Even Mr. Miyagi Had Student Buy-In Issues Initially (Humor)

Even Mr. Miyagi had student buy-in issues. If you've seen the movie, The Karate Kid, you know these "wax on, wax off" training scenes, which is clearly active, Daniel-san-centered teaching. You wouldn't just want to only watch videos or watch demos, if you need to face real humans in a karate tournament. It seems like avoiding a kick to the head might require more than factual knowledge of what a kick is and knowing about the existence of a block or an avoidance move.

Let's take a look at a key segment, where Daniel doesn't see the point of all his practice, and has a blow up.

When viewing this scene from a teaching point of view, it comes down to Mr. Miyagi not framing and signposting the activities.  "You're doing this to get stronger at ..."  Instead, he assigned Daniel exercises, and did not tell him what these exercises were for. So naturally Daniel was upset, because he could not see the connection to learning karate. Finally, Mr. Miyagi does some student buy-in work, and has Daniel demonstrate that he actually has strengthened his defense abilities. At that point, Daniel made a big step forward in student buy-in, after getting some positive feedback from this teacher.

(Now of course this a movie, and drama is needed. I wouldn't change the movie, nor is this a film critique.)

If we boil things down to their essence, the situation is (a) instructors know what the connections are and the purpose of the work, however (b) students don't always see (or can't see) these connections, since they lack expert insight.  Hence, it's vital for teachers to signpost, "We are learning in this way, because..."

Returning to The Karate Kid, at some point, there has to be authentic meaning to the work. Daniel fully buys in after the "anniversary scene", where it is revealed that Mr. Miyagi had suffered tragedy in his family life, while earning a congressional medal of honor for his military service to the United States. This experience provides much needed perspective for the young man. The next scene is Daniel practicing with intent on his own - a sign of full buy-in.  Game on!

This suggests that buy-in has multiple levels. It's one thing to see why you are doing an exercise. It's another to be fully committed to the path forward. This is where assignments and activities focused on the meaning and value of the work can be useful. This can include but is not limited to the value of problem solving, growth mindset, and inspirational content, where students have an opportunity to learn universal lessons about what their education is for.

Wax on, wax off,
Wax on, wax off...

Cold Calling Pitfalls

This blog post is about cold calling. Randomly calling on students can go well, but it's not so easy as pulling a name and asking, "What's the answer!?"

The pitfalls of basic random cold calling is that it's not an equitable practice in its barebones form. Some issues include (but are not limited to) the following.

1. Making a mistake in front of the whole class can be stressful. This is a high risk situation.
2. Not everyone thinks fast, so they may be in the process of figuring something out, and then called on the spot to have the goods, right then and there. 
3. Thinking fast is not necessarily smart, and thinking slowly is not necessarily not-smart. But having to be quick on your feet biases the definition of smart as having the answer quickly in class on the spot.
4. Stereotype threat can be triggered. Some students are the only one of their identity in your class. If this student makes a mistake, then the stereotypes could be "validated." 

What can we do?

Randomizing who contributes does have a positive facet. It spreads the chances around. That's good. The key is to do it in an inclusive way.

Here's one example:

Instead of going with something like "What's the answer!?"you can add think-pair-share into the mix.  First, state the question or task, and ask students to think first and the talk to their partner. Then when you select a person at random, the prompt could be, "Share with us what you discussed with your partner." What students share could be a partial answer, a question, a comment, the whole answer, or perhaps asking for another minute to finish their conversation. If framed as a way to generate discussion and engagement, rather than having to be right, this can reduce anxiety and be a more inviting experience.

Riffs: We can think of think-pair-share as the base layer, and add on or adapt layers above it. Instead of randomly calling on a pair, you could visit a few groups and see what they tried. You can usually very quickly find a pair willing to share. Quiet students who have a useful idea can be encouraged to share, and this specific teacher move is where you enact inclusion! The quiet student is invited in by the instructor and is validated for having something worthy of being shared.  

Keeping track of who has shared will then help you spread chances equitably.  This riff works well earlier in the term, as you are developing student buy-in and comfort with talking about and discussing math. It's lower stakes, and doesn't put people on the spot.

Another riff is for classes that include student presentations. Assigning randomly the first chimers is a way to spread who makes the comments. Otherwise, it's the usual people raising their hands again and again. This can be done by selecting two students, then asking everyone to talk to their partner about the presented work. The selected students chime in first. They can ask a question, comment, or give a compliment. Again the contributions are done in a way, where students have time to think, discuss, and prepare remarks. Once the first chimers have made their comments, you can open the floor for further comments.

