Thursday, December 30, 2010
Sunday, December 19, 2010
Enjoy, and Merry Christmas!! No:ia, No:ia!!
Wednesday, December 15, 2010
For Meg Ormiston, it's a wonder sometimes that teachers don't just give up. Restrictive Internet policies in schools, coupled with unresponsive IT departments and beleaguered administrators, present teachers with a nearly impossible situation: They're being pressured to incorporate 21st century teaching and learning into their classrooms, but they're not being allowed to use the tools they need to do that. They're being hamstrung. And so are their students.
Ormiston has served as a curriculum coach, school board member, conference presenter, professional development specialist, and grant facilitator. Currently, she consults with schools on incorporating technology into the classroom to reach 21st century learners. And that requires her to continue speaking up for teachers who aren't yet trusted with Internet access in their classrooms.
In this interview, Ormiston told us that while there are legitimate barriers to using some Internet technologies in classrooms, the justifications in many cases are much flimsier. Bandwidth might be too limited for the widespread use of streaming video, granted, but in a lot of cases, the reasons for the restrictive policies aren't very clear. Schools seem simply not to trust teachers, the very individuals they've hired for their training and certification as professionals formally qualified to care for children in a classroom setting.
And, as she observed, if schools by this point can't trust teachers to decide whether a given Web site is appropriate for their students, how can they trust those teachers in the classroom at all?
Ormiston will be speaking at three sessions on these topics at the FETC 2011 conference, being held Jan. 31 through Feb. 3, 2011 in Florida: "Playing School or Preparing for Life?" and "Bringing the World to Your Classroom Using Web 2.0 Tools."
THE Journal: A lot of schools are blocking access to the Internet--especially to social networking sites and resources. Why is this happening?
Meg Ormiston: I'm a parent, and I think it's important for us to protect children. But we have to look at teaching and learning too. We want to keep kids safe, and I'm all good with locking pornography. But we have to remember to teach responsible computing. That includes social networking. We have to help students make good choices with networking resources and sites they visit and help them know right from wrong. We can't blanket-block everything because that's also blocking learning.
One of the examples I use is YouTube. Yes, there are inappropriate things on YouTube. But there are such rich wonderful learning opportunities too. As budgets continue to be slashed, YouTube offers a lot of learning opportunities. Should we filter and check them? Absolutely. Nobody should be trusted in the classroom with students if they can't also be trusted to use YouTube appropriately.
When I started teaching, we had to make sure to preview videos and filmstrips before we showed them. Teachers need to be the filters to make sure that what's on YouTube is appropriate. But that means they need to be given the opportunity to access YouTube for teaching and learning.
THE Journal: What's the hold-up on unblocking filters?
Ormiston: For some schools, it's a legitimate problem of bandwidth. There's just not enough network power coming into those buildings for kids to be streaming videos. In those situations I can see restricting it for certain times. Or in some buildings they limit it during their peak hours. I understand the bandwidth issues.
Another issue is that people who are not certified educators are making decisions about what is blocked. Or a lot of times, it's the piece of software that the district has purchased that makes the blanket decisions. Social networking on many tools will be blocked. That will cut out all opportunities to use images on Flickr, VoiceThread, Blogster.... A piece of software is running the Web filter and blocking full categories, which means we're blocking a lot of learning because of the label of "social networking." Most of the software has the ability to overwrite the filter. But some districts don't give anybody the opportunity to overwrite it.
But I know it can be done. On the flip side, I [work with] one high school where all that they're blocking is Facebook and the whole category of pornography. Everything else is up to the discretion of the educators.
THE Journal: What's the opportunity that's lost when schools are more restrictive?
Ormiston: If you're doing nothing but blocking all day long, teachers are going to give up using technology. If I were to keep hitting the wall again and again, I'd give up. I'd go back to the tools that I had before the computer was around. It's a turn-off for teachers. When I go into those districts, I hear, "You can't get it here." They give up. And so would I.
But the biggest part of the problem is that when students go home, it's the Wild West out there. There's no blocking in most cases. There's no filtering. There's usually not an adult to help them make good choices. And they haven't been instructed in the schools about what's appropriate and what's not. That's my biggest fear. We're letting kids wander around on the prairie with no guidance.
