Sunday, October 30, 2011

Going to AMATYC? Experience an MLCS lesson

If you will be attending the 2011 AMATYC conference in Austin next month, consider our workshop on Saturday November 12 at 10:45 am to 12:45 pm.  Anyone can attend; there is no advanced registration or special fee.

Below is the description from the program guide.  We will explain where the MLCS course (in the Quantway pathway) came from and what it includes, showing examples as we go.  We'll take a large portion of the workshop to do a lesson from the course so that attendees can experience how the classroom feels.  We'll debrief that lesson, talk about the pilot, and ways the cousre can be implemented in a school's sequence.  There are many options including some very simple ones for emporium redesigns.

We hope to see you there!

Mathematical Literacy for College Students: Bringing New Life to Life

New Life is an AMATYC initiative to create a new experience in developmental mathematics. This workshop will explain the project history as well as allow attendees to experience the new course, MLCS, by participating in a class activity. Attendees will receive ideas for course development and a sample course outline.

Friday, October 28, 2011

Pilot Recap, Week 10: Tough, but necessary

Great class periods with exciting content?  Check.

Engaged students appreciating math?  Check.

Improved performance? 

Nope, no checkmark there yet.  That's where Heather and I sit now, dealing with the frustration of students not accomplishing what we want for them.  The open-ended problems we graded for this unit were excellent.  I saw real progress made with them in terms of students building models and using graphs, algebra, and numbers to solve a big problem at hand.  They enjoyed the problem too.  But today was test day and that's altogether different.  Showing what they know individually without being able to work with someone else or look something up is a real challenge, but a necessary one.  I enjoy students talking and working on math as much as anyone but I also want to see what they can do on their own.  Whether it's a test or quiz or in-class assignment, as a teacher I've got to have that kind of information to assess students.

After two hours of Heather and I hashing out the issues at hand and solutions to them, we know that we can't solve all of them ourselves.  Sure, we'll do more quizzes in MML and more time in class discussing problems they've tried for homework.  We'll work more on metacognition, something many incoming freshmen lack.  But a big part of the problem is lack of motivation on the students' parts.  Yes, they enjoy class.  But going home and doing work on their own is work, hence the name.  They have MML assignments and conceptual work that is really challenging, but again, necessary.  That's where learning happens, not when I'm speaking but when they start doing.  And some are just not doing what they should.  You can lead a horse to water...

So what's the take-away?  The course is solid and has phenomenal potential.  We see that and so do students.  We've gotten comments like, "this is first time I could see why we do the things we do in math."  "This is the first time math has really made sense."  But we are dealing with a student who is not really ready for college and not just mathematically.  They still have skills to learn and habits to form.  That process is tough but necessary.  We are actively cultivating the skills, thought processes, and behaviors necessary to succeed in this course, college, and work.  Still, a lot rides on them.  I have the same challenges as a parent, that you prepare them but ultimately they have to sink or swim on their own.  And it's a painful process to watch when it doesn't go well.  But, like I do with my kids, I will be there on the sidelines when they come to me for help.  I will do my part and eventually, I hope, so will they.

Saturday, October 22, 2011

Pilot Recap, Week 9: Attractive Algebra

We reached a new milestone in the MLCS pilot this week.  Students actually wanted to use algebra to solve a problem when they weren't required to.

Upon hearing that, I immediately thought:  I can retire now.

But seriously, I have never had an experience teaching developmental math where students wanted to use algebra.  In a traditional curriculum, we force it on them promising a world of brain calisthenics unmet by any other means.  They balk because they don't like it and find it useless.  Whether it's useful for everyone is a matter of debate, but there are many folks like myself who will use algebra to solve problems in real life because we know how to.  I see it as a tool in my tool belt along with pictures, graphs, numerical approaches, and technology.  And now, so do my students.

This week began with us solving all kinds of equations physically with manipulatives and then in written form.  Students did not like using manipulatives at first but we forged ahead, telling them, "this is a broccoli moment.  You may not like it but you need it."  And it did help.  They understood why we subtract something from both sides or add it.  They could see why we don't divide off 2x on both sides when finishing a problem that ends with 2x = -16.  They saw that adding 3x to both sides is not the same adding 3.  But our goal in the course is not algebraic manipulation for the sake of it.  We want to solve big, interesting problems and let the algebra come along for the ride.  And it does.

