Math Lit Toolbox
- 2017 Webinar Math Lit 5 Years Later
- Math Lit Forum
- MLCS Book: Math Lit
- 2014 Math Literacy webinar (Youtube)
- Math Literacy Training
- 2013 MLCS Presentation: What is Math Literacy? (Youtube webinar)
- MLCS syllabi (objectives and outcomes)
- 4 Credit Hour Math Literacy Course Syllabi
- A Typical Day: Math Lit classroom videos
- Math Lit instructor support
- Math Lit FAQ's
- Implementing Math Lit Presentation (Youtube webinar, PPTs, & handouts)
- Implementation blog series
Thursday, December 13, 2012
Here are some common obstacles that come up when trying to pilot a Math Literacy course and some ideas for overcoming them. All of the ideas shared are above board and do not ignore the rules in place. I'm a big believer in following the rules and learning ways to work within them. Some schools are saying they are teaching intermediate algebra but really are piloting MLCS instead. I don't advise doing that. It could backfire in a big way in terms of your state regulations and articulation.
1. Intermediate algebra
Many states, including mine, have a requirement of intermediate algebra before college level courses. Some states are beginning to allow alternative courses in an attempt to see if they can be successful. If you are not lucky enough to be in one of those states, here are some things you can try:
a. Create a large enough course in terms of credit hours and content, making sure all the big ideas from intermediate algebra are addressed. This means including factoring, quadratics, exponentials, rational functions, and radical functions. That's not to say that you need to teach all those topics the way we do in intermediate algebra. Otherwise, what's the point of the course? But you can show students the typical intermediate algebra topics in a different light, one that focuses on modeling and concepts and applications.
b. If that's still not enough to get approval for a pilot, go around that intermediate algebra requirement with placement. Placement is something that nearly every school is in control of. Use that to your advantage. We started our pilot with making every student in the course take the placement test at the beginning of the course and at the end. The data was quite interesting. Many students placed into college algebra and those who didn't were close. Our school is contemplating a different placement cutoff for liberal arts math and statistics anyway since being at the college algebra level on the placement test is not necessary for success in those two courses. It's only necessary for college algebra and precalculus. That new cutoff would be just slightly less than the college algebra cutoff, similar to how we use ACT scores. If you have a specific placement cutoff for stats and liberal arts math, you can verify that students passing the course meet that placement number using the exit placement test. And even if you don't have a special cutoff score, you can still use the placement test at the end.
This approach allows students to use the Math Literacy course as basically a bridge to non-STEM college level math. They take the course and then retake the placement test. If your state won't allow the course as entry to statistics or liberal arts math, the placement test result can. This approach allows you to pilot but still follow state rules.
2. Faculty opposition
Sometimes faculty in your department will be skeptical that standards will be reduced or students will not be prepared for the outcome courses. But the reality is they don't know that for a fact. The data will bear out the truth. In this situation, ask for a pilot with the stipulation of gathering data and re-evaluating the course after 2 years. It takes that long to teach the course and track the students after it. Some faculty, especially ones in math, need hard data to convince them. Still, some folks just don't like something different than algebra, even if students perform well in the next course. That kind of emotional reaction is very hard to address because it's not based on facts or logic.
Another suggestion is to make the course an option and not a requirement in your department. That allows students and faculty who believe in the course to be a part of it and those that don't, aren't.
Of all the traditional topics, this one creates the most conversation and conflict. Fundamentally, many instructors believe students should learn to factor. Here are the most common cases and what can be done:
a. Faculty are concerned that students won't be ready for a traditional intermediate algebra class after MLCS if they don't learn all the factoring techniques. The reality is that students who pass beginning algebra aren't even ready for using factoring in intermediate algebra. We as educators like to think if we've taught a topic, that it equates to students learning the topic. But that's just not the case all the time. Many beginning algebra students still need massive amounts of review of factoring when they go into intermediate algebra, even if it's just a few weeks later. We saw this firsthand in our redesign. We tried to address factoring "just-in-time" in intermediate algebra and it never worked. We saw our intermediate algebra pass rates soar once we added in intermediate algebra as a unit and just taught it directly. All the students benefited.
So my suggestion in this case is to add factoring to your intermediate algebra class if it's not. And if it is, it will be enough to help an MLCS student succeed. Most students moving from MLCS to a STEM path are stronger academically. That lurking variable matters and benefits the issue greatly. And nearly all of these students have seen factoring before intermediate algebra. Remember, because we teach algebra so early in U.S., most students have seen 3-5 years of algebra prior to starting developmental math.
b. The other concern faculty have is the idea of removing an old standby. Even if factoring is not useful, many instructors believe we should teach it for historical reasons and for critical thinking. First, students are not getting the brain exercise we like to think with factoring. The are ways to make students work hard and think critically AND learn content that will help them in the next course. We don't have to do topics just for the sake of mental exercise. We also don't have the luxury of time to do that anyway in MLCS.
But doing something just because we always have doesn't make sense. My father is a retired math professor. He knows how to calculate square roots by hand and use a slide rule, but I don't. I learned trig with trig tables and stats with stats tables, but my students know neither. Times change and so does content. 100 years ago, a college student had to know Latin to graduate. We laugh at that now, but at one time it was considered essential to being college educated. Again, times change, and mathematics education has to evolve with those changes. We have precious little time with students and need to prepare them for their next course and college in general. If a topic is not going to serve those goals, it needs to re-evaluated for inclusion in a course.
These are some of the big obstacles and some ideas. Hopefully they will help some. If you've tried something that worked and helped you gain a pilot, please share in the comments or send me an email.