THE Journal: So how can an educator make a successful case for opening up access to the Internet?
Ormiston: Unfortunately, this is the worst part. You have to send your teachers home to learn because they can't learn Web 2.0 tools or any of these social networking tools at school--because they're all blocked. Once your teacher goes home to learn, then they have to come back and say, "I'd really like to use this for this purpose. This aligns with my curriculum. This is age appropriate..."
But here's the hard part. Even if those teachers go home and find VoiceThread, what then? Many teachers don't even have anybody in their building to go [to]. They might be able to fill out a form for a service desk or ask the principal, who's already overwhelmed, but a lot of them don't have a point person to say, "This is really useful, and I'd like to use it with my class." They don't have any options. If I were them, I would give up.
Another thing:. These tools are constantly changing. We need to be able to get to the locking and unlocking at the moment you need it for teaching and learning. [In] one of my districts it takes two and a half weeks to get an answer about whether the site will be open or not. Most people just give up the site because they know the answer is going to come back from some central office, and the answer is going to be no. So we give up. Then somebody comes with questions: "Why aren't we using more technologies in the schools? Why isn't it making difference?"
What's crazy is that I can walk into a high school and have a student show me how to get around any filter put up. So the students know the work-arounds, and the teachers' hands are tied.
THE Journal: What needs to be in place for a school to open up access?
Ormiston: A lot of really focused professional development. It's not enough to say, "Woo-hoo! We're open today!" We've locked teachers down for so long, they need to know what's appropriate, what's not, what to preview, what the best sites are for getting started if they're new to this. And we need professional development not only for our teachers but also for our administrators.
THE Journal: Why the administrators?
Ormiston: The leader has to have the vision to make change. Many leaders don't have deep technical backgrounds. So when the expert in the IT department says, "No, no, no," it's hard for the school administrator to say, "Yes, yes, yes," if [he or she] hasn't been exposed to social networking sites or to the possible teaching and learning opportunities. The easy answer is to block everything. Then we'll be safe. But we're really not.
THE Journal: Say the filtering is lifted. Suddenly, the riches of the kingdom are available to educators. What should they do next?
Ormiston: A tiered approach is great. Most of the filtering software is tiered. Let's start off by opening access for teachers, and let them explore and begin to figure out how to use YouTube appropriately in the classroom. Let's see what happens. Everything is going to be fine. Then let's start changing permissions for students.
When I'm working with a blocked and filtered school, and they're starting to think about coming out of it, I often recommend opening one site a month or one site a week, if they can handle it: "This week we're going to try Wordle and make tag clouds.... We're all going to try VoiceThread...."
THE Journal: Do you think you'll ever be able to stop talking about this stuff?
Ormiston: Sometimes I just say, can't we talk about something else? I feel like it's so old. When are we going to snap out of it? When are we going to realize that you can block and filter until you're blue. But [then kids] open up their smart phones, and there's not a block or filter, and they're sitting in your schools.
Education is the key. Leadership is absolutely the key. The leader has to understand why this is important, then advocate to others [on behalf of] the faculty and students that this is about teaching and learning today.
People say to me, you don't understand the network, and I keep saying, no, I don't. I focus on teaching and learning. I'll say to IT people, you'd be happiest if nobody ever came to school, because then there'd be nobody to block, filter, cause problems, hack.... They'd have nothing to worry about.
But this is about a living, breathing, and ever-changing community. Every time we get one of these new tools, we have an opportunity to engage students. That's what it's about. It's not about locking things behind the gate. It's about appropriate engagement. We have to find the tools that we can embed into curriculum that students will really enjoy. They do not enjoy another packet of papers. They want multimedia. They crave the opportunity to work with other people--and other people outside of our schools. With a lot of these tools, we have that opportunity--of course, with supervision.
We lose so many opportunities when a network person says, "No Skyping in our school district...."
