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Even though I am a high school algebra teacher, I have decided to go back and spend some time trying to get students to understand fractions and to stop thinking of them as the monster of mathematics. I especially think this is important, because fractions are such a real world skill. So this is what I think will happen as we go through the stages.
Unconsciously Incompetent–The students have no true understanding of what a fraction actually is, what it represents.
Consciously Incompetent–The students begin to gain an understanding of what a fraction is (a part of a whole), but still have no idea how to do math with fractions, but now they start to see that they don’t really have any idea.
Consciously Competent–Through practice with manipulatives and visuals, students gain an understanding of fractions and learn how to begin do math with fractions.
Unconsciously Competent–The students can now look at the fractions and understand concepts such as a fraction of a fraction is a smaller number than the original fraction.
Consciously Masterful–Students have become comfortable working with fractions and are now ready to start the process over with mixed numbers.