not.

“Research shows that all children are born with an innate sense of number and simple computation,” she says. “It is the responsibility of parents and early childhood teachers to build upon this capacity.”

Everyone has the potential to be successful in mathematics, Colgan says, “just not on the same day, and not in the same way.”

Attitude and disposition are key factors in student achievement. Parents are a child’s first role models and their most important teachers, so don’t pretend that being able to do math isn’t an important skill.

“There is research to show that we become who we are when we are 10. Interestingly, this is the age at which 50% of elementary schoolchildren in Ontario say that math is hard, they are not good at math, and that they do not like math,” she says. “I suspect this is another example of nurture versus nature.”

http://www.torontosun.com/2011/07/08/summer-school-is-hot

First posted: Saturday, July 9, 2011 4:04:57 EDT PM

June 20, 2011

Ellen Roseman

http://www.moneyville.ca/article/1010830–roseman-perrcent-vs-percentage-take-my-quiz

Do you know how to calculate percentages? And do you understand the difference between “per cent” and “percentage point?”

I hope you had a perfect score in my quiz below. You’ll find the answers at the end of the column.

Many people are poor with percentages, even if they had great math marks in school.

Even large companies can make mistakes. Check out a computer ad published in the late 1990s.

“Why cruise at 60 when you can speed at 75?” the headline said, referring to the new Dell Dimension 75 MHz Pentium-chip based system.

“You get 15 per cent more processing power than a 60 MHz system. That’s one heck of a machine for under $2,000.”

Dell’s processing speed was impressive at the time, says Jack Weiner, a mathematics and statistics professor at the University of Guelph.

However, going from 60 MHz to 75 MHz was a 25 per cent increase — not 15 per cent, as the ad said.

Today, you can buy a $450 Dell laptop with 2.5 GHz of processing power. One MHz (or megahertz) equals one million cycles per second, while one GHz (or gigahertz) equals one billion cycles per second — or 1,000 MHz.

To calculate the increase in this case, you subtract the earlier amount (60) from the later amount (75). That’s 15.

Then, you divide 15 by 60 and multiply it by 100. The result: A 25 per cent increase.

A common mistake is to divide 15 by 75 and multiply by 100, producing a 20 per cent increase.

You have to use the earlier amount, not the later amount, as the divisor.

(The divisor is the number used to divide another. In the equation 15/3 = 5, the number 3 is the divisor.)

Confusion about calculating percentage increases and decreases is common. This can lead to money management problems.

Here’s a real case, involving mortgages sold to low-income U.S. consumers before the 2008 market crash.

Many subprime mortgages, not available in Canada, had low “teaser rates” in the first year, followed by stiff increases in subsequent years.

Sellers often exploited a common misunderstanding of “per cent” and “percentage point” to bamboozle borrowers about the increases they faced.

Suppose you started with a 2 per cent mortgage rate. The bank has told you that rates would be going up 10 per cent in the next year.

That could mean two things:

1) Your rate would go from 2 per cent to 2.2 per cent (an increase of one-tenth of a percentage point).

2) Your rate would go from 2 per cent to 12 per cent (an increase of 10 percentage points or 500 per cent).

Scenario one was comfortable. Scenario two was catastrophic.

The widespread confusion about calculating percentages helped bring about a collapse in the U.S. real estate market. Luckily, Canada’s banks never entered subprime territory.

Percentage points are used to show the arithmetical difference between rates. For example, if a rate jumps from 2 per cent to 10 per cent, that’s an increase of 8 percentage points.

We in the media find it easier to use per cent instead of percentage point. If the Bank of Canada rate goes from 2 per cent to 3 per cent, that’s an increase of one percentage point — not 1 per cent, as reporters often say.

By downplaying an actual rate increase of 50 per cent, we create a climate of misunderstanding and possible disaster.

The difference between per cent and percentage points was a mystery to me until I became a full-time business writer. Now I’m aware of how often they’re confused.

I asked Alan Goldhar, who teaches business at York University, if students know the difference.

“For business students, I’d guess about half would understand the concepts right away,” he said.

“For non-business majors, I suspect one in five students would understand without explanations or examples by me. I’m usually amazed at how little most of them know about finance concepts.”

Let’s hope practical life skills are added to school curricula, so that students learn the skills needed for successful money management at a younger age.

Here are the questions

a)       10 per cent

b)       11 per cent

c)       Neither

2. You hope to buy a $30,000 car, but end up with a $45,000 model. You blew your budget by how much in percentage terms?

a)       33 per cent

b)       45 per cent

c)       50 per cent

3. You have a mortgage with a 3 per cent interest rate for one year. The rate goes up to 6 per cent in the second year. What is the percentage increase?

a)       3 per cent

b)       50  per cent

Big drop in math skills of entering students

On that point there’s no argument, but educators don’t agree about how much it matters.

by Anne Kershaw

http://www.universityaffairs.ca/big-drop-in-math-skills-of-entering-students.aspx

Deteriorating math skills among high school graduates is not just a North American phenomenon, experts say.

The math skills of students entering Canadian universities have declined sharply in recent years, with many students unable to do basic arithmetic. Whether this is a learning crisis with dire implications for Canada’s citizenry and its future science and engineering base or simply an inevitable result of the ubiquity of calculators and computers is a matter of debate.