Cold calling can be warmed up with some additions and tweak. Using a small amount of time, allowing for thinking and talking, and taking perceived judgment off the table, creates an environment where students are less concerned about how they might appear and more focused on the Math. 

Student Buy-In Strikes Back

An Arstechnica article is making the rounds essentially about student buy-in. There are several layers to unpack here.

First, here's a link to the article: College students think they learn less with an effective teaching method They don't even realize they've learned more.

The key point of the article is that students liked lectures more, but did statistically better when taught via active learning. The article ends with suggesting that instructors give a short lecture on the benefits of active learning to deal with the issue.  Giving a pep talk is a good starting point, but not enough.

Why do we even need to work on student buy-in? The overarching reason is because teaching is a cultural activity. When people walk into a classroom, they have default, often unacknowledged assumptions about what is "supposed to happen." Deviations from the norms can create tension.

We need to unpack this further. In math, we have Math anxiety that messes up a lot of students. In general, we could describe this as having fixed mindsets about intelligence. "I'm not a math person" or "I learn best when shown all the steps that I can memorize..." come up as signals of this. This matters when we get to a point where students get stuck. Getting stuck is exactly the point where we have to confront our images of ourselves.  Getting stuck has been implicitly learned as equivalent to being stupid. The "smart" ones get it fast, and if you're not fast you're not smart. This is actually something that comes in education research (under the heading "Nonavailing beliefs", which are beliefs that inhibit or do not support learning).

When an instructor uses active learning that sets students up to have to make sense of something actively, then it's natural for students to get stuck sometimes. And when students get stuck, all those issues mentioned above get activated.

Another layer is the "answer getting" culture we've created. Much of school success has been about getting the answer. The most common questions that are asked in class are "What's the answer?" and "Is this right?" Rarely is it about, "Why is this true?" or "How else could we approach this idea?" So when we ask students to process ideas at a deep level, rather than crank out answers, then it creates yet another tension -- "Is this going to be on the test?"

Smart has been co-opted. Let's re-co-opt smart. Smart is working on ideas and problems, getting stuck, trying new ideas, collaborating, and so on... Smart is thinking of education as a journey. We need to educate students (and parents) what being smart is. With growth mindset research, we have a framework to have productive discussions about this.

Teaching is also a system. So if you teach X, but test Y, there's a problem obviously. But life is more subtle. If we focus on process in active learning, but test the easy-to-test things for whatever reason, then our assessments are saying we value Y, but our activities are saying we value X. Actions speak louder than words, and assessment is where you put your money where your mouth is as a teacher. The point here is the conditioning students go through is not just about what happens in class, but about the whole experience. Assessment is one of the big pieces of a class, and affects how students view learning. It's not just what activities we use in class. We also need to align our assessments (both summative and formative).

Perhaps one of the more troubling ideas from the article is that students can't identify they learned more. This made me pause.  This isn't new news, but it's a reminder.  Let's think about this.  In almost any other context this is truly odd. If you're learning to play the trumpet and are learning to hit high notes, you know when you've learned it. Of course, there's nuance in learning music, so I'm not trying to make it a binary learning outcome. But if students don't recognize they have learned more, it's a sign that there's more than just the specific teaching that's not right. One thing that jumps out is feedback and coaching. Students need regular feedback that they are learning and making good progress. Pointing out successes regularly and equitably is essential and goes a long way. "We learned this... Way to go, and we learned this because we worked on it, got stuck, and figured it out. That's smart!"

Now all this sounds like I might be blaming students to some extent. I'm not. Not in the slightest. This is about unpacking the layers of our system. Circling back and putting the layers together, we get the outcomes our teaching culture is designed to achieve, whether we realize it or not. We still have holdovers from the roots of the industrial revolution, where our model for education was created using a factory model. You know, bolt on the knowledge and you're good to go. But our goals are different today, and we are shifting towards humanistic education. That is education for developing people as human intellectuals.

Student buy-in is generally about this broader cultural shift. When students walk in the door it's our job as teachers to help them make this transition in mindset and purpose. If we just change the way we teach, and don't inform students, it's on us if they walk away with a bitter aftertaste.

