![Mathematical Misconceptions
■ A misconception is the result of a lack of understanding or in many cases
misapplication of a rule or mathematical generalization
■ An the other hand, An error might be caused due to a misconception. Other factors
may include carelessness, problems in reading or interpreting a question and lack of
numbers knowledge (Spooner, 2002)
■ A misconception is “a mistaken idea or view resulting from a misunderstanding of
something.”
■ Certain conceptual relations that are acquired may be inappropriate within a certain
context. We terms such relations as "misconceptions." A misconception does not exist
independently, but is contingent upon a certain existing conceptual framework.
Misconceptions can change or disappear with the framework changes. [Pines, 1985]](https://image.slidesharecdn.com/pptonerrorsandmisconceptionsinmathematics-250131103902-398ed28d/85/PPT-on-Errors-and-Misconceptions-in-Mathematics-pptx-2-320.jpg)
![Ginsburg [1977] offers a number of observations
about errors
Ginsburg [1977] offers a number of observations about errors:
■ Errors result from unorganized strategies and rules.
■ Faulty rules underlying errors have sensible origins.
■ Too often children see arithmetic as an activity isolated from their ordinary
concerns. (many misconceptions and faulty thinking in algebra are related to
misconceptions and faulty thinking with arithmetic (e.g. fractions).
■ Children often demonstrate a gap between formal and informal knowledge.](https://image.slidesharecdn.com/pptonerrorsandmisconceptionsinmathematics-250131103902-398ed28d/85/PPT-on-Errors-and-Misconceptions-in-Mathematics-pptx-5-320.jpg)
PPT on Errors and Misconceptions in Mathematics.pptx
- 1. MATHEMATICAL MISCONCEPTIONS Dr Ibrahima Haneef Mathematical Misconceptions © 2023 by Dr Ibrahima Haneef is licensed under CC BY 4.0
- 2. Mathematical Misconceptions ■ A misconception is the result of a lack of understanding or in many cases misapplication of a rule or mathematical generalization ■ An the other hand, An error might be caused due to a misconception. Other factors may include carelessness, problems in reading or interpreting a question and lack of numbers knowledge (Spooner, 2002) ■ A misconception is “a mistaken idea or view resulting from a misunderstanding of something.” ■ Certain conceptual relations that are acquired may be inappropriate within a certain context. We terms such relations as "misconceptions." A misconception does not exist independently, but is contingent upon a certain existing conceptual framework. Misconceptions can change or disappear with the framework changes. [Pines, 1985]
- 3. Error An error takes place when a person chooses the false as the truth. When the actual result is different from the objective (erroneous result); when the procedure adopted is different from the accepted procedures (erroneous actions) erroneous conceptions might be hindering problem solving and producing irrational results. Errors are of various types and hence difficult to classify accurately.
- 4. How to remove misconception? ■ The misconception must be changed internally partly through the student’s belief systems and partly through their own cognition. ■ It is very important to recognize student misconceptions and to re-educate students to correct mathematical thinking
- 5. Ginsburg [1977] offers a number of observations about errors Ginsburg [1977] offers a number of observations about errors: ■ Errors result from unorganized strategies and rules. ■ Faulty rules underlying errors have sensible origins. ■ Too often children see arithmetic as an activity isolated from their ordinary concerns. (many misconceptions and faulty thinking in algebra are related to misconceptions and faulty thinking with arithmetic (e.g. fractions). ■ Children often demonstrate a gap between formal and informal knowledge.
- 6. Misconceptions about math — in general 1. Mathematics is incorrectly viewed as a collection of rigid rules and mysterious procedures that seem to be unrelated to each other and require total mastery with little or no understanding. 2. Mathematics is perceived by many to be difficult and demanding and is considered to be a subject in which it is socially acceptable to do poorly. 3. Mathematical thinking is regarded as essentially unimportant to people that do not actually "do" mathematics in their employment capacity. 4. The pervasive role of mathematics is underestimated in the world of everyday living.