Showing posts with label Mastery-Based Grading. Show all posts
Showing posts with label Mastery-Based Grading. Show all posts

Monday, October 26, 2020

Seven Ideas to Help with Reopening K-5 Schools from an Educator Perspective

The focus on reopening has primarily been about health and safety for good reasons. It's a good time for us to add another layer to this discussion, which is to think about how we can improve teaching and other related factors to help reopen smarter.

A typical situation parents might find themselves in is this... Their child is doing math homework on their own, and gets stuck. This is added stress on top of all the pandemic stresses. Dinner needs to be cooked, like is hard as is.  It gets emotional, parents are frustrated, Math feels awful, and then everyone wants to get back to in-person school ASAP! 

I totally get it. For many of us with kids at home, it's been a huge struggle during this pandemic. Juggling parental duties, work, taking care of yourself, it's a tough. We all want to go back to something normal. 

In this post, I share some thoughts about actions educators can take to help improve our situation. This is really important, because we want to make the decision to go back to in-person because spread is low and we have the resources to do it right. We shouldn't be reopening prematurely, because virtual teaching is bad. It puts people in harm's way for the wrong reasons. As of this writing, the US is hitting all-time highs in case counts, hospitalizations are increasing, and the government has literally said it's given up.

What this means for schools is that virtual is going to be a big part of reality for a long time. I don't see a way for us to go back and it's magically 2019. 

Many families can't go back to in person, because they have a high-risk member. They deserve a good education.  Others need to go back, because they have essential jobs. We need space for them.  Little children should be in some form of in-person school (assuming it's safe), because they are so young and it's what they need. Secondary and college students should be largely virtual, because we need to set aside precious space and in-person time for the youngest and neediest. But we can make virtual better, and in some cases much better. 

Caveats: I'll focus on Math, because it is my area. The ideas are generally applicable to other subjects.  Education is an extremely large sector. In California, there are over 6 million students in public K-12 schools. This means that the comments I write here are not going to cover all the cases due to the sheer size and range of scenarios that are present. But there are things we can do to (a) alleviate some of the pain and stress of virtual learning and (b) use better virtual learning as part of a larger strategy to carve out time and space for some in-person learning. 

I'm not commenting in detail about things like masks, coronavirus testing, or other health and safety measures. That's an area of expertise that I have been following closely, but it is not my area of expertise.  

Below is a list of some ideas to help with thinking through reopening schools from an educator perspective.  The perspective I can offer as a professional developer in Math Education is that I see areas where we can improve teaching and learning that have benefits with dealing with the pandemic and can have lasting upside even afterwards. 

1. Prioritize the youngest, neediest tiers of students, teacher safety
The top priority should be to the youngest and neediest students and the safety of teachers. If a child can't read yet, because they are in kindergarten, then zoom isn't the best format for this child.  Further, there are other situations for all grades (K-12), such as students who are homeless, who are not safe at their homes, or have special education needs or other needs. These students need to be on school campuses for their wellbeing.  Hence the priority grades are K-2. And other priority groups can be also be identified and put into this top priority tier.  

As our pandemic situation improves, we can add in more tiers. The tiers are preK-2 and high needs, grades 3-5, middle school, and high school. 

Teachers should be classified as essential workers, and they should be in the early phase of vaccinations. They work with large numbers of people, indoors, for long periods of time. Teachers deserve all the support we can give them, because they do so much for our society. Sick or dead teachers are devastating to schools, just as losing HCW in medical settings.

2. Try to decouple academics, socialization activities, and daycare
This section is about rethinking services provided by schools in a different way.  In 2019 and before, schools provided all three of academic training, socialization, and daycare.  What would help our problem-solving approach during a pandemic is to try and split these three things apart, as much as is reasonably doable. This doesn't mean we won't have overlapping areas with these three areas, but that we don't need to bundle them as all-or-nothing. Bundled, all-or-nothing thinking limits what we might possibly be able to do to help more children and families.

For instance we could have academics taught mostly or completely virtually (depending on the grade tier), have socialization events in person and virtually so that children can learn social skills and just have fun and be kids, and daycare could be provided in smaller group sizes, so parents who can't stay home have safer options.  

For example there are families, where the parents are essential workers and the family has an at-risk member. In-person could be too risky.  Families in this situation are put in a tough spot. Consequently, de-coupling the services schools provide opens the door for more solutions. In this case, daycare could be provided in a small setting nearby, while the children do mostly virtual learning, allowing the parents to work while mitigating risks. 

Secondary school students in virtual learning could do some in-person socializing, such as some organized activities in gyms or outdoor fields to do normal things like hangout with friends and get off of screens for a while. Of course properly distanced, masked, etc. 