How to get started? Let's get practical. After all that blabbing above, we need things we can do in class that work.  Linked below is a post from earlier this summer with a collection of links from what to do on Day 1 to ongoing strategies to digging deeper into Math Anxiety.

Student Buy-In In Practice Overview

And just yesterday I wrote a letter to students that can be used as a starting point to get students on board.

Letter: Dear Student

Letter: Dear Student

This letter is to students in college math classes, but might apply in other settings such as secondary math or other subjects.

Dear Student,
I am writing this letter to you, because your instructor, other instructors, all of us care. We care deeply about your success. We care about your future, and the future of others. That's why we went into teaching in the first place, a profession notorious for long hours, high commitment, and not the highest wages. Teaching is a calling, and our calling specifically is to help young people today to prepare them to solve tomorrow's problems. Teaching is a social responsibility to young people, to prepare young people with the knowledge, creative thinking, and values needed to live healthy, successful, impactful and meaningful lives.

Consider this next idea for a few minutes about time... Children who are in kindergarten today will retire in about  60 years. I write this in 2019, and that means a student in kindergarten will retire around the year 2079.  2079!  Think of the difference between what your life is like today, compared to 1959. The world has changed drastically in ways that people in 1959 could not predict. No way they could foresee smart phones, google, climate change, automation, globalization, etc.   The main point I want to get to is that there are questions and problems that young people (you) will have to solve that have not even been thought of yet by anyone on the planet. Your education today must prepare you to solve these unstated, problems far out into future.

What this means is that getting the answer in the back of the book isn't nearly enough.  Yes, it's good to check your answers sometimes, but that's just a small part of your education. Yes, it might have worked to get you into college or through your last math class. I totally get it. But learning isn't a set of check boxes or getting the answer that is in the back of the book. The people who invented the iPhone or the people who put the first human on the moon or your favorite band or your pediatrician or whomever else you admire or appreciate, they solved real-world problems and looked far beyond the back of the book. At some point, logic, reason, and creativity is what you need. Answers might be good for checking things off, but really the learning is the process to getting to the answer and being stuck on good questions that make you think.

Let's unpack some of the details. It's okay to ask, "Is this right?"  Please ask for help, and ask for help every time you need it, even for small questions. But I hope you also go farther, and ask questions that expand your thinking. "Why does this work?" or "Why doesn't this work?" or "Is there another way to look at this?" Memorizing isn't thinking, by the way. We can teach computers to memorize better than humans, and thus memorizing isn't as important as it might seem. Sure it might help you get back a multiple-choice test, but really in your future life multiple-choice tests won't be how we tackle something big like climate change.  The big goals of your education include deep understanding, being able to explain complex ideas with nuance, being able to learn from others, and being able to use ideas creatively in new ways often collaboratively.  Hence asking for help should be part of a larger process to make sense and expand your understanding and thinking. Learning is fun when it makes sense! And if it doesn't make sense, then keep on trying to understand and get help.

You can get help from various resources. Resource number 1 is your instructor. That's the person who is responsible to your learning. Next there are your classmates, your textbook, the tutoring center, and perhaps the internet. Try and talk to as many humans beings as you can first. Math is learned better with more human interaction.

Office Hours: Office hours are for you, and if you are stuck on something, even a small thing, go to office hours. It's not an imposition when you show up, and your instructors want to help you. Even if you instructor seems completely different than you, you can and should ask for help. While it might seem a bit scary, it's ok. I know a ton of math instructors, and so far all of them are human beings, and are really nice in office hours. Some even have a sense of humor! I know that might be shocking, but it's true. And when they go home, they go home to things like cats and children, and watch TV or text their friends about Friday plans, just like you.

Yes, there exist legends of math geniuses, who work in their attics for years to invent math. That works for them in certain contexts, but none of them worked alone or got to that  point all by themselves. They have collaborators, consultants, books,... they actually went to school with other human beings at some point in their lives (and interacted with them). They read journal articles, they attend seminars, they go to conferences. Some people gave them a job, so opportunities were given to them. No one is 100% self made. Therefore, work with other people regularly, even if you don't view yourself as "social" in the everyday sense of the word or are introverted. In this letter, I mean social in a school or workplace sense. We all have to communicate with others to give and receive feedback, as well as brainstorm new ideas.

