Misconceptions in School Math 2

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Fractions

Integers
 * 1) Calling 5/7 as &ldquo;5 out of 7&rdquo; encourages an image of 5 physically take out of 7. This can cause a mental block in visualizing fraction addition &amp; subtractions 				Encourage calling 5/ 7 as five sevenths.It also discourages a fraction to be seen as made of 2 separate numbers. We need to encourage seeing them as an integrated pair.
 * 2) Writing 6/4 as 3/2 is not &ldquo;reducing&rdquo; the fraction. 				It reduces the numbers (to the smallest possible values) with which the fraction can be written.Equivalent fractions are all equal, though they may look different.
 * 3) While computing, always convert a mixed number into an improper fraction 				It depends on the context. A problem like 2 &frac34; + 3 &frac14; does not need any conversion. Even a problem like 3 &frac12; - 1 1/3 does not need conversion.

Geometry
 * 1) Two negatives always make a positive 				This is true only for multiplication and not subtraction and addition</li></ol>

These are misconceptions which I learnt through my teachers who observed them in their classes.


 * 1) Straight Line 				Many students think that only horizontal or vertical lines are straight lines. This is possibly because most teachers draw straight lines on the board in this manner, possibly by force of practice.</li>Many also think that the opposite of straight line is a slanting line, which is not a geometrical object at all. This confusion could also arise due to the fact that in the corridors &amp; during PT exercises the term &ldquo;straight&rdquo; is used in a sense which is slightly different from its geometrical meaning.</li></ol>
 * 2) Right Angle 				Many students think that a right angle gets its name since the horizontal line of the angle is drawn to the right.</li></ol>
 * 3) Triangle 				When drawing a general triangle, a teacher usually draws an equilateral triangle which is a specific case.</li></ol>

Remediation


 * 1) It may be necessary for a teacher to use a rule at her class level. But as the grade level changes, the new teacher needs to revisit these &ldquo;rules&rdquo; and inform the students in advance that the rules need to be modified. It is best if the teacher can also explain why the rule needs to be modified.
 * 2) Teachers need to be aware of the possible misconceptions which students may carry when they come into their class. It is then necessary for teachers to clear them as and when necessary. If they are not explicitly brought out in the class, discussed and the deeper idea presented, the misconceptions may remain and hinder understanding of concepts built on these earlier concepts.
 * 3) In case of misconceptions related to some fundamental concepts, quick remediation is not possible. The root cause has to be located and retaught. If Place Value is not understood well in the lower primary classes, the student will have difficulty in mastering the 4 operations in the higher primary classes. Any amount of practice of problems will not solve the problem.
 * 4) It would be a good idea for teachers to document the common misconceptions that they see students having and then collectively work towards avoiding or remediating them.

< 30.5 Misconceptions in School Math 1 | Topic Index | 30.7 Unstated Assumptions >