So once we had established how and why we solve equations like we do, we got back to the task at hand:  solving a problem and determining if we should write an equation or use numbers or a table or graph.  And that's when we heard something very satisfying for a math teacher:  "Can we use algebra to solve this?  It would be so much easier."

Why yes, you can.

We started with a fun problem setup that was completely real:  you only have so much money (a $20 bill) and are heading to a restaurant for dinner with your friends.  How much of something can you get for your money?  We started simple with just the food items and then built all the way up to incorporating tax and tip.  Not calculating tax and tip, but solving a problem like this:  you have $20, you want to figure out how much of an item you can buy knowing its price and that after you purchase it, you'll add on 7% tax and a 20% tip.  That's not a trivial problem.  And we told them:  solve it with just numbers and then with algebra.  And along the way, we asked them to determine which method they preferred with each problem and why.  When we finally got to this scenario (with tax and tip), students could not see their way out of it numerically.  But they could with algebra.  This is the equation they built and then solved:

1.20[1.07(1.50 + 5 + 0.25w)]=20

And without question, the solving was the easy part.  It was creating that monster that was hard.  By the time we got to the solving, they were breathing a sigh of relief. 

But the best part was that they were completely engaged and really thinking.  One student said, "my brain hurts but I like this."  Heather said it's like they're sweating on the inside, meaning really working their brain.  I used to say to my algebra classes that algebra will do that but often it doesn't.  It just frustrates students and reduces their motivation to enjoy and succeed at math.  When you tell them they can solve a problem however it makes sense and not force a method on them, they'll gravitate towards the things (like algebra) that we know can be quicker and more useful.  It's just human nature:  we like choice, we don't like mandates.

We ended the week with more problem solving that resulted in equation building, graphs, looking at linearity vs. other types of graphs.  And then out of nowhere today, we saw a connection and had them build a rational function.  We explored fitting data with the best type of function and how the graph doesn't tell you the whole story about data.  But a table and an equation together with it can tell you everything you need to know.  Again, algebra came out of nowhere (seemingly to them but we had planned as such).  We had a situation that we wanted to understand more about and doing the calculations to be able to make the graph was getting time consuming.  So we went to Excel.  They've started to see the power of Excel.  We talked them through programming the columns to do the calculations we wanted, filling in cells, and then graphing.  To do that programming, they have to understand the calculations at hand to generalize them. 

It's amazing how motivating something can be when it has an immediate point.  I love math just for its own sake, for the beauty of it.  But most of my students don't and need more to keep them interested and willing to work.  Just having a real reason to do something that isn't contrived can go a long way to keeping them in the game and moving forward.

Altogether, a good week.

Friday, October 14, 2011

Pilot Recap, Week 8: They get it

That title sums up where Heather and I have gotten to:  they get it.  We have finally gotten to the point where students have completely bought in and more than that, they like it.  Meaning, they like the course, the approach, the goals, and the execution.  Sure, there are about 1000 things we can do to improve and we will.  That's the nature of a pilot with a brand new course.  But in the meantime, they like coming to math class.  They like seeing what's going to happen next.  And here's what I care about:  they are learning. 

A sample of what we did this week:

Topic: Study census data on median weekly earnings vs. unemployment rates as well as educational attainment vs. unemployment rates.
Goal: Develop scatterplots, idea of association, best fit lines, predictions. Discuss how level of education affects potential earnings and likelihood of unemployment.

Topic:  Origami done in a roundtable group relay
Goal:  Analyzing the role of steps, their order, precision, and teamwork

Topic:  Looking at proportions within recipes and chemical equations, balancing chemical equations
Goal:  Work on developing proportional reasoning; see similarities between chemical equations and algebraic equations (terms, coefficients, checking work, strategy for starting a problem)

Topic:  Students measured an ingredient by volume, then weighed results.  Found standard deviation.
Goal:  Looked at role of variability and how it can measured, that measures of centers are not enough to tell the full story about data.  Used numeracy and algebra to develop the standard deviation formula, order of operations to utilize it.