Monday, December 13, 2010
Wednesday, December 8, 2010
Friday, December 3, 2010
Thursday, December 2, 2010
It’s no coincidence that the occurrence of ADHD has risen in parallel with the growth of standardized testing. These kids are being given Ritalin and Adderall and all sorts of other things—often quite dangerous drugs—in order to get them focused and to calm them down. It's a fictitious epidemic. Anyone who knows anything about anything knows that the secret to success and focus in the classroom has nothing to do with drugs or discipline or anything like that. The secret to success is about developing an engaging methodology that engages students to want to be there. It's not about getting them to learn, it's about getting them to want to learn. Without motivation, there will be no learning. posted by Ian Jukes
Read the article Ian Jukes is writing about here.
Wednesday, December 1, 2010
Six Nations District Numeracy Committee Meeting Minutes
Wednesday, October 27th, 2010
District Teacher Room, J.C.Hill School
12:30 p.m ‑ 4:00 p.m.
In attendance: Joe Restoule General, Marlene Martin, Tammy Clause, Jessi Skye, Alice Anderson, Luanne Martin, Anne Noyes, Carrie Froman (late)
1. The positions (co‑chair and secretary) were nominated and selected for 2010/2011 school year. The positions are as follows: Co‑chair ‑ Marlene Martin, Secretary ‑ Jessi Skye/Luanne Martin alternating every other month
2. Terms of Reference were discussed. A motion was set to finalize the terms of reference at next PAC meeting. Mr. Restoule General typed up the purpose of the committee, Responsibilities of the Committee, and Recommendation Procedures. It was recommended by the committee for the Numeracy District Teacher to attend all PAC meetings to provide a brief Numeracy Committee update to keep all principals informed.
Functions of the District Numeracy Committee:
*Focus of the NC – Improvement of student achievement through improvement to classroom math experiences (includes using the Mathematical Processes, using manipulatives)
*Using assessment data for, of and as learning
*develop PLCs at each school according to school needs
* ensure connection w/PD committee
*generate teacher resources such as a user’s guide
*desk book example, added on to with additional topics (3 part lesson; Big Ideas, scopes of sequence)
*adjust DNP (District Numeracy Plan) to meet new template of SSP (School Success Plan)
Responsibilities of Numeracy Committee:
*Get District Numeracy Plan approved and sent to PAC for Nov. 9th
*complete final draft of minutes within 1 week of the NC meeting
*2 days for the first draft (sent to all NC members); 2 days for revisions (from NC members) in advance of sending to DNT
*DNT share minutes with Ps and VPs and NC (Ps and VPs would share minutes w/ALL staff (electronically/hard copy)
*report back to staff at the next scheduled staff meeting
*co‑chairs sign by next NC meeting
*targeted information sessions as need be (priority items)
*recommendation that DNT attend each PAC to present a monthly update/recommendations/reviews and field/respond to questions and/or concerns
*in the event of closed/cancelled PAC an e‑mail to all Ps and VPs from DNT for any time sensitive items
*Numeracy committee NOT to share items with general staff until P and VPs see it first
3. Approval of minutes was agreed by last year committee members (L.Martin, A.Anderson, J.Restoule General).
4. A review of the District Numeracy Plan was made. Changes were made by the committee. A new draft will be sent out via email by J.Restoule General. A motion was set to finalize the Plan at next PAC meeting.
5. Meeting adjourned
Tuesday, November 30, 2010
Wednesday, November 24, 2010
Tuesday, November 23, 2010
Children with home computers likely to have lower test scores, study finds
ScienceDaily (2010-06-19) -- Around the country and throughout the world, politicians and education activists have sought to eliminate the "digital divide" by guaranteeing universal access to home computers, and in some cases to high-speed Internet service. However, according to a new study, these efforts would actually widen the achievement gap in math and reading scores. ... > read full article
Monday, November 22, 2010
Saturday, November 20, 2010
These are tips that incorporate the liberal use of digital tools such as blogging and personal mobile devices which, among others, are getting a big spotlight in regards to their relevancy in the digital learning experience.
posted by Ian Jukes
Jun 28, 2010
view the original source for this post
10 Techniques to Massively Increase Retention
Do you like this story?
This is the classic ‘forgetting curve’ by Ebbinghaus, a fundamental truth in memory theory, totally ignored by most educators and trainers. Most fixed ’courses’ or ‘lectures’ take no notice of the phenomenon, condemning much of their effort to the world of lost memories. Most educational and training pedagogies are hopelessly inefficient because they fail to recognise this basic truth. Smart learners get it. They revise over a period, with regular doses to consolidate their memories.