Wednesday, November 28, 2012
Einstein said, "We can't solve problems by using the same kind of thinking we used when we created them." To get to the point we want students to be at the end of the math literacy course, which is college readiness, we use very different approaches. And they do work, but they do not look like what instructors expect, especially in terms of the printed page. For example, I taught a lesson today that started with reviewing linearity and building a model, then moved into solving literal equations, and concluded with factoring the GCF. All of this worked together in the context of building a model and then working with the most useful and simple form of it. Everything had a purpose, but nothing was easy. Beyond that, those topics never appear together in an algebra book. But they need to if we want students to see connections. And while that mix of topics may be strange to us as instructors, it can make sense when solving a bigger problem.
College readiness is more than a skill set, but possessing the ability to use that skill set. To get students there, we use open-ended problems each unit. This unit, we're having students work on problems framed around the question, "how big is big?" We want students to grasp the largeness or smallness of numbers in a variety of settings. We ask students questions like, "could you carpet the U.S. with its own debt if it was in $1 bills?" $16 trillion is a large number but how large is it really? Putting it in perspective helps to make sense of it. That idea is pervasive in real life. I just used an example: $16 trillion instead of $16,000,000,000,000. Writing "trillion" allows me to work with a number that's more manageable: 16.
We ask students to take the U.S. debt and find its weight in quarters, its height if it was stacked in $1 bills, its area, etc. But the numbers are enormous, so we ask students to make a comparison that's useful and helpful. To make this idea and goal concrete, we use the example of blue whales, the largest mammal. But how big are they? We could find their length or weight but those are just large numbers. So put them in perspective. This interactive app provides a great demonstration. For me, seeing that a blue whale is the length of a basketball court is really illuminating.
This unit project has an amazing amount of math in it to be solved. Students have to work with scientific notation, dimensional analysis, concepts from geometry as well as do research on quantities and find objects of comparable size to make comparisons against. If you want a fun challenge, find the weight of the U.S. debt in quarters and then something on the earth to make sense of that number. It's not a trivial exercise.
Like the quarter problem, the entire open-ended problem description is brief and there are no mathematical symbols in it. But to complete the project takes pages of calculations and research. That isn't how we typically provide "word problems" to students because it's really hard for students to complete. We don't provide short statements and tell the students to figure it out. As educators, we want to make math accessible so we try to find ways through problems, be it decoding word problems or finding key words or recognizing problem 'types.' That approach is full of good intentions but the outcome is a student who can't really solve problems. Students can often mimic their way through, but true understanding is not often gained. It's like we've left the training wheels on the bike and then expect students to ride without them. If they never have to ride on their own, we shouldn't be surprised when they can't.
As with the project description, there are lessons throughout the book we've written that are devoid of symbols, at first glance. Take a look at this page from the manuscript:
It begs the questions, "where's the math?" Take a look after students complete the lesson:
Like the national debt problem, students start with few words and a problem to solve. But getting there requires a serious amount of work. The mathematics is evident and abundant but it was not given to students but instead created by students.
The level of expectation is higher and so is the difficulty level. But the understanding is deeper. Students move past skills alone and work to use those skills without constant prompting on when or how. Not easy, but the payoff is greater.
A colleague of mine said years ago when we began redesigning our developmental math program, "what we're doing is good, but I wish we could do more mathematics with students." I just looked at him puzzled because what else are we doing with them in an algebra class if not mathematics? But I understand his point now. Doing mathematics is rich and complicated and messy and often, circuitous. Algebra is neat and linear and simplified to a set of procedures. Do we need those procedures? Absolutely. But focusing on them alone is akin to learning all the scales in music. If we never move past the scales and into the songs, how can we say we've made music?
Thursday, November 8, 2012
Saturday, October 27, 2012
Thursday 1:40 - 2:30
MLCS: Redesigning a New Pathway for Non-STEM Majors
Kathleen Almy, Heather Foes
On Friday, November 9, I'm part of the Developmental Math Committee's (DMC) themed session on redesigns. In 10 minutes, I will very briefly overview our version of MLCS including challenges, progress made, and plans going forward. If you or a colleague want a quick snapshot of this redesign and others, consider this themed session.
Friday 9:00 am - 10:55 am
Evidence-based Developmental Math Redesigns (DMC Themed Session)
Embedding Student Success Strategies into Math
Courses Amy Getz
MLCS: One Year Later
A First Look at Developmental Math Students After Course Redesign
Developmental Math I and II Redesign at Valencia College
A Developmental Math Boot Camp
Washington State’s Developmental Math
Michael Nevins, Carren Walker
On Friday afternoon, I'll assist with Jack Rotman's workshop on the two New Life courses, MLCS and Transitions.
Friday 1:45 pm - 3:45 pm
New Life Courses: Mathematical Literacy and Transitions
Additionally, there are more talks on MLCS, Dana Center's New Mathways Project, Carnegie's Quantway initiative, and other schools trying pathways of their own design. Definitely the concept of pathways through developmental math beyond beginning and intermediate algebra is taking hold. The DMC will have a committee meeting on Friday afternoon that anyone can attend. At it, we'll be voting on an intermediate algebra position statement. The statement addresses the concept of allowing for innovation and moving away from a universal college-level math prerequisite, intermediate algebra, for all. Instead, the statement promotes appropriate preparation for all students based on the courses they will be taking.
Lastly, we'll be at the Pearson booth if you have questions. Also at the booth will be copies of the sampler of our book, Math Lit, in both student and instructor versions. If you want to talk more, please stop by. Or, if you'd like to set up a time to meet, please email me.
See you in Jacksonville!
