Answer-Getting and: Mastery Quizzes

See Previously: Some Thoughts on Interventions & Answer-Getting

So here’s another thing I did a few times in my class this year with dramatic effect: Mastery Quizzes

A Mastery Quiz Is: A collection of skill-based questions designed to be completed in 10-15 minutes. The types of problems on the quiz should be very similar to the ones they’ve done in class – no surprises. For full effect, some problems should be procedurally difficult in the sense that they are multi-step and require you to be careful with all the little details of the problem. Think along the lines of “Perseveres in Solving Problems” for the remedial student. It is not multiple choice.

A Mastery Quiz Works Well With: Skills that have some kind of concrete or procedural foundation that, if students just relied on this foundation, they would get it right. Examples include:

• Integers for students who know how to use the number line but try to take shortcuts and make little mistakes
• Multiplication for students who can use the box model but get stuck with the standard algorithm and make little mistakes
• Exponent Rules for students who understand the individual rules but try to do too many steps at once and make little mistakes
• (Procedural Skill) for students who understand (the foundation grounded in a process or scaffold) but (do this bad thing) and make little mistakes

Here’s my Mastery Quiz for Integers:

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Here comes the important one:

You Grade a Mastery Quiz By: Everyone Either Gets a 0% or 100%

The gist is: students take the quiz, its graded on the spot, then returned to the student for them to fix the ones they missed. This process repeats itself as many times as it takes for a student to get 100%. This causes the quiz to take the entire period to complete as students continually re-evaluate their work. If a student doesn’t finish the quiz during the class period, they get a 0%. This is why its important for the quiz to be designed to take 10-15 minutes, even with the longer problems. If a student makes a mistake, there is no feedback about what the mistake could be – it’s the student’s responsibility to find it (more on this later).

The way I’ve given these quizzes in the past, I tell the students ahead of time that we’ll be having a quiz but wait until I’m about to pass them out to tell them the details above. The reaction has been mixed, but I remember it being generally positive since students like the idea of getting a 100% on a quiz – for many, this may be the first time this has ever happened. Once I’ve passed out the quiz, I sit at the front of the room with the answer key and wait for students to finish. As they do, they bring up their quiz and I grade it on the spot. I put a little X next to the problems they’ve missed and a Check next to the problems they get correct, then tell them to return to their seat and fix them. If a student misses the same problem several times, multiple X’s appear next to the problem.

Eventually, some students finish. I make a note of students who got 100% the first time in order to congratulate them later. Everyone gets a high five and start quietly working on other things.

Eventually, some students get frustrated. They’ve missed the same question 2-3 times. They don’t know what they’re doing wrong. They want to give up. “This is stupid – I’m never going to get it”. I tell them not to panic and not to give up. I tell them to take their time and trust themselves. I remind them of all those concrete strategies we’ve been working on. I remind them not to skip steps and to take their time. I remind them to do whatever scaffolding strategies have worked for them – there’s no time rush today, and they’ve already tried the short-cut method. I tell them to erase all of their work, take a 30-second break, then try the problem all over again from scratch. These students begrudgingly return to their seats so they can try again. They finish and approach with trepidation – they desperately don’t want another X on their page. Usually these students get all Checks – eventually. They breathe a huge sigh of relief – they never want to have a moment like this again. They’d rather get it right the first time than have to keep doing it over and over and over and over again. Mission Accomplished.

Eventually, some students get angry. They put their head down. They refuse to finish. They’ll take the zero. These are the ones I work with 1-on-1 when everyone else has finished up. I don’t let them give up. I sit next to them and ask them to try the problem again. I am kind and patient but persistent and unyielding. I ask them to use the strategies that we’ve been working on in class. I watch them do their work and don’t let them take shortcuts. I coach them on how to show their work. I’m careful to always ask questions while never explicitly telling them what comes next. This group of students is tricky – these quizzes can either empower them beyond belief or reinforce everything they’ve been led to believe about themselves. Hopefully the former happens, but a lot of that depends on Trust:

I need to trust that I’ve seen enough successes in the days leading up to this quiz so that I know my students are capable of reaching the correct answer even after several mistakes. My students need to trust me as someone who is genuinely there to help them and believes that they can do it – that I wouldn’t give them this quiz because I thought they would fail it. Lastly, and most importantly, my students need to trust in their ability to work carefully and correctly to solve problems – that their perseverance guided by careful procedures will lead to correct answers.

