Upcoming MLCS Webinar

I'm giving a webinar for AMATYC on April 24 at 2 pm CST.  Here is the description and registration information.

Title: New Pathways for Developmental Math: A Look into Mathematical Literacy for College Students

Presenter: Kathleen Almy, Rock Valley College

Description: Mathematical Literacy for College Students (MLCS) is a new course that is part of an AMATYC initiative called New Life for Developmental Math as well as the Carnegie Quantway project. It is an innovative way to redesign the developmental curriculum, providing pathways for the non-STEM student. The course uses integrated, contextual lessons to develop conceptual understanding and technology to improve mastery of skills. In one semester, a student placing into beginning algebra will gain the mathematical maturity to be successful in statistics, liberal arts math, or intermediate algebra. Reading, writing, critical thinking, and problem solving are key components to reaching that goal. Webinar participants will learn much more about the course as well as receive ideas for course development including a sample course outline and a sample lesson.

Date: April 24, 2012

Time: 3pm EDT / 2pm CDT / 1pm MDT / 12pm PDT

Committee: Developmental Math Committee

Click here to register.

MLCS Presentation

Below is a recent presentation on MLCS given at ICTCM and IMACC.  It is related to but different from the workshops I've been giving since November. 

Are you interested in developing MLCS at your school?  If you have questions or would like to see a sample of a unit or would like a training workshop, please contact me. 

View more PowerPoint from kathleenalmy

MLCS Video Excerpt: Shortest Distance

This past week we taught a lesson that begins with a hands-on component.  The video excerpt will show some of the whole class parts of the lesson.  Here is a run-down of the lesson:

Lesson:  Shortest Distance
Objective:  Develop and apply the distance formula

This lesson appears late in unit two.  This unit focuses on understanding numbers and operations.  To that end, we work with many situations that allow us to explore how numbers behave and introduce algebraic ideas at the same time.  By the time we see this lesson, students have learned signed numbers and their operations, number properties, order of operations, exponent rules, Pythagorean Theorem, and slope. 

To begin the lesson, we measure the classroom and make a scale drawing of it using a scale of 1 unit on a grid = 1 foot in the room.  We then decide to place objects from the classroom on the drawing by establishing an origin and axis system based on that origin.  This process of setting an origin and determining locations based on it emulates a simplistic version of what surveyors do.

This leads to a good discussion on where in the room the origin should be and what would make it easiest to work with.  Eventually students settle on the back left corner of the classroom (from their perspective) since that makes the classroom the 1st quadrant.  This choice creates all positive ordered pairs.

Since the measuring tapes are only 25 feet, measuring becomes an interesting challenge.  Discussion quickly ensues on logistics and the role of accuracy.  We try to measure with the tape on the floor, but are careful to keep the tape taut if measuring off the ground.  Students then find ordered pairs for objects in the room they choose.  We pick up the lesson at this point being taught by Heather Foes:



NOTE:  This is not a professional quality video. 

The lesson continues, moving between whole group discussion and small groups with students practicing tasks and digging deeper into the ideas of the lesson.  I've described below what occurred but was not shown on the video.

After finding a few specific distances, we generalize the process using Pythagorean Theorem with generic ordered pairs.  Students need to really understand the order of operations to use the formula accurately.

Students practice using the formula.  As a class, we discuss how a graph can be used to avoid using the distance formula but there are limitations to that method as well.  Lastly, we connect this idea to slope.  Both slope and Pythagorean Theorem can be used on or off a grid.  We want students to see how the formulas look with a grid and without as well as the pros and cons of each method.  The goal is not just apply the distance formula to two random points.  Instead, the goal is to see how the formula can come about and why it is necessary.

A discussion always arises about what can be measured and what cannot.  We also discuss the pros and cons of physical measurement vs. math on paper.  Students usually surprise us by liking the idea of working on paper.  Measuring doesn't require much math, but it is challenging to do it accurately.  Also, it requires them to move and they don't always enjoy that element.

