Module 2: Procedural Knowledge
Objectives:
Learners will be able to:
- Describe the importance of procedural knowledge.
- Explain why procedural knowledge is important in mathematics.
- Identify the applications of procedural knowledge.
Time for a Refresher!
What is procedural knowledge?
Write down your thoughts in this Google Form link:
Procedural Knowledge Refresher
*This may be a wise time to refer back to your journal! You may want to add to your journal as well.*
Quick Recap: For a quick recap, let's recall that the root word of procedural knowledge is "procedure." Therefore, it can be looked at as the knowledge of knowing the procedures of something. We often use our procedural knowledge as a means of executing a specific skill. Some refer to procedural knowledge as "know-how" knowledge.
Quick Self-Reflection: Does this quick recap match what you said in the Google Form above?
Before reading any further, what are some things that you hope to learn? Do you have any areas of confusion? Please add these to your journal under "Module 2."
I hope to answer any questions that you may have in the coming lessons and modules!
Why is Procedural Knowledge Important?
Procedural knowledge is something that we use on a daily basis. Most of what we learn, as humans, is through experience. When we attempt to do something new, our brains are faced with a new problem. Once we figure out how to solve the issue or problem, then we are able to develop a sense of muscle memory. In other words, when we face that same problem again in the future, we are able to know how to figure it out.
So, you might be asking: "what is an example of procedural knowledge?"
A prime example of procedural knowledge is driving a car. We all learned to drive a car by using our procedural knowledge. Driving a car is a skill. The more you drive, the better you become at that skill. The reason this example is such a great one for procedural knowledge is because procedural knowledge is more than just reading a book and being able to spit out some facts. Procedural knowledge is NOT the same thing as factual knowledge. In order to gain procedural knowledge, you must put yourself in the situation and practice the skill until you feel that you have mastered it.
If you would like to read more about procedural knowledge this is a great website:
https://www.edapp.com/blog/procedural-knowledge/
There are many examples of procedural knowledge in our daily lives. What are some examples that you can think of?
Post them here:
List your example of procedural knowledge!
Procedural Knowledge in a Mathematics Classroom:
According to the National Council of Teachers of Mathematics, "Procedural fluency is a critical component of mathematical proficiency." Do not let the idea of procedural fluency confuse you. Procedural fluency is just the ability to apply procedures effectively and appropriately. As most of you already know, mathematics is a very skill-based subject in education. Yes, there are plenty of concepts (which we will discuss in Module 3) but there are also plenty of procedures that we teach to our students. Solving equations is a prime example.
One-Step Equations: Let's take a look at a common example of procedural knowledge in a middle school mathematics lesson. Teaching students how to solve one-step equations is a perfect example of procedural fluency.
Let's use this example:
3x=15
Students would be asked to solve for x.
When teaching how to solve for x, the teacher would explain a procedure to follow. The teacher would explain that when solving equations we need to use the inverse property. We essentially are "undoing" the problem. So, in the expression 3x, the 3 is being multiplied to the x. Thus we would have to do the opposite of multiplication, which is division. Then, we need to divide by 3 on both sides. When doing that, we are left with x by itself (which is what we want!) on the left and 15 divided by 3 on the right. 15 divided by 3 is 5. Therefore our answer is x=5.
As you can see, explaining how to solve a one-step equations is very step-based. In other words, there is a set procedure to follow. There are certain questions students need to ask themselves in each equation that they are trying to solve.
Two-Step Equations: Another very common example of procedural fluency is two step equations. Here is a short tutorial video on how to solve two-step equations.
As you can see, procedures are taking the forefront in this tutorial. In every single solving equations problem, the student needs to get the variable (letters in math) by itself. To accomplish this goal, there are steps that need to be followed. As in the car example above, more practice with solving equations can lead to students achieving mastery of the skill. Solving equations is a skill! Once students start to get the hang of following the correct procedure, they can use those procedures to solve other equations that may have a slightly different format.
Solving equations is just one of many ways that procedural knowledge is developed.
Is Procedural Knowledge the Same as Memorization?
What do you think? Is procedural knowledge the same as memorization? Place your answer in your online journal under "Module 2 Notes."
According to the National Council of Teachers of Mathematics, procedural knowledge is much more than just memorization. It's also much more than just mastering one single procedure. Memorization is just not the same as procedural knowledge in mathematics because every question is a little bit different. For instance, I just gave the example 3x=15. What happens if the next example is (3/2)x=15. Well, now we have a fraction out front. Students who just memorized the initial example will not know what to do next. Procedures are steps. Not every single equation needs the same steps to solve it!
How Can Teachers Make Procedural Knowledge Easier for Students?
Teachers can make procedural knowledge easier for students by being clear and concise.
Have you ever had to read an instructions manual to put something together? Is it very easy to follow when it is overly wordy and is not straight to the point?
This is exactly the question you need to ask yourself when teaching procedural fluency. When teaching students how to follow a series of steps, you should be as clear and concise as possible. It will garner the best results!
Game-Based Learning Involving Procedural Knowledge:
One very popular way that teachers can have students practice their procedural fluency is through the use of game-based learning. Game-based learning is a way to help increase student engagement. Students often become excited when mathematics is put into a game format.
A couple very popular game-based software programs:
- Kahoot
- Gimkit
Kahoot is a game-based program that uses multiple-choice quizzes as it's driving force. Students earn points based off the correct answer as well as the speed in which they answer the question. I have noticed that students absolutely love Kahoot. However, Kahoot is designed to answer questions quickly. Thus, it's important as a teacher to keep this in mind. If you plan on using Kahoot as a game-based platform in a math classroom, then you should be using questions that test students' quick math skills. These questions should be procedural questions that take 30 seconds or less.
Here is a link to a kahoot that you can try!
In your online journal, answer the following question:
- How many seconds do the students get for each question?
- Are most of the questions indeed procedural?
Gimkit is another game-based program that students enjoy to play. Similarly to Kahoot, Gimkit also uses multiple choice questions. However, these questions are not timed! Gimkit does not have a timer, but it is important to realize that the point of the game is to make as much virtual money as possible. The more questions you answer the more money you're going to get. Therefore, students will be working at a fast pace. Thus, the questions in Gimkit are usually skill based as well. They are very procedural!
Here is a link to a Gimkit that you can try!
Both Kahoot and Gimkit are game-based programs that I have used. I have realized that if I want students to use these games productively then I have to understand their strengths and weaknesses. Their strength is definitely to help students build on their procedural fluency. This is not a time to build a lot of conceptual knowledge! We will dive further into conceptual knowledge in module 3.
Here is a link to proceed to Module 3: Conceptual Knowledge:
Module 3: Conceptual Knowledge