This has gotten easier over the past few months. Instead of painting up the math with exciting colours, I have stripped it bare. I stopped forcing them to work on an assigned list of problems that is due the following day.
Originally, my students had less freedom.
Term 1: Traditional. Assigned seating. Students quietly face 'front', listening, taking notes. Practice problems build in difficulty. Homework checks (when I remembered).
Term 2: Non-traditional. Random groups every day. Work standing at whiteboards. Big problems.
In the last little while, I have been allowing them some more freedom.
1. Work however you want. (Paper or Whiteboard. Standing or sitting.)
2. Work with whomever you want.
3. Work on whatever you want.
Strangely enough, they push themselves more! Instead of resisting and complaining about a list of assigned practice problems that are too hard... they are choosing to work on the problems that are hard! Why? Because those are the ones that they know they need to practice.
Here's an example what happened in a review lesson.
Students walked in to 4 questions on the board, from 4 completely different units. On a scale of 1 to difficult, most of them pushed difficult.
On another board I wrote:
1 - No idea what to do ( ~ 40%)
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2 - Understand what to do after checking textbook or talking to somebody. (~60%)
3 - Understand what to do, but made a mistake. (~80%)
4 - Understand what to do, completely correct. (~100%)
I told them to try each of these problems to see what level of understanding they have so they know what needs work. This worked as a great 'quiz' replacement. Students were 'willing' themselves to get a 3 or a 4. They were sitting elbow to elbow. Perfect environment for cheating on a quiz. But if its not for mark, who are you cheating? The class was quiet for about 10 minutes as they sweated over the problems individually. Slowly a few students pulled out their textbook (their resource) for some ideas. A few whispered to each other. They studied their textbooks in pairs.
Suddenly, it was no longer about right or wrong. How many points can the student earn. It was about 'How well do I actually understand this?' For me to assess my class, I did not need a quiz average. I just needed to watch and listen.
At the end, students did not ask me what the right answer is. They asked me good questions. How do I multiply terms with exponents? When might I need to use the tan inverse function? Why is any number to the power of 0 equal to 1? They frowned at me when I gave them a little exponent rule 'x^0 = 1' because they wanted to understand the rule. Check. Check. Check!!
Following this 'quiz', I told students to flip to the cumulative review of the whole year and work on whichever problems they want, however they want, with whoever they want. Here's a few pictures.
You will see students working on paper, portable whiteboards, and vertical whiteboards.
True, the classroom was fairly buzzing with noise and students regularly go into off-topic conversations. I haven't figured out how to totally prevent the off-topic-ness, but I believe that quality working time trumps quantity working time.
A few things that really stand out lately in this approach are:
1. Hope. Instead of writing themselves off as a failure when they make mistakes... they have a sense of hope that they can master difficult concepts.
2. Fun. Instead of complaining about work, students enjoy the casual, stress-free atmosphere where they have freedom to choose.
3. Challenge. Nobody truly likes working on tasks that are 'brainless' or 'useless' when they are working for themselves. So with the freedom to choose what they want to work on, students challenge themselves to questions that look difficult.
As a teacher, this environment of students working independently and collaboratively gives me the time to informally assess the needs of individual students, coach where needed, and to teach small groups when they require it.
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