Is Cramming for a Test a Form of Cheating?

How Can Some Math Students Learn So Little in 12 Years of Classes? This afternoon, my Fulbright colleague and math teacher Elizabeth Agro Radday and I were considering this question. Despite a decade of effort, many young students learn little about mathematics except that they hate it. How, we wondered, could twelve years of schooling in math result in such poor outcomes for so many?

The same could be said for history, my discipline, of course. (I have often fretted at how little my students remember about the French Revolution, studied just one year before.) But Liz and I were chatting after visiting the classroom of Pekka Peura, a respected math teacher at the Martinlaakson Lukio, here in Helsinki.

Coincidentally, several years ago Peura came to ask himself the same question Liz and I were kicking around this afternoon. The answers he came up with are really not new, but based on a century’s research about motivation and students’ ownership  of their learning.

Peura has implemented a mastery-based, student-controlled math curriculum in his classes.  He floats around the room, helping when needed, but allows the students to manage their own learning, to the point of scoring their own final exam.

It isn’t a simple system and must have taken an enormous amount of labor. Peura has uploaded a detailed solution to every problem so his students can see how they are doing as they go–and which skills are the most essential to learn before moving on. When I asked how it worked, Peura pulled out his iPhone and quickly brought up a sample problem. Once the students complete a given “quiz,” they score themselves by using Peura’s rubric. Such a solution is what he showed me on his phone:


Students also have a large card listing each lesson in the course. They score their own work, see where they need more work, and mark down their score on their card. They are constantly asked to reflect on whether they need more help, have a basic grasp on a topic, or fell they have mastered a lesson. They decide when they are ready to tackle a new topic. Grades are based on how far students progress into more complex topics.

Won’t the students cheat and inflate their scores I asked? He smiled and said some might, but he knows where they are in their learning after checking in with them every day. He also inferred that those in charge of their learning begin to take outcomes seriously and understand that moving on to more complex math without mastery of what comes before is a recipe for failure and stress. And students cheat on traditional assessments as well, while often learning less.

Peura even characterized cramming for a test as “cheating” because it is a way of avoiding doing the learning that is really the chief object of study. We teach them to forget as well as to learn, he told me. We make them learn a lot for an exam and then encourage them to forget it so they can cram more information for the next test into their short-term memory. Since this doesn’t lead to real learning but may result in an inflated grade, it is arguably a dishonest or at least inaccurate assessment of their learning. Teachers should find a way to discourage this kind of preparation. One way is to eliminate high-stakes summative assessments.

dunning-krugerAt lunch, Peura talked about his students’ process of math learning in reference to the Dunning-Kruger Effect. I didn’t know what this was, so he showed me a graph of it on his phone. Many
math students, he argued, at first have an inflated sense of their abilities but are then crushed by their inevitable failure. A teacher’s job is, in part, to move them to the part of the curve at which they can see the relationship between their rising confidence and their growing expertise. Putting students in charge of their own learning, Peura seemed to be arguing, gets them to the right side of the graph more quickly. It makes sense: by offering his students clear and lengthy rubrics that require constant self-reflection and self-assessment, he has removed much if not all of the dark arts from his students’ experience of math.

As a social studies teacher, I wonder how I can make use of such a teaching style. The objective nature of much mathematics makes the self-reflection model fitting. Could it work in teaching the causes and impact of the French Revolution?


“Peura’s Theses”: from Suomen Kuvalehti,  “A Teacher Who Does Not Teach,” translated by Google’s miraculous-but-clearly-not-Finnish robot translator, with a few edits by yours truly.

  • All students are able to learn when given a suitable pace;
  • Teaching characterized by lecture is appropriate for only a small percentage of students. For most it is too slow or two fast;
  • Too slow a pace frustrates; too fast a pace prevents proper training for building new data upon knowledge already learned, making it more difficult to absorb; the result is a negative spiral;
  • Learning is more effective when the student is required to reflect upon lessons and discusses them with others;
  • The teacher’s job is to help students identify their skills and their own way of learning;
  • Most traditional assessments are pointless and do not measure actual know-how. Instead, they cause undue stress for many students and decrease their quality of life. Therefore, teachers must work to develop new metrics;
  • This method is applicable to mathematics in addition to other subjects as well as primary school teaching.