And really I hope you get stuck a bunch of times in your learning process (in a safe learning environment, not on tests).  Get stuck??? Yes, get stuck. Because you need to push your personal abilities. Each time you get stuck and unstuck, you learn what works and what doesn't work and you get smarter. Through working on problem solving in math (or any field), you are doing something like going to the gym for your brain. Your brain will get stronger, and you'll learn new ways to think, see, and feel.

Math anxiety is a real thing. I've written about it many times on this blog. I've talked to hundreds of students about it. I'm sorry about this. Math anxiety should not exist. Not everything in the world is right, and math anxiety is one of those wrongs that we are trying to fix.  In the meantime, if you had experiences that led you to math anxiety, what you need to know is that it's not your fault! You're not dumb, you're capable, and there is a way out.

The way out is doable. It's shifting from a fixed mindset (where one views their math abilities as fixed at birth), to a growth mindset, where one views effort and practice as the ingredients for getting smarter.  Think about one of your hobbies or interests. How did you get better at it? You practiced. You might have had a teacher or coach or watched videos, but at the end of the day you put in the focused, dedicated hours, and did the work. That's being smart, and from now on, we are co-opting the word smart.  Getting smarter at math is exactly same. A good teacher will provide you with a positive class environment and support you through your specific learning challenges, and when you practice, think, ask questions, collaborate, and do all those things people do in every profession and hobby, you'll make real progress.

Only watching videos of other people doing the math isn't going to cut it. Look I get it. Khan Academy is one click away. It's a useful resource, and I even watch KA sometimes to see which ones might help my students. Whenever I need to fix something in my house, I find a video on how to fix it. That's a good way to get information that you lack. However, learning math is like learning to be a musician or athlete. It's not just information and facts, but also about developing thinking and problem-solving skills. Doing better at math requires thinking mathematically, which is analogous to learning to ride a bicycle. You can't be taught to ride a bicycle beyond the basics by watching a video, because there are things your brain and body have to construct by actually doing it in order to build that skill.  Mathematical thinking is the same in that you can't just get info uploaded into your brain like a firmware update. You also need to construct understanding and meaning for yourself, just like your body and brain have to construct things in order to ride a bicycle safely.

Another example is learning how to hit a baseball/softball. We could watch tutorials all day and understand what we need to do. Basically it's swing a bat and hit a ball. But only watching videos is obviously not enough.  We need to actually swing a real bat and hit a real ball and get ongoing feedback from coaches. And then practice, play games, strike out, reflect, rest, repeat.  It takes time to get good at it. That's the perspective you should have about Math and watching videos. Sure watch videos sometimes to get some info, but don't stop there. Start there, and do the work. Do your own reps on real problems. Otherwise, you'd just watching, and that is just sitting in the stands. You need to be on the field, because this is your life and your future. Get in the game!

Hopefully, your instructor will ask you to work with your classmates sometimes on a question or task. In education this is called active learning and is part of inquiry-based learning (IBL). These methods are designed specifically for you to engage and think for yourself. Listening to someone isn't enough. Sometimes we need to hear ideas from the instructor that we can't easily build ourselves, but like sports or music or any hobby, you ultimately need to be the one engaged in the process, asking questions, and taking ownership of your development.

Learning to work with others is critically important. Working in groups is not only about helping one another, although that's a good aspect of group work. One of the main benefits of group work is learning through discourse. Sometimes we need to talk things out in order to make sense of what is going on, and hearing other people's ideas can also benefit all of us, and helps us engage in the process of trying and refining new ideas. Another benefit of group work is learning to communicate. In an era when more and more repetitive tasks are being automated, the ability to do humanistic work, such as communication and problem solving, is much more important and valuable.

Try to contribute to group discussions and regularly invite your group mates to share... "So what do you think? What did you get? [smile]"  It's not about one person getting the answer for the group, and everyone else copies. It's about giving everyone a chance to think, try, share, refine, and see ideas from multiple perspectives. That's good for you!

In summary, focus on problem solving as a process, embrace and be patient with being stuck and not having answers right away, think about the long game of your personal intellectual development, develop a growth mindset, and work on learning with your classmates. These are things you need to prepare for your future. All people, especially young people, have immense capacity to learn, grow and get a lot smarter! Believe in yourself by actively investing in how you learn.

Best wishes on a successful new school year!

