Frequency of use regarding the conceptions of differentials found of the analysis in the different textbooks
| . | Varian ( | Perloff ( | Wetzstein ( | Sydsæter et al. ( | Hoy et al. | Jacques ( |
|---|---|---|---|---|---|---|
| 1. Differentials as a mere sign for derivative or slope | 33.3% | 63.0% | 69.7% | 39.0% | 54.7% | 82.8% |
| 2. Differentials as an operator | 4.4% | 14.8% | 6.7% | 41.5% | 3.8% | 1.7% |
| 3. Differentials as shorthand for limits | 2.2% | 1.2% | 4.5% | 4.9% | 5.7% | 3.4% |
| 4. Quotient of differentials interpreted as a rate of change | 13.3% | 4.9% | 10.1% | 7.3% | 3.8% | - |
| 5. Quotient of differentials with discrete interpretation | 2.2% | 18.5% | 5.6% | 12.2% | 9.4% | 10.3% |
| 6. Differentials as symbols to be manipulated | - | 1.2% | 1.1% | - | 1.9% | - |
| 7. Differentials as variables in a linear approximation | - | - | 1.1% | 7.3% | 13.2% | - |
| 8. Differentials as infinitesimally small quantities | 8.9% | 1.2% | - | - | - | - |
| 9. Differential as a finite increment | 40.0% | 7.4% | 13.5% | 2.4% | 11.3% | - |
| . | Varian ( | Perloff ( | Wetzstein ( | Sydsæter et al. ( | Hoy et al. | Jacques ( |
|---|---|---|---|---|---|---|
| 1. Differentials as a mere sign for derivative or slope | 33.3% | 63.0% | 69.7% | 39.0% | 54.7% | 82.8% |
| 2. Differentials as an operator | 4.4% | 14.8% | 6.7% | 41.5% | 3.8% | 1.7% |
| 3. Differentials as shorthand for limits | 2.2% | 1.2% | 4.5% | 4.9% | 5.7% | 3.4% |
| 4. Quotient of differentials interpreted as a rate of change | 13.3% | 4.9% | 10.1% | 7.3% | 3.8% | - |
| 5. Quotient of differentials with discrete interpretation | 2.2% | 18.5% | 5.6% | 12.2% | 9.4% | 10.3% |
| 6. Differentials as symbols to be manipulated | - | 1.2% | 1.1% | - | 1.9% | - |
| 7. Differentials as variables in a linear approximation | - | - | 1.1% | 7.3% | 13.2% | - |
| 8. Differentials as infinitesimally small quantities | 8.9% | 1.2% | - | - | - | - |
| 9. Differential as a finite increment | 40.0% | 7.4% | 13.5% | 2.4% | 11.3% | - |
Frequency of use regarding the conceptions of differentials found of the analysis in the different textbooks
| . | Varian ( | Perloff ( | Wetzstein ( | Sydsæter et al. ( | Hoy et al. | Jacques ( |
|---|---|---|---|---|---|---|
| 1. Differentials as a mere sign for derivative or slope | 33.3% | 63.0% | 69.7% | 39.0% | 54.7% | 82.8% |
| 2. Differentials as an operator | 4.4% | 14.8% | 6.7% | 41.5% | 3.8% | 1.7% |
| 3. Differentials as shorthand for limits | 2.2% | 1.2% | 4.5% | 4.9% | 5.7% | 3.4% |
| 4. Quotient of differentials interpreted as a rate of change | 13.3% | 4.9% | 10.1% | 7.3% | 3.8% | - |
| 5. Quotient of differentials with discrete interpretation | 2.2% | 18.5% | 5.6% | 12.2% | 9.4% | 10.3% |
| 6. Differentials as symbols to be manipulated | - | 1.2% | 1.1% | - | 1.9% | - |
| 7. Differentials as variables in a linear approximation | - | - | 1.1% | 7.3% | 13.2% | - |
| 8. Differentials as infinitesimally small quantities | 8.9% | 1.2% | - | - | - | - |
| 9. Differential as a finite increment | 40.0% | 7.4% | 13.5% | 2.4% | 11.3% | - |
| . | Varian ( | Perloff ( | Wetzstein ( | Sydsæter et al. ( | Hoy et al. | Jacques ( |
|---|---|---|---|---|---|---|
| 1. Differentials as a mere sign for derivative or slope | 33.3% | 63.0% | 69.7% | 39.0% | 54.7% | 82.8% |
| 2. Differentials as an operator | 4.4% | 14.8% | 6.7% | 41.5% | 3.8% | 1.7% |
| 3. Differentials as shorthand for limits | 2.2% | 1.2% | 4.5% | 4.9% | 5.7% | 3.4% |
| 4. Quotient of differentials interpreted as a rate of change | 13.3% | 4.9% | 10.1% | 7.3% | 3.8% | - |
| 5. Quotient of differentials with discrete interpretation | 2.2% | 18.5% | 5.6% | 12.2% | 9.4% | 10.3% |
| 6. Differentials as symbols to be manipulated | - | 1.2% | 1.1% | - | 1.9% | - |
| 7. Differentials as variables in a linear approximation | - | - | 1.1% | 7.3% | 13.2% | - |
| 8. Differentials as infinitesimally small quantities | 8.9% | 1.2% | - | - | - | - |
| 9. Differential as a finite increment | 40.0% | 7.4% | 13.5% | 2.4% | 11.3% | - |
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