Sources:; (using Google Translate, which struggles with Finnish!)

The Movement North

europe-crisisThe image here is linked to a terrific website, and a great resource for teachers, visually demonstrating the enormous movement of people into Europe over the past few years. You can click on any country and see its outgoing or incoming migrants.

Many thanks to Marjo Sassali at the normal school here in Jyväskylä for sharing this with me! It complements a lecture I attended the other day by Dr. Erka Caro, a post-doc researcher whose work focuses on migration from the Balkans into the EU.

I hoped to find a similar animation of the the post-1945 movement of peoples but without luck. One article, published in 1950 in Economic Geography, estimated the number of refugees in Germany alone at 14,000,000 in 1950. During the same period, during the partition of India and Pakistan, “one of the largest and most rapid migrations in human history” took place, “an estimated 14.5 million people migrated within four years.”

There was tremendous violence during both these migrations and, like today, most of the victims were utterly blameless people caught in unimaginable situations.

Dr. Caro points out that today’s mass migrations take place against a backdrop of greater migration in general. The number of people living and working away from their homelands has been growing consistently over the past decades and doesn’t show signs of stopping. Transportation is less expensive than ever, new technologies increase communication between people everywhere and make the world seem smaller. A third cause, Caro argues, is the decades-long export to developing nations of alluring images of lifestyles in the North, a “trigger” to those who now have the means to move in the direction of such promises.

From on March 16: “The UN Refugee Agency said today that more than one million people, mostly refugees from Syria, Iraq and Afghanistan, have now crossed in to Greece since the start of 2015.”

Human migration, usually individual, is a feature of globalization, like the flow of information or goods. And while nations have spent years negotiating free-trade treaties, there is not the same international cooperative effort given to managing and regulating the flows of the millions of people on the move.

So even as thousands pour into Macedonia from Syria and elsewhere, tens of thousands of Macedonians leave for Germany and other wealthier nations in the EU. (Macedonia is not a member of the EU but its citizens can travel to the Schengen countries without a visa. The fact that the EU does not yet even recognize the name “Macedonia” but calls the nation “The former Yugoslav Republic of Macedonia,” suggests there is still some way to go.) Macedonia then is both a giving and receiving nation in terms of the flow of migrant people.

Here in Central Finland, most of the migrants are from Iraq. They are primarily young and male. Will they stay? Will they be sent elsewhere or back to Iraq? Will they be taught Finnish and allowed to join the mainstream of society? Or will they remain here and become an isolated community cut off from the social welfare state?

According to Dr. Caro, seeing the Macedonians in Germany as temporary migrants who will automatically leave when their time there is over is not a usable alternative. Since World War II, short-term migration plans, whether in the US, Germany, or Australia, have not led to the outcomes policy-makers hoped. What to do? Even encouraging economic growth in the less developed nation might create more outmigration as it becomes more affordable.

Finland’s migrants come not for economic opportunity but to flee violent conflict. I am very curious to see which choices the Finns make as they confront a new era of immigration and a likely re-definition of what it means to be “Finnish.”

English and Finnishness, First Thoughts

Whehqdefault1n I flip on “Radio Kompassi,” 88.0 FM, what do I hear? Tonight, “The Logical Song,” by Supertramp followed by “Army of Two,” by Olly Murs. Then ads in Finnish. “Halo,” by Beyoncé and more local ads. Then Springsteen and a mailed-in duet by Sir Elton and LeAnn Rimes. Ads (in Finnish) and then, at last! A song in Finnish!

My mind goes back eleven years, when popular musicians in Germany unsuccessfully petitioned the government to create a law mandating a minimum percentage of music on the radio to be in German. France has had such a law since 1994, though it is subject to ongoing controversy and resistance from radio stations.

But I have heard about nothing along these lines in my two months in Fihqdefaultnland. I have heard about right-wing groups “patrolling” the streets of Turku or Tampere, but their concern is a small number of poor and socially isolated people. Is there not irony in the fact that these defenders of Finland wear sweatshirts emblazoned with “Soldiers of Odin” in English? It sounds like a joke, but wouldn’t a nativist slogan be in the mother tongue?

