We use item response theory (IRT) to determine mastery based on responses to problems of varying difficulties.  The difficulties of problems are determined from a combination of

  1. How our team of expert mathematicians and teachers rate the questions and 
  2. The results of every student who has ever done those questions.

Using IRT also helps us find the best question to ask a student next in order to get the most information from their response. For example, as a student progresses to a higher mastery level they will receive more difficult questions.

Mathspace takes the IRT and applies a growth mindset lens. In order to motivate students to keep answering questions, we show them a mastery score only capable of increasing.  This way, students have 'seemingly' nothing to lose by answering questions.

If a student starts demonstrating mastery at a calculated IRT level significantly lower than their displayed mastery score (by answering questions incorrectly), Mathspace will intervene with the "helping hand" message.  Teachers will see the red exclamation point in the mastery dashboard.

Once a student has mastered a topic, if they decide to continue practicing they will cycle through all the questions in the exercise again with different numbers.

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