Below are the handouts from the talk we gave at ICTCM today since we ran out. They include objectives from the course, a sample lesson, flowcharts to show possible implementation options, and a flyer for the book Math Lit with the unit structure and math topics listed.
The presentation today was brief and therefore it did not have as much detail as we often use. To compensate for that, I've included a youtube video below the handouts of a similar but more detailed version of the presentation we gave today. If you have questions, please email me.
This video was recorded in September 2012 so several things have changed since then. The book is almost finished and is coming out in July of this year. It will have a full MyMathLab course using Pearson's new design, releasing this summer. A sample MyMathLab course already exists. Please search for the book title, Math Lit, in MyMathLab to create a course. Several schools have been class testing our materials and interim MML course over the past academic year. We have conducted several workshops and plan to do more with training. We will be offering an online training course in June using the LMS Canvas. Registration information will be posted on this blog next month.
We don't approach algebra in the traditional order or using traditional methods in the MLCS course. One reason for that is the audience. The student taking this course has taken somewhere between 1 and 3 years of algebra, and yet they have placed into an algebra class at the high school level. Taking the same approach, when it was not effective the first or second or third time, will likely not yield a new result.
So we approach problems and ways to solve them, not algebra and then problems using it. It seems like a subtle change but the emphasis is incredibly different. In MLCS, algebra is a means to an end, not the end itself. We value algebra tremendously. But there is an overemphasis on this wonderful subject at the developmental level. I've often thought calling this area "developmental math" is a misnomer. It should be called developmental algebra, because that's what we spend 80% of the time working on. The remaining 20% is spent on numbers, geometry, and applications.
In reality, students will face problems with numbers in their lives and future classes, not necessarily algebra problems. Knowing when and how to use algebra matters more if we really do believe this subject is important. But that's not the traditional focus. It's just on the mechanics, as though linear equations and polynomials are falling from the sky waiting to be solved and factored.
Another reality is that in real life, the numbers aren't nice. Polynomials exist but they often don't factor. And graphing by m and b is a lovely idea but real data doesn't make it nice to do. And it's often possible to come up with an equation that is not easily solved without technology or numeric methods. We do students a disservice by shielding them from these truths. And in teaching them how to deal with them, the problems are far more interesting and students are more engaged.
Our approach is to always begin concrete and with numbers. Bring in the algebra when it will make the problem easier in terms of solving and/or organizing the details. Students will gravitate toward it often if they are not forced to use it because it is so powerful and often helpful. And sometimes algebra completely obscures the issue at hand and is overkill. Again, knowing when to use it is just as important as being able to use it.
This can be a difficult shift at first, especially if an instructor has taught traditional algebra for many years. Nearly every book has the same ordering of topics and the same emphases. So it's unusual at first to see commutative property after integer operations have been addressed. But students can still be successful with integer operations because they've been using the commutative property since first grade as a natural behavior for numbers and certain operations. It's not the name that matters; it's the understanding of the concept so that it can be used. Intuitively, students can solve many problems without the formality we often put on them.
Take Pythagorean theorem for example, a topic I taught this week. We came at the theorem and its uses from every angle. Using it requires algebra but really an understanding of numbers, something we've been working on for weeks, will suffice when solving the equations involved. When we get to equations like this, this is the approach we used since we haven't gotten to formal equation solving:
We need to find what adds with 225 to achieve 484. That can be found by subtracting 225 from 484. This approach uses the concept of addition and subtraction being inverse operations. The result is 259.
leg2 = 259
The length of the leg will be a positive number and it should square to be 259. That is the definition of the principal square root of 259. We write that next and then use the calculator to get a decimal approximation.
leg = √259 ≈ 16.1
It was also interesting when using the calculator for this problem. Students used the square button and then the square root button. I asked them if they notice anything about the placement of those functions on the calculator we typically use, the TI-30. They are paired on one button with one function being the direct operation and one requiring the 2nd function to get to it. I told students this is not a coincidence and asked if they could figure out why. A student's eyes lit up and said, "they're inverses of each other!" Exactly! That's a valuable concept to know.
Can students solve problems like this without formal equation solving techniques? Absolutely! And it makes sense because we are working at the numeric level. When we get to the formality of algebraic manipulation, it is always easier because a strong foundation in numbers has been established.
Some students remember equation solving from a previous course and prefer to use those steps. We encourage them daily in this course to use methods that make sense. Every concept that is taught uses multiple approaches to understand it, be it visual, numeric, algebraic, or verbal. After we learn those methods, we ask students to reflect on the method they prefer going forward. Learning how they learn provides a student tremendous insight on their understanding and is very helpful throughout college.