This lesson illustrates the depth of the lessons in the MLCS course.  The algebra or an algorithm are not the only goals of the lesson.  It's the process and discussion of getting there that elicits the most learning and improvement of students' conceptual understanding.  Students quickly see that real life problems are almost always much more complicated than traditional textbook problems.  But those same real life problems are also very rich and interesting.  They are worth the effort necessary to solve them.

MLCS Course Development and Training

Non-STEM courses like Quantway, Statway/Statpath, and MLCS are taking flight across the country and with that comes a lot of questions.  Because we've been working on a course and implementation for over a year, we've learned some things to help make it work.  Here are some tips for course development:

1.  Identify your goal.

We wanted appropriate preparation for the student heading to liberal arts math or statistics.  Sometimes the goal is acceleration.  While that wasn't our first goal per se, we are certainly happy for that to be a by-product of the course. 

Knowing your goals defines your next step.

2.  Determine the course content.

Look forward to where students will go and see what they need when they get there.  For us, that was statistics, liberal arts math, or intermediate algebra.  While we have many intermediate algebra topics in our course, they are covered in a conceptual, applied way that uses modeling.  So yes, we look at rational functions but no, we don't add rational expressions.  If a student will eventually take college algebra or precalculus, they'll need those algebraic manipulation skills.  We wanted them to be able to go into an intermediate algebra (IA) course without issue.  Our IA course has factoring in it, as most do.  So we were comfortable with exposing students to the concept of factoring in the MLCS course and doing one very useful type:  GCF.  Again, they can get the rest of the factoring techniques in an IA course.

Using IA as our bridge forced us to add in a few more objectives on polynomials.  It was funny; at first we didn't like that because it felt contrived.  It seemed like we were only adding them for a next course that many wouldn't take and therefore felt disconnected from the content.  But as we taught the course in the fall, there were times where polynomials came up and I needed to be able to say "degree" or "binomial" and students know what I mean.  They were necessary topics to our end goal.  That was great!  So we embedded them in the second unit of our course to ensure students have that basis for later material.  It also further prepares them for the bridge course.  In so doing, we solved two problems.

How much content you have affects the next step.

3.  Determine the number of credit hours.

It was very important to us that this course not be like all the other developmental math courses we teach:  rushed.  This learner needs time to discuss and think and learn.  We need that time too and we wanted it in the classroom with them.  Plus, our state has a lot of requirements to make this course something that can be articulated.  Add that up and we have 6 credit hours.  It's unlikely that schools outside of Illinois will need anywhere near that many.  The mode for this course as it's being developed around the country is 4 credits. 

Also consider if you want a lab hour embedded within the credit hours or in addition to them.  We use MyMathLab and have considered having an hour with students in a lab while they're working on skills.  We haven't needed to go to that yet but it's something to think about.  Doing this is kind of a hybrid of a self-paced emporium model and a pathways model.

4.  Write a course outline.

Now comes the fun part:  goals and objectives.  State succinctly but clearly the course description, goals, objectives, and content.  Here is our course outline that went to the college curriculum committee if you'd like to see an example.  You can download it as a Word document so that it's editable. 

5.  Choose materials.

In our course outline, you'll read that we have a MLCS course packet and MyMathLab.  The course packet is the book that we're writing for this course that isn't yet in print.  If you're interested in seeing a unit, please email me.  I can request a copy be sent to you from the publisher, Pearson.  It is available for testing this fall if you want to pilot MLCS and will be officially in print in summer 2013.

We started writing because we wanted materials to match the content and goals of this course.  Because this course is new, they did not exist.  You can piecemeal books together but it will be awkward for the teacher and student.  You can also write lessons, but that is a time-consuming undertaking.  Open source materials will be available eventually but that content doesn't cover all the objectives in our course or state.  Plus, we wanted MML.  It was an important requirement with any materials we used.  Lastly, we wanted materials that addressed every possible need for any instructor.  So we have written and designed many tools for instructors in the book.

6.  Plan the execution of the course.

This is the step where you think about how many sections you will offer, when they'll be offered, who will teach them, and how they'll be taught.  If possible, plan schedules so that teachers can get to each other's classes and observe occasionally.  Heather and I did this throughout the fall semester and it was invaluable.  It has improved the materials greatly and educated us on ways to make the class experience even better.  You see things in the back of the room that aren't obvious from the front.  So consider this step.