David Tow, a Fulbrighter in Finland, has interviewed many young Finns about their ideas of Finnishness. He told the audience at the Fulbright Forum yesterday at the University of Jyväskylä, that young Finns see themselves differently than their parents’ generation. They are millennials, more international and cosmopolitan, less introverted. Add the waves of new immigrants to smartphones, Instagram, and snapchat, and what “Finnish” means seems to be shifting quickly.

Yet I hear little about a threat to some distinct, authentic Finnishness. What I hear from many Finns is this: Finland is a small country so know it must internationalize in order to thrive. Few Finns seem worried about American cultural influence, in part, they say, because Finnish culture is so strong.

One of the pillars at the center of this culture is language. Fluency in Finnish seems to be a crucial marker, though even this is complicated by the fact that Swedish is also an official language and competence in Swedish also qualifies an applicant for citizenship. But the complexity of Finnish and the difficulty of a visitor achieving any kind of comfort with the language makes it a fortress for Finnishness, housing history, belief, shared values, etc.

I wonder if, even as Finland diversifies (a trend treated as a given by people I meet here), the difficulty of learning the Finnish language will become an even more dramatic marker of who is Finnish and who is not. Not in a nativist, anti-immigrant fashion I hope, but as the carrier of inherited ideals and values, a shared past, and so on. Where once “Finnish” meant not Russian and not Swedish, perhaps in the future, the Finnish language will either be an embattled tongue riddled with English words and phrases, or it will function in an affirmative fashion, as the voice of a newly redefined people.



How Not to Educate Students for the Future

The current political climate in the US is so harsh and it seems every topic cleaves us into two antagonistic camps.  Take climate change and migration, for example.

Looking through the new Finnish Core Curriculum,  on the other hand, I am powerfully struck by the calm assurance of the authors. In an English-language report about global citizenship in the new curriculum, Liisa Jääskeläinen of the Finnish National Board of Education provides translated paragraphs that I find stunning. For example (the emphasis is mine):

“Pupils are guided in how to live modestly and to share what they have. They will also learn how to act as enlightened consumers. The intangible elements of welfare will be highlighted. Pupils are encouraged to reflect on how to transform their lifestyles so that raw materials and energy can be saved and biodiversity safeguarded. Special attention is to be paid to climate change. Basic education will open views to global responsibility beyond generations. Through their choices and actions schools express their responsible relationship to the environment, and choices that may be harmful to the existence of raw materials, energy or biodiversity are to be altered in a sustainable manner.”

An easy contrast to this comes from presidential candidates who deny climate change or try to brush it away. Senator Marco Rubio, for example, recently admitted that, “Sure, the climate is changing. And one of the reasons why the climate is changing is because the climate has always been changing. There has never been a time when the climate is not changed.” And of course, there is Donald Trump and his imagined wall on the US-Mexican border. As you can see from the nice graphic below from the Wall Street Journal, both immigration from Mexico and the number of undocumented immigrants from Mexico in the US have been falling throughout the Obama years.


So our political class cannot be trusted to educate the people about these complex issues. They have too much to gain by muddying the facts. The mainstream media has not proven very helpful either. So, once again, it is up to the public schools.

Since education is largely left to the states in the US, what they do matters in terms of preparing American children for the challenges ahead, like climate change or the loss of American manufacturing jobs. These are not issues touched by Common Core or by most state standards, including in my liberal home state of Oregon.

Instead, many states are turning to private education companies for solutions. Twenty states are working with a company called the Partnership for 21st Century Learning. (Am I wrong to be annoyed by the missing hyphen in the name?)

Guess what? This company, which calls itself P21 for short, will create even more standards for students and teachers to follow, will hand teachers content to teach, and will “Implement a recognition system—such as badging–for teachers, principals, and school district instructional support personnel to support and inspire professional development on global issues and competencies.” Yuck.

Not surprisingly, sponsors of P21 include large corporations with complicated outlooks on global education, including Ford and Disney. Pearson, the world largest publisher of books is also a “platinum member.”

P21’s documents call for a lot of involvement of “business leaders.” Why? Why not let teachers craft what they teach?

P21’s website has a whole section on “Citizenship.” But what is striking (and keep in mind, twenty states work with this group) is the complete absence of the term “global citizenship” in the materials of a group focused on teaching students about the skills needed for the future.