Sincerely,
Professor Stan Yoshinobu

Pronouns, Early Term Simple Survey

Many thanks to the NSF PRODUCT team for bringing this up in an email discussion! This short post is on pronouns, and a result of that discussion. These are not my ideas, and I'm sharing the main ideas from that discussion.

Pronouns matter, and it makes a difference if we ask students to tell us their pronouns without assuming what they are. Why does this matter? Here's a quote from www.mypronouns.org

"Often, people make assumptions about the gender of another person based on the person’s appearance or name. These assumptions aren’t always correct, and the act of making an assumption (even if correct) sends a potentially harmful message -- that people have to look a certain way to demonstrate the gender that they are or are not."

One way to get this information is to ask. And while you're asking, you might as well find out what they preferred to be called and what might help them succeed.

1. Your name____ (and email optional)
2. Please call me by this name (please add a phonetic pronunciation, if people often pronounce your name incorrectly) _____ 
3. Please use these pronouns for me (don't want to share this? no problem; not sure what this means? read about pronouns here: https://www.mypronouns.org/) ____
4. For me to be successful in this class, I need you to know that ____

Working towards an equitable classroom is an important consideration today (as the 4th pillar of IBL), and we should be more conscious of the issues and be action oriented. The last question on what would help students succeed can help you understand specific needs right at the start of the term, which can make a significant difference for student success.

One more thing. I put "he/him/his" in my email signature. An easy and impactful thing to do.

In short, I learned not to assume. I learned that we should simply ask and share with our students why we are asking, since they may need to learn as well.

Student Buy-In In Practice Overview

Student buy-in is one of the issues that comes up frequently at workshops and in hallway conversations. Student buy-in isn't a simple thing. I've written about it previously on this blog, and I think this topic needs to be visited regularly.

Getting stuck is hard. Fruitful struggle and productive failure aren't usually taught and learned. Making mistakes has often been equated with failure (in the negative sense of the term). Students aren't usually encouraged to explore, experiment, and tinker.  Thus, the conundrum is that in order for learners to grow, they need to be challenged appropriately, which means being stuck on some ideas, yet being stuck is equated to being dumb.

Luckily today we have the advantages that can help change learning experiences into authentically positive ones.  Growth mindset work has zeroed in on beliefs that lead to becoming smarter. We know more about how to use active learning to open up learning spaces, and we have a growing collection of videos on productive failure that can direct students toward successful mathematical practices. Instructors can assign videos as homework with reflective writing prompts every week or so for the first part of the term.

Day 1 of a course is important. Linked below is one way to open a course, by starting with students' hobbies and how they got better at the hobby.
https://theiblblog.blogspot.com/2019/01/opening-course-and-launching-winter.html

See also Dana Ernst's "Setting the Stage" opening.
http://danaernst.com/setting-the-stage/

Ongoing strategies for student buy-in are posted here. It's not enough to only do something on day 1, because it's a journey.
http://theiblblog.blogspot.com/2019/01/ongoing-student-buy-in-strategies.html

Nudging students to engage more is one way to address student buy-in. We all need a break sometimes, and we can all use a bit of support. One way to keep students going is to nudge them.
http://theiblblog.blogspot.com/2018/11/nudges-as-teaching-technique.html

Attend to Math Anxiety, because knowing where students are coming from can help us be better teachers. Math anxiety is a thing, and most students have some level of anxiety. Ignoring it only limits student learning, so we might as well deal with it. Math anxiety is linked to (lack of) productive failure, and fixed mindsets. Here's a post on the iceberg diagram and math anxiety and how instructors can detect math anxiety and fixed mindsets from statements like, "I don't learn this way..."
http://theiblblog.blogspot.com/2018/01/iceberg-diagram-fixed-mindset-math.html

Digging deeper, math anxiety is something you can read about from students directly. Here's a collection of math anxiety quotes to give you a sense what lies underneath. If you've never asked, try adding a math autobiography assignment at the start of the term. Let students share their experiences.
https://theiblblog.blogspot.com/2015/03/math-anxiety-realities-student-voices.html

Sharpening your IBL skills is also important, because a well-taught class is part of the equation. Problems that are too hard or leaving students struggling for too long works against student buy-in.  Also making things too easy is also. The IBL Blog Playlist is collection of posts organize by topic. If you are new to IBL, we also have a video series to get you going.