If this step isn't possible (or even if it is), plan how the instructors teaching the course can converse after lessons to debrief and improve them.  We meet after our classes and talk.  If you can't do that, set up a discussion board.  But this step is so important that it shouldn't be skipped over.  This is not an algebra course.  It's new for everyone.  Having the security of people to talk to helps everyone entering into the course for the first time.  And it helps the course get better and better over time.  This technique is like a Japanese lesson study.  Not identical, but it emulates their philosophy of teaching a lesson and refining it with other instructors over time. 

7.  Training

You may want training before you begin your pilot to understand better what a class feels like, how to make groups function well, what kinds of pitfalls there are to be aware of, etc.  I've been helping schools who are developing the course and will continue to do so.  Experiencing a lesson is so important so that you can see what the classroom will feel like and what you need to prepare for.  I can say without question that teaching in this way has made it very hard to go back to my 100% lecture, traditional courses.  Students are engaged and discussions are rich.  I truly enjoy what we do in the classroom in a way I never have.  And I've always loved teaching so that's saying something.  Yes, it's an adjustment but one that's made quickly for everyone. 

I'm also thinking about creating a training workshop that would allow several schools to come to one location so that I can work with them.  If this is of interest to you, please email me.  If there is sufficient interest, I can try to work out the logistics of making it happen.

My main goal with this post is to let you know you're not alone.  I've been working with schools on various redesign initiatives for years.  I will continue to do that with this course as well.  Having someone to ask questions of and bounce ideas with really helps everyone involved have more confidence in the process.

Student Success and MLCS

Here is a blog post I recently wrote for Jack Rotman's Developmental Math Revival blog.  It outlines how student success is integrated into the MLCS course at our school.

The six major areas of focus of the MLCS course at Rock Valley College are numeracy, proportional reasoning, algebraic reasoning, functions, mathematical success, and student success. Each unit addresses all of these facets. Specifically, the course and accompanying lessons are designed to improve a student’s chance of success in a math class. Here are some examples:

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.

Considering Statway? Consider MLCS

Statway provides a two-semester integrated approach to statistics, taking a developmental learner to and through stats with developmental content addressed just-in-time.  It's a great idea and can work for students who definitely know they only need statistics for their math requirement and major.  The problem is that many developmental students are undecided in terms of their major, so nailing down the exact math requirements can prove challenging.

So what can be done?

MLCS (Mathematical Literacy for College Students) is like Carnegie's Quantway course.  Instead of two semesters, this one-semester course takes the student who places into beginning algebra and builds their mathematical maturity.  At the end of the course, they are ready for intermediate algebra, liberal arts math, or statistics.  Unlike Statway, there is a considerable number of algebra objectives addressed enabling the student to move into intermediate algebra upon completion.  But they're also able to move into more than one non-STEM course. 

This course design is deliberate in giving students options because it's possible that this student will change their mind and major at some point.  That decision may be as small as needing a liberal arts math class instead of statistics, but it's possible that they move to a field requiring much more math.  If they decide to go into a STEM route and need more algebra, they will only need one additional semester of it after MLCS.  For most students, MLCS reduces their time in developmental math to one semester and gets them into a credit bearing course upon completion.

What I have found that I like best about this course, beyond the fact that it accelerates the developmental sequence, is that it does it differently.  We know that this student has had algebra.  But what most of them do not have is an understanding of algebra, nor numbers for that matter.  They didn't retain the algebra they learned well enough to place out of it or use it.  So instead of repeating that process, we come at the course differently.  Our materials start with interesting problems that this student could encounter and explore them mathematically.  Everything integrates, everything connects.  And more than that, everything has an immediate use.  A topic need not be useful to be valuable, but when it is, motivation is much higher.  Motivation is a key component for success in developmental math so this is a helpful characteristic of the course.  And beyond that, it's fun for both the instructor and student.  Again, a course need not be fun to be successful, but it sure is nice when it is.

But what about statistics? 

