This is the second in a series of posts about learning acceleration in math. As I wrote in the first post, I'm a huge proponent of bringing focus to math instruction and see it as central to acceleration. In the same way that the "big chunks" of math curriculum (core scope and sequences, intervention scope and sequences, and interim assessments) require a lens of focus, so do individual lessons and activities if we are to increase
proficiency with grade-level mathematics. This is what I have come to think of as "micro focus."
Focus on a single, clear lesson goal
In what ways are lessons sometimes unfocused? Lack of focus can start with having multiple learning targets or objectives. Student thinking, problem-solving, and practice are then not sustained for a full class period on a single outcome; focus is diffused across two or more different outcomes. Further, it can be unduly challenging to provide support for students when there are multiple objectives, as each learning target brings its own set of skills, knowledge, and prerequisites to consider. Finally, assessing progress and decision-making about further support is challenging when students will demonstrate different levels of understanding across multiple learning targets. The portrait of understanding from a single lesson may be too complex for us to reasonably act on.
So, then, a key move that accelerates learning is focusing each lesson on a single, clear objective. Doing so ensures that students have adequate time and opportunity to be successful with the objective, allows for multiple, strategic supports to meet the objective, and makes analyzing student performance more straightforward and actionable. For example, a typical lesson on equivalent ratios in sixth grade might have three learning targets, such as:
"I can determine whether two ratios are equivalent or not."
"I can explain what equivalent ratios are."
"I can generate an equivalent ratio from a given ratio."
What mathematics should students spend most of their time doing? What skills and understandings should be continuously assessed to check whether students are being successful? What scaffolds and supports might I consider to ensure students are being successful? There aren't easy answers to these questions when there are several objectives.
While a lesson about equivalent ratios will likely involve students doing all of the things named in these learning targets at different times, I've come to appreciate the value in focusing the lesson on a single grade-level learning goal. In this case, I might choose to focus on the following single, clear goal for a few reasons:
"I can generate an equivalent ratio from a given ratio."
For one, it's relatively straightforward to observe and assess whether students are getting it. For another, the first two learning targets come along for the ride. It's most likely that students will be able to generate equivalent ratios if they first know what equivalent ratios are and can determine whether or not two ratios are equivalent; in this way, this learning target can be thought of as a culmination of the first two. And finally, generating a ratio that is equivalent to a given ratio is highly applicable to later work.
Sometimes, it's relatively easy to choose a single learning target from a group of them; other times, it's more difficult and might require significant revision. In all cases, it can feel like you are losing something of the original intent of the lesson. But the value gained in focusing the lesson is the pay off.
Now, focus the activities
Once a lesson is focused on a single learning target, our attention can turn to the activities. The exit ticket or other formative assessment, along with the problems, exercises, and other activities need to be focused on the single clear learning target. Once the lesson is "micro focused," we are on the road to acceleration! We can next further amplify the opportunities for learning the grade-level goal through what I like to call a lesson-level "barrier analysis," by considering: What are all the challenges that might get in the way of students being successful with the single, clear goal?
To illustrate this idea, let's consider another sixth grade example. Think of this learning target:
"I can use unit rates to make comparisons."
What are all the related skills that students might need to be successful with this learning target, but might not be explicitly attended to in the lesson itself? What are the potential barriers to success with this grade-level goal? Here are some that I came up with:
Setting up unit rate calculations
Performing computations, especially division, in cases that involve non-whole numbers
Interpreting the meaning of the unit rate
Interpreting entries in a table or other representations
A list like this helps us create even more focus, by adapting the lesson to minimize these barriers. For example, if setting up a unit rate calculation is a barrier, a warm up involving a worked example can help to prime students to be able to set up the calculation later in the lesson. For a computational barrier, we can provide tools like multiplication tables or calculators or reduce computational loads by focusing some problems on writing expressions, rather than computing with them (see this post from 2023 for more on this idea). If interpreting the meaning of the unit rate is a barrier, we can choose opportune moments to provide explanations of unit rates (i.e., "You can think of the 'best deal' as the lowest unit rate." "You can think of the 'best gas mileage' as the highest unit rate.") I've found that ideas like these can sometimes produce resistance in math educators, perhaps due to culturally ingrained ideas about what math class is supposed to be like. ("It's supposed to be hard!" "They should have learned that years ago!") But I firmly believe that activating and providing necessary background knowledge (in ways described by UDL guidelines) can really open up grade-level learning for all students.
"Micro focus" means more focused lessons and activities, allowing for sustained attention to a specific grade-level goal and the inclusion of thoughtful scaffolds that can help more students get there, making it an essential component of accelerating learning in math.
Note: It is a best practice to include both mathematics and language learning objectives, as described in the English Learners Success Forum's guidelines. My intent in this piece is to focus each lesson's mathematics learning objective on a single, clear outcome, not to eliminate language learning objectives.
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