Decoupling the three services is a complex task, requiring input from all groups, including parents, students, teachers, staff, and local officials. It'd be interesting to see existing solutions in this area, and my sense is that daycare is the key piece. If parents had good daycare, some safe options for socialization, and virtual teaching was good enough, we'd be in a very different context regarding the pressure to reopen schools.

3. Improve virtual (and in-person) teaching via active, student-centered teaching
This item applies more to older grades and upper elementary. But all grades will likely have to be virtual part of the time.   

So, imagine a world where virtual teaching is fun. Your kids are okay with it, and they are learning. This releases some (a lot?) of the pressure to rush back to in-person school, and gives time for scientists and the government to develop better testing and treatments.  

Good teaching is good teaching, whether virtual or in person. Teaching is a complex system and cultural activity. I can't do it justice in this space. The short version is that we can use active, student-centered methods like inquiry-based learning (IBL) to shift classes to engaging, collaborative spaces.  Uptake of active, student-centered teaching is still low in the US, and this is an area of need, whether or not we are in a pandemic. 

The four pillars of IBL teaching in Math are:
  1. Deep engagement in rich mathematical tasks
  2. Opportunities for regular collaboration between students and with the teacher
  3. Instructor inquiry into student thinking
  4. Instructor focus on equity
These pillars aren't specific to Math, and you can substitute in whatever subject.  On a typical day, roughly 2/3rds of class time should be spent on students doing tasks or engaged in thinking through questions, where students are guided by their teacher to think and discuss math questions, such that the process of answering these questions leads to authentic learning.  

Generally speaking, there exist ways to implement IBL methods in virtual settings that are promising for upper elementary and certainly for secondary. Professional development training for teachers is one way to get these kinds of teaching methods into our classrooms. Younger children need more hands-on learning, hence the need to prioritize bringing them back in the first round. 

More information about IBL is available on the AIBL website and on this blog.

4. No math homework in K-5!  
No matter the teaching methods used, one thing that can be done across the board is to eliminate or significantly change homework. Homework is not shown to help learning outcomes in K-5, and I'd argue that it's not needed everyday in secondary either. 

Homework for points adds stress, and even if students do it, many leave disliking Math due to the accumulation of negative experiences.  When students are asked to do problem after problem after problem without help, all alone, it can really frustrating for students who struggle, and entire families feels this, and just makes them want to go back to in-person, whether it's the right thing to do or not.

Math anxiety is a real issue. Many students carry math anxiety into adulthood. See this post on Math Anxiety Realities, where college students speak about their painful experiences from math classes. Teaching in ways that increases stress is not good for student learning, and sometimes leaves lasting scars. 

The best option is to eliminate math homework for K-5. Just don't do it. Do all the learning together synchronously or in-person where possible. 

For secondary, one option is to assign modernized, optional homework, where students are given handout to read about a math idea, technique, a solution to a problem, looking back at recently completed material just to name a few ideas.  

Another option, and a really easy one to implement is to state a problem or question and provide a detailed solution with an explanation. Ask students to try the problem first, and then have them compare their thinking with the provided explanation. 

5. Use mastery-based grading 
There are many reasons to update assessment. A points system is an extrinsic values framing of grades, which is actually not a good motivator, can lead to inequities, and isn't tied necessarily to actual learning. Students are told that homework is worth X points and tests are worth Y points, and it's all about getting points.  While this has been the standard, it's not as good as a system with intrinsic values framing, such as mastery-based grading. In mastery-based grading, students are given transparent learning goals, and given multiple opportunities to learn them. The focus then is on learning.  

A simple example of mastery grading is to give frequent quizzes/tests, where students are given two possible scores. One is "meets standard" and the other is "not yet."   For problems that students earn a "not yet," they are given chances to retry the problem until they earn a "meets the standard."  Quiz/test questions are centered on students explaining why things work, so that they the emphasis is on critical reasoning and problem solving.  Basic skills and concepts should be practiced in class together with informal assessments to give feedback to students and teachers. This feedback then informs the class whether they should practice more or move on.

Other mastery-based grading systems exist that are more sophisticated and tuned for student learning. The example provided is an easy-to-implement version that is compatible with the challenges and constraints teachers face in a pandemic.  See www.masterygrading.com 

One key potential benefit of mastery-based grading is equity. I'll argue via an example. Suppose student A learns a topic in week 7 and student B figures it out in week 9.  The test is in week 8. Student A get a higher grade than student B, but both have learned the same thing.  Now let's say student A is in a middle class family with parents with college degrees who can work from home, and student B has to work or has parents who are working long hours, and student B has more non-school responsibilities.  In this case, mastery grading would result in the students getting the same grade, because they learned the same things. 

