Procedural knowledge
From WikEd
This web page is focused on use of procedural knowledge for junior high age students with a primary focus on mathematical learning.
Contents |
Definition
Procedural knowledge is knowing how to control the revant factors for examing some phenomenon (Reber & Reber, 2001), performing a certain task or completing an activity. Procedure knolwedge also means knowing the method of manipulating a specific condition or the technique for implementing a task. This may include the procedures we use to do a science experiment, write an essay or solve a mathematical equation.
Procedural knowledge is often thought about as certain skills we possess, tasks we can complete or processes we are able to follow.
A skill typically refers to a specific set of steps performed in a faily strict order and, ideally, without much conscious thought. A process is a more general set of steps that is performed with more conscious thought and careful consideration of what needs to be done next.(Marzano, et.al.,1997 p. 49)
Use of Procedural Knowledge in the Math classroom
Procedures and processes are a big part of learning math. Many of the concepts we learn in math involve memorizing and following steps to get the correct answer. Basic addition involves a step by step process. [Problem solving] is a process. Solving an Algebraic equation involves following steps. As the students learn to complete basic math computations, they should be immersed in the processes they need to follow. The processes of the basic skills serve as building blocks for the future, more complex, skills they will learn. There are three phases of acquiring procedural knowledge, construct models, shape and internalize. (Marzano, et al, 1997. p. 93)
In the construct models phase, a model of the process to be learned is displayed and the steps involved shown. An math example could be working out a multi-digit multiplication problem. As the problem is being worked out, the steps should be discussed that are needed to complete the problem in a manner that is understandable to the learner. Work out the example, discussing or listing each step, so the learner has a model as a point of reference. Students can construct their own models and list their own steps, in their own words, which would demonstrate their understanding of the process.
In the shape phase, the process originally followed will be modified to make it better. Adjustments should be made to improve the process and make it more efficient to use. Some aspects may be added or dropped depending on what will make the process understandable to the learner. The learner may come up with ways of making the problem easier to solve and want to add to the steps they follow. In this phase it is important for the students to gain an understanding of the procedure they are performing.
In the internalize phase, the learner needs extensive practice in order to get to a level of "automaticity" or "fluency".(Marzano, et al, 1997. p.101). Certain skills need to be automatic, without having to think about what we are doing. Recognizing which basic math skill is being indicated by a mathematical sign should become automatic, not requiring much conscious thought. Other skills need to become fluent, requiring a thought process, but known well enough to perform them with ease.
Most mathematical concepts require the above phases to be repeated with additions to the knowledge base of the student. For example, when students originally learn long division they should go through the phases above. Then when they learn to do long division with the addition of decimal numbers, they will again need to go through the phases to allow for integration of the new knowledge. The process is made more difficult and should be repeated when the students do not reach mastery of the procedures they are to learn.
Interviews with teachers of other academic areas on use of Procedural Knowledge
Science Teacher
Mrs. Forbes teaches 6th and 8th grade Science. She predominately uses procedural knowledge in her Science classroom two ways.
1. The more obvious one is for the scientific method steps. There are different ways to present the scientific method, but for Jr. High age students, she has them follow a basic format which is used throughout the school year. They have to memorize the five basic steps; Problem Title, Hypothesis, Procedure, Results, Conclusion, and are tested on their knowledge of them. For use in experiments, she has printed sheets posted in her room and available for them to use. Inside the Procedure, Results and Conclusion steps, there are an additional set of steps to follow on each. So, there are procedures inside the overall procedure.
2. In Mrs. Forbes science class, the students are also expected to follow a set of procedures for mathematic problem solving. She uses this to teach force, velocity and other science/math related concepts. The steps to follow for problem solving are: Given (knowns, unknown), Formula, Substitute and Solve, Final Answer (Reasonable?).
Language Arts Teacher
Mrs. Reinhart teaches 7th grade Language Arts. She was able to come up with three ways she uses procedural knowledge is her classes.
1. When having her students identify different parts of speech, she has them cross out the parts which are obviously not what they are looking for. For example, when looking for the subject, she has them start by crossing out the prepositional phrases, then verbs, etc., until they are left with few things to choose from. She describes it as a "step by step process...like a puzzle." She tells her students if they follow the steps the correct way, they should get the assignment right.