One of our goals is that a student can go into a statistics course upon completion and be successful.  To get them ready, our approach is to take some of the key ideas they will learn in statistics and come at them conceptually and physically.  The idea is to take some time with these ideas that will be covered quickly in a statistics course so that students really grasp the intricacies.  For example, we work with means many times from many different perspectives.  That topic will be covered in 1 or 2 class periods in a stats class.  We see means throughout this course, each time differently, to explore them and go deeper with the concept.  We also explore weighted averages, medians, correlation, and variation.

Also, the approach to the course is to build mathematical maturity.  That includes being able to make and a read graphs, being able to read critically, being able to use percentages, and being able to use technology appropriately.  All of these skills factor into a building a strong base for a statistics course and all are present throughout the MLCS course.

Since there are many terrific statistics courses and books that exist, we do not aim to do statistics topics in MLCS as they would be done in a stats course.  They'll experience a college-level approach when they take a statistics course.  Instead, we approach statistics knowing that we have a developmental learner.  They need time to explore, see ideas in a hands-on way, and see them applied in accessible situations.  They won't be bored when they take a stats class.  Instead, they'll feel ready to take it on while being aware of some of the main ideas that will be explored deeply but also quickly.

MLCS & Presentation Update

Another week of MLCS and it was a good one.  Students remarked that their initial conjectures about the course were wrong.  Some thought group work would be a waste of time, but have found that talking about math and hearing how others think is actually very enlightening.  Some were pleasantly surprised that they could learn so much without a teacher standing at the board the entire time writing notes.  One student remarked that she felt she was learning more with our approach. 

We do have direct instruction, but it doesn't dominate the class period.  I would say the breakdown between it and group work is about 50/50.  That time in groups helps students investigate, practice, and solidify concepts. 

I'm also seeing a trend:  it takes right around 2 weeks to get student buy-in.  But most if not all will buy-in.  I've heard many instructors comment that is a fear, that students won't go for a course that's not in the traditional format.  And we did feel that at first in the fall semester.  But getting the materials and policies of the course into a good place has made a tremendous difference.  If your course structure has some routine, is stable, and is well organized, students will tolerate different approaches to instruction.  They won't if everything feels new, but they will if the new facets are in a tolerable amount and they find them valuable.

One takeaway I've continually had is that students are capable of learning real mathematics.  Yes, we can teach them skills.  But we can teach them more:  how to apply the skills, how to connect concepts, how to understand and solve complex problems.  And it's rewarding for the student and the faculty member to do so.  I find the class flies by, that we're always busy with discussion or problem solving.  Students have remarked the same.

One issue we've had since the course started is with tutoring.  When our students go to a tutor to get help, they sometimes get the reaction, "why are they doing it that way?  It would be so much faster to ...."  For example, why do we teach students to scale a fraction like 12/40 down to 6/20 and then up 30/100 instead of using cross multiplication [12/40 = x/100] or the calculator if we want a percent?  Well, we do use the calculator,when it makes sense.  And we do use algebraic solving methods for proportions when they make sense.  But often, those methods make math seem mysterious and dependent on technology or rules.  Technology and algebra are valuable, so we pull them out of our toolbox when they are needed.  We want students to build numeracy.  To do so, they need to work with numbers all the time in various ways and often, in their head.  It's like a muscle; the more they work at it, the better their agility with numbers will become.

Also, when students learn "tricks" or rules without understanding, they do not retain them nor can they apply them.  This course is about retention and application so our first means of getting there is understanding.  Yes, it sometimes takes longer and requires some thought, but that time and process is valuable.  Students gain confidence that they can work through a tough problem and they learn more about the topic while they're at it.

As we often say, there's a method to our madness.

I'm gearing up for the presentation trail again.  Here's an update:

February 16:  MLCS Workshop at Triton College
February 24:  Redesign presentation in San Antonio
February 25:  Panel discussion on MLCS in IL (Southwestern Illinois College)
February 28:  MLCS Worskhop at Wright College
March 2:  Redesign webinar for Pearson
March 17:  Cherry Blossom Congress keynote
March 24:  MLCS Presentation at ICTCM (Orlando)
March 30:  MLCS Presentation at IMACC (Monticello, IL)