I enjoy watching Food Network. There are a number of shows that, as I’m flipping through the stations, I will always stop to watch. Two of my favorites are Good Eats and Cutthroat Kitchen, both hosted by Alton Brown.
Good Eats doesn’t appeal to everyone, as Alton goes beyond the usual format of a cooking show and explains why all of the ingredients interact the way they do, and oftentimes makes suggestions as to what you could use as a substitute for some of the ingredients. This makes the show sort of a hybrid between the standard PBS cooking shows and chemistry class.
Cutthroat Kitchen, on the other hand, is more of a game show where the contestants are told they will be making a certain type of dish (not a specific recipe), but then Alton throws different sabotages at them that force them to think on their feet without the assistance of any new ingredients or utensils. Most of the sabotages are ridiculous and would never be experienced in a real kitchen, but the entertainment value is high and the dishes actually turn out well in most cases - at least that’s what the judges on the show say.
Those who watch Good Eats purely for the recipes are usually annoyed by the chemistry part. They don’t care about why the recipe works. All they want is to have the recipe in hand, watch Alton make the recipe, and then try it themselves. Substitutions aren’t important. Variations aren’t important. The only thing that matters is to be given step-by-step instructions to create the recipe.
But what happens when you have to change the recipe, either because you forgot to buy one of the ingredients at the store or because you have a friend who is allergic to something in the original recipe? For those who rely on step-by-step instructions, the answer is to go back to the store or to pick a different recipe. For those who understand how the recipe works, a quick (or a planned) substitution can be made, and the dish will turn out just fine.
Sound familiar? All that matters in many math classes, to both students and teachers alike, is that the students are able to follow a set of step-by-step instructions to get the right answer. Why it all works isn’t important, just follow the directions. Variations aren’t important, since there won’t be any variations on the tests, at least not the ones given in class. So the teacher sees their job as being to present the material in as many ways as necessary for the students to be able to follow the step-by-step algorithm. Students repeat the refrain “just tell me what to do” because they see their role as being to memorize the steps and reproduce them on the test.
Ummm...this isn’t math. Not really.
Real math involves understanding why the algorithm works, and being able adjust it to fit a new situation. This is why both teachers and students struggle with preparing for some standardized tests - namely, the ones that make it a habit of throwing in exercises that rely on the appropriate concepts but that are not like the standard exercises found in a textbook. The AIR test last spring is a good example of this. At times, AP tests can be. When this happens, the students complain that the test wasn’t fair because they had never seen any problems like these before. The teachers complain that if they had known “that kind of problem” was going to be on the test, they would have made sure the kids saw some of them. In other words, both the students and the teachers see memorizing the algorithm for a specific type of exercise as the purpose of math class.
Ummm...no...no, it’s not.
Math class is supposed to be about empowering the students with both the basic concepts and mechanics as well as with the problem-solving skills to flexibly use them in new situations - even if the situation occurs on a standardized test.
The implications for what needs to happen in the classroom are deep. Teachers are told that they need to differentiate the instruction to meet the needs of every student. Students come to expect the teacher to “teach the way they learn best”. Let’s be honest: we all learn differently. That means a high school teacher would need to teach the same lesson in over a hundred different ways each day, assuming the teacher knows the way each student learns best. This is not reasonable. Actually, it’s not even possible. Twenty-four hours wouldn’t be enough time for this to happen, let alone the seven hours in a school day. And besides that, this would still focus on the basic algorithms and not on the flexible problem solving.
So what is possible? Does the method of instruction exist that empowers the students to take responsibility for their learning? Can one method actually be used every day that provides the opportunity for every student to learn how to problem solve the way they learn best?
Yep. Any of the discussion-based methods - project-based learning, problem-based learning, and Harkness, for example - do exactly this. It’s not necessary to change the instruction for each student. What is necessary is to give the kids the freedom to learn the material in the way they are most comfortable, and have a deep enough understanding of the material ourselves to be able to support them when they get stuck without resorting to “here, let me show you how to do this”. And by learn, I don’t mean memorize the algorithm. I mean learn the material to the point that they can use the content and skills flexibly.
The kids can’t stop once they are able to make dinner from the recipe. The standardized tests - and life, for that matter - demand more than the ability to reproduce a recipe they've seen on an episode of Good Eats. They need to be ready to compete on Cutthroat Kitchen.