Tuesday, October 23, 2012
Tuesday, October 2, 2012
Saturday, September 29, 2012
The following week, I'll be at Oakton Community College in the Chicago suburbs doing two MLCS sessions. The first is a general talk overviewing the course. The second is an interactive session designed to help schools plan their pilots. The Pearson site has the session descriptions.
Tuesday, September 25, 2012
Looking for new teaching strategies and techniques, especially regarding using technology with your courses? Learn from your colleagues for FREE and from the comfort of your own home or office!
Speaking about Math & Stats Online Conference – Friday, September 28th from 10am-4pm Eastern
• This full day online conference is filled with sessions given by mathematicians and statisticians.
• You can join just one session or you can join multiple sessions; it is up to you.
• To join on September 28th, all you need is a computer and internet connection.
• There are NO REGISTRATION FEES!
Check out the great topics and fabulous speakers! (All times Eastern)
10am - Eric Schulz from Walla Walla Community College on Teaching and Learning with Interactivity
11am - Scott McDaniel from Middle Tennessee State University on Flipping the Math Class at the College Level
noon - Greta Harris-Hardland from Tarrant County College, NE on Mod Math: A Redesign Option for Mastery and Acceleration of Developmental Mathematics
1pm - Kim McHale from Heartland Community College on Using Statistics in Online and Hybrid Statistics Courses to Improve Student Learning
2pm - Kathy Almy from Rock Valley College on New Pathways for Developmental Math: A Look into Mathematical Literacy for College Students
3pm - George Woodbury from College of the Sequoias on Using MyMathLab to Promote Mastery Learning
For more information and to register for this free event, check out www.pearsonhighered.com/speakingabout/mathandstats/
Thursday, September 20, 2012
This week was the end of the first unit of MLCS for the semester and with that came the grading of their open-ended project and their first test. And to say the least, I am thrilled with the progression of this course and what we're seeing. Here's what's happening:
1. Because the text is such good shape and the goals of the course are clear, students never really had an adjustment period where we had to hope they'd buy in. They just quickly learned how we run this course and adapted without an issue. That is a major change from last year where students took about 2 weeks each semester to accept how the course would operate.
2. Along with that, we are seeing terrific things with the projects and tests. The level of quality is much higher than what we got from students last year. We're not necessarily attributing that to the level of students (although it's possible), because they are similar to our classes from the spring. What is different is the cohesiveness of the content and clarity of the goals and expectations. Basically, we get what we're trying to do and we can articulate that well. Consequently, students better understand what we want from them and can provide it. As Heather put it well, we're more confident and students sense that.
But there's something I noticed this week that I had never thought of before. We know the goal of a course like MLCS is college readiness. It's not about solving equations or graphing lines (even though we do that too). It's about maturity in terms of college and mathematics. To get there, we push students and ask more of them than they're used to. At first, it's intimidating because the open-ended projects are not simplistic. The tests aren't easy either. Most math students at community colleges do not take tests that are half word problems. But students rise to these challenges and really gain something in the process of that struggle.
It's like my 8 year old and how he reads. He's a terrific reader but he didn't get that way by reading 2nd or 3rd grade books. He got that way by first reading a lot but also by always pushing into new and harder books. The same principle applies with developmental students and the traditional developmental sequence. If we want them to be college ready, how can we expect that to happen if they're just redoing what they did in high school? Pushing them beyond the familiar and comfortable exercises new parts of their brains and helps them make gains where we need them. It makes sense. You build strength by lifting heavier weights than are initially comfortable and adapting to the challenges they pose. Mental muscle works the same way.
3. We are starting to figure out better ways to elicit the behaviors we want from students in the course. Attendance policies matter and grading MML homework helps too. But we need students really working with paper homework to solidify concepts and get to the point of being able to use the ideas learned. However, the idea of grading their homework each day is not appealing to me or Heather. So we've added longer quizzes given twice each unit that cover the paper homework in addition to MML quizzes that cover skills. Still, some students won't do the work. So we're now randomly collecting pages from their binders to give them that little extra push to do their homework. It should help some, although there will still be some students who are not motivated by measures like these.
Another related change I've made this semester is what I call an "intervention." We are a quarter of the way through the course. If students are going to pass and aren't currently, they have to make major changes now. Usually I either do a pep talk or a gripe session when I give back tests if they're not that good. This time the tests were good (I graded my first perfect MLCS test!) but there were still some D's and F's. To address the specific issues with those students, I wrote a letter to students and stapled it to the back of their test for privacy. It outlined what they need to do to pass the course. I also showed them the timeline to finish their college level math course if they pass this class as opposed to the timeline if they need to repeat MLCS or change to beginning algebra. The difference is more than a year of their lives. That fact alone seemed to get the attention of several students. I'm hoping this intervention strategy will prove successful. We'll see...
Are we there yet? Meaning, is the course perfect? No, but most courses aren't. The book is still being tweaked and the MML course is still a work in progress. But the growth and improvement we are seeing is not a fluke; it's real and consistent amongst all our sections. That is reason to celebrate.
Tuesday, September 18, 2012
Wednesday, September 12, 2012
The Math Lit sampler will be available in early October 2012. Contact your Pearson rep for a copy.
Tuesday, September 11, 2012
Sunday, September 9, 2012
I'm continually pleased with the progress that's been made in a year. The materials are working beautifully. Students adapt quickly to the style of the class. Maybe it's because Heather and I better understand what we're doing, but issues of "buy-in" were pretty non-existent. Students accepted that this is how the class would roll and have been very positive as well.