Little and often
The real solution, to this massive problem of forgetfulness, is spaced practice, little and often, the regular rehearsal and practice of the knowledge/skill over a period of time to elaborate and allow deep processing to fix long-term memories. If we get this right, increases on the productivity of learning can be enormous. We are not talking small increase in knowledge and retention but increases of 200-700%.
It has the potential to radically alter the attainment levels in schools, colleges, universities and organisations. OK, that’s the theory, what about the practice?
What strategies enable spaced practice?
I’ll start with a few ‘learner’ tips, then a few ‘teacher/trainer’ practices and end on some technical techniques.
1. Self- rehearsal – This is very powerful, but needs self-discipline. You sit quietly, and recall the learning on a regular, spaced practice basis. The hour/day/week/month model is one, but a more regular pattern of reinforcement will be more successful. Research suggests that the spacing different for individuals and that it is good to rehearse when you have a quiet moment and feel you are in the mood to reflect. Recent research has shown that rehearsal just prior to sleep is a powerful technique. Another bizarre, but effective, model is to place the textbook/notes in your toilet. It’s something you do daily, and offers the perfect opportunity for repeated practice!
2. Take notes – write up your learning experience, in your own words, diagrams, analogies. This can result in dramatic increases in learning (20-30%). Then re-read a few times afterwards or type up as a more coherent piece. It is important to summarise and re-read your notes as soon as possible after the learning experience.
3. Blogging – if the learner blogs his/her learning experience after the course, then responds to the tutors’, and others’ comments for a few weeks afterwards, we have repeated consolidation, and the content has a much higher chance of being retained.
4. Repetition – within the course, but also at the start of every subsequent period, lesson or lecture, repeat (not in parrot fashion) the ground that was covered previously. Take five or ten minutes at the start to ask key questions about the previous content.
5. Delayed assessment – give learners exercises to do after the course and explain that you will assess them a few weeks, months after the course has finished. This prevents reliance on short-term memory and gives them a chance to consolidate their knowledge/skills.
6. Record – it is education and training’ great act of stupidity, not to record talks, lectures and presentations. They give the learner subsequent access to the content and therefore spaced practice.
7. Games pedagogy – Games have powerful pedagogies. They have to as they are hard. It works through repeated attempts and failure. You only progress as your acquired competence allows. Most games involve huge amounts of repetition and failure with levels of attainment that take days, weeks and months to complete.
8. Spaced e-learning – schedule a pattern in your online learning, so that learners do less in one sitting and spread their learning over a longer period of time, with shorter episodes. Free your learners from the tyranny of time and location, allowing them to do little and often. In education this is homework and assignments, in training subsequent talks that need to be emailed back to the trainer/tutor.
9. Mobile technology – the drip feed of assessment over a number of weeks after the course or redesign the whole course as a drip-feed experience. We have the ideal device in our pockets – mobiles. They’re powerful, portable and personal. Push out small chunks or banks of questions, structured so that repetition and consolidation happens. This usually involves the repeated testing of the individual until you feel that the learning has succeeded.
10. Less long holidays – it terms of public policy, increasing school results would be better served by avoiding the long summer holiday and restructuring the school, college and University years around more regular terms and less long vacations.
The retention benefit works like compound interest as you’re building on previous learning, deepening the processing and consolidating long-term memory. It is, in my opinion, the single most effective strategic change we could make to our learning interventions.
Friday, November 19, 2010
Thursday, November 18, 2010
Wednesday, November 17, 2010
Tuesday, November 16, 2010
Click the "Caribou Contest" keyword below to see previous posts regarding the contest. There is also a link on the side to go directly to the Caribou page for details.
Thanks to those teachers who are challenging their students and approaching problem solving, math and technology in this integrated way.
(Note: Caribou Cup pictured at right is NOT the actual Caribou Cup, nor is it a reasonable fascimile. Actual Caribou Cup may differ in size, material and likeness.)
