The calculus concept inventory: a psychometric analysis and implications for use

Gleason, Jim; Bagley, Spencer; Thomas, Matthew; Rice, Lisa; White, Diana

doi:10.1080/0020739x.2018.1538466

Cited by 9 publications

(10 citation statements)

References 34 publications

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“…After this study was undertaken, Gleason et al (2016) published a psychometric analysis outlining weaknesses in the validity of the CCI to measure conceptual knowledge in calculus. Their findings explain that usage of terminology (e.g., "derivative") and notation (e.g., f'(x)) in the CCI items may afford an advantage to students who have already seen calculus.…”

Section: Methodsmentioning

confidence: 99%

Spatial Training and Calculus Ability: Investigating Impacts on Student Performance and Cognitive Style

McCunn

Cilli-Turner

2020

JERAP

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Undergraduate calculus is a foundational mathematics sequence that previews the sophistication students will need to succeed in higher-level courses. However, students often struggle with concepts in calculus because they are more abstract and visual than those in other foundational mathematics courses. Additionally, women continue to be underrepresented in the STEM fields. This study builds on previous work indicating a malleability in spatial ability by testing whether improvement occurs in students’ spatial and mathematics ability after implementing spatial training in calculus courses. The researchers also measured associations between spatial training and self-reported cognitive style. While spatial training did not significantly improve calculus and spatial skills, the researchers measured impacts on the psychological correlate of cognitive learning style. This is important as non-spatial cognitive preferences can result in students not recognizing the dynamic information encapsulated in graphical images, which is a large component of calculus. These results may have practical implications for teaching calculus at the undergraduate level and may, with further research, help to narrow the gender gap in the STEM fields.

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Section: Methodsmentioning

confidence: 99%

Spatial Training and Calculus Ability: Investigating Impacts on Student Performance and Cognitive Style

McCunn

Cilli-Turner

2020

JERAP

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“…The objective was to have a tool for population-scale comparisons of samples of responses from students who experiences two different modes of instruction. There has been very limited work on the validity analysis of Epstein's Calculus Concept Inventory, but there are no other calculus concept inventories at this time (Gleason et al, 2015(Gleason et al, , 2018. Carlson and collaborators developed a Precalculus Concept Assessment and a Calculus Concept Readiness instrument, both focused on precalculus concepts (Carlson et al, 2010(Carlson et al, , 2015.…”

Section: Introductionmentioning

confidence: 99%

“…Carlson and collaborators developed a Precalculus Concept Assessment and a Calculus Concept Readiness instrument, both focused on precalculus concepts (Carlson et al, 2010(Carlson et al, , 2015. Gleason et al (2018) critiqued the Calculus Concept Inventory, concluding that their data, from 1800 students enrolled in Calculus 1 courses, were consistent with a unidimensional model but expressing concerns about its content validity and reliability. The focus in their analysis was not on the comparision of alternative modes of instruction, which was the reason for which the inventory was developed.…”

Section: Introductionmentioning

confidence: 99%

“…There has been very limited work on the validity analysis of Epstein’s Calculus Concept Inventory, but there are no other calculus concept inventories at this time ( Gleason et al. , 2015 , 2018 ). Carlson and collaborators developed a Precalculus Concept Assessment and a Calculus Concept Readiness instrument, both focused on precalculus concepts ( Carlson et al.…”

Section: Introductionmentioning

confidence: 99%

“…, 2010 , 2015 ). Gleason et al. (2018) critiqued the Calculus Concept Inventory, concluding that their data, from 1800 students enrolled in Calculus 1 courses, were consistent with a unidimensional model but expressing concerns about its content validity and reliability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Development of the BioCalculus Assessment (BCA)

Taylor¹,

Bishop

Lenhart

et al. 2020

LSE

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We describe the development and initial validity assessment of the 20-item BioCalculus Assessment (BCA), with the objective of comparing undergraduate life science students’ understanding of calculus concepts in different courses with alternative emphases (with and without focus on biological applications). The development process of the BCA included obtaining input from a large network of scientists and educators as well as students in calculus and biocalculus courses to accumulate evidential support of the instrument’s content validity and response processes of test takers. We used the Rasch model to examine the internal structure of scores from students who have experienced calculus instruction in the two methods. The analysis involved three populations (Calculus 1, Calculus 2, and Biocalculus) for which the Calc 1 and Calc 2 students were not exposed to calculus concepts in a life science setting, while the Biocalculus students were presented concepts explicitly with a life science emphasis. Overall, our findings indicate that the BCA has reasonable validity properties, providing a diagnostic tool to assess the relative learning success and calculus comprehension of undergraduate biology majors from alternative methods of instruction that do or do not emphasize life science examples.

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Concept maps as assessment for learning in university mathematics

Evans

Jeong

2023

Educ Stud Math

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A concept map is a visualisation of a group of related concepts with their relationships identified by directed arrows, which can be viewed as an externalisation of a schema encoded in a learner’s long-term memory. Concept maps have become popular learning tools in various educational settings. However, the existing research has not fully explored the effectiveness of concept mapping as a learning tool nor analysed its utility as an assessment tool in mathematics. This study reports on the implementation and evaluation of a novel assessment, concept mapping, in a university mathematics course (N = 219). We investigated relationships between concept mapping performance and two major outcome variables: academic achievement and assessment self-efficacy (a two-factor measure comprising Comprehension and Execution and Emotional Regulation). Hierarchical multiple regression showed that concept mapping performance explains a statistically significant amount of variance in both the final exam scores and the Emotional Regulation factor of assessment self-efficacy after accounting for other conventional coursework assessments. The explained variance in the final exam suggests that concept mapping used as an assessment tool can detect and evaluate learners’ distinct capabilities that are not discerned by conventional assessments. Hence, concept mapping’s potential to assess conceptual understanding warrants further investigations. Moreover, the association with the emotional regulation efficacy measure suggests that concept mapping as a learning activity involves more positivity about the ability to succeed in facing challenges than a typical assignment. This potentially indicates more perseverance and effortful learning while actively engaged in meaning-making and the type of relational reasoning elicited by concept mapping.

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The calculus concept inventory: a psychometric analysis and implications for use

Cited by 9 publications

References 34 publications

Spatial Training and Calculus Ability: Investigating Impacts on Student Performance and Cognitive Style

Spatial Training and Calculus Ability: Investigating Impacts on Student Performance and Cognitive Style

Development of the BioCalculus Assessment (BCA)

Concept maps as assessment for learning in university mathematics

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