Mastery grading can be bias resistant. That is, it is less likely to penalize the student who has more in life to deal with and/or fewer resources.

In states like California, standards-based grading is already used in elementary schools. Where teachers can further make improvements is to drop timed tests, and use oral exams/interviews and other task-based live sessions to see if students are making progress. All these should allow for retakes after getting support. 

Online proctoring software raises many questions about whether they are ethical. Lockdown, surveillance testing is not morally sound, expensive, and completely avoidable. We can use better assessments that are more humane and aligned with learning outcomes that we value, such as critical reasoning and justification. (See this disturbing account reported on by The Washington Post, where a student asks a proctor if she can *vomit* Link).

6. Cull unnecessary or less important topics, and focus more on core topics
A typical math textbook has a lot of material in it. Most teachers and college instructors will say things like, "There's so much to cover."  This really doesn't have to be the reality and shortchanges time on better, high-level goals such as problem solving and communication.  

In every course, some topics can be covered less intensely, because they are less important or tangential to the main learning goals. Each subject area can be culled down to essential topics using the state standards as a starting point. Culling the list of topics can help teachers and students by giving more time for core topics, which actually matter in the long-run. 

Connecting back to the revised homework ideas above, secondary math teachers can cover less important topics by assigning reading, a video, or a handout for students to read and try something. In this way, students get exposure to additional topics, but it's not taking up valuable class time that could be better spent on larger goals.

The reality is that students use Khan Academy and other resources. Harnessing this for a range of uses opens time and space for educators to hone in on key ideas. 

7. Focus on community solidarity
More than any other time in our lives, we need community. We are living through a global humanitarian crisis, and it affects all of us in many ways.  Thus, building community should be one of the core goals of every class. To do this, some class time can be used to build community on a regular or daily basis. We don't only teach Math (or insert your subject).  We teach students, and they deserve an education that is humanistic, empathetic, and compassionate, especially in time like this. 

Why is building community so important? If students feel disconnected and stop caring about their education or worse their futures, then what's the point of learning how to add fractions or complete the square? Thinking of reopening schools purely and solely as a medical problem is incomplete and possibly dehumanizing or invalidating. Putting humanity first is the right move. 

Even in virtual learning, we can build community. Teachers can do this using chat, breakout rooms, padlet, jamboards, discussions, and others. Some socializing virtually can benefit students, and help them feel more involved connected to their classmates and teachers.  

Sample openers for class are fun polls like "What is your preference (a) oatmeal, (b) toast, (c) cereal?" Or "How many cups of coffee did your teacher need this morning?" Mix it up, have fun, be human and authentic!

Common misconception RE rigor
A common misconception area is that hard equals rigor. This is especially true in STEM subjects, where low grades, lots of homework, and lots of students doing poorly means the class is "rigorous."  The corollary to this is that classes where students do better is less rigorous and watered down.  

All of the suggestions above are not about reducing rigor or lowering standards or "dumbing it down." They are adjusting how we teach or assess to improve learning. It should feel easier, more doable, and more enjoyable, if done right. If a student learns more their grades will go up. That's not a sign of less rigor, it's a sign of student success.  If anything, regressive methods are ironically less rigorous, because many of the exam questions can be solved with google or looked up on Chegg.com. This means AI can do much of the usual tests tests, which is less rigorous than having to explain or justify why something works or doesn't work. 

Colleges messed things up
Colleges should have been bailed out and been virtual. We effectively spent significant "in-person budget" on the tier of students most capable of learning virtually, all the while seeding more outbreaks. Bad policy and planning is directly affecting your school's ability to reopen safely. I won't go into details, but here are some links, if you want to dig deeper.

The coronavirus, poor leadership and being understanding
The pandemic is causing our problems. Let's be clear about this. While we may disagree about how to reopen or what to prioritize, the real problem, the real thing causing us all the pain and suffering is the coronavirus and the mismanagement of the pandemic. We need to acknowledge this and not unfairly blame schools or teachers or superintendents for the predicament we are in. Their job is to educate, not to do infectious disease public health. 

Further, East Asian countries have done a much better job managing this crisis, and they can run their schools close to normal. Lack of national leadership in the US, and a catastrophic lack of empathy have created this Groundhog Day cycle we are experiencing. The obstacles of reopening schools are unnecessary, avoidable, and directly a result of failed leadership. 

