First-Grade students should not figure out facts as needed by finger counting. It eats up valuable working memory space and is a bad habit. Instead, they should memorize single-digit number facts to avoid cognitive load when solving problems. Ton de Jong writes, "The basic idea of cognitive load theory is that cognitive capacity in working memory is limited so that if a learning task requires too much capacity, learning will be hampered. The recommended remedy is to design instructional systems that optimize the use of a [very limited] working memory capacity and avoid cognitive overload." (Also, any classroom distraction increases the cognitive load in working memory, so it is important that students focus and pay close attention in class which is much more difficult when students sit in small groups facing each other.)
Cognitive load indicates the amount of mental effort needed in working memory. For example, if a student has automated 5 x 7 = 35 in long-term memory, then, as needed, it pops into working memory effortlessly. But, when the student needs to figure out 5 x 7 each time it is needed in working memory, then the mental effort or cognitive load increases and the cognitive capacity shrinks. Learning is impeded. The goal is to get the important stuff (i.e., the fundamentals) into long-term memory, which requires practice-practice-practice. Students should overlearn the basics of arithmetic and algebra.
Learning the standard algorithms of arithmetic in the primary grades is a key step. The standard algorithms organize and simplify place value and apply single-digit number facts. These fundamentals must be in long-term memory to solve problems and perform arithmetic well.
In other words, the student hasn't learned 5 + 7 = 12 because he can't remember it. Learning is remembering from long-term memory. You don't want kids to work it out each time, which is the essence of constructivism, discovery learning, and other minimal guidance approaches that are inefficient.
To reduce cognitive load when solving a problem in math, students should have automated single-digit number facts and standard algorithms as early as possible (Grades 1-3). Working Memory space is very limited.
Human processing power in working memory is limited, so it is important to decrease cognitive load as much as possible when students deal with the demands of solving a math problem. Essential factual and procedural knowledge should be automated in long-term memory "leaving room to attend to the details of the problem."
Math problems should be stated clearly without extraneous information that increases the cognitive load in working memory. Requiring students to show different ways to find a solution increases the cognitive load in working memory.
Sweller writes, "Providing unnecessary information can be a major reason for instructional failure."
Don't permit 1st-grade students to count on their fingers. It's a bad habit. After the 1st month of school, the number line and charts should be removed, too. Kids should memorize the single-digit addition facts, not calculate them as needed on their fingers or a number line.
Note: The discovery and problem-solving approaches, which are commonplace, are not a good learning stratagem compared to explicit teaching and worked examples.
Also, there are ways to move working memory information to long-term memory via repetition, imitation, and practice. Students must drill to develop skill.
In summary, not knowing the single-digit number facts for instant recall or the standard algorithms, for example, may create a cognitive load that often interferes with solving problems and learning.
To Be Revised
Last update: 10-1-17, 10-4-17
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