Topic:  Analyze problems and write 1-step equations to solve them.  Solve them numerically and compare/contrast methods.
Goal:  Understand basic priniciples behind solving equations to set foundation for more involved problems next week.  Analyze the role of numerical and algebraic methods, when each has an advantage.

This is just a taste but I think it shows the variety.  We've found a way to make the topics connect within a unit and have some relationship to each other.  We're always moving forward, building their numerical and algebraic skill set.  But with that, we work on proportional reasoning constantly, functions, and bring in geometry and stats whenever possible. 

If you're wondering how origami could end up in a unit that has solving equations, the idea is this:  show, don't tell.  We want students to understand that you can't "wing" everything in real life.  Sometimes order, accuracy, and precision really matter.  I can say that till the cows come home; it will mean little.  But put students in a situation where they experience that firsthand and all of sudden, the message is very clear.  And beyond that, it's just fun to see 20 year olds fold paper boats.  :)

Tuesday, October 11, 2011

Emporium Models & Quantway/Statway: Living in Harmony

It may seem counter intuitive that these two initiatives could work together, but I believe there is a way to make that happen.  Most faculty are in one camp or the other.  That seems logical since emporium models are about lab-based learning, working on an individualized program of study at one's own pace.  The Pathways initiatives are about students working together in a classroom at the same pace.

So how could they marry and live happily ever after?

Well, consider this:  both need the same things but offer them in different percentages.  Both want to offer the student a new experience that serves their needs more than the traditional lecture-based approach.  How they achieve that is different, for sure.  But both want students to get the skills and connections.

Emporium models focus heavily on skills and at many schools, solely so.  But ask instructors and students and they will say that they do want interaction, they just don't want lecture.  Students want to gather together and instructors want to talk with them as a group.  But problem solving together would be the ideal, not just answering questions as a group to students who are at different places content-wise.

The Pathways models focus on group interaction and problem solving, but skills have to be included.  Skills exist in the classroom as does lecture, but in lesser proportion to problem solving and connections.  They're often reserved for time outside of the classroom so that students can spend as little or as much time as they need.

Both models use interaction for connections and online homework systems for skills. 

In our course, we've already seen students need more skill work than we can do in the classroom, so we're beefing up the online component to allow for that.  Emporium schools often complain that they need more than just skills so they try to beef that up with a once weekly problem solving session.

How about the best of both worlds?

Emporium schools could use Quantway or Statway lessons during their once-a-week problem solving sessions to make connections and solidify understanding.  Students who haven't seen the topic will get an introduction in a way different than the static, online lecture.  Students who have learned the topic will make connections.  Everyone gets something out of it even though they're on different skills they rest of the week.

Pathways schools could have once-a-week lab time just for skills.  That would give students who need more time for skill development just what they need along with the instructor there to support their individual needs.

What I like about this idea is that it gets the best of both worlds and would not be that involved (or costly) for either camp to implement.  What do you think?

Saturday, October 8, 2011

Pilot Recap Week 7: What's STEM got to do with it?

One of the first reasons for implementing the MLCS course was the desire to tailor the traditional developmental math curriculum and move away from the one-size-fits-all approach.  There is a large sector of the community college population who are not STEM (science, technology, engineering, mathematics) bound.  Many students want an Associates in Arts degree of which typically has a statistics or general education math requirement.  I believe, as do many other faculty members, that intermediate algebra is overkill on certain topics for these students but that it is light on topics they will need.  So MLCS has been a great option (so far) for this population. 

However, an interesting discovery was made this week.  Heather has a strong background in science with a degree in chemistry in addition to mathematics as well as a specialty in physcial chemistry.  Watch her teach and you'll see it's clearly a love.  I respect and value science but favored pure mathematics when I was a graduate student.  We wanted to blend these loves into the MLCS course by inserting mathematical theory when it made sense but in an accessible way.  So far, that's been fun.  We've shown students why we need negative numbers, zero, fraction, percents, decimals, irrational numbers, and even complex numbers.  We've gotten at ideas of proof, again in unexpected ways.  That's just a sample of the math side.  For the science side, we are embedding lessons and problems throughout that have a scientific focus.  This week we worked on ions and atoms, finding the numbers of protons and electrons based on the charge.  Next week, we'll be balancing chemical equations and in the next unit, the majority of lessons have a science flair.