The deterioration of math skills is apparent across North American, says Brenda Smith-Chant, a psychology professor at Trent University who specializes in the development of mathematical cognition. And it’s not merely a matter of students being unable to handle trigonometry or algebra, she says. “Even basic arithmetic is throwing them, and we’re talking about adding three two-digit numbers.”

Dr. Smith-Chant says that students’ deficiency in math is affecting their course choices and educational paths. For example, many psychology students decide to leave the field because they’re put off by the requirement to take a statistics course.

For the past 20 years, Carleton University psychology professor Jo-Anne LeFevre has been researching how well first- and second-year students solve simple arithmetic problems, such as adding 25+73+16. She has seen a marked decline in paper-and-pencil computation skills. In 1990, students were solving an average of 80 problems in a set time period; 15 years later that had dropped to an average of 60. “It’s a significant change, statistically,” she concludes.

Dr. Smith-Chant, for her part, has seen a similar decline, using similar methodology. In 1984, first-year psychology students answered an average of 80 questions correctly. In 2004, the number had dropped to 73 correct answers, and last year it was 56.

While most educators agree that numeracy has declined, there’s no consensus on how much it matters. Some argue that in an age of calculators, people don’t need basic skills to acquire higher level mathematical knowledge and that it’s more valuable for students to spend their time learning larger concepts.

But others say that the more fluent you are in the basics, the more easily you can grasp more advanced math. Sherry Mantyka, a professor of mathematics and statistics at Memorial University and director of the mathematics learning centre, has spent years helping students improve their core math skills. In a controlled experiment several years ago, Dr. Mantyka and a psychology researcher found that students who didn’t know basic numerical facts and numeric processes were disadvantaged when grappling with more complex math problems. “Their working memory was insufficient and they would start making mistakes,” she says. She adds that the need for remedial math courses at Memorial “seems to be getting worse,” with about 500 first-year students requiring remedial math in each of the last five years.

Many observers say this erosion in basic computation skills is a result of the mathematical reform movement spearheaded by the National Council of Teachers of Mathematics (NCTM) about two decades ago. This philosophical shift in math pedagogy to emphasizing conceptual thinking from what some saw as rote memorization brought about curriculum change across North America.

Now, many are seeing unintended consequences. Robert Mann, a professor of physics and applied mathematics at the University of Waterloo and president of the Canadian Association of Physicists, hears concerns about math skills from colleagues across a number of disciplines including economics, math, physics and chemistry. In his own classes he has found that, a decade ago, students were strong in technique and weaker at grasping concepts, but that has almost reversed. “Now, they know what to do but they don’t know how to do it,” he says.

“The changes [in teaching approach] paid off in one way but they also had this alternative impact that we didn’t really expect,” he says. “I think pedagogically teachers at all levels are not really comfortable with how to teach in the computer or calculator age.”

Gordon Robinson, a biologist at the University of Manitoba, believes that the level of math skill being seen at universities across Canada is of widespread concern. “I think the answer you would get from anybody who teaches first-year math at a university is that they are just aghast at the quality of the students they are having to deal with. We’re talking baby calculus, not rocket science.”

The deterioration of math skills is far from just a Canadian or North American phenomenon. “There have been a number of wide-ranging studies out of OECD countries that have found that preparedness for math in postsecondary education is really bad and it’s getting worse,” says Dr. Robinson.

So how is it, then, that Canada ranks highly in math in the international Program for International Student Assessment (PISA), which compares skills of 15-year-old students in OECD countries? In the most recent scores for math assessment, administered every three years, Canada placed fifth out of 30 OECD countries.

That’s because, say Drs. Mantyka and Smith-Chant, the PISA tests “math literacy” or how to apply math knowledge in the real world, and there is no correlation between “math literacy” and the level of basic math fluency found in students entering university.

In fact, the leading Aalto University School of Science and Technology in Finland, the country that came first in math under PISA, recently sought Dr. Mantyka’s advice after noticing that Finnish students are entering university with weaker math skills than expected. Dr. Mantyka is now collaborating with the Finns on developing remedial programs and has joined them in an on-line remedial software project for the European Union.

While the debate continues about the importance of numeracy, researchers in the field aren’t ready to concede that the need to perform math in our heads has become obsolete. Dr. Smith-Chant says the lack of math skills may have even contributed to the recent recession in North America, with people getting themselves into risky financial situations, including mortgages with ballooning payments, because they didn’t understand how interest rates work.

Dr. Mantyka agrees. “How can you make a sensible decision about a mortgage or your ability to pay back that mortgage if you have no ability to work with percents, other than punching numbers on a calculator and hoping you get the decimal in the right place? Yes, it’s very scary.”

A new study shows a third of first-year college students in Ontario are in danger of not graduating because they flunked or barely scraped through their math course.

Researchers at Seneca College who conducted the study say that equates to about 10,000 students.

About 67 per cent of students achieved good grades — As, Bs, and Cs — slightly better than last year.

The governing Liberals are focusing on post-secondary education as a way to pull Ontario out of a major economic recession.

Monday’s throne speech promised to increase the portion of the province’s population that has a university or colleges education to 70 per cent from 62 per cent.

The government also promised to create 20,000 new post-secondary spaces this fall and increase the number of foreign students to about 54,000 from 37,000.

The Seneca study focused on the math results of 30,000 college students, but also examined the records of almost 80,000 students who enrolled in college in the fall of 2008.