Thursday, November 11, 2010
Wednesday, November 10, 2010
Wednesday, November 3, 2010
Monday, November 1, 2010
Friday, October 29, 2010
Thursday, October 28, 2010
Friday, October 22, 2010
Thursday, October 21, 2010
Election platform aims to put focus back on education, not ineffective testing
Ontario teachers are tired of feeding government's insatiable appetite for evidence that its top-down initiatives are working.
In anticipation of the October 2011 provincial election, the Elementary Teachers' Federation of Ontario (ETFO) has prepared an education platform
ETFO, which represents more than 76,000 education workers, believes the system can do a better job of addressing the learning needs of diverse student population and ensuring that graduating students are well-prepared for higher education, training, and citizenship. "Strengthening the education system will contribute to a healthy, vibrant society in the future," writes ETFO President Sam Hammond.
A top issue for ETFO is a standardized testing and how this deprives more important educational priorities of needed resources.
ETFO says that current Liberal government has focused on increasing the achievement levels in literacy and numeracy as measured by the grade 3 and 6 tests administered by the Educational Quality and Accountability Office (EQAO). "The political imperative to see 75 percent of grade 6 students achieving an above average level 3 in these tests has led to a disproportionate amount of classroom time and resources being allocated to teaching literacy and numeracy."
Teachers, ETFO says, are spending increasing amounts of time collecting assessment data related to EQAO "to feed the government's insatiable appetite for evidence that its myriad top-down initiatives are leading to improved student test scores. Consequently, not all students receive a balanced curriculum that pays sufficient attention to social studies, science, the arts, or health and physical education. Scaling back on the literacy and numeracy assessment initiatives is the top concern identified by ETFO members."
There are alternatives. Finland, a top-performing nation on international assessments conducted by the Organization for Economic Cooperation and Development uses random sample tests to occasionally check to see if its curriculum and teaching approaches are appropriate. Ontario should adopt the same approach, ETFO says.
"The most effective assessment of student progress is the assessment that teachers do every day in the classroom," the platform states. "If the government is truly interested in improving the levels of student success, it should put its focus on supporting teachers' skills in ongoing classroom assessment rather than on the limited measurement of EQAO tests."
Meanwhile, the number of specialist teachers at the elementary level has significantly declined since 1997-1998 as the result of a funding formula introduced by the Mike Harris Conservatives. Recent small increases in funding for specialist teachers "still leave elementary students significantly short-changed in terms of their access to quality programs in the arts and health and physical education," says ETFO.
Tuesday, October 19, 2010
Please refer to this post for Frequently Asked Questions regarding the Progress Report Card. We will be adding FAQs as they occur. Feel free to add your own question by clicking on the "comment" link below and they will be answered as soon as possible. If you have your own answer or discovered some alternative method or idea other than the one provided, please feel free to add them!!
Tuesday, October 12, 2010
A reminder to all teachers and students that the first Caribou Math Contest is tomorrow for grades 3 to 8. This year students and schools will be competing for the Caribou Cup!
We have some exciting updates to the competition this 2010-2011 testing year that we could not wait to share with you! Available to all students, teachers and parents with a Facebook account, is our friendly math contest mascot, Carl Caribou. He is an excellent resource for students who need some tips on how to answer questions for practice tests, need hints to difficult problems and receive helpful reminders of current events and updates in regards to the Caribou Cup. This is also an exciting chance for all participants to connect with friends across Canada and develop great relationships through an educational experience.
To access this great resource, please go to
We really encourage you to join the group so that you can not only improve your math skills, but also be a part of a great community.
Thank You and Good Luck,
The Caribou Team
Wednesday, October 6, 2010
Fear of Numbers | By Cynthia Macdonald | Why Kids Hate Math, Math Tutoring Services Toronto | University of Toronto Magazine
Why do so many kids struggle with math?
The first time it happened, we were in Grade 11: six or seven teenagers, in line at a doughnut shop. I felt an urgent tug at my sleeve.
“Cynthia,” my friend D. whispered, pulling me away. “Do I have enough for coffee?”
He opened his palm to reveal a damp cluster of nickels, dimes and quarters. It was far more than the 50 cents needed for a cup, but D. had no way of knowing that.
Now, I wasn’t much of a math student myself, but at least I could count change. Later, I found out that several others in the group had also been acting as after-school accountants for D. – an eloquent, funny boy who nonetheless lacked even the most basic arithmetic skills.