Thus, it's important we start from a position of understanding and kindness. Schools are not responsible for getting us into this mess, and we shouldn't place unfair responsibility on schools to get us out of this predicament, especially when many schools lack resources to even meet basic needs even before this pandemic. The predicament is on us as a society. Own it. 

Outro
Other major issues in education need to be addressed eventually on a societal level. Specifically we also need to take more action on inequality, old buildings, overcrowding, poverty, school segregation, lack of or inadequate healthcare, and more, because all these things directly affect our schools and prevent us from forming a stronger, more just society.  These issues overlap with the pandemic and can't be solved with improvements to classroom instruction alone. I mention this to contextualize the broader issues at play and the limitations of focusing on teaching.

What is outlined here isn't attempting to solve all the problems, because many issues are outside the locus of control of educators. With that said, real, practical, implementable actions we can make things a whole lot better right now. 
  1. Prioritize the youngest and neediest
  2. Try to decouple academics, socialization, daycare
  3. Use active, student-centered learning like IBL
  4. No math homework in K-5
  5. Mastery grading
  6. Cull content from course that are not essential
  7. Focus on community solidarity
Stay safe and healthy!


Wednesday, September 30, 2020

Mastery-Based Grading: Interviewing Sharona Krinsky, David Clark

SY: Massive thanks to Sharona Krinsky and David Clark for sharing their thoughts on the topic of mastery-based grading or MBG for short. This interview grew out of a different conversation Sharona, David, and I had about a separate topic. MBG is an excellent framework for assessing students for learning with a focus on equity and is compatible with IBL methods and non-IBL methods. 


Question 1: First, tell us a bit about yourselves.

Sharona: I’m a full-time lecturer in the math department at California State University Los Angeles. I’m also the executive producer of Encore South Bay (Link), a community and youth theater company in Los Angeles. I have degrees in math from UC Berkeley and The Ohio State University, as well as an MBA from The Ohio State University. In addition to working, I love Israeli dancing, scrapbooking, and traveling.


David: I’m an associate professor in the math department at Grand Valley State University, in west Michigan. I’m also a boardgamer (although not a very good one…), hiker and backpacker, and amateur photographer. I’ve lived my entire life in Michigan and nearby. For grad school, I moved from Michigan south into Canada.



Question 2: How did you get involved in MBG?


Sharona: A few years ago I was looking for more ways to bring active learning into my Calculus classroom and stumbled across Kate Owens’ blog about SBG [standards-based grading]. Started reading it and then joined the Google+ group run by Robert Talbert. This led me down a rabbit hole that included Robert’s blog and posts by Josh Bowman. I dove in head first, converting three separate classes at the same time to standards based grading and never looked back. From there, I had the incredible fortune to meet Kate at MathFest a few years ago in Denver which connected me with Dave, Drew Lewis, and TJ Hitchman. This was followed by a serendipitous run-in with Robert Talbert at Poly Teach at Cal Poly Pomona. A year later, I was asked to redesign and coordinate our GE statistics class, which has over 1,500 students in 50+ sections every fall and about 600+ students and 20+ sections in spring. I convinced my co-coordinator to do standard-based, mastery grading and brought about 30 other instructors along for the ride.


David: As an undergrad, I took a few classes that used (what I now recognize as) Inquiry-Based Learning and Ungrading. They encouraged me to learn and persevere much more than my other classes. That experience lived in the back of my head throughout grad school, while I got more and more disappointed with the incentives that points brought into my classes (think: “Why isn’t this 8/10 instead of 7/10?”). After graduating, I heard a talk from TJ Hitchman during a Project:NExT session in which he offhandedly mentioned how he used standards-based grading in a geometry class. That started me down the rabbit hole, and I ended up completely re-working my syllabus to use SBG -- just weeks before I started teaching that course. That class was an amazing experience, and I couldn’t believe how much it improved my students’ experiences (they begged me to give them a quiz on the day before Thanksgiving break). Since then I’ve been slowly learning and converting more courses to use various forms of mastery grading.


Question 3: What are some of the key benefits to students?


Sharona:

  • Allows for growth through failure: Getting students to understand that failure is not only OK but a better way to learn is a huge breakthrough. De-programming the idea that only immediate success is how you succeed allows time to build on growth mindset ideas and build grit in our students.

  • Talking Math, Not Arithmetic (of Grades): Students get to focus on questions such as “what do I not understand about the math?” instead of “how am I going to get enough points to get the grade I want?”. Conversations with students are positive, encouraging, and about MATH. They learn more, and they discover that they can succeed by not giving up.

  • Encourages deeper thinking and communication: Students learn that there are a lot of ways to show that they understand the material. AND that understanding is not the same as getting the right answer. They learn to show what they know, even if what they know is partial or incomplete.


