Direct Instruction, Part 1

Direct Instruction, Part 1

Several months ago, in the NCTM regional conference in Boston, I attended a session on Direct Instruction. It immediately dawned on me that our high school series, Integrated Algebra 1, Geometry, and Algebra 2 and Trigonome! try uses elements of direct instruction.

We purchased a book, Designing Effective Mathematics Instruction: A Direct Instruction Approach, 4th Edition, so that I could better acquaint myself with direct instruction.

So what is direct instruction? According to the National Institute for Direct Instruction, direct instruction is

…a model for teaching that emphasizes well-developed and carefully planned lessons designed around small learning increments and clearly defined and prescribed teaching tasks.

Of course, no program is perfect and you'll need to use your experience and common sense. For example, if you take this definition to its logical conclusion, you may stifle student creativity. If you've recently learned something new and complex, you know what I'm talking about—as you first struggled to understand the new topic or skill (whether it's a home improvement project, an arts and crafts project, or a work project), you appreciated the gentle learning curve (small learning increments). But as you gained confidence and mastery, you had to take "leaps and bounds"; otherwise, the project would have never been finished.

Applying this to the classroom, students need a gentle learning curve when approaching new and intimidating topics. But, eventually, once students start to master the topic, it's OK to provide a more challenging environment.

Tip #1: Topic Order Is Important

In retrospect, it seems obvious that the order in which you present topics and skills matters. Yet, when creating a lesson, we are always tempted to mindlessly mix topics together. Direct instruction recommends to:

• Teach pre-skills first
• Teach easy skills before more difficult ones
• Don't teach complex strategies and/or concepts that are likely to be confused one after the other.

Some examples are in order: When teaching how to graph linear functions, make sure students know how to plot points on a coordinates axes. That's teaching pre-skills first. When teaching the rules of exponents, it may be a good idea to explain the rules with concrete numerical examples before using variables. The average student may struggle with variables.

The third bullet above caught my attention. At first glance, it may appear that teaching similar complex topics one after the other is a good idea. After all, students can use compare-and-contrast to better understand the two concepts, right? Unfortunately, that view assumes that the student is talented or at least motivated to want to keep the concepts straight. That's not always the case (as I'm sure you well know). It's better to keep similar complex topics separate. For example, at the lower grades, students may confuse congruence and similarity. But what do you think? Leave your comments below.

By the way, a strategy is a set of skills. For example, how to factor a quadratic is a strategy that uses the skills factoring a perfect square, etc. Pre-skills are skills that students need to master before learning the current topic. An easy example is: students need to first know how to plot points on a coordinate axes before attempting to graph linear functions.

Well ,that's it for this time. Over the course of the next few months, I'll be blogging my journey as I (more formally) explore direct instruction.

how to graph linear functions