How many people like D. walk among us? There may be many. According to a recent federal government report, only half of Canadians have the numeric skills and knowledge “necessary to function well” in society. Illiteracy is a much discussed problem, but its sibling – innumeracy – goes relatively unnoticed. Perhaps it’s because we have long internalized the idea that, while reading is necessary, mathematical ability is the gift of a chosen few.
“Stand firm in your refusal to remain conscious during algebra,” Fran Lebowitz once wrote. “In real life, I assure you, there is no such thing.” Lebowitz was wrong, of course: mathematical reasoning is necessary all through life, affecting decisions we make in personal finance, travel, cooking and real estate, to name just a few. Our collective inability to analyze data has left us at the mercy of politicians and their advisers, who likely also quail in the face of math. “Innumeracy,” wrote math professor Lynn Arthur Steen in his 1997 book, Why Numbers Count, “perpetuates warfare, harms health and weakens families.”
Today, the Canadian public school system still turns out teenagers who are left puzzled at the cash register. Earlier this year, the Toronto Star reported that one-third of community college students in Ontario are in danger of failing first-year math. This could be linked to the fact that one-third of all high school students are currently registered in applied (non-academic) courses. A 2004 study showed that 60 per cent of these students were also failing, or close to it.
A small cohort of kids have always “just gotten it,” but the situation is frightening for those who don’t – especially in a work climate where some firms now administer standardized math tests to prospective employees.
Newfangled instructional methods are always being tried in an effort to right things. The 1960s saw the introduction of “new math” as a panicked response to Russia’s Sputnik program, which was thought to be the result of the country’s superior educational system. The method confused parents, was roundly mocked by satirists such as Tom Lehrer and Charles Schulz, and died within 10 years. More recently, President George W. Bush convened the National Mathematics Advisory Panel to arrest the lag in American science and engineering capability. (In 2006, the United States scored 25th out of 30 countries on the math portion of the Program of International Student Assessment. Canada, reassuringly, scored 7th.) Its final report advocated yet another overhaul of how math is taught.
John Mighton (BA 1978 VIC, MSc 1994, PhD 2000) would agree that the state of North American math education is far from ideal. The eminent playwright, teacher, author and U of T adjunct math professor has long been the Chicken Little of arithmetic, using words such as “disaster” to describe the state of student numeracy in Canada’s public schools. The tutoring program he started in his Toronto apartment 10 years ago (known as JUMP, short for Junior Undiscovered Math Prodigies) was originally designed for struggling inner-city kids, but is now gaining respect in classrooms as far afield as England and South Africa.
Mighton is routinely portrayed as a back-to-basics saviour, rescuing children from the inquiry-based (also known as reform) math that is currently the fashion in Toronto schools. It’s a reputation that makes JUMP attractive to those of a more conservative educational bent. But while it’s true that his system stresses pencil-and-paper work, learning concepts in steps, computational fluency and extensive review, it would be wrong to say he wants things the way they used to be.
More than anything, Mighton says, we need to change the culture of self-defeat that persists in so many math classrooms. The change he seeks is as psychological as it is pedagogical. “As early as Grade 3 the kids notice which kids in the class are smarter, and which ones are less capable academically,” says the 50-year-old polymath, who’s also the author of two books (The Myth of Ability and The End of Ignorance) that reinforce this point. Mighton contends that the time-honoured practice of sorting children into A, B and C groups only worsens math phobia: “By the time kids are streamed in high school, they’ve lost any motivation to do math or engage in it.” Two separate studies on JUMP, conducted by the Ontario Institute for Studies in Education at U of T, suggest that the program increases math confidence.
Despite this, Mighton can’t get a break at home. This past May, consultants employed by the Toronto District School Board reached into their pencil cases and jabbed him with a set square. The board issued a position paper on his methods, condemning JUMP as a form of “rote, procedural learning where students memorize very small computational steps with little to no conceptual understanding.” This is another way of saying that Mighton wants to give students the topdown directive that 4 x 4 = 16, instead of guiding them to discover on their own that 16 is equal to four groups of four.