This is contrast to Finland where the national curriculum states,”Basic education will set out the foundation of global citizenship based on the respect of human rights and it will encourage pupils to act as agents of change.”

To P21, although students in the US need to be trained for “success” in a global economy, citizenship in the 21st century is not global, it’s … “21st Century.” Citizenship has a time but not a place.

I can only think that this brings us back to Trump and Rubio & co. It appears to be too political to call for empathy and solidarity with others, even as we live in a globalized world–of shrinking glaciers and rising seas (like in Miami Beach, as Marco Rubio has seen). We have Zika and other health threats that do not stop at borders. We have radicalized groups seeking to destabilize modern society.

We can only solve these problems together. Rubio is correct in a way when he says a law can’t change the weather. We need hundreds of laws and binding international agreements to slow the impact of climate change. But the organization seeking to shape our students’ vision of the world, will not say the words “global citizenship” in its documents.

As Corey Robin wrote, at “Global society, 21st-century skills: These are buzzwords for … international capitalism ….  Education is the quintessential American hustle.”

Alternatively, Americans could, like the Finns, at least express the desire that “Global education [work towards] the preconditions for just and sustainable development in line with the development goals of the UN.”


Equality and Justice in Education?

This cartoon, floating around on Facebook and elsewhere, makes me think about how we offer education to children.

What does giving the smallest child here a second box do for or to that child? What does the group gain when all three kids can see over the wall?


This seems true to me on the level of the individual as well as on the level of the community. Some schools, some communities need more so their children can have access, but also so they can contribute their talents to society.

When this comes to global education, we can see it as an unnecessary luxury for students in poor districts to study multiple languages, learn about climate science, and travel abroad (or art and music, for that matter). Or we can see it as a form of justice from which we all benefit.



Teaching the Migration Crisis

“Refugees Welcome,” Regensburg, Germany

Riding the 21 bus from the Altstadt of Salzburg, Austria, to our comfortable rooms at Haus Ballwein, just where the fields begin at the edge of the city, we stopped near the wonderful Augustiner monastary-brewery. The rear double doors opened to let a grandmother push her stroller onto the bus.

Standing there, holding my rolling suitcases, I was struck by the emblems of the Red Cross, emblazoned over a dilapidated building. On its gates, stenciled paintings of running figures and the words, in English, “Refugees Welcome.” We had stopped outside a center for people fleeing Syria, Afghanistan, Iraq and other nations in crisis.

In Regensburg, Germany, we had seen similar signs. Outside Jyväskylä, Finland, where we are living until July, unaccompanied minors, mostly Iraqi I’m told, live in a camp, their futures uncertain. In Oulu and Turku, an anti-immigrant group calling itself “Soldiers of Odin,” patrols the streets. A new chapter has appeared in Estonia, despite the fact that that country hosts virtually no refugees at all.

The current “migration crisis” gripping all of Europe is a topic all students deserve to wrestle with. What is to be done to help settle the millions of people roaming Europe, cut lose from their homelands by war, instability and economic uncertainty? What of the millions more taking shelter for who-knows-how-long in camps and cities across the Middle East?

IMG_4672.jpg“Kein Mensch ist Illegal” (“No Person is Illegal”), Regensburg Germany

This is not an issue that will soon disappear. Politicians from the US to Hungary to France will make or destroy their political careers by responding to this new, mass migration–as well as the others already underway around the world.

And how many people will be forced to leave their homes in coming years as the impacts of climate change become more widespread? According to the World Bank, “In Bangladesh, 40% of productive land is projected to be lost in the southern region of Bangladesh for a 65cm sea level rise by the 2080s. About 20 million people in the coastal areas of Bangladesh are already affected by salinity in drinking water.” Bangladesh alone could produce millions of climate refugees.

Upper-secondary students will have a chance to weigh in soon as voters, as politicians seek to protect or transform challenged notions of national identity. How can young people learn to evaluate this issue?

