This week was the last week of new content. We decided to spend next week (the last week of regular semester) to work on getting ready for the final exam. It's not a typical thing for either Heather or me to take a week to do that in any class but we thought it could help them do better on the final exam. They will work on MML and paper problems that recap the course and cover all the key content. And in the spirit of full disclosure, we're exhausted after this pilot so this idea for the last week was a welcome relief.
So what did we learn this semester?
There's not enough space to list it all so I'll be brief but still use two blog posts to cover it. In short, we learned a lot. Here's the first half:
1. As I've said numerous times on this blog, you can make a really hard, rigorous course without all the algebraic skills of a typical beginning and intermediate algebra course. We did that and then some. The course was a real challenge for students. We found ways to make it more accessible but the fact remains, it's quite hard to read and solve word problems all day, every day throughout the course. But it's a worthy challenge.
2. It can be really fun to do real mathematics with developmental students. Not canned problems, not rote skills, but real, rich mathematics. Problems that don't have a quick, pat answer. Situations that are fuzzy and ill formed. The discussions we had and the engagement of the students was really enjoyable. They were thinking and talking and learning about the power of mathematics. That's valuable regardless of passing or failing or what happens next semester.
3. Balance is everything. We finally got there but wow, was that a rough road. Finding just the right amount of MML vs. paper homework, lecture vs. group work, open-ended vs. single solution problems, skills vs. applications, the list never seems to end. Basically, this course turned our regular course approach upside down. So all the things we knew how to do well inside and out didn't work so well anymore. Finding ways to take students with us on this journey and make it work for all involved was hard but now I feel like we know what works. Or at least we're a whole lot closer to that point.
4. It's frightening to see how little numeracy and literacy skills our developmental students have. But I tend to not to focus on that. We get what we get and there's no point in getting upset over it. Instead, we consistently challenged them to read, research, and think in ways they hadn't. We stretched them. For that, I'm proud.
5. Developmental students really lack metacognitive skills. They don't know how they think or learn. We constantly asked them to take a problem that started out in words and translate it 3 more ways: numerically, graphically, and algebraically. But when we were done, another goal was to find out which way made sense to them. While we worked and worked on that, I think more work needs to occur there in an overt way. We focused so much on other student success skills, not knowing that metacognition would be a key one throughout. Usually student success is about attitude, test strategies, and time management. Those are included in our course but so are ideas about majors such as STEM fields, how to calculate and understand grading practices, and how to understand themselves and their learning processes.
6. Technology need not be that lightening rod of controversy it often is in mathematics education. Our approach was simple: use technology the people do in the workplace. That is, they use whatever they have or makes the most sense given a situation. So that's usually a calculator (scientific, could be graphing or not) and a computer but it could just be a pencil. We used Excel nonstop, and students really liked that. The graphing calculator was zero advantage to the students who had it. We're not doing a lot of "graph: y=3x + 2" so it's no leg up to have one. And the numeracy required is so consistent and involved that having a calculator didn't mean they had all the answers. Plus, our tests pushed them to explain calculations and delve deeper, beyond simple calculations. The calculator was just a tool, not a crutch.
7. My last lesson in this part is for all those instructors out there who are feeling disenfranchised by some of the approaches of redesign which seem to be replacing us with technology. Computers are just tools. The human element matters in learning. It always has and it always will. The role we had in the classroom was essential. We lectured some, not a lot, but were constantly questioning them, challenging them, and keeping them moving forward when they got stuck. We weren't guides on the side or sages on the stage. We were their teachers, in every sense of that word. Heather and I both walked around every inch of our classroom every class period, moving to where we needed to be and doing what needed to be done. Sometimes that's whole group, sometimes it's small group, sometimes it's with individuals. Whatever was necessary, we adapted.
I truly enjoyed it and feel re-energized towards teaching. I've also joked that I'm ruined on traditional classes. Now that I've had the opportunity to teach a course that every aspect is real and relevant, that's interesting and not contrived, and that students really enjoy, I can't go back to teaching traditional algebra face to face. I may continue teaching it online and will definitely continue teaching statistics, general education math, math for elementary teachers, and calculus face to face. I need to get college algebra using this approach but that will happen down the road. My goal is to take this approach to as many classes as I have the time and energy to do so. It's just too rewarding for them and me not to.
That's all for now. Next week, I'll recap the lessons we learned about the course structure like grading, advising, etc.
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