Documents like this infuriate Mighton (to the extent that he can be infuriated: quiet and firm, he shares a birthday with Gandhi). The statement, he says, is “completely full of misinformation. They’ll say this is the correct way to teach – but we didn’t say that wasn’t the correct way to teach! We actually advocate the same thing, but they’ve never looked closely at our program.”
The Toronto board adheres to the reform style of teaching that has become increasingly popular over the last 15 years. Reformers tend not to be as pencil-and-paper-bound as Mighton is. They believe a dependence on traditional algorithms prevents children from understanding the processes behind a given problem. To this end, they often link math concepts to real-life situations, use concrete objects and encourage group work. They emphasize the importance of understanding mathematical concepts over computational ability, stressing the “why” over the “how.”
But are the two camps really so far apart? Thumbing through Mighton’s Grade 4 workbook, I see that he, too, advocates the use of materials such as card games, coins and fingers. He also stresses that a concept be learned before an algorithm (such as long division) is introduced. “John Mighton is a friend of mine,” says reform math advocate Barry Onslow, a retired professor of education who contributed to the development of the current Ontario math curriculum: in short, someone you’d think would be Mighton’s enemy. “People want to have this polarization,” he says. “They want things to be black or white. They aren’t. There are many shades of grey.”
Nevertheless, other reformers still view Mighton as Mr. Drill and Kill. Some Toronto teachers who want to use JUMP are specifically told not to by their principals, and have to sneak its tenets into their lessons. This is not the case in Vancouver, where JUMP methods are openly embraced. “Are people more backward out west?” Mighton asks. “Why is it we are being welcomed there, when people are forced underground here? And would they welcome our program if they weren’t getting results?”
A similar battle is being waged in California, the centre of what’s become known as the Math Wars. For almost two decades now, reform and basics advocates have been at each others’ throats, amassing research and mounting publicity campaigns to support their respective sides. Remember the Reading Wars, which pitted whole-language modernists against phonics traditionalists? Trade letters for numbers and you get the idea.
Some reformers condemned the National Mathematics Advisory Panel’s final report, released this spring. They thought it was too rigidly basics-oriented in nature. Reading it, however, one sees that its language is quite even-handed: “To prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency and problem-solving skills,” it says. “Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive.”
The fact is that traditionalists such as Mighton and reformers such as Onslow share many ideas. Perhaps the way to mathematical salvation lies in seeing what they have in common, instead of what divides them. We forget that when a war is being waged, children know about it. In the 1970s, students such as D. and myself saw “new math” disparaged every day in cartoons and newspapers. It made us mistrust the entire subject.
If there is one idea that unites the math fixers, it is this: Children must understand what they are doing. Today, D. would likely be diagnosed with a learning disability, but no matter. Both Mighton and Onslow believe that if he’d only been taught why he was performing mathematical operations, he too could have succeeded. “Why do we invert and multiply?” Mighton asks a group of teachers gathered for one of his training sessions on a sunny spring morning. We are all learning how to divide fractions, something we’d done in Grade 7 and now have completely forgotten. There is a rule for it, but no one’s ever taken it apart to show us the machinery. Mighton does, and we all breathe a sigh of relief before putting the idea into practice ourselves. We do not move on until everyone gets it.
Barry Onslow’s approach is more direct, but that might not be a reform thing – that might be Barry Onslow. “What’s 10 divided by a half?” he asks me. “If I said that to you, what might be your instant reaction?”
“My instant reaction would be to freeze up completely,” I tell him.
“But if I said you have to give me an answer…”
“Oh, all right then,” I stammer. “Five.”
“That is the answer that most people would give,” he says, “because you think of 10 sheared in half. But that’s not what it means. What it means is, how many halves are there in 10 wholes?”
Even I can easily see that it’s 20; divorced of meaningless symbolism, the idea makes perfect sense. But will I remember this later? “Your experience in school was one of memorizing rules,” Onslow tells me. “And if you forget those rules, then you forget your math. But if mathematics makes sense, you don’t need a lot of rules, because it fits into a framework.”
The scary reality remains, however, that math failure seems to persist for some kids, no matter what instructional method is used. When I speak to my own children’s math teachers, they complain about everything except methods. Scarce resources, disparate knowledge among students and their own anxiety are much bigger problems.