The discovery was for us more than our students.  We realized how much science we are bringing in which is so valuable to students regardless of their future paths.  Those who will major in non-STEM areas need to know more about STEM fields and have scientific literacy as well as math literacy.  For our students who will head towards STEM fields, which is a fair number, they are getting their feet wet in situations that aren't contrived but are very real.  They're also getting a preview of topics to come in their science courses with time to understand the math behind those topics.  By the end of this course, students will have seen a wide variety of topics from biology, chemistry, and physics. 

Additionally, we are doing some STEM recruitment as well. We have a lesson that will allow students to study STEM fields in terms of their earning potential, unemployment rates, and skills necessary (both math/science related and not). These fields are so valuable to the U.S., so we want students to have a chance to see what they entail, that they are interesting, and that they have strong salaries to boot.

Just something unexpected in this process. I'm not sure why I'm still surprised by things like this but I am. This process has been so organic and non-linear. The act of discovery and problem solving, like we use in mathematics, is a very satisfying thing. Not easy, but incredibly fun.

RVC Developmental Math Redesign 2011

I've updated a PDF packet I made a while back that gives you a brief summary of what our redesign looked like in terms of broad ideas and many specific ideas, our flowchart, and our data.  I've added information to this packet about the new MLCS course and how it is being incorporated.  Check out the link below to download the packet:

RVC Developmental Math Model 2011

Saturday, October 1, 2011

Pilot Recap Week 6: Hitting our stride

This was a great week in the pilot because for the first time, every lesson had the right mix of instruction vs. small group work.  We had challenging problems that drew their interest, enough theory to explain how to complete the problems that arose, and time to solidify skills with additional problems.  The biggest challenge of this whole project is determining its structure and order.  There isn't any course like it anywhere or any book to model off of so we just have to try, fail, correct, and try again.  Some days that's tough because solutions are so obvious in the classroom whereas they're not so apparent on the page. 

One really fun thing students encountered this week was the difference in finding a measurement in real life compared to finding it on paper.  Students are often put off by traditional math approaches that try to keep everything on paper.  They want to experience the situation at hand, not just talk about it.  But when we did that (find measurements physically), they could see there are all kinds of additional issues that come up.  Solving them makes for good discussion and an interesting class period.  They could also see the advantages of paper:  it's often more accurate and it can be faster.  That's not to say that finding a real life measurement isn't valuable.  It is.  But it's worthwhile to talk about the advantages and disadvantages of each approach as well as when each is the most useful or appropriate.  Like calculators and computers, the less we are completely dependent on one means of solving a problem, the more skillful we become as mathematical problem solvers.

We also realized that we are flipping the classroom in our own way.  MyMathLab is used throughout the course but for skills only.  We don't have 10 skill examples written out on paper in any lesson, like a traditional text would.  We do a few key skill examples, which Heather refers to as naked problems:  problems stripped of all context.  But practicing more of those can be done outside of class in MyMathLab own their own time.  If they need 10 minutes or 2 hours, they can get that.  What the classroom provides is a completely different experience, one that is built on talking about and doing mathematics, not skills.  There is a movement nationally to put students in a computer lab and have them complete skill problem after skill problem, all the while calling that mathematics.  Certainly skills matter but they are not enough.  Being able to recognize when to do a skill in a context is one of the key uses of mathematics.  I constantly tell my students, no one is going to come to you in real life and say:

Simplify:  3 - 2(x - 1) + 8.

It's not happening outside of a math class or math test.  But will they be faced with complex problems where having mathematical skills could serve useful?  Yes.  That's why I like this course so much.  They are talking, arguing, and explaining mathematics to each other, not skills.  We had problems yesterday that were pretty meaty and within them they had to simplify an expression like the one I listed above.  What was interesting to see was that virtually no one had trouble with the algebra; that was the easy part.  The hard part was solving the original problem at hand that required generalizing a situation into an expression.  But they figured it out and it was pretty satisfying for them and us.

Next week wraps up another unit and we test.  I'm not as nervous as the first time around.  They are getting the goal of the course and how it operates.  But I still keep my fingers crossed that they'll do well.