Heather and I have been working for over two years writing a text that completely embodies the goals of MLCS. Those goals are as follows:
1. Prepare students for non-STEM college level courses like statistics and general education math
2. Develop the maturity necessary to be successful in college level courses
3. Develop an algebraic base to give students the option of intermediate algebra upon completion
Ultimately, we began with the goal of appropriate preparation for non-STEM math, which is not intermediate algebra. Having a student who is able to add rational expressions enough to pass a test but with no real understanding of them has no use to me as a statistics teacher. Intermediate algebra has been used a prerequisite because it gives us a student who has a certain level of cognitive ability and maturity. In other words, it's been used a hoop for statistics and general education math. I believe all developmental courses should prepare students for where they're headed and that passing them means the student is college ready. But each course in the developmental sequence should be supportive of the courses that come after it. If your path includes college algebra or precalculus, then intermediate algebra is an excellent preparatory vehicle. For other college courses, it is insufficient.
So that mindset of where these students will actually go has been at the forefront of our book development. It drives every decision and omission. Nothing is accidental. Absolute value equations serve no purpose in this course so we don't do them. If a school wants to add that topic to their developmental math sequence, it would make more sense to add them where they are a benefit (intermediate algebra) instead of where they feel like an odd add-on in MLCS. All the topics in MLCS have to serve a greater point than "we've always taught this topic" or "I had to learn it." We're not letting history guide our decisions other than the fact that history has taught us the current developmental math sequence is not working.
But we want schools to have options when using this book. Our version of MLCS is large and won't always match what other schools want to do verbatim. The same goes with most developmental courses in that variability is large. So we have a large number of topics to accommodate a variety of needs. One of those needs is that a student can go straight into intermediate algebra after our course and not have to go back to beginning algebra if they change their mind and head towards STEM courses. And students do change their minds. We have plenty of algebra in the book and students can go onto intermediate algebra and pass it. But MLCS is not a beginning algebra course even though there is a large amount of overlap between the two. We have incorporated many intermediate algebra topics but do so differently. Our students who go onto intermediate algebra will see many familiar topics, but in that course will get the procedural aspect to them. We do some procedures with quadratics, rational functions, radical functions, and exponentials but that's not our goal. We spend our time modeling, graphing, exploring, and understanding them. We build the base that intermediate algebra can add onto if further skills are needed there.
The key thing we did was throw out old conventions and expectations of the type and order of topics often seen in developmental math. In other words, this is not an algebra book. And it's not an algebra book repurposed either. The beauty of not having written an algebra book is that we don't have that to work from. We started from scratch, which was incredibly daunting. But ultimately that served us and our students well because we didn't feel tied to a model that isn't working. Like in home building, it's often easier to start from nothing than to remodel.
To address the second goal mentioned that I skipped over with all this talk of intermediate algebra, we were intentionally building a cohesive product. It's not a collection of neat lessons. Its order is intentional and thoughtful and when used, works. Students slowly but surely grow mathematically and become stronger problem solvers. And along the way they get algebraic skills. If reordered to make an algebra book, our lessons would certainly support the development of algebraic skills and they would show students why the skills matter. They show the relevance of algebra. But the mathematical maturity would not necessarily come. The whole is greater than the sum of its parts, as Aristotle said. In this case, order matters.
It was important that we establish and maintain rigor. The bar is so high after this course, college level math, that we have to make sure students can handle that. I speak often on this course and I always say, "I teach the college level courses on the other side. Why would we want to pass students to put them in a course they will fail? That is a hollow victory that ultimately hurts the student." And the rigor is definitely there, even without adding rational expressions. It's a tough course when done the way we do it in Illinois because it's a very large course. It would still be a challenging course with fewer topics and more time on them, but it would have a less rushed feel. This is something we're dealing with. I guess it's better to have more content and cut than to find our students are underprepared and have to add. But I always err on the side that more is better.
We had other goals too, like the book being successful in any developmental classroom, not just ones with very experienced full time instructors. So it has a wealth of support and tools to help any instructor. Plus, it's built with the instructor in mind. We do unusual lessons that involve things like chemistry and nursing applications and physics. I say unusual, not because they've never occurred in a math classroom, but because they are unheard of in a developmental math classroom. Developmental math classrooms are primarily about algebraic manipulation and a small set of contrived applications that involve numbers, investments, trains, coins, and mixtures. Occasionally a projectile will pop up (and then down, ha) but that's about it. Our book has one new context after the other. New is exciting but can make some instructors uneasy at first. I was certainly nervous the first time I taught order of magnitude. Now it's one of my favorite topics and lessons; I can't imagine not teaching it. So we were thoughtful to make sure the background is sufficient for the instructor to feel confident, and that the focus is always mathematical and not the context itself. The whole point is to build mathematical problem solvers, not movers of the letter x or chemists, for that matter.
Our perspective is one of the teacher. We worked on this book because we believe in this particular pathways movement. That's why we haven't worked on a Statway book. It's a great philosophy but not one that we can implement at our school or perhaps even in our state. It was important that we piloted every lesson and really work and finesse the lessons until they are class tested, instructor approved. If you build this course, you have to get it through your curriculum committees and state level rules. You will likely have adjuncts teaching the course. We love MyMathLab but feel there's more to mathematics than algorithmically generated problems. We want students who do math on paper and on the computer. Being in the classroom, we have empathy for these issues and have worked to find solutions.
I've been asked why we are getting a book published and not just using the materials ourselves. Well, there are two reasons. First, we know the hurdle of finding good materials is huge and daunting and therefore can stall out the best laid plans. Getting this initiative off the ground matters deeply so we wanted to eliminate the worry about locating good materials. We want instructors to be able to focus on logistics and getting the course approved, which is plenty enough to think about. But second, we've had very positive responses to our written materials used in the classroom for years for other courses like developmental algebra, statistics, general education math, precalculus, college algebra, and math for elementary teachers. Heather and I have long written workbooks that support the text they're based on so well that students usually don't buy the text. They use our workbooks and MyMathLab. Using that approach as a stepping-off point, we started researching and reading about interesting contexts and situations where math pops up. Then we crafted the lessons, organized them to achieve the goal of mathematical maturity, and tied sets of them together to form cohesive units. We then worked, reworked, and reworked again the book formatting so that the content functions on the page and in the classroom. It's been a very organic process.
What is exciting now is that the book has been through our field tests for a year now. And it branches out to other schools starting this fall. If you are interested in class testing some or all of the book, please contact me. That feedback from instructors and students only makes the product better. It's been a time-consuming process writing a book, possibly only matched by all the years I worked on our redesign. But the publishing process vets the work in a thorough way, helping create a product that works on a large scale. The book has already been reviewed multiple times. Add to that editors, a team who is producing it, and all the class testing so far and to come, and the work keeps improving. It's been a labor of love, but ultimately worth it. Our goal was not to think outside the box, but instead to throw the box away. That's a scary thing to do because it's so unfamiliar. But algebra books are not achieving all the goals we have in developmental classes, so we figured we had nothing to lose. If you're searching for an algebra book, please look for one of the excellent ones that already exist. But if you want something different that works and supports this course, we may have just the book for you.
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