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Math Misconceptions and Considerations HSG-C.B.5

Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.

Which formula do I use to convert to radians? The formulas for converting radians to degrees and vice versa are easily confused. Misconception: Here the student used the wrong version of the formula to convert the degrees. Notice that the student completely dropped the degree measurements in the numerator in order to have an answer in radians.

What to do: Explain to the students that when they set up the formula they should be able to cancel out the old units because they are in the numerator and denominator when the proper formula is used. The result is an answer in the desired units.

Arc length and arc measure are the same thing After spending time working extensively with central angles, students have finally mastered the concept that the central angle is congruent to the intercepted arc. Yay! Now, the problem is that anytime they are looking at an arc length they assume that it’s measured in degrees. Misconception: Instead of finding arc length, this student found arc measure.

What to do: Point out to students that arc length is a fraction of the circumference. Students think that arc length is a degree measurement when in reality it should be measured in the same units (inches, centimeters, etc.) as the radius.

Vocabulary for mathematics isn’t that important Sometimes linking mathematics terminology to everyday vocabulary can really solidify a concept for students. Unfortunately, there are instances when this may cause a hindrance rather than help. Misconception: Sectors and segments are an example of this problem. In the English language, we often use these two terms interchangeably to mean a piece or part of something. What to do: As you are introducing new vocabulary to students, care should be taken to distinguish between these two geometric concepts. Additionally, as you talk mathematics in your classroom continue to use proper terminology (i.e., “point” instead of “dot”).