It's a valid concern because we are changing the focus off traditional algebra. Whenever that happens, educators worry that we'll be expecting less of students. I cannot say strongly enough that this concern is not an issue whatsoever. Actually, quite the opposite is the reality.
Students in a beginning or intermediate algebra class see content that's very prescriptive. And while they may not understand it, they can often get by with mimicking and memorization. As good intentioned as we all are to bring in conceptual understanding, applications, and understanding of the processes going on, the bulk of the content is rote use of skills that usually can be classified by a "type": one step equations, "work" problems, mixture problems, etc. A student who doesn't really know what they're doing can find ways to pass tests despite their lack of understanding.
In this class, the skills are not the focus. They exist and are plentiful but they're just one cog in a much bigger machine. The approach is something like this:
- Rich situation initially explored
- Skills identified that need development
- Development of skills
- Application of the new skill in the original context
- Further exploration of the situation in a deeper way while making connections
In the U.S., we have a well-defined view of what a math classroom should look like. It may or may not be the best view for employers or jobs but it's one we know and understand. Many instructors and from what we've seen, many students, believe that to do math, it must look something like this:
Solve: -3(2 - x) = 4- 2x
Certainly that is in the spectrum of mathematics, albeit in the skill band. But this is mathematics too:
There are two pay structures, a 5% raise or a 3% raise with a $1000 bonus. For whom is each option best?
Because these students are so new to a large problem like this, we're walking them through it and taking the opportunity to show graphs, tables, patterns, the role of variables, and develop numeracy whenever possible. But at the end of the day, solving that problem requires solving this equation (that they wrote): 1.05S = 1.03S + 1000. So we still get to equations of all sorts just as you would in an algebra class. This is simpler equation that they'll solve in the course. The large ones are seen as well.
The reality is when you do the skills and the concepts and make connections and apply every skill developed in multiple contexts, you get a hard course. It's an interesting course, but it's hard nonetheless. We're watching closely to see how students fare in the pilot and studying the methods we use such as sequencing and pacing of topics to ensure they'll understand them. But regardless, this is a tough approach for students. They can't fake it or mimic anything and that can be frustrating, because that's a technique they may have come to trust in times of struggle. The ones who are successful will do well in a college level course, that we're confident of. At this point, we're just hoping that most can be successful at this course and make it to the college level course.
We're not going to walk away with a 90% pass rate so worries of this being an easy course to make students feel good that puts them in college level math for which they're unprepared are unfounded. The ones who succeed will be excellently prepared.
I hope that we will work our way through this journey this semester, over the hills and valleys, and come out on the other side with the great majority of the students with us and better for having the experience. My Pollyanna ways just expect that to happen. But we have to wait and see.
Enough with the metaphors and referencing of old movies. It's time to get back to work.
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