Here are some questions for students to consider:

  • What rights do people have to cross international borders in time of crisis?
  • Do people have a general right to move freely throughout the world? Why or why not?
  • What are the international agreements on this issue? (Look here.) What do you feel is the morally just answer?
  • When can a nation rightfully announce it can take no more refugees or migrants, no matter how worthy their need?
  • Should nations refuse entry to refugees but still admit wealthy or skilled foreigners seeking to immigrate?
  • Should there be a global agreement to collectively fund long-term refugee support efforts no matter where the refugees initially go?
  • What determines if a person a “refugee” or a “migrant?”
  • Should unaccompanied minors, migrating across international borders, have different rights than those with adults?
  • What is my country’s policy for taking in refugees?

There are, of course, many more important questions for students to ask. As an American, I wonder why the Finnish government is facing tough questions regarding migrants from Iraq while my government is not. This just doesn’t seem fair, somehow. Why should Germany take in so many more people than France or the UK? Should the EU be paying for the maintenance of its southern border or is this the responsibility of the (often poorer) nations that happen to be situated there?






Bavaria and West Virginia

Erneuerbare Energien in Oberstdorf Photovoltaik-SolaranlagenA few days ago, I traveled from Finland to Munich to Regensburg, a small city in eastern Bavaria. I spent a year here, 2004-5, and much looks just a it did. My family and I dined at our favorite pizzaria in Regensburg, L’Osteria, for the first time in eleven years. I bought Regensburger rolls at a number of bakeries I remember fondly. In the toy store where I once took my two-year old–now thirteen–displays of wooden Christmas ornaments stood on the same shelves.6898303724_ee5400b2cf_b

But something has changed. The countryside between Munich and Regensburg is transformed. Numerous fields are filled with vast arrays of solar panels. Seemingly half the buildings in central Bavaria have panels. Countless barns and industrial buildings are covered in them.

When I lived here a decade ago, I was struck how Germans ascribed any warm day to climate change, something Americans just didn’t do in the early Bush years. Ten years on, they aren’t just talking about the weather but putting there concerns into action.

It is heartening that Germany and its Conservative leader, Angela Merkel, have taken the lead in pursuit of a modern economy fuelled by sustainable power. In 2015, as one headline announced, “Almost 33% Of German Electricity Came From Renewables in 2015.” Things are looking up.


And then …  I read this, in the Daily Telegraph of Blue Field, West Virginia:

CHARLESTON — Fears that global warming would be taught to West Virginia students provoked members of the House of Delegates to act on staving off education in the state on the topic while repealing Common Core Standards Friday. The bill that will prohibit the State Board of Education from using Common Core and related testing measures passed the House of Delegates by an overwhelming 73-20 vote, with seven members absent.

Really, it shouldn’t be a surprise that a legislator, quoted in the article, claims they are getting rid of their science standards because legislators didn’t want to “politicize” science by teaching about climate change. But reading about it in Germany is a stark reminder of the work to be done.

“Delegate Jim Butler, R-Mason, said his review of the standards revealed measures to have students show causes for global warming and ways to prevent it. ‘In an energy producing state, we are teaching our kids we are doing immoral things here in order to make a living in our state,’ Butler said.”

(Sure, the Obama administration is doing what it can despite such action on the state level, but I don’t rest easier knowing it also spied on communication between Chancellor Merkel and UN Secretary-General Ban Ki-moon about the Paris climate conference.)

As a teacher, I worry about another generation of students raised with little attention paid to climate change–or, as other recent journalism has shown, ignoring it or getting it wrong. I find the argument that  we do a poor job teaching climate change and its impacts because most important research has been done since most teachers left school unpersuasive.

I am lucky (and everyone should have this luck) to teach at a school where science isn’t politicized and where teachers are trusted to know what they are talking about. But this clearly isn’t the case everywhere. When will West Virginia or Texas ever teach students according to scientific knowledge rather than the interests of each “energy-producing state”?

I have come to wonder if the only way for American education to change, nationally, is for teachers and students to go to jail.

Without picking up the tempting comparisons to the Civil Rights Act or the Voting Rights Act, I think the federal government must compel the states to mandate the teaching of science in science classrooms by threatening the education funding such states have come to rely upon (and other funding–remember how state drinking ages rose to 21 in the 1980s when the Reagan Administration threatened to withhold transportation funding?) .

But no such movement has ever begun from the top down. There have always had to be arrests and other shows of civil disobedience before the federal government acted. In this case, we may once again need the young to show the way. How else will state departments of education ever help prepare students for the challenges ahead?