- Title: A Study of Students’ Readiness to Learn Calculus
- Authors: Carlson, Madison, and West
- Access the original paper here
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Paper summary
This research article investigates the readiness of college students for calculus, revealing significant weaknesses in foundational knowledge and reasoning abilities. The authors developed the Calculus Concept Readiness (CCR) instrument, a 25-item multiple-choice test, to assess these areas and predict student success in calculus. Analysis of CCR results from a large sample of students demonstrates a strong correlation between CCR scores and calculus grades, highlighting specific precalculus concepts where improved instruction is needed. The study uses both quantitative data from administering the CCR and qualitative data from student interviews to identify these weaknesses. The CCR taxonomy details the reasoning abilities and understandings assessed by the instrument, emphasizing the importance of covariational reasoning and a process view of functions.
What are the key implications for teachers in the classroom?
Teachers should assess prerequisite knowledge because it:
- Identifies gaps in student understanding so that instruction can be adjusted accordingly. For example, if students do not have a strong understanding of functions, they will struggle to understand calculus concepts that build upon this foundational knowledge.
- Improves student learning and preparation for more advanced coursework. The Calculus Concept Readiness (CCR) instrument is a tool that can be used to identify areas where precalculus instruction can be improved to better prepare students for calculus.
- Can be used to place students into appropriate courses. By assessing students’ prerequisite knowledge, teachers can ensure that students are placed in courses where they will be successful.
- Predicts student success in future courses. Studies have shown that students who score well on the CCR instrument are more likely to earn higher grades in calculus courses.
The CCR instrument is a valuable tool for assessing prerequisite knowledge for calculus. It assesses a variety of foundational understandings and reasoning abilities that are essential for success in calculus, including:
- Covariational Reasoning
- Understanding the Function Concept
- Proportional Reasoning
- Angle Measure
- Sine and Cosine Functions
The CCR instrument can also be used to identify areas where precalculus instruction can be improved. For example, the study found that many students did not have a strong understanding of angle measure or the sine function. This suggests that precalculus courses should place more emphasis on these topics.
Overall, assessing prerequisite knowledge is essential for ensuring that students are successful in mathematics courses. By identifying gaps in student understanding and providing targeted instruction, teachers can help students develop the foundational knowledge they need to succeed in more advanced courses.
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These data in combination with our examination of the percentages of correct CCR answers further supports that many student are taking and passing first semester calculus with severe deficiencies in their reasoning abilities and knowledge base