Children in Asian countries persistently score higher on international tests than their counterparts in North America, but this is not necessarily because they are taught differently. Maybe they just study harder. With more homework, shorter holidays and fewer extracurricular distractions, it’s said that an average Chinese pupil enters university with two more years of education than a Canadian one.
And teacher quality is important. “I read this paper recently where they looked at factors such as gender and socioeconomic background, and they found that everything was washed out by teacher effect,” Mighton says. “If you have a good teacher, all those other things aren’t so important.”
Regardless of the teaching method, learning math is like walking a tightrope – it requires sharp attention and a constantly active mind. One slip and you fall off. Expecting each student in a class of 30 to follow along at the same pace is asking a lot, especially in an era of video games and three minute music videos.
“The research in psychology suggests that attention is the key to everything,” Mighton says. “If you’re not harnessing attention, keeping it focused, then the brain is not developing. I think a lot of things that used to train attention, like how to stay on task, to focus, how to look for patterns in things – all those deeply important cognitive skills – aren’t being fostered in kids. One of the effects is that kids have more attention problems now.”
Culturally, we have also done children a disservice by depicting mathematicians as geniuses, lunatics or both. Movies such as A Beautiful Mind and Good Will Hunting (in which John Mighton played a small part, both as a consultant and an actor) and the television show Numb3rs all command public interest, but their heroes tend to be tortured loners who sit above and apart from the rest of us.
According to Onslow, math is anything but a solitary pursuit. “How do we learn?” he asks. “Do we learn in isolation? We have to get our ideas out in the open where people can discuss them. That way, they can see why some of their thinking might be faulty.” Similary, Mighton stresses active, rather than passive learning, though JUMP is less language-based than most reform classes (so that, among other things, ESL students will not be at a disadvantage).
It should be mentioned that Mighton himself was no child math prodigy. “Sometimes I did well, but sometimes I did terribly,” he says. Although he eventually earned a PhD in mathematics, he almost failed calculus in his undergraduate years at the University of Toronto. None of this surprised him. As a child, a glance into his older sister’s psychology textbook had convinced him that geniuses reveal themselves early; he was not one.
Mighton turned to the consolations of philosophy, earning a master’s degree in the subject from McMaster University in 1978. It was during this time that he developed his own life philosophy: that genius – or at the very least, extreme success – might just be something you can program. He read Sylvia Plath’s Letters Home, which was revelatory. “It was clear that she taught herself to write by sheer determination,” he says. “She did everything she could to train herself, including writing imitations of the poems she liked.”
Plath’s method worked for Mighton, and he has since become one of the country’s most successful playwrights. His approach is strikingly methodical. For Mighton, a so-called creative work does not erupt like Krakatoa in the artist’s mind. It is a tightly constructed puzzle, given shape and nurtured by the proofs of those who’ve gone before. “There are patterns, structure and logic in the arts,” he says. “It’s very similar to mathematics.”
His is a highly democratic vision of genius, open to the hardworking and the strongly encouraged as well as the gifted. Ironically, this is something Mighton figured out on his own. The traditionalist’s journey, then, has actually been reformist in nature, built on ideas he discovered and mastered for himself. It’s an example of how patterns and the connections between them can be found in so much of what we do – proof that mathematical thinking, rather than the memorization of formulas, is an essential skill to develop.
Every good math teacher agrees on at least one thing: math is a subject of lifelong importance, and not a childhood torture on the order of bra-snapping or dodgeball. Onslow advocates family math nights to reacquaint math-anxious adults with the subject. Mighton believes in later math learning, particularly in a climate of rising concern about brain fitness in the aging population. “It’s almost an evangelical experience when adults go back and find that they’re smart enough, because many people carry a great burden of feeling stupid from school. It has a great psychological effect. People forget the adjustments they went through to deal with this stuff,” Mighton says.
“Don’t know much about algebra,” Sam Cooke once sang; “don’t know what a slide rule is for.” Cooke thought the mere knowledge that one and one is two would be all he needed for true happiness, but math educators such as John Mighton and Barry Onslow think differently. They believe that happiness and advanced math are not necessarily mutually exclusive. One day, the rest of the world may even agree with them. Now, what a wonderful world that would be.