David: MBG...

  • Gives students time to learn. It gives students a chance to come back from early failures without penalty. Compare that to how, in a traditionally graded class, doing poorly on an early midterm exam can tank a student’s grade for the rest of the semester. Similarly, if a student doesn’t have some background that an instructor expected, MBG helps identify this and give students a way to learn background material without penalty.

  • Decreases test anxiety. Because assessments are lower stakes, there’s less pressure on each individual assessment.
  • Encourages students to develop a growth mindset, which can benefit them beyond any individual class.
  • Sets up a clear path to success. Clear objectives, and grade requirements stated in terms of those objectives, let students see exactly what they need to do to succeed in a class. It removes the sense that grades are something that happen to students, and gives them agency.



Question 4: The covid-19 pandemic has highlighted serious limitations of timed, (high-stakes) tests.  How do you see MBG helping in this current era? 

Sharona: In my opinion, MBG is the answer to the serious limitations of high-stakes tests. Although I still give timed assessments, the knowledge that the worst thing that happens as a result of the test is that they might have to test again tremendously lowers both the anxiety of the students and the incentives to cheat. Most students WANT to learn. That’s why they are in college. They want to do well, and they want the time spent studying to be worth it. If they can show what they know, get feedback, and then get to show it again, they quickly learn that it is worth it to do the work themselves. It also allows for tremendous customization of the learning process to meet students where they are, without placing undue burden on the instructor.


David: During the Big Pivot online last March, the one thing about my classes that didn’t need to change was my assessments: My MBG setup was flexible enough to keep working. MBG lowers the stakes on every assessment. Even if an instructor uses timed tests, each one becomes lower stakes, since students have opportunities to retake or revise later. MBG also supports instructors in using assessments that fit the COVID era better, such as portfolios, interviews, or student-made videos. These kinds of assessments aren’t inherent to MBG, but they work well with the philosophy of determining if students have demonstrated overall proficiency in their work.



Question 5: How does someone get started with MBG?  And if someone has a question, where can they go?


Sharona: In addition to reading about MBG and joining the community, instructors need to begin learning about and using Backwards Design principles to design the course. Begin by asking the big question “What should my students know and be able to do” after taking my course. And really hone in on that answer. Don’t just accept the list of skills that we have traditionally taught. For example, I really thought about what the core concepts of Calculus II were and came up with the math of “accumulation”, “the infinite” and “position and motion in space”. I then organized my learning targets around those core concepts. If you visit www.MasteryGrading.com you will have links to over 16 hours of recordings from our first Mastery Grading conference, held online in Summer 2020.

David: Start by reading one or two of these articles to get an overall idea of how MBG works: Kate Owens’s standards-based grading blog post, Robert Talbert’s Specifications grading blog series, or my MBT article. Then check out the articles in the PRIMUS Special Issue on MBG. These articles are detailed explanations of how instructors have used MBG in many different classes, and they are free to all MAA members. Two great places to ask questions and get inspiration: Robert Talbert’s Mastery Grading Slack Workspace (the link invites you to join the workspace) and the super-friendly MBG community on Twitter. Follow @MasteryGrading, check out this list of MBG tweeters, and look at hashtags like #masterygrading, #sbgchat, and #pointlessgrading.



Question 6: Anything else you’d like to add?  


Sharona: MBG has been the single highest impact practice that I’ve adopted in over 30 years of teaching. I did workshops on “cooperative learning” in the 90’s and have used active learning for decades. I was an early adopter of the Hughes-Hallett Calculus text. Despite all of that, I never really succeeded in getting most of my students to really engage in the actual mathematics until I started MBG. The depth of content in my conversations with my students is incredible. And I really enjoy giving really high grades that my students worked incredibly hard to get. (My grades are bi-modal, all A’s, B’s and F’s). I call myself an MBG evangelist for a reason :)


David: My first time using MBG was a “glass shattering” moment. I’ve never again been satisfied using points in a class. It’s changed not just how I do assessment, but my whole focus when designing a class. MBG also fits well with active learning pedagogies like IBL: We’re trying to inquire into what students know and set up opportunities for them to demonstrate their understanding -- rather than forcing limited assessments with punitive results. Finally, the huge variety of ways that people use MBG, and all the acronyms that go with it -- SBG/MBT/Specifications/etc. -- can seem intimidating at first. There’s a lot out there, and everyone ends up finding the best way for themselves. You can dip your toe into MBG (maybe using it only with tests or quizzes) rather than blowing up your entire class plan.



Monday, June 24, 2019

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). 

---

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.