Without question, I'm sold on this course and what it can do for developmental math students. More than just mastery of specific mathematical objectives, MLCS builds college readiness. We push them, no doubt. Students say this is a tough course. But it's also an accessible and enjoyable one. If students will work, they will be successful. That cannot always be said in an algebra class, or most math classes for that matter, because math is linear. If you lack the prerequisite skills, you are at a huge disadvantage. But the prerequisite skill knowledge needed in MLCS is fairly minimal and we review that content to begin the semester anyway. What we need are students open to learning, willing to think, and willing to put in serious hours of work. The payoff is large: one semester and they are done with developmental math. But beyond that, they are ready for college level work and expectations upon successful completion of the course. They've had to write, read, think, problem solve, communicate, and persevere. Not all will make it, but many do.
In other exciting news, we have been working on a sampler of the MLCS book we're writing. It is nearly finished and will be in print in early October. Pearson representatives will have copies. It is one full unit, completely designed and professionally laid out. The cover has also been designed and is part of this sampler. I'll post a picture when I have the final copy.
The book is written and has been through several rounds of edits. If you would like to see the full manuscript, please contact your Pearson representative. It is currently being class tested at schools across the U.S. Additional class tests are available for the spring semester. We will begin copyedits and design edits of the remaining units soon with a publish goal date of next summer. After seeing the sampler, I'm very anxious to get the rest of the book to that level.
|Students in MLCS class working together.|
Tuesday, August 14, 2012
My concerns are many when it comes to this use of the model. For one, I do not believe learning is mimicking what is seen on a computer screen. It's a far more complicated process that involves humans because the brain is complex. And learning math is not just moving letters and numbers on a page or screen; it is also complex. Two students figuring out an exercise or an instructor talking a student through steps is not the human interaction I'm speaking of. Of course, those types are necessary. But beyond that, there are deeper aspects that only a qualified instructor can offer, insights needed to truly build understanding in a greater way.
I have a colleague who will joke that no doctor would ever say, "I don't need to understand how to do the liver surgery. Just point me in the right direction and I'll cut." That's absurd. But the type of "learning" we offer through emporium models, particularly in developmental math, is little more than procedures and "how's" with very little "why" along the way. We break math down into tiny bits so that students can learn them, but we never connect the dots and put the puzzle back together so that students can see the bigger picture. They get a set of disconnected skills that have no meaning between them, something that is necessary to use the skills in later courses.
It begs the question: what is our goal here? As a country we are in a huge rush to get students through developmental math, even to the detriment of the student. We want great statistics, not great learning. As an educator, good pass rates are important to me because they are a measure of our programs. But I'm more interested that my students learned something, that they were pushed and came out on the other side better for the experience. That they did more than endure a series of tests and checked off a set of skills they can do. Math is a amazing subject, but you have to step back away from the trees to see that beautiful forest. And it takes a well-versed guide to make sense of what you're seeing.
I'm not saying technology shouldn't be used or that lecture is the number one way to offer instruction. Quite the opposite actually. I believe we need balance and emporium models are too extreme, offering an unbalanced method of math education. Like the Khan academy, I think they have a place and offer something additional to developmental math programs for particular populations of students. But as a replacement across the board for all sections and students? I don't think that respects the great variety of needs or learning styles for students nor the variety of teaching styles and strengths of instructors. For a redesign to work, respect must be present or faculty will resist. Or they will succumb temporarily only to reject the model when administration changes.
What got me thinking about this topic was an opinion piece in the Chronicle, Don't Confuse Technology with College Teaching. One part in particular caught my eye:
A set of podcasts is the 21st-century equivalent of a textbook, not the 21st-century equivalent of a teacher. Every age has its autodidacts, gifted people able to teach themselves with only their books. Woe unto us if we require all citizens to manifest that ability.
Most people find math intimidating. And most returning adult students find technology intimidating. So a course on a subject that they struggle with that is solely using technology for instruction and help is a person answering their questions only, is not usually a welcoming prospect. Students want and deserve more.
Students usually do not move faster through the content either, a often used selling feature of the emporium model. More often than not, they will move slower. So policies and deadlines become very important. The most success our emporium ever had years ago was when it is was so rigid that self-paced could not even be used in the description. And "success" was a pass rate on paper. Ask the students and they disliked the model for two reasons: the experience in the course was not what they wanted and they feared that hadn't really learned anything, causing them to be at a disadvantage in the next course. After years of trying to make this model work, we dropped it, taking the elements we liked from it and working them into a new, hybrid model of instruction. That model is just an option in our program, not an approach that every student experiences unless they want to.
My other big concern are the unspoken reasons for choosing the model. Administrators are often picking this model and imposing it for the sole reason of cutting costs. While a successful developmental math program can save the college costs down the road, that is not usually where the cost-savings come from. Administrators quickly do the math and realize that when the computer is offering the instruction and grading the assignments, there's really no need to cap class sizes at 24 or 30. Some colleges assign several hundred students to an instructor for a section and use tutors or teaching assistants to staff them. The need for qualified, full-time instructors drops quickly. This is the unsaid way of saving money.
From the Chronicle article:
Can technology make education less expensive? College is expensive, but colleges do things other than educate. Many courses simply convey information and provide technical vocational skills. These could be automated, presumably at savings. The price tag includes the campus experience—an education of a different sort—with all its lovely, cherished amenities.
But the core task of training minds is labor-intensive; it requires the time and effort of smart, highly trained individuals. We will not make it significantly less time-consuming without sacrificing quality. And so, I am afraid, we will not make that core task significantly less expensive without cheapening it.
Food for thought.
