Procedural Fluency in a Problem-Based Classroom

One of the biggest struggles I’ve had during the process of changing to a problem-based learning classroom is the balance between building problem-solving skills and conceptual understanding with procedural fluency. In fact, this dilemma is one of the most frequent questions I hear when talking about problem-based learning. Where does procedural fluency fit-in? When is it taught? How is it taught? These are great questions that I’ve struggled to answer, and I’m hoping you can help me.

Background:

I recently read Robert Kaplinsky’s FAQ blog post about PBL, and this quote really hit home:

“The Common Core State Standards (CCSS) call for educators to pursue with “equal intensity” the three aspects of the Rigor shift: procedural skill and fluency, conceptual understanding, and application. Regardless of your support for the CCSS, it seems reasonable that students should have strength in all three components. So with that in mind, consider the following scenarios.

If you do two or more problem-based lessons per week you would be spending at least 2-4 days per week on these lessons. That would take you away from the balanced rigorous understanding we are striving for. Their procedural skill and fluency as well as conceptual understanding would suffer…”

Through all my excitement and effort to create and implement great problems, I haven’t focused enough time on improving my approach to teaching procedural fluency. The CCSS call for an equal intensity that looks like this:

Pie Chart

But my focus and attention has looked more like this:

Other Pie Chart

I can imagine that there are others striving to improve as well, so let’s work together to find some solutions.

Teaching Procedural Skills:

When I say teaching procedural skills, I’m talking about the part after the problem-based lesson has taken place. One goal of a PBL task is to create an intellectual need for a concept. For example, a goal for stacking cups is to create a need for y = mx + b. Who really wants to count one by one when there’s this useful formula? A need arises for the student, and the procedural skill now has context.

But, in this post, I don’t want to focus on when to teach the skill. I want to find better strategies for teaching procedural fluency after the need has been created. The students are curious, you have them where you want them, now you need to teach them slope-intercept form. How do you structure this initial launch?

At this point, I’ve got nothin’…

Straight Rows

The only tool I have (if you can call it that) is for all students to face me…hang with me guys let’s get through this…traditional, straight row teaching. I don’t know how to teach a new procedural skill with students in groups. I haven’t found a way to get enough focus in my direction without physically facing all students toward me. I’m not happy with this arrangement because it definitely compromises the curiosity I’m trying to develop in my students, and I know I can’t reach every student when they’re in rows.

Jenn Oramous shared a strategy that she uses in her project-based learning classroom. When teaching a new skill, she has one member from each group come to her table to learn the new tool. After teaching this smaller group, each member returns back to his or her team and teaches what was learned. If students are still struggling or want more instruction, they can go to the teacher’s table after the student-led session. I like the sound of this because it encourages collaboration and student ownership of learning.

What are the strategies, techniques and structures you use to introduce and teach a procedural skill?

Practicing Procedural Skills:

The skill has been taught, and it’s time to give the students an opportunity to build procedural fluency. I want to maintain a collaborative, inquiry-based atmosphere so I’d prefer not to have students working independently. What do I do?

Jon Orr gave me great advice about how to approach skills practice. He said that he likes to have the class play a game in order to bring some excitement to an otherwise boring situation. The games are usually played with small groups, and reteaching can take place during this time.

My favorite game he introduced me to is Math Race. I tried it with my students, and it was a big success. The kids work on practice problems together, and once a group has an answer, a member brings the work to the teacher for review. If the answer is correct, the group gets a sticky note to place on a number board. In addition, the group gets to shoot one trashketball shot. A made shot results in an extra sticky note. At the end of the game, a randomizer is used to pick the winning number, and the corresponding group wins a prize.

Game Board

I really like this game because the winner is not dependent upon which group has the strongest students. Even if a group only has one sticky note on the board, they can still win (a similar situation occurred the first day we played). Also, I have “random” students from each group explain, in detail, their thought process for each answer. The “random” student is usually someone who may not be contributing the way he or she should so this forces everyone to get involved. Many times, group members had to explain to the reporting student the thought process, and this created the type of dialogue that’s ideal in group work. Overall, the game created a lot more student buy-in than what is normally seen during traditional practice time.

Other than games, the only intriguing technique I’ve heard of (but haven’t used) is speed dating. Just another way to mix it up a bit.

I need your help because there has to be so much more out there that I’m missing. What other strategies and structures have been successful in your classroom?

Feedback:

  • Geoff Krall provided two helpful links including 7 activities that can make practicing procedural skills better.
  • David Griswold knocked it out of the park with his breakdown of student motivation within games.
  • Robert Kaplinsky made an excellent distinction between “application” defined by CCSS and general ideas. He also mentioned the effectiveness of Open Middle problems. Check them out!
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