Standards-Based Grading Example in an IBL Course

I'm sharing an outline of standards-based grading I've recently used in a course for future elementary school teachers, although much of this is generally applicable to other courses. I'll list the main features and then get into some of the details below.  Also this is just one example, so do not assume that what I am sharing is representative. It's really a form that works for the specific course.

Here are the main features:

1. Gateway exams
2. Reading assignments
3. Homework assignments
4. Productive failure
5. Class contributions and participation
6. Final project

How these fit together is that if a student earns a passing grade on all items, they earn a B in the course. Students can raise their grade to an A/A-/B+ with an excellent grade on the final project. Students earning one or more non-passing scores in any of the categories will earn a grade lower than a B, with specific grades reductions based on the nature and quantity of the unsatisfactory grades.

1. Gateway exams: These exams are based on the IBL units we work on regularly in class, and are based on the math being learned in the course. Students are required to pass all of the problems on the gateway exams (i.e. get the correct). For any problem that was not successfully passed, a student must retake that problem on the retake exam.  The retake exam is given about two weeks after the initial exam. Problem done correctly do not have to be retaken.  The first retake is done in class. Subsequent retakes are completed in office hours or alternatively completed in writing and submitted for review.  This past term, I gave 2 exams, and was limited by the quarter system (10 week terms) in how many retakes can be given in class.

Retakes can become a logistical challenge for large classes or in courses where there is a significant amount of material to cover. One has to weigh the costs and benefits of this and plan accordingly. The strategy I've taken is to start with a course that I thought would be relatively easier to manage, and then work my way to other courses where I feel I would be better off with more experience.

2 and 3. Reading assignments and homework assignments are graded for process and completeness. Accuracy feedback is given, however, the goal of these assignments are for students to think and reflect on math and math knowledge for teaching. Points are not taken off for mistakes or incorrect answers, and instead feedback is given when necessary and points are awarded for good process. For example, if a student gets a problem wrong, but writes questions or explains what they did and what they still need to work on, then they earn full credit for the problem. 

4. Each student is required to present one productive failure (i.e. #PF) per term (in a 10-week quarter) about a mistake or something the student was stuck on. The format is to discuss (1) the mistake or issue, and (2) to share what they learned from the process.  (In some courses the number of #PF presentations is 2.)

5. Student contributions to the class discourse is another component. Students work in groups and are expected to show up to every class, contribute to discussions, be effective group mates (i.e. be good at listening, supporting, and sharing), and present math ideas sometimes. More or less this is participation grade, but with stipulations about expected behavior. 

6. In lieu of a final exam, students must submit a final report. The report is based on 4 tracks related to mathematics teaching in the elementary school and the course content (in this case fractions for teachers).  Each track has a lead source (article or book). Students are required to do library research, branching out from the lead source, to find learning challenges (for children) established in the Math Ed literature. Lastly, students are required to create rich mathematical tasks that address the identified challenges that build from starter problems to middle problems to goal problems. 

I get asked if creating math tasks is pedagogy.  The answer is no. Creating math tasks to address specific math learning goals is a teaching specific math activity. Identifying the main math ideas, ordering and sequencing math problems, and building up from first principals is doing a math (applied to teaching children). 

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Some general comments.

Gateway exams require students to learn all the standards of the course. There's no partial credit for problems, and students are required to demonstrate they know the math they need as teachers. Students have multiple chances to make sure they get problem completely correct. The retakes can be logistically challenging, if you are not organized. Overall, the workload is about the same, because retakes eliminates the time needed to determine partial credit, and there's a tradeoff that more or less washes out (for me).

Further, the overall assessment structure aligns the class to the mathematical work of teachers and the philosophy of IBL. The focus is on learning, and guiding students to what they know well and what they need to work on further. What students need to work on is clear, and this I find one of the main benefits of standards-based grading.

The reading assignments, homework, productive failure, and class contributions, as an ensemble focuses on process and prospective teacher beliefs. The shift is away from "answer-getting" without deep understanding.

Final projects or final exams can be implemented in ways that work with standards-based grading. In this specific case, I decided on final projects, since it gives future teachers the opportunity to connect they math they are learning, the research literature, and connect that to the classroom. In other courses, I have used standards-based final exams. 

If you're thinking about trying standards-based grading, I highly recommend giving it a go.  If you have been using standards-based grading, please share what you do! 

Edit: Dr. Kate Owens published A Beginner's Guide to Standards-Based Grading the AMS Blog.