To that end, we use MyMathLab when it is superior and we use paper when it is more appropriate. Here are some ideas for use of MyMathLab:
1. Practice skills in MyMathLab.
As part of the book I am writing with Heather, we will have a MyMathLab course with assignments for all skills addressed. We have a working MML course that can be used when class testing. But the final course will have many more problems and bells and whistles.
2. Build self-checks for students.
One of the downsides to MML is the ease of misusing the help aids. Students like to mimic View an Example, which is not learning. This course is about understanding, not mimicking. To help students better assess where they are learning and where they have deficits, we have quizzes regularly on skills without help aids. These quizzes are done in MML.
Additionally, we have a few questions on every homework assignment in the book with a MML assignment. These questions are on paper, mirror the MML problems, and do not have help aids. So students get a feel of what it would be like to be tested on skill problems without using a computer.
3. Use paper when it is more appropriate.
To push students to connect ideas and apply concepts, we have paper homework with problems. There are fewer problems and students are expected to do all of them. Again, they are not exercises. The odd numbered problems aren't like the even numbered problems with numbers changed. Each problem is unique and requires students to push past skill-based understanding. They don't have the typical "word problem" feel because they are like problems students have already been working with in the lesson, and they are realistic. That doesn't make them easy, but it does remove the "story problem" feel, which causes instant anxiety in many students. My students find the paper homework is harder, but necessary. And thus, it's not their favorite. They prefer MML problems because they are rote and prescriptive. But since the goal of the course is to think and solve problems, we push students past the skill problems alone. And unlike traditional algebra classes where skill problems encompass 80-95% of the course, skill problems only take up 50% of the course.
This approach marries technology and traditional methods for doing homework in a math class; it's a happy medium between paper only and MML only. Similarly, we assess in a similar pattern: skill quizzes are done in MML and conceptual/applied problem quizzes are done on paper in class. Because we do not have the facilities for testing online, our exams are done on paper and have both skill and applied problems.
Next up: Training
Tuesday, August 7, 2012
Here are some ways the course is structured to address student success (from a previous blog post):
The approach of the course begins with real, relevant content and covers topics differently than they are in a traditional text. That automatically increases motivation, an important component of student success. Students have commented repeatedly that the course is interesting; they like what is taught as well as how it is taught. For example, direct instruction and group work are balanced with each lesson beginning and ending with group work. This improves attention, understanding, and engagement. Students are shown respect for their prior knowledge by allowing them to tackle real mathematical problems instead of working from a premise that all the content is new. Many of the specific skills of the course are not new to these students because in reality, most of them have had several years of algebra prior to the course. What they lack is understanding, retention, and application. To improve that, considerable time is spent on solving thought-provoking problems and seeing traditional topics from a unique perspective. All problems are taught through a context and do not start with abstract ideas. Instead, the development moves from concrete to abstract, which builds student confidence and understanding. Further, students are treated like adults, most of whom work and have many varied experiences. They learn how math is used in the workplace and see those ideas in practice in class. For example, they learn how Excel is used. They also learn how the concepts taught can be used to solve problems they will likely face in and out of college.
Next, specific student success activities are included in every unit. Each student success lesson is different but all have mathematical ideas in them. So beyond the traditional ideas of time management and test anxiety, issues that these students will face are covered. For example, students learn how college math is different than high school math. This is done in the context of determining what components are necessary to be successful in a college math class. To visualize the various components, students hone their skills with graphs and percentages. They study job statistics to compare STEM and non-STEM fields in terms of their earning potential and unemployment rates. This approach brings in some statistics concepts. The topic of grades is addressed often and deeply. Components include how grades can be figured (points vs. weights), how GPA is figured and how it can be increased, and why it is difficult to pick up points at the end of the semester as opposed to the beginning of the semester. Students learn about means, weighted means, what can and cannot be averaged, and how algebra can help solve problems that arise in this context. Additionally, the first week has many activities to help students begin the semester on the right foot in terms of prerequisite skills, working in groups, and understanding course expectations.
Another component of the course is helping students learn how to study. Students think they should just “study more” but do not understand what that means in practice. To remedy this problem, students are given very specific and explicit strategies that they can act upon. Students receive a detailed list with actions they can do before class, during class, between classes, before tests, during tests and after tests. Also, students tend to really like online homework but they can get dependent on help aids and sometimes can’t write out their work. So every online assignment has an accompanying brief paper set of problems similar to the online ones, but they must write them out and have no online help aids. With skill homework, they have conceptual homework on paper that is about quality over quantity. That is, they have fewer problems that take more time so as to work deeply with the concepts at hand. The test review has a detailed plan to teach students how to study for math tests, beyond just working problems. Additionally, students are held accountable for all the work assigned so that they learn good study habits and personal responsibility.
Lastly, metacognition is emphasized regularly. The developmental student often doesn’t fully understand how they think or learn. Most problems are taught using 3-4 approaches to work at verbal, conceptual, graphical, and algebraic understanding. For example, when students solve equations, they do so first with tables, then with algebra, and last with graphs. Once they have learned all those techniques, they are asked to think about which makes most sense for them and keep that in mind going forward. This approach of solving problems in multiple ways is used often in the course to broaden their mathematical skills, but also give them a deeper understanding of the topics. This method has an additional benefit for students on test day. They have several tools in their tool belt to use if one technique is not making sense or their anxiety is affecting their memory.
Together, these techniques support the developmental student in being successful in this course and future math courses.
Next up: MyMathLab
Monday, August 6, 2012
1. Attendance is everything.
MLCS hinges on students interacting while working on rich problems and having lively discussions. That cannot be replicated by watching a video or getting a friend's notes. Those measures can help on rare occasions but they are not sufficient on a regular basis. We have seen attendance and work ethic as two of the strongest indicators of success in the course. Students have to be in class and do the work there as well as go home and do more work there.