There are many people who feel this way about algebra, that our focus could use some updating. But often they are the ones using the mathematics instead of teaching it. I think it's worth listening to the people who use math for a living. Of course not every concept has to be immediately useful to be worth learning. But with the current traditional approach, there is too little that is useful and too many topics developed in a way that is unrealistic in terms of the real world uses. For more on this idea, please watch this short video by Richard Feynman, Nobel prize winning physicist.
If you'd like to see what the MyMathLab course will look like for our book, Math Lit, you can preview it by creating a course in MyMathLab. Go to "Create/Copy Course" and search by the book name or Almy or Foes.
Click on any graphic below to enlarge it for easier viewing.
Once it is copied, this is what you'll see.
We use MML for the skill component of the course so that students can practice all the skills that are developed in a way that will help them develop mastery. Additionally, an ebook is available as well answers to the conceptual homework in the text.
To guide students through the book structure, tabs correlating to cycle parts are available, each with the set of steps students complete to learn a lesson. They include participating in the lesson, doing MML homework, and doing conceptual homework with answers provided for checking their work.
Within the instructor resources is a link to the Instructor Appendix, a document that supports instructors in teaching the course, cycle, and lessons. Additionally, there is a link to a webinar I gave about the MLCS course.
Although travel season never really ends for me, it does have its busy and less busy times. I'm in the busy season now, traveling every weekend for the foreseeable future. Recently I worked with the Maricopa college system in Phoenix on redesign. It's interesting to see how large college systems work to implement change. There are always challenges to redesign; they just vary due to things like size, funding, culture, and facilities.
I've been speaking at a series of three sessions to educate faculty in Illinois on new pathways courses. We've had events at Southwestern Illinois College and Parkland College. Our remaining event is on March 2 from 10 am to 1 pm at College of DuPage. Any faculty or administrator in Illinois is welcome to attend and learn more about the types of pathways courses we're testing in Illinois, the data to date, and when we'll be voting as a state.
Intermixed with the Illinois events, I'm speaking on MLCS in Houston this week for TCCTA. Next month I'll be in Washington state (both Seattle and Spokane) for events to talk about pathways courses. Then it's on to ICTCM in Boston and then IMACC at Robert Allerton Park in Monticello, IL.
Throughout this time, I'm doing training workshops with schools as they plan pilots. Heather and I are working on the online course we'll teach on pathways this summer. Information for registration should be coming in the next month or so. Communication is often easier with face-to-face workshops, but it's hard to be everywhere at once. The online course will give us an opportunity to provide training for MLCS on a much larger scale and in the convenience of your own home.
Lastly, we are in the home stretch of finishing the book, Math Lit. A demo course in MyMathLab will be available very soon. We've already seen a sample of it and it's fantastic.
It's been a lot of work for me and many, many others around the country who are committed to providing new developmental math avenues for students. Seeing that work come to fruition is truly exciting. Hearing about students enjoying new courses and feeling success in a math class for the first time makes all of it worthwhile.
We're back in the swing of things at our school, entering our second week of the semester and our fourth semester of piloting MLCS. Things are never dull on the pathways front. I'm waiting for more information that I'll post soon on the blog, but until then, here's a sneak peek:
Online MLCS Training
Heather and I will be teaching an online course this summer about teaching pathways courses like MLCS. It will be 4 weeks and in June. If you're thinking about teaching MLCS but want much more detailed help and the chance to talk to other educators in the same boat, this course is for you. Plus, you don't have to travel! This will be a great opportunity for faculty or administrators prior to a pilot or for schools who want a more detailed look at pathways courses than a webinar or presentation can provide.
Registration information will be posted on the blog soon.
If there is interest, we will teach the online course on a regular basis. I'm very grateful to be asked to do this by a company that can facilitate online classes like this. Doing so allows us to offer the training on a large scale that we have heard so many requests for. We will continue to do face-to-face workshops but it is hard to reach all the schools who want more help. The online course will help that issue greatly.
We are committed to making MLCS possible at any school and have worked to make that happen through education, materials, training, and support. Schools that class test with our materials are eligible for webinars with Heather and me to get their questions answered and brainstorm solutions to challenges.
Would you be interested in a discussion board about MLCS and/or the Math Lit book? Email me or post in the comments if you are. I can set up a discussion board that would be free and allow us to have an ongoing dialogue and resource for schools.
