A few months ago, I decided to deliver math lessons to my fifth grade digitally. It was the last subject area that I brought into this form. I was reluctant because typesetting needed for math was confusing and frustrating. Beyond that, I was quite pleased with how I conducted math lessons, and my results have been positive.
There is a lot of direct instruction in my math lessons. I make no apology for this. My school and community expect it. The demands of state curriculum and standardized testing demand we cover a lot of material. However, I have long approached math differently from many others. Rather than worksheets or exercises from the book, students in my class have done their work and respond using 9×12 dry erase boards. I have been presenting mini lessons on the chalkboard and putting up problems one by one for students to do. If they grasp it, I continue to new material. If they have not, I reteach and practice more.
While still largely direct instruction, I have found this approach significantly different in that it is social. Instead of students receiving direct instruction, guided, and independent practice, there is constant interaction with rapid shifts in lessons because of the feedback given by the students. I have been better able to scaffold my lessons by starting with simpler work, checking for understanding, then moving on to more complex as appropriate.
OpenOffice Impress is a capable open source presentation application available on all platforms. Windows users may have PowerPoint. I use Keynote along with a multimedia projector and project onto a screen or my chalkboard.
Unfortunately, iWork applications, unlike those in Microsoft Office, do not have an integrated equation editor. I made a brief attempt to get LaTeXiT to work on my computer, but I just did not have the time to fiddle with it and learn the markup language. I ended up buying MathType (also available in Windows) because it integrates with iWork. It was pricey and has an interface that leaves much to be desired, but it does the job. For the amount of time saved, it has been worth it. Bottom line is that you need an equation editor to digitize math instruction. If you use MS Office, you have a tool set sufficient for intermediate mathematics. I found the Open Office tools too limited (unless you learn LaTeX). Grapher, which comes with Mac OSX, has about the same features as Open Office’s Formula. Outside of MS Office, you need third-party party software. If you are willing to learn LaTeX, there are many free options. If you run a Mac, I recommend the MacTeX distribution. It takes care of all the dependent software in one easy installation. Now LaTeXiT and related software run on my computer.
Presentation software packages include capable graphics and charting tools. Learning accompanying spreadsheet software extends the range. Nonetheless, you will need to create graphics beyond the on board tools. Windows users may have MS Visio. ConceptDraw is a premium choice on Mac or Windows. I use OmniGraffle, a less expensive Mac alternative. Dia, an open source diagram tool, is available for Linux and Windows.
While exploring math resources, I was shocked to find Mathematica for $49 in a special offer for K-12 and community college educators. Mathematica is an advanced mathematics and scientific programming environment. I use Mathematica, but I just scratch the surface. I have done some basic formulas and graphing; however, I usually used it with the huge library of Mathematica demonstrations. They can be downloaded freely and played using the software or a free player. Using Mathematica allows me to hack or modify the demonstrations to customize them to my needs. It is also a capable math typesetting application.
Committing lessons to slides, I have focused on the structure and sequence of my lesson in more detail than I had. Laying out the minute details slide by slide makes it clear if anything is missing. Having the lesson laid out as such also has kept the structure and sequence within a lesson tighter. I reflect upon my work more closely.
I have also learned a lot about math. Searching for materials, I have discovered different approaches to teaching a given concept. I have seen many educators’ lessons on YouTube. They have given me deeper understanding and innovative ideas about both mathematics and pedagogy. Beyond that, the Internet provides access to diverse cultures that sometimes use methods different from those prevalent here.
Students are more focused. Delivery of lessons is faster and more efficient. While I interact with the projected material upon the chalkboard, time spent writing is significantly diminished. I work easily with grids, graphics, and multimedia. We have more time for extension, exploration, and review.
The downside has been the substantial time investment. It takes time to become efficient with the applications and develop a work flow. Time is lost in trial and error. Creating problem sets is tedious. Now and then time constraints have forced me to compromise quality or take shortcuts such as copying unaltered problem sets from textbooks.
As the year draws to an end, I now have half a year of math instruction presentations created. I have implemented many shortcuts and efficiencies, so completing the rest will be easier. I think that my teaching has improved dramatically as a result of this work.The next step is to share these lessons with others which brings up another set of issues to be addressed in another blog post.