To ensure good attendance, we have an incredibly strict attendance policy: after the 3rd absence (for a course meeting 3x a week), the student receives an F. There are no exceptions for pregnancies, military service, or long term illness. That sounds very cruel. In the past, we did make some exceptions and those students did not pass because they were not in class. So the student who has to leave for military service for an extended period of time, while possibly very conscientious and dedicated, cannot overcome the structure of the course and be successful. So we eliminate the possibly of a student thinking they'll be the exception and have a strict policy. The reality is that students who miss 4, 5, 6 or more times don't pass. Might as well have a policy that addresses that upfront.
This is the same approach many lab-based science classes like chemistry and biology take. Labs cannot be made up; you are present or you get a zero. Some things cannot be replicated at a student's convenience.
We've debated about having points for attendance, but instead opted for the real world approach that employers take. There is no reward in real-life for showing up; it's an expected part of the job. But there are absolutely consequences for failing to show up.
What does it mean to attend? Students must be present from the beginning to the end of the period, awake, and participating. Texting, coming in late or leaving early, or just generally doing nothing does not count as present. Students do not like this but again, it's really no different than what an employer expects.
2. Points for tests are a substantial part of the grade.
It is very important to us that we have some very typical components to the course so that students can transition into a more traditional course without issue. One of those components is a test each unit. The tests count for 60-70% of the course grade. We also give a comprehensive final exam that counts twice as much as a unit test.
Our tests mirror the emphasis of the course: skills and applications are in equal proportion. Skill questions (worth 50% of the test grade) give students a way to show their skill knowledge in a theoretical format. Applications questions (worth 50% of the test grade) show if students can apply those skills in context. All test questions have a similar feel as homework and quiz problems but are not necessarily identical. The course isn't about memorizing a "type" of problem and mimicking a solution. It's intended to grow students into problem solvers who are prepared for college level expectations. Thus, we do not give practice tests that look like the real test with numbers changed. Instead, we lay out a 5-step process for studying in the book so that students really understand what it means to "study" math. In that 5-step plan are many helpful problems that look like test questions, giving students a good preparation without reducing standards.
3. Hold students accountable with homework and quizzes.
Students need to practice regularly so we use MyMathLab for homework and quizzes for skills in the course. Students have MML assignments often, with several due dates each week. All assignments earn points.
The other type of homework in the course is paper, conceptual homework. These problems (not exercises) are more involved and require connecting skills and concepts. They are challenging and because of that, there are not 50 of them in a lesson. There are fewer and students are expected to do them all.
The problem with paper homework is holding students accountable. I'm not willing to collect homework and grade it. If we create worksheets with a sampling of homework problems, students just copy from one another. We tried that approach of collecting worksheets regularly, hoping students would appreciate the time out of class to work on problems. They just cheated. We also tried short quizzes to start each class over one problem from paper homework. These quizzes took too much time and didn't encourage students to work enough.
So this fall we will have regular quizzes, around once per week, on paper based on paper homework. They will be announced ahead of time so that students can make sure all paper homework is done and understood. Students can't use their notes. If they've really done the paperwork and worked with problems until they understand them, the quiz will be easy. If they are only doing MML work, the quiz will be very hard. But students need that wake up call when the consequences (in terms of points) are lower so that the same mistake is not made on the test. That would be a much more costly error.
We will budget enough time to allow for the quizzes in class. We've used this approach in other classes with success. Some students will still not do the paper homework, but this measure is as good as any as encouraging that type of work while keeping the instructor's workload manageable and maintaining integrity in the grades.
4. Encourage accountability on projects.
We use a unit project that is done in groups each unit. Students get a group grade, meaning there is one grade and all students in the group earn the same number of points. There is one exception: if a student has not pulled his or her weight, we reserve the right to reduce the points they would receive or to give them 0 points.
The problem is that there will always be students who allow others to do the work and benefit from it. To combat this, we have a substantial number of points on each test with a problem related to the project. It becomes very clear who did the work.
We want students to work very hard and to reward the growth they make. So in the spring we tried a very non-traditional grading scheme that was built on a gaming/mastery approach. In some ways it succeeded, but students felt confused about their grades and we were not able to use MML to list their grades the way we wanted. The negatives seemed to outweigh the positives. Since the course is so non-traditional, we've learned that there must be some typical elements for students to not feel anxious. One of those elements includes a grading scheme that is like their other classes. All of the grading components listed above are worth a certain number of points; we've also used a weights structure, but students struggle with understanding their grade in that format too.
These ideas are not the only way to grade in the course; they're just approaches we've seen have a reasonable level of success. If you pilot the course and find something that works well for you and/or your students, please share with us.
Next up: Student Success
Wednesday, July 18, 2012
1. Create the first set of groups
2. Play with group composition
When we first piloted the course, we thought mixing abilities would be key to a group's success. But that didn't pan out to be the case. Some lower students could be shy about asking for help, and some stronger students could be overbearing and unsympathetic to students who didn't work as quickly. Grouping students who work well together in terms of personality and who are similar in ability level has shown to work fairly well. Group interaction is a complex thing, so there's not one right way to compose groups. Play with it throughout the semester to find what works for your class and you.
Sunday, July 8, 2012
1. Determine entry requirements.
We use the placement cut score for beginning algebra as our entry to the course or that the student has passed prealgebra. Whatever you choose, determine if placement will be a part of it and if so, what the placement procedure will be.
2. Implement placement procedures.
Communicate and work with whoever at your college facilitates placement to implement the procedures you've chosen.