2. Her students follow a procedure when writing an essay. She has them start by brainstorming their topic, outline, paragraphing, organizing the paragraphs, write the paper.
3. Mrs. Reinharts students use a certain process to improve [reading comprehension]. The students have bookmarks with the "steps" to follow and think about while reading to improve their comprehension of the story.
Depending on what the students are working on, Mrs. Reinhart puts the steps they are to follow on the board for them to review or copy to their notes. They are allowed to refer to the steps during the assignment, but she feels it is important for students to memorize the procedures for tests they may take.
Use of Procedure Posters in my classroom
I chose to incorporate this subject into the professional development plan I am doing this year for self evaluation. My class of sixth grade Math students will be creating a "procedure" poster for the subject areas we cover that step-by-step procedures can aide their learning. We started this process in the past week with procedures to follow for comparing decimal numbers. The kids were eager to help create the poster. From this activity I hope to find that better knowledge of the step by step procedures will help with comprehension.
Since originally starting the plan for the procedure posters, my students have created posters of the steps needed to add and subtract decimals numbers and multiply and divide decimal numbers. I found the addition and subtraction steps were beneficial, however the steps for multiplication and division did not help as much. I feel this is due to the lack of mastery of the basic skills of multiplication and division rather than the not knowing the procedures to follow.
Wikipedia Link
Wikipedia Procedural knowledge
Other Web-Sites
Encyclopedia: Procedural knowledge
Representation of Cognitive Skills
Math Skills Has a procedural knowledge based test with answers.
References
Reber, A. S., & Reber, E. (2001). The penguin dictionary of psychology (3rd ed.). London: Penguin Books Ltd, England.
Robert J. Marzano, Debra J. Pickering with Daisy E. Arredondo, Guy J. Blackburn, Ronald S. Brandt, Cerylle A. Moffett, Diane E. Paynter, Jane E. Pollock and Jo Sue Whisler, 1997, Dimensions of Learning. McREL (Mid-continent Regional Educational Laboratory), 2550 S. Parker Road, Suite 500, Aurora, Colorado 80014.
Testimonials
Procedures are definitely an important part of any classroom. In the band rehearsal room, there are procedures to learn many things. Students follow a procedure when they learn how to put together their instrument. A procedure is followed for learning a new piece of music. Procedures also govern how they practice their instruments outside of class, assuming that they actually practice! Some of these procedures, such as putting together the instrument or practicing, must become unconsciously done so as to become skill. Other procedures, such as reading a new piece of music, must remain procedures, and be done with much thought and consideration. Elizabeth Giger
Procedural Knowledge is fascinating. It is the type of knowledge that many students are unaware that they posess. I recall in Kindergarten, instinctively knowing that as soon as we entered the classroom, we put our coats away. We also knew that when it was time for naptime, we would get our milk and find our mats. Although children aren't aware that they hold this knowledge it is there. A prime example...tying the shoes. We practice and practice, and now, as an adult...it's instinct.
I have used procedure posters in my classroom as well. The procedural posters range from what to do when the morning bell rings to how to choose a book for independent reading. They serve as reminders for students. Sometimes I would just ask students to reread the posters to get them back on task. E. Elrick
In my math classes, procedures play an important role in the class running smoothly, as students know the procedure for asking a question, sharpening a pencil, taking notes, and completing homework. As for mathematical content, procedures are important in some mathematical processes such as simplifying expressions using the order of operations, but some teachers turn topics such as "equation solving" into a procedure with definite steps to be taken in a specified order. Equation-solving skill in which concepts need to be understood. Procedures can help in the process, but in an equation such as
2x + 8 = 32
where most students are taught to subtract 8 from both sides of the equation as a required first step, it may be helpful for the student to understand that both sides of this equation can be divided by 2 as a first step, resulting in
x + 4 = 16
which can then be solved by subtracting 4 from both sides. The concept is that the equation remains balanced, and there are certain procedures that we follow to ensure that it does. L. Wilkinson
