# Studies point to smarter way to learn procedures, solve problems

Easy as 1, 2, 3! Such claims have touted the ease of use of a new gadget, although a closer look would reveal that it would take dozens of steps to make it work. Just ask School of Psychology Professor Richard Catrambone.

In his research, Catrambone often undertakes a task analysis. It involves recording in excruciating detail the to accomplish a procedural task, such as executing a pirouette, solving an algebra problem, or programming a Lego toy tank to pivot from any of its two wheels.

For the experts explaining the detailed procedure to Catrambone, the analysis can be overwhelming. They've solved these so many times before that the solutions have become second nature. Going over each step in detail is like moving in plodding motion.

For Catrambone, task analysis yields copious notes. The process, he says, is necessary in creating effective materials and tools for education and training, because they enable identification of the subgoals embedded in a procedure of multiple steps.

Catrambone and his award-winning former Ph.D. Lauren Margulieux, now an assistant professor at Georgia State University, have shown in various studies that when problem-solving procedures are taught through subgoals, learners can apply them to a wider variety of problems.

"Imagine you're in an algebra class and the teacher solves a problem on the board. Then the teacher erases the problem and gives you another that is just like it," Catrambone says. "Most students can rip out the old numbers, shove in the new numbers, and get an answer. They've memorized what the teacher did."

When students get a conceptually similar problem but is not solved in the exact set of steps, they fail.

Margulieux offers an example. Solving equation A, 2x – 4 = 4x + 8, is conceptually similar to solving equation B, 6x – 15 = 3x/4 + 2x. Solving either equation involves two subgoals: isolate the variable and simplify it. The specific subgoal steps, however, are different for equations A and B. Students who only memorize the solution to equation A will unlikely solve equation B.

At Play, At Home, At Work

Subgoal-based learning is good for learning procedures and solving problems with knowable correct answers, Margulieux says. Applications are everywhere.

Catrambone says he often creates wacky poker games that annoy his friends by varying the steps within each subgoal of the game. The subgoals include dealing a certain number of cards, designating a common pool of cards, and assigning certain cards as wild. "Whether the number of cards dealt is 5 or 4 or 3 is irrelevant," he says. "All I do is create new games that meet the subgoals."

Meanwhile, Margulieux sees the principle in cooking. To cook vegetables, a subgoal cook would "pick a vegetable, pick a way to cook it, and pick the flavors to go with it," Margulieux says.

A by-the-recipe cook would get a cup of broccoli, get a tablespoon of olive oil, roast the broccoli in the oven, and garnish it with salt and pepper, all the while checking the recipe again and again in between steps. If the menu calls for Brussel sprouts, the cook would need another recipe.

An important application is in education. Catrambone observes that many learning tools often do not work as intended. "Especially at Georgia Tech, we can get caught up in creating widgets and learning environments and multimedia simulations for education and training," he says. "But you need to do the task analysis first to identify what the learner needs to know – the subgoals and associated steps – and then use that knowledge to guide the creation of learning materials and tools. Otherwise, those materials and tools will be much less effective."

Margulieux aims to apply these findings to online learning. In a real classroom, she says, struggling students have the advantage of the teacher seeing the difficulty they are having – even if they are not asking the exact right questions – and doing something about it.

Online, where the student and instructor are not in the same space, the barrier to asking a question is high, Margulieux says. "The cost of asking follow-up questions is even higher because if students don't get an answer that makes sense, they probably won't ask another question. They will just try to figure it out themselves, and if they don't have the knowledge to do this, it could be detrimental for learning."

"My interest is to make instructions very explicit in what students need to know to understand procedural problem solving so that they can perform well even if they don't have anyone online to help them," Margulieux says.

How else can learning be made more effective?

Catrambone and Margulieux have established that subgoal-labeled worked examples improve learning outcomes. For equation A, that would look like this:

• Original problem: 2x – 4 = 4x + 8
• Isolate variable: 2x – 4 – 2x – 8 = 4x + 8 – 2x – 8
• Isolate variable: –12 = 2x
• Simplify variable: –12/2 = 2x/2
• Answer: –6 = x

Furthermore, they have shown that in some fields, computer programming for example, combining the subgoal-labeled worked example with subgoal-labeled expository text improves learning even more.

Their latest work, with Ph.D. student Laura Schaeffer, shows, however, that the improvement does not play out the same way in other fields. "While subgoal-oriented examples help learning in all domains tested so far, subgoal-oriented expository text seems to help in some domains but not others," Margulieux says. "Why this might be the case is a focus of ongoing research."

Explore further

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More information: Lauren E. Margulieux et al. Varying effects of subgoal labeled expository text in programming, chemistry, and statistics, Instructional Science (2018). DOI: 10.1007/s11251-018-9451-7

Feedback to editors

Mar 08, 2018
Maybe sometimes it is not the goal that is important, but the way to get there (or somewhere else).

Mar 08, 2018
mack, in my opinion. This research was not about learning algebra. But, rather, learning how to apply subgoals as a tool, to accomplish complex procedures.

For instance, you are given a project to assemble the accessories for a barebones desktop computer. Your first subgoal is to create a wishlist of what you want to add to the basic computer to make it useful for your projected needs.

Your second subgoal would be to track down those parts. A sub-subgoal is to find who actually has a key to where those parts are stored.

Good luck! You will hear the mantra "Not my department." a lot!

Additional sub-sub-subgroups will be things like filling out invoices too accounting and reports justifying your progress to your boss.

Extraneous complications such as the computer's base language is not compatible with your department's database.

Good times, had by all... Not!

Mar 08, 2018
The article sorta reminds me of a passage from Dune where the bene Gesserit say they were the first to learn how to learn. (unfortunately it's not quite that easy because different people learn in different ways)

he often creates wacky poker games that annoy his friends by varying the steps within each subgoal of the game. The subgoals include dealing a certain number of cards, designating a common pool of cards, and assigning certain cards as wild.

Ewww. Poker with wild cards? That is just...ewwww.

For instance, you are given a project to assemble the accessories for a barebones desktop computer. Your first subgoal is to create a wishlist of what you want to add to the basic computer to make it useful for your projected needs.

The FIRST step is always: Has someone done this before?...then proceed.

The savings potential by spending a bit of time on that one question at the beginning of any task is enormous.

Mar 09, 2018
a_p, yeah it would have been even better if I wasn't the sap stuck with figuring out how to get things working when no one else in the department was willing and able to help out. Corporate bureaucracy is just as stultifying as all other hierarchies.

And, "wild cards". In poker? If you are not related to all the other players? By blood or marriage? RUN!!! And if it's my family members? I would run twice as fast.

Come to think of it, I'd guess wild cards in strip poker could be fun.

Mar 09, 2018
I would disagree @anti. The first task is to determine what the task is, and the second is to break it down into subtasks. Then you have some things to ask the question, "Has anyone done this before?" about.

Mar 09, 2018
I have used this sort of strategy for both problem solving and product design. In fact, in the best (and most successful) organizations I've worked in this has long been tacitly recognized as a generally successful strategy and is ingrained in the corporate culture.

After that, probably the most important factor affecting success is suppression of feature/mission creep.

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