3. Create and implement an advising plan.
This is critical to the success of the course. The advisers at your school need to know about and understand the goal and audience for this course so that they can best advise students about taking it. It will be helpful to draw up a new flowchart with the course and a short summary sheet of important information about it. Copy and distribute this sheet to anyone who will be advising developmental math students.
Additionally, students in the class will need advising when choosing their next math course. We create a sheet to summarize key facts and questions and use it for in-class advising a week or so prior to open registration.
4. Consider recruitment.
You may also want to recruit students specifically for the course through an advertising program. You can create flyers and/or send an email to specific groups of students (non-STEM majors, for example) to get the appropriate student in your sections.
5. Address intermediate algebra.
Feeding into general education math or statistics is not an issue for MLCS since it was designed with those courses in mind. Feeding into your intermediate algebra smoothly is another issue. Some schools want to add in traditional topics like trinomial factoring or absolute value equations into MLCS so that students can move into intermediate algebra. This would not be my first choice. Those topics will feel odd in MLCS; students will notice when you're covering something just for the sake of doing so. All the other topics in the course have a reason for their inclusion and students will come to expect that as the course continues.
Instead, it's easier to add topics to intermediate algebra, like trinomial factoring. Our school's intermediate algebra course already includes factoring because students don't recall it, even if they just completed that chapter in beginning algebra a month before. So including factoring there helps everyone, but especially students coming from MLCS.
Next in the series: Groups
Thursday, July 5, 2012
1. Determine your goal.
Why do you want to create this course? Is it to diversify content and provide more realistic problems to developmental students? Is it to provide a pathway for non-STEM students? Is it to accelerate the time in the developmental sequence? Whatever it is, state it and acknowledge it amongst the faculty who will work on the development of the course. It's important that everyone is on the same page for bringing the course to life. Your goal will affect how much and what kind of content is covered. Knowing your goal will also help you measure its success. More on that in another blog post.
If you decide to create this course to replace one or more courses across your sequence and/or creation of this course will be met with a lot of skepticism, skip to #8 next before proceeding.
2. Determine your audience.
Who will take the course? At my school, it is a student who placed into beginning algebra or passed prealgebra and only needs statistics or liberal arts math for their program of study. In other words, it is for our non-STEM students at the beginning algebra level. Some schools want students who have passed only basic math, not prealgebra, to be allowed to take the course. Whatever you decide will affect the content necessary to make that student successful. If you allow students who have not taken prealgebra, you may want to give more time to the lessons on fractions and integers.
3. Decide on the outcome courses.
This is very important as it will have a direct effect on the content covered. Investigate the outcome courses you will feed into to ensure prerequisite skills are addressed. Make a list of skills and/or topics students need to learn to be successful in those courses. We wanted intermediate algebra to be on the list of outcome courses so that students wouldn't have to backtrack if they changed paths. Setting that as a goal has a large impact on what must be taught.
4. List the content and objectives.
What do your students need to learn to be successful for the places they'll go and what would you like them to learn beyond that? We added a few more algebra topics to our course to ensure students could flow into our intermediate algebra. We also made sure our intermediate algebra covers factoring to the point that a student could take MLCS and then intermediate algebra and be successful. More on that in the next blog post. But we also considered that our students would feed into a few key science courses. And these students need to be well rounded citizens. That governed some choices and broadened our initial list of objectives.
At this point, you may also need to consider 4 year schools you feed into and/or state requirements to ensure you have the necessary content for the course to be piloted.
If you'd like to see our course outline and objectives, check it out here.
5. Choose materials.
You need materials that support your goals and vision for the course. A traditional algebra text will likely not suffice. MLCS is not just different in terms of the order of topics, but also the treatment and emphasis. We could not accomplish our goals with the materials available. One option is to piece things together that you can find and write materials to supplement them. That will have a choppy feeling to students and instructors, creating even more challenges than will already be present with a new course.
We have worked to write materials that would encompass the vast majority of content needs for this course. In this document, I have listed the four units and lessons in each as well as included some sample materials. We also worked to make the materials work for any student or instructor. Many instructor supports are created to ease the instructor into a new course and philosophy successfully. But the student also gets many important help aids so that they can navigate a new kind of course and content.
If you would like to see a larger sample of our materials and/or class test them, please contact me.
6. Choose the credit hours for the course.
Once you see how big or small your course is, you can decide on the credit hours necessary to teach the content. But also include enough credit hours for the students to learn the content. These students need time. Err on the side of more credit hours than fewer. One 5-credit course passed the first time is still less financial aid than a 4-credit course repeated. The number of credit hours will have a direct impact on pace, which should not feel rushed. This is one place where my college's version of the course needs improvement; we feel rushed all the time. Nobody likes that feeling. A little more time for discussion and problem solving is very helpful at the developmental level.
7. Get approval to offer the course.
You will likely have to apply to your college's curriculum committee, but there may also be state-level permissions to acquire. Investigate the protocol for adding developmental courses and follow any necessary procedures.
8. Introduce the course to the full department.
If you have all the interested players part of your course task force, it's not always necessary to explain the course to the entire department until there's something to show. We waited until our course was approved before presenting it to everyone so as to not get people excited or worried about a non-event.
To make the course a success, it's a good idea to make sure everyone understands what the course is and why it's being created. If you are concerned about buy-in, offer the course as a pilot and only as an option in the sequence, not a requirement. Some schools are using MLCS to replace beginning algebra. We are not because many faculty and students will balk at that approach. You'll need to consider your school's culture when choosing how to bring the course into the developmental sequence. The method that will garner the least resistance is to create an alternative, optional pathway with MLCS in it. That allows only faculty and students who are interested in the pathway to take part in it. Faculty that are opposed to it will not have to teach it, nor will their classes be affected.
