Math Misconceptions and Considerations HSS-CP.A.1-5
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Students rely on their own experiences to determine probability Lacking the prior knowledge necessary in mathematics, students rely on their own experiences to draw conclusions. Misconception: “I have never rolled 4 sixes in a row in my life, so the probability must be zero.” What to do: This may be a good opportunity to revisit experimental and theoretical probability with students. Posing questions such as “Just because it did not occur in your experiment, does that mean it will never happen?” Also, discuss with students the concept of the law of large numbers and how it can impact probability. Utilizing the probability simulator on a calculator can provide students with experiences that imitate repeated experiments that would be too time consuming otherwise.
Mutually exclusive versus independent events Probability has a lot of new terms that students must become familiar with and many words that have different meanings in a non-mathematical context. Misconception: Not having experience with the mathematical definitions of mutually exclusive and independent events, students may think that they are interchangeable when discussing probability. What to do: Expose students to problems where an experiment yields mutually exclusive events and independent events so that students can see that there is a difference between the two.
What’s a club? Many students do not have any experience playing with a deck of cards in this day and age. Misconception: Students improperly identify the sample space when using a deck of cards.
What to do: Involve students in activities at the start of the unit where they manipulate a deck of cards, determining various sample spaces (whole deck, red cards, clubs, face cards, etc.).