An Anecdote

I gave this quiz earlier in the year when I had a student who was intelligent and confident, but tried to do too much in his head and made little mistakes but didn’t think they were important – “But mister, it’s just a negative! Its basically the same thing!”. He was an active participant in class and could always tell me what to do next. He would say “It’s okay – I already know how to do this” and shrug off practice assignments. He was convinced he didn’t belong in my Math Lab class, and was convinced he’d get a 100% the first time. When he took this quiz, he was the first one done in his class – he missed 10 problems. He was a little shocked, but he went back and started to fix his quiz. When he returned, he only had two incorrect answers. He came back a third time and the same two problems were still incorrect. There was a pause before he went back to his seat. Something was happening. I said “Start each problem over from the beginning. Don’t do anything in your head. Don’t take shortcuts. Double-check your work. You’ve got this if you take your time”. His return to his seat was slow and somber. He restarted both problems from the beginning. He took his time and checked his work. He was careful – every step mattered. By the time he came back up, over half the class had already finished. He had gotten both problems correct. I raised my head to acknowledge his accomplishment – but, before I could say anything, he muttered with earnest “I need to be more careful and start taking my time”. If I had said this to him, it would have been the 100th time he’d heard it. Watching him say it to himself, this was the first time he really heard it and it really meant something.

What About the Student Who Gets a 0%?

When I’ve given these quizzes, it becomes pretty apparent when a student or two won’t finish. As class winds down, I find time to talk to this student one-on-one. I make the point that these skills are important – they’re not going away. And based on today, something needs to change – either how we do these problems or the way we think we know how to do these problems. Whatever it is, something’s not working and we need to fix it. We’ll work more on this in the coming weeks. But right now, this goes in as a 0. When I think you’re ready – once I’ve seen growth – we’ll find a time for you to retake this.

In Summary: I see these quizzes as the sobering experience for Answer-Getting and “I Don’t Need Help” students that is absolutely necessary for growth to happen. For many, its the catalyst that breaks down the “I Don’t Need/Want Help” wall and opens them up to trying new ways of doing problems and new ways of working through their thought process.

Push-Back Against Answer-Getting

• Mastery Quizzes, by their very nature, don’t let students be uncaring about incorrect answers. On formative assessments, I may try to tell a student that they’ve got an incorrect answer, only to be met with “Oh – well, whatever. I’ll turn it in anyway”, which is frustrating to me because it completely defeats the point of the formative assessment. However, a Mastery Quiz forces students come face-to-face with their mistakes and forces them to address them. No more passing the buck.
• I can tell them that incorrect work wastes time in the long run, but that’s usually something I’m more conscious of than the student. Mastery Quizzes force students to face this truth head-on – they see that speed and accuracy don’t always go together. Hopefully they begin to see that its better to go slow but be correct rather than fast and incorrect – and this is usually validated by the people who are first to get 100% rather than the people who are the first to finish.
• The students who struggle the most are the ones who try to ‘guess’ the answer just so the teacher will move on – “What is -3 + 7?”, “10! -10! 4! -4!”. Watching those incorrect X’s accumulate on their paper is sobering and makes them rethink this strategy. These are the students who tend to get the most frustrated, but this is also a vital experience for them – to see that mindlessly spouting answers isn’t valuable and ultimately is a waste of time.
• I get to have this conversation with students after the quiz: “I’m going to make a prediction about your past math classes: you’re someone who can do the work in class, can follow along with the teacher, and can even do the homework that night. But when you come in the next day and check your answers, you see that most of your answers are wrong and you don’t know why. This is why. It’s these little mistakes. Once these get fixed – once you start taking your time and getting all the steps in between – everything will start going so much smoother”.