When he teaches a math lesson, Tom Fisher wants students to feel confused. At least he wants them to feel this way from time to time and temporarily.
Especially the administrator these days, Fisher still teaches the algebra of honors in Breakwater, an independent pre-K-8th school in Portland, Maine.
For Fisher, it is important to mingle with mathematics and to play.
This is not the conventional way to teach the subject, says Fisher. Too often, mathematics teachers present information through conferences and working sheets to students, forcing learners to decipher the context and usefulness by themselves.
But for Fisher, there is a reason why students of the last year often wonder why they learn mathematics. This is because when the instruction is designed for tests, it is not sensitive to the question of whether the knowledge it transmit is sustainable, says Fisher. Worse, such a heavy approach prevents students from developing tolerance for confusion resulting in problems by themselves, he supports. This deprives students of the precious experience of conquering the problems that seem impossible at the beginning.
Thus, in class, Fisher tries to focus on the development of a feeling of play, and he found that he helps to focus on examples of the real world. These examples are disorderly and can cause temporary suffocation. “Everything is not pleasant and neat,” says Fisher, adding: “It requires additional reflection and additional reflections.”
For example, when the time recently came to build a lesson on fractions, Fisher made comparisons.
A pair of children in his class ended up comparing the person with the most geese in the person with less toes.
Another compared the duration of the videos.
Another has still watched the temperature over several days.
Fisher asked them to consider what made these questions easier or more difficult to understand, and they discovered that when a number was twice as much than another, it was easier because of the obvious relationship, but when they compared a hottest video of 403 seconds to a hottest day – it was more difficult. The discovery captures a characteristic of the relationships between numbers and the way we use them, says Fisher.
What made the lessons work is that the students selected what to compare, says Fisher. This gave them a feeling of agency and motivated them to tackle complex problems.
It is an approach that some researchers think they are too often absent from the class. Regarding mathematics, do they argue, there is not enough emphasis on the game. But with concerns about the development of students in these areas, especially postpandemic, would it focus more on the game to help mathematics?
Learn the game book
There is a false dichotomy between mathematics and the game that is common, especially in early childhood, explains Doug Clements, professor at the University of Denver, Colorado. Even among the researchers, this can cause “bulimic” partisan commitments to one or the other, he adds. This is unfortunate, because research has shown that they are deeply connected, says Clements. For example, a study have shown that the best “social -dramatic game” – where children occupy roles and interact on the rules – occurs in classrooms where there are both mathematics and literacy programs. So, an intentional teaching time and the game seems to be the most powerful to support learning, adds Clements.
The general usefulness of the game for learning is well established, especially in young years. For example, playing in early education reinforcement The development of socio-emotional skills and critical thinking. Some research has even suggested that she had the ability to Reduce socioeconomic inequalities.
But what do we mean by play?
For researchers, the “game” occurs when students take control of what they are doing. It is flexible, chosen voluntarily and yes, fun.
But that doesn’t mean it’s chaos, a free for everyone.
As when learning sports, language or music, structured practice is really important for mathematics, Barbara Oakley, a distinguished engineering professor for the University of Oakland, wrote in an email in Esurge. So, more pleasure can be useful, provided that it is based on automatic mathematical knowledge paths in the students’ brain. But at the same time, focusing on “pleasure” in mathematics can be harmful if it neglects structured practice. “The problem is that if it is not done correctly,` `Fun ” in mathematics is the equivalent of teaching a child to play the guitar by teaching them to play the aerial guitar. I mean, it’s fun! It’s easy! But that goes through all the movements without teaching playing the guitar, “she added.
Part of the objective is therefore to develop these skills. For this, researchers also see usefulness in an unstructured time.
An important element is to mix the free game with “guided game“, Which has a certain direction of an instructor. The National Association for the Education of Young Children has cataloged a game continuum: from “free game”, where students play without direction, to class education, where students receive an endless teaching flow. The different forms of play can be complementary, according to researchers as well as the University of Colorado, Denver. Basically, it is important to have both guided sequential development, where students are initiated into new mathematical concepts, as well as free games where they can try these concepts, says Clements.
How does it translate into class? In early teaching, where Clements specializes, he generally builds intentional lessons, then set up the classroom so that, as students play, they come up against mathematics at each turn. This could mean preparing the classroom with labels and blocks and other spatial and mathematical items. But another way is to teach a small group of students a game and divert them, says Clements. This appeals to the minds of students, he says, and it gives them more ideas to play. The objective is that students recognize themselves spontaneous mathematical concepts in the world. Once, a mother returned to point out that her preschool child had noticed that the bridge they trotted was made of hexagons, said Clements.
But the approaches reflected in class that mix the game and the teaching are rare, depending on Clements. Instead, many schools give students too little teaching in mathematics – or too little game.
Some also wonder if the emphasis on mathematics game can also transmit an involuntary message.
Another word for fun?
These days, almost all mathematics programs in early childhood and primary school include games, generally a game or dice, explains Yvonne Liu-Constant, a specialist in practitioners for Project Zero. At the start of the progress of a student, there are also a lot of articles for students to be handled physically, such as binding colorful cubes or bears that students use to count, she says. This is the result of a push to make mathematics more fun in recent decades, she said.
When Liu-Constant started teaching, it was all about it.
But lately, she wondered if it is not somewhat wrong. The problem? Over the years, he gradually entered the Liu-Constant that she continued to hit a wall in mathematics. Finally, she blamed it to a hidden message: when you devote yourself to making mathematics “funny”, you almost imply that mathematics are not already pleasant, known as Liu-Constant. We will never say only about art, she adds. The hypothesis is that art is intrinsically interesting. And for people who love mathematics, it’s already like art, she says.
It is crucial that the feeling of game in mathematics extends beyond activities and games, she said. It should be more omnipresent. It’s like that with his brother, an engineer in Taiwan, who finds mathematics so absorbent that he could spend all his free time thinking about figures, says Liu-Constant.
So, these days, in his work with the pedagogy of the project of Project Zero, a research arm in Harvard by relying on an “whole school approach” of learning, Liu-Constant has tried to rebuild the game as a learning strategy, and not simply a set of activities for which teachers must find time.
It is a question of discovering the pleasure which is already in mathematics, rather than trying to use games as an apology to teach mathematics, she says.
For those who are in class, the game works.
Model search
Back in Maine, Fisher argues that his approach has an impact.
The Fisher school, Breakwater, is small, with around 180 students and class sizes of around 15 students. Unsurprisingly, it exerts different pressures on teachers than public schools. Breakwater also stopped standardized tests years ago, according to Fisher. Although they still rely on state standards, they no longer regularly perform NWEA assessments, a widely used evaluation company affiliated with the manual publisher K-12 HMH. Fisher admits that this makes it difficult to compare the long -term effects of this approach to alternatives such as regional public schools. Everyone at school does not use this approach either.
But Fisher, who uses this approach, notices a difference.
In the end, Fisher feels that a playful approach makes mathematics more memorable, the less sticky lessons. He teaches students to find strategies to perform mathematics, he says. In his eyes, the thoughtful game raises the teaching of mathematics.
In older notes, it is difficult for people to imagine what the game looks like, he said. But a pivot component is self-directing. It can happen in small ways. Sometimes said Fisher, it’s as simple as letting students discover a concept rather than making them explain. It is a question of giving an agency to the students, he adds.
