The Latest False Dichotomy in Education

Years ago when I was a student teacher, there was a battle of sorts being waged in the language arts curriculum: the phonics vs. whole-word approaches to teaching reading. On one hand, students were asked to sound-out all words they did not know, and on the other, students were asked to memorize thousands of words. Reality: fluent readers use a variety of techniques including but not limited to the ones espoused by such methods. When some people tried to call this approach "whole language" it created confusion as many missed the difference between "whole word" where individual words are memorized out of context with 'whole language" in which context, along with phonics and sight words is an important component.

Many moons later, we see a similar battle being waged in the teaching of mathematics. 

There are the traditionalists who value "sage on the stage" and "drill and kill" methods in which students memorize algorithms and focus on answer-driven tests. Students become walking calculators, and weaker students are often left without the conceptual understanding to allow them to know when and how to apply these algorithms to solve everyday problems. Mnemonics such as "Yours is not to reason why, just invert and multiply", "FOIL" (which only works for up to two terms), and what I've only recently discovered, the "butterfly method" for multiplying fractions are examples of how conceptual understanding is replaced with memory tricks in order to gain a correct answer on a standardized test.

Then there are the constructivists who believe that students must create their own knowledge set through experimentation. They offer an overwhelming range of options for students to explore, but often neglect the final stages of consolidation and review, as well as time for practice with additional problems. Critics argue that since it took centuries to develop the fields of mathematics, expecting students to "reinvent the wheel" is a waste of time for everyone. Such teaching can also be time-consuming, and students who are struggling can become overwhelmed and confused with the large variety of methods to solve a given problem.

Again, just as in the reading example, the polar extremes reflect a false dichotomy when it comes to learning.

Since there seems to be a reluctance for educators, policy makers and the general public to consult the literature, examine what we know about cognitive development and read the studies, there becomes a tendency to grasp onto the methods one is familiar with and hold these as sacred. In many cases in North America, this means that the traditionalist methods are held in higher regard than the constructivist methods. Looking to other countries that tend to do well in mathematics, there are some interesting cultural differences that appear in the approach to teaching and evaluation. One example can be seen in this video with Phil Daro http://vimeo.com/30924981.

In the middle, is student inquiry (again, the name is often used as a substitute for pure constructivism, which causes confusion) in which students are encouraged to try out problems using whatever means they can, discuss the various methods that worked and didn't, share and yes, memorize the methods that work consistently, and connect these methods and patterns to problems they encounter in everyday life. There is structure to the lesson, but there is also a place for students to work with problems on their own terms, experiment and make connections with prior learning. Lessons are scaffolded so that they build on concepts already mastered. Consolidation happens with the whole class and is reviewed again at the start of the next lesson. Students still memorize times tables and formulas, but they also understand where these come from and what is happening with them. They can use a matrix to show multiplication and can tell you why ax + by + c= 0 is a different way of showing y=mx +b, and how various different values of "m" will change the slope of a line when graphed. They can relate this to situations in their everyday life. They know what to do when confronted with 

(2x + y)(3x +2y -z)

 because they have learned the underlying pattern of how this works, rather than just a convenient but limited mnemonic. The understand that BEDMAS is an mnemonic shortcut that helps them use the distributive property, and that the multiplication/division are interchangeable as are addition/subtraction.

Without context, understanding of the underlying pattern, and sufficient understanding to apply the concept widely, a math student's abilities are no more useful than a calculator, and are likely much slower at that. We need people who can not only calculate, but choose the appropriate algorithm and problem-solve in a variety of situations. We need people who understand how to program the algorithms in the first place. Math is not a religion to be taken on faith; it is a science that stands up to scrutiny. We would do well to remember this as we approach the subject in the classroom.

Students learn by doing and thinking, by struggling through problems. When this is connected to their everyday experiences, it becomes meaningful. If we can recognize this in other subject areas, then why not in math?

Halloween Science

 It's Halloween! Time to don your lab coat Mwahaha!

There are lots of strange & spooky science activities on Lemonade that are perfect for sharing at  Halloween, so I thought it might be a good idea to put them all together here so they can be easily accessed from one place. 

Halloween lends itself to lots of strange science activities, from spooky dry ice experiments, to cosmic black light effects and strange magical potions that disappear and reappear, that change colour unexpectedly or become slimy and ooze.

You can make your own shrunken heads from carved and dried apples (it will be as if those apple dolls your grandparents made became apple zombies).

It's also a time to look at some truly bizarre creatures , even more bizarre creatures and maybe do a little owl pellet detective work. If you have access to a microscope, you can see a whole world of alien-looking creatures--from pond critters & close-up insects to bacteria (in fact, you may want to try and culture some bacteria of your own--see below). Strange & spooky science effects can also be found in the kitchen with possessed dancing raisins & living sludge bread (yeast & sourdough).

To culture bacteria, you will need a petri dish (or clean, clear container), some powdered agar (you can find this at health food stores and science suppliers), chicken broth (to use as a nutrient base), cotton swabs, and a place to store the samples. Boil the chicken broth then add the agar and stir well. Pour the mixture into petri dishes, cover and refrigerate to set.

Use the cotton swabs to collect samples from anywhere you suspect germs & bacteria may be found. Try doorknobs, computer keyboards, pet mouths, human mouths--and so on. Gently brush each swab along the top of a gel, label and seal the dish. Repeat for each sample. Store the samples at room temperature, or experiment with making several copies and storing at various temperatures for several days or even weeks. Examine your results under a microscope if possible.

Of course, if you are doing this as a controlled experiment, you will need to be much more careful about preparing and storing the cultures in order to avoid contamination, but for pure exploration, these instructions should suffice.

Other ways to culture bacteria can be edible, such as making your own yogurt or cheese. In fact, when you eat yogurt, you are actually eating live bacterial cultures--poor things! They're being EATEN ALIVE!!!

More weird science can be found here.

Happy haunting!