1. We have figured out what we are doing and can communicate that clearly. When Heather and I started teaching the course in August, it was still a fuzzy idea. Now we know that are working to develop mathematical maturity in a very specific way. The goal is college readiness in one semester. The order of lessons is very intentional so that the development progresses continually. And it works. For example, we started working with linearity and exponential change in the first unit. Just numerically to start, as we do with every concept, but we built to graphs, algebraic models, and problem solving with the models. This progression has happened with all the topics be it writing and solving an equation, working with units, using proportional reasoning, or working with graphs. Our approach to content seems like a lot of interesting activities. But underneath is a very specific design to ensure students have the skills and vocabulary they need and are putting ideas together continuously.

2. We've learned how valuable open-ended problem solving is. It's so valuable and rich that we intend to count it for more in the course points and may progress to an individual open-ended problem solving assignment at the end of the semester. Students do these types of problems in groups because they are very hard. But we believe some of the greatest learning of the semester happens through them. The problems force students to connect a myriad of ideas, do research, work together, write a coherent solution, and work over an extended period of time. The mathematical lessons are great, but it's the student success skills that they come away with are also so valuable.

3. The two most important elements for success in MLCS are work ethic and attendance. Simply put, students must attend, period. If they miss, they can't just watch a skill-based video or phone a friend. The interaction that happens in the class as well as the questioning and discussion can't be easily duplicated. Heather and I still have a goal that the course can be done in a hybrid or possibly fully online format. We're not there yet, but it's a goal. We want the course to function well face to face first before branching out to other modalities. But the face to face experience requires excellent attendance. Just like missing work at a job, there are consequences. A student recently said that when he misses a class, it feels like a week was a missed. And if you miss a week, it feels like a month. I don't see that as a bad thing. If anything, it's bothersome to me when students can miss multiple class periods of a class and there's no negative outcome. The classroom experience should be of benefit to students.

The question comes up, "what about student's lives and the natural things that happen?" That is a reality of working with developmental students, but the fact is you can't get out of developmental math in one semester and it be easy. If it was easy, we wouldn't have the nationwide crisis we do right now. If life happens and a student has to miss a lot, it will be incredibly difficult to catch up. He or she may have to drop and try again another time. That is a reality to any course. Most students cannot miss long periods of time and pick up again without issue. If they had that level of knowledge, they probably wouldn't be in the course in the first place.

4. At our school, this course is not for everyone. Due to the strict requirements of my state, we have a lot more content than many states will with their versions of MLCS. So we have a giant, 6 credit course. That's a tough thing to take on for a developmental student. That's why at our school we have so many options like 8 week courses that move slow and steady as well as online and hybrid offerings for our traditional courses. We offer an accelerated combined algebra course too. It's also very challenging. But again, you don't get out of developmental math in one semester without doing some major work.

5. Accountability is everything. This is something Heather and I are still finessing. We need more measures in place to check on each student's paper conceptual homework that don't include collecting homework every class period. We're reflecting on the semester, like we ask students to reflect on each lesson and unit, to determine what worked and what needs improvement.

6. The idea of getting the content eventually is a helpful approach to grading in this course. Students don't have to ace every test to pass. They have to work really hard and "get" the content eventually. We used a version of gamified grading courtesy of my friend George Woodbury. Students could earn up to 10 points on each of the 4 units. The final exam was 100 points, giving the class total 140 points. The 10 unit points were based on how well students did on their open ended project (2 points), MyMathLab (2 points), in-class quizzes (2 points), and the test (4 points). For example, an A on a test is worth 4 points. B's are worth 3 and so forth. We will adjust the breakdown of points and what's needed to attain a 2 in a category because that's not quite right yet. But it was still successful this semester. It worked more in terms of mastery and a

*level*of success instead of students constantly worrying about how many points something was worth. The idea has really good bones but with more discussion and research, I think we'll get it to an even better place.

7. Our placement tool is not sufficient. We use Accuplacer and it's not enough. It only tests algebra skills and this isn't an algebra course. However, students can do algebra (more on that later). We're looking at additional measures that students have to complete prior to registering, to ensure we get students who are willing to really work and/or a critical thinking test instrument as an additional placement measure. Those ideas will be worked on this fall. I don't need a student with incredible algebra skills. I need instead someone who has a sufficient cognitive level for this much reading and critical thinking and who is willing to work. We've had several students who would not consider themselves a traditionally successful student in a math class, but they've shined in this course. I've had students tell me that they love that the course is not about pushing symbols around but that every skill has a point and every lesson is grounded in something real. As I said earlier, work ethic and attitude matter far more than prerequisite skills.

8. Everyone who comes in contact with these students must understand the approach and methodology of the course. It's not enough for the instructors to understand the approach. Anyone who tutors these students must be on board too. I've recently worked more with faculty tutors in our Math Lab to talk about the goals of the course and how to help these students. The most common problem is wanting to throw techniques at the student that we aren't using yet or ever. For example, we build exponential models as a comparison to other models. We'll ask students to solve an exponential equation, but with the graph, a table, or guess and check. We don't take the log of each side of the equation to solve it. Sometimes a tutor will jump to a technique like logs instead of going with the approach taught. There's no malice intended, but it's still an issue all the same. The main goal we have is understanding and knowing when and why a technique makes sense, not just getting every algebraic tool possible to say we can. Pushing symbols with no real understanding of them is not our goal.

9. We are seeing success in a traditional numerical sense like pass rates, placement scores, and the like. I had 55% pass and Heather had 62% pass. Keep in mind our sample is small, but I'm still encouraged. We also have students take the placement test at the end of the course just to see how that measure is affected. All but 2 students in a each class went way up on their placement score. The most common outcome was a placement score at the very upper end of our intermediate algebra range (almost college level) and several placed into college level. There are many students who are near the college level cutoff who could be successful in a statistics or general education math course, so I'm buoyed by those results. Our college level cutoff is really meant for college algebra and statistics and is too high for our non-STEM college level courses. It's also very comforting to see that all the algebra we do is enough. No, we don't do every algebra topic under the sun. But we do cover a large amount and certainly everything they need in the outcome courses.

Beyond numbers, I see and hear so many encouraging things in this class. Students really talk about math and mathematical ideas. And I see progression and growth in the students as the semester progresses. Heather and I will sometimes get frustrated if attendance is down or students are getting lazy about homework. But then they'll say something in class that we have never seen or heard in a beginning or intermediate algebra class. And then we know something new and something good is happening. That makes all the work and time worth it.

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