9. Work with the course logistics.
At this point, you need to determine day patterns, length of class periods, times the class will be offered, number of sections, who will teach them, what semester will the pilot begin, etc. It's helpful if you can teach this course in a room large enough to move desks into groups and one that has a document camera. A lecture hall is not the ideal environment for this class. If you can schedule sections to not be held at the same time, that will help in case a sub is needed at a later date or if the instructors want to observe each other. Also, consider who will teach it and their schedules so that hopefully a common time can be found for the pilot instructors to meet and talk. The instructors will want that, so it's important that time is planned for it from the beginning.
Next up: Integrating MLCS into your sequence
Friday, June 29, 2012
Because you may want more information, I've also attached a sampler packet with the following items:
- Contact information
- Overview of MLCS project and history
- Course objectives and outcomes
- Topics in each unit of the course
- Implementation options and tips
- 3 sample lessons (1 instructor version with instructor notes in red and 2 student versions)
A professionally designed sampler will be available later this fall through Pearson.
Sunday, June 24, 2012
- Course design and development
- Integrating MLCS into your sequence
- Student success
- Building your collaboratory
- Tracking success
- Final thoughts
More to come!
Thursday, June 14, 2012
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.
Tuesday, June 5, 2012
1. Successful redesigns hinge on good follow-through.
I cannot stress this tip enough. Many schools and especially administrators get very fixated on a new idea and grants to support them. New ideas are great and energizing, but the newness will wear off. What's left is work, and that's not the fun part. Grant funding will not keep the momentum going, but people can. It's just like a person who loses a large amount of weight or runs a marathon: what sets them apart with their success is that they started and kept going. When things got boring or hard, they kept going. And both boredom and struggles are unavoidable with redesign. This leads to the second aspect:
2. Disagreement is unavoidable. How it is dealt with makes the difference in success or failure.
This is a difficult one to stomach. I really struggled with this on a personal level. It's very hard to work well with colleagues for years and suddenly be on the opposite side from them. We've weathered the storm at my school, but it was no small feat to do so. When you upset the apple cart, people will notice and they will voice discontent. Change can be very uncomfortable. Because even though a system is unsuccessful, there is something innately comforting in the familiar. As humans, we crave consistency and fear the unknown. I've often said that I like being a guinea pig and am happy to try anything, even if it fails. Many faculty do not echo this mantra. And that's ok. You can fall into groupthink quite quickly if no one gives a dissenting opinion. You need a variety of perspectives to have the pragmatism that's necessary to make logistics work. However, some instructors are very opposed to trying new things for fear they will fail. The outcome of failure always comes with risk. But so can success.
So those very nice and well meaning colleagues can become barriers. What is hard is what remains unspoken. Often it's not only the fear of failure that causes instructors to object to a redesign. It can also be the unwillingness to write new materials or tests or the anxiety of having to learn how to use a new computer system. These concerns are rarely voiced, but they often sit at the root of inertia. To overcome these issues, it's important to make change as easy as possible with as many support structures as possible for faculty. Make master courses in MyMathLab that instructors can copy. Offer multiple training sessions. Show tools like testbanks and other instructor resources available with your text. Create materials that reduce faculty workload during the change process. These ideas won't always solve every problem, but they will reduce many. And above all, create some process to assess and improve all implemented changes. If instructors know that things will change if a policy or course is not working, they will often be less anxious. I said often, "nothing is set in stone." And I kept my word. We still meet as a task force and tweak policies and courses. The process of improvement never really ends.
The other alternative is to pursue departmental peace at all costs. That's attainable but change will not come with it.
3. Real change comes from doing some really different.
We had hoped, like many schools, that if we just did X or Y that success would come our way. Like trying out an attendance policy or using online homework. And the reality is it's not enough. It's akin to saying, "I want to lose weight so I'm going to try eating one salad a month." It's certainly not going to hurt you, but it's not going to make a dent in the problem. When our redesign really took off in terms of pass rates and outcomes was when we instituted our 8 week modules and required MML across the board in addition to the changes in place like standardized policies, adjunct training, and new placement procedures. The modules were very hard to create and implement but they made a real difference because they were really different.
Likewise, MLCS takes work to throw in the mix because it's a true change. It has to be approved at a school and possibly a state. But more than that, it takes a mindset shift from "developmental math is algebraic manipulation" to "developmental math is about preparing students for the courses they will take." Not everyone buys into this philosophy. That's why I believe in adding pathways courses into the traditional slate of courses, instead of replacing them. If you've got a school that is totally on board with replacing your traditional courses, have at it. But most aren't. Again, a lot of very nice and well meaning instructors cannot part with the idea of factoring, adding rational expressions, and rationalizing denominators before taking a college level course. It's a large change that not everyone supports. Instead of forcing pathways on students or instructors, allow them to be an option. If they become the favored option, they'll grow and the number of traditional course offerings will naturally shrink. But that would be a natural consequence to what people in your school want. So it can work. Forced change is sometimes necessary, but all changes cannot be forced.
Basically, it comes down to how much do you want things to get better? Are you willing to experience some discomfort and disagreement? Are you willing to try new things even if they aren't guaranteed to work straight out of the gate? Are you willing to learn new content or a new system? If you are, you can see true improvement and growth. It won't come day 1 and it won't be easy, but it can happen. The alternative is assured: continue working in a system that does not work. As Robert Kennedy said, "Only those who dare to fail greatly can ever achieve greatly."
Wednesday, May 23, 2012
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.