A frequent concern that arises when courses like MLCS are proposed is the issue of rigor. Often, it is assumed that an alternative to intermediate algebra is being developed because students can't pass intermediate algebra. And with that comes the debate of whether someone should get a college degree without being able to prove competency in high school algebra 2. The insinuation is that our current system is just too hard and folks looking for change are really looking to reduce standards.
I do believe students are capable of passing intermediate algebra. Students in our school do very well in that course through our redesign. And through that success, they fare extremely well in college algebra, the true goal of intermediate algebra. I also believe intermediate algebra is a good course and one that we should not eliminate.
The question is
should they have to take that course? And are our reasons for requiring it outdated?
Intermediate algebra is commonly used as a prerequisite for college level math because it weeds out students who are not college ready. In other words, it's a hoop. If our goal is evidence of college readiness and therefore rigor and high standards, we can get there in other ways than intermediate algebra. And in doing so, we can accomplish what I believe to be the real goal of developmental math: preparing students for the college level math courses they will take.
We teach intermediate algebra because of history and tradition, which is not sufficient. For students headed to statistics or liberal arts math, there are no skills in intermediate algebra that will help them be successful. Most students see the course as an exercise in moving letters on a page and are often quite irritated in those two follow-up courses when they discover they didn't need any of the skills they worked so hard on.
But intermediate algebra does have rigor and high standards. So it does accomplish one goal: putting stronger students in college level courses. Using it as one size fits all prerequisite is my issue. Read any article about the job market and what employers need and a theme is common: graduates lack skills necessary for the workforce. I believe the time we spend with students should be meaningful and of value to them. Not everything has to be immediately useful, but much should be. Or at least much more than we currently do should be useful. And the processes used to develop content should have meaning beyond the course. We should be preparing them for what's next in their program of study but also to be productive citizens and employees.
In MLCS, there are some skills we work on that I'm very confident students will not use in real life. So why do we still include them? Because of the way they're developed and the additional skills and techniques students get along the way. For example, we do a problem about a school increasing tuition and the effects of loss of credit hour enrollment due to increases. We build a cost model, which is quadratic, and analyze it numerically and graphically. We then learn about the vertex, how to find it, what it signifies, and how to use it.
In an intermediate algebra class, students are given quadratic functions and asked for the vertex. Then there are a handful of applications for students to practice using it. But the focus is on the symbolic manipulation. In MLCS, the focus is on problem solving, new functions that arise when problem solving, and ways to work with them. Students exercise skills they've already learned and extend their ability to analyze a situation. It's rigorous and difficult, but worth the class time spent on it. While I can't guarantee they'll use the skill developed in their daily life, I strongly believe they'll use the processes involved.
When I'm teaching algebra to students who are not headed on the calculus track, I don't understand our goal anymore. That's why I've stopped teaching developmental algebra for students heading to statistics. I can't sell a course based on exercising one's brain. We could do Sudoku and chess for a semester and exercise our brains. That sounds absurd, but so does moving letters around for 4 months when students will never use that skill again.
And do their brains really get exercised? We like to believe that happens because it justifies what we do. But I really question how much learning is taking place in developmental math classrooms. Students are mimicking and enduring but they're not retaining and applying. Learning is defined as:
The acquisition of knowledge or skills through experience, practice, or study, or by being taught.
Notice it's not the
exposure to knowledge or skills; it's the
acquisition of them. I don't believe our students are acquiring much from our developmental algebra classes. And with the amount of time and cost they spend there, that's not acceptable.
So back to rigor: why does MLCS have it? And how is it possible to have a comparable level of rigor of intermediate algebra without the symbolic manipulation that intermediate algebra includes?
Here's how: depth and expectations.
Whatever we do in MLCS, we do it deeply and frequently. There is very little "one and done" of a topic. Every skill is developed because we need to use it. If we develop a Venn diagram, it's so that we can use it as a tool to make comparisons and gain further insight on a situation. For example, we use Venn diagrams to compare and contrast high school and college. We also use them to compare and contrast variables and constants, which is an important distinction.
It's not, "graph y = 3x - 8." It's determining if a situation is linear, if a model will help solve further problems, and using that model's equation and graph to answer questions.
Using a skill after you determined it should be used is much more difficult than performing a skill after being told when and how. But that's how life is. I don't get new projects with a detailed roadmap attached to them and "view an example." I get new projects and the instruction "make it happen." What, when, how and why is up to me to figure out. That's the way of the world and certainly the job environment. It's very beneficial for students to experience those types of challenges in the safe environment of the classroom.
But every time you decide to go deeper with a skill, you lose time that would allow you to go further in breadth. That approach is one I've used for years in my statistics courses. I never get to ANOVA, but my students can collect real data and test hypotheses using it. They can obtain and analyze statistics. I sacrifice more topics for fewer topics done deeper, where real life activities are the norm. The end result is a hard course with great value. And I never once get asked "when am I going to use this?" A slight perk, but one that I cherish.
The other component that ensures rigor are the expectations of the course. In our version of MLCS, we make students write, explain, and research problems including open ended problems. This approach makes them love MyMathLab problems because they're a very simple, boiled-down part of the course. But learning is about understanding (and showing that) as well as application. So half of their tests are applications. And not routine, previously seen, canned applications. Problems are truly problems and challenging. I've never given a developmental algebra test with more than 10% of the problems being word problems. 50% almost seems cruel. Yet that is far from the case in MLCS. And students can do them.
The old adage of depth over breadth is truly exhibited in this challenging course. But students can rise to the challenges and in so doing, they reach the level of college ready. No, it's not intermediate algebra. It's just as hard, but it prepares the students for what's ahead of them. I absolutely believe intermediate algebra has value, just not for every student. The same could be said for my math for elementary teachers courses. They're wonderful, but I can't imagine a pre-med major getting much out of them.
