Module 4 – Procedure Using is a main design theory which will be applied to your next two CSTE Courses – Web Application and Technology Plan.
Case Study:
Your team should be working together to select a short procedure lesson which can be learned in less than an hour. Review the examples of “Principles for learning procedural skills” and “A sample Procedure Lesson” to complete the following tasks:
1. Identify all the steps, break them down to entry level, and write a generality that includes the goal and the steps at entry level.
2. Share the reasons why procedural tasks are important. References are needed.
Question #1:
ReplyDeleteStudents at my school struggle with every year and we are always looking teachers are always looking for resources. Teaching students to convert fractions to decimals is a linear procedure with no branching procedures or decision steps.
The learner will be able to convert a fraction to a percent.
1. Divide the numerator by the denominator
2. Multiply the answer by 100
3. Round the answer to the specified place value
4. Add a percent sign
Question #2:
Reigeluth (1999) states that we use procedures in almost everything we do. In mathematics it is agreed that procedural knowledge is important (though there is debate about whether conceptual knowledge or procedural knowledge comes first). The National Mathematics Advisory Panel in its 2008 report states that “procedural knowledge is also essential and is likely to enhance conceptual knowledge and vice versa”. Fractions are one area in which conceptual and procedural knowledge reinforce one another.
References:
National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: Department of Education.
Reigeluth, C. (1999). Principles for teaching invariant tasks. Retrieved March 19, 2012, from http://www.indiana.edu/~idtheory/methods/m2e.html
Most times in math, students need to follow steps (procedures) in order to arrive to a unique answer. This is evident as we often teach our students PEMDAS when simplifying expressions.
ReplyDeleteQuestion #1:
ReplyDeleteMath is a very procedural subject. Just about every lesson is about what steps are needed to solve a problem. There are also different ways and/or steps to get to the correct answer. For the same case study, converting a fraction to a percent, you can also write it as:
Step 1: Find a number you can multiply the bottom of the fraction by to get 100.
Step 2: Multiply both top and bottom of the fraction by that number.
Step 3. Then write down just the top number with the "%" sign.
It is the same steps, but worded in a slightly different way.
Question #2:
Procedural task analysis is useful because it helps "break a task into component parts, organize relationships between the parts of the task, and produce an appropriate representation of the task" (Barba & Rubba 1992). It helps chuck the information in bite-size manageable pieces. It is helpful to visual learners to make a flow-chart of the steps needed to take in order to solve the problem. Most students that I work with can see the big picture, but it is the small details/steps that they have difficulty understanding. Understanding procedural knowledge is the opposite of declarative knowledge (recall information). Teaching and learning procedural tasks helps the student understand the process instead of recalling the information.
Reference:
Barba, R. H. & Rubba, P. A. (1992). Procedural task analysis: a tool for science education problem-solving research. School science and mathematics. 92(4). 188-192.
I agree with you that teaching and learning procedural tasks help the students understand the process instead of just recalling the information. The tricky part is making sure they know when to apply the procedure. I think that is what is difficult about word problems. The kids sometimes are not sure which procedure to apply.
DeleteIdentify all the steps, break them down to entry level, and write a generality that includes the goal and the steps at entry level.
ReplyDeleteSteps for solving equations
I would instruct students to always try to solve equations in the order below.
Note: Most algebra problems only have some of the steps - not all those listed below.
First - get rid of any fractions
Second - get rid of any parentheses
Third - combine like terms to get all the variable terms together and the number terms together
Fourth - move all the variable terms by adding or subtracting (using the property of opposites) on both sides of the equal sign so the variable terms are all on one side of the equal sign
Fifth - move any number terms by adding or subtracting (using the property of opposites) on both sides of the equal sign so the number terms are all on the other side of the equal sign from the variable term
Sixth - if there is a number multiplied by the variable, get rid of it by dividing
Share the reasons why procedural tasks are important. References are needed.
Catrambone (1990) pointed out that more detailed instructions have the benefit of being definite and make the task easier to complete initially as they describe exactly what needs to be done to accomplish the task. Furthermore, procedural instructions are an important condition for determining learning and transfer.
Catrambone, R. (1990). Specific versus general procedures in instructions. Human-Computer Interaction, 5(1), 49-93.
Do you teach the kids a mnemonic to remember the steps? Is PEMDAS that you mentioned above part of these steps?
DeleteNo, I do not teach a mnemonic when solving equations. The reason is that the above steps are my preference of order of steps some may be interchanged. Another teacher may teach the steps in a different order and still arrive at the correct answer. However with PEMDAS regardless steps must be followed in order to get the correct answer.
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