Thinking Conceptually General approaches The initial approach to this should be a recap of the work on indices. This forms the foundation of understanding of the work on logarithms. The work on the introduction of the exponential function should be done graphically so that it is clear how this function works. This graphical process can also be used to show the inverse function through its reflection in the line . This helps justify the impossibility of a negative value within the logarithm. With the work on indices reviewed, proving and demonstrating the laws of logarithms becomes a more natural process. There are a multitude of examples of modelling with exponential functions within many other subject areas, including physics, chemistry, biology, economics, geography, psychology. This is not an area that will ever run dry and provides a depth of applications to stimulate interest. Common misconceptions or difficulties learners may have The failure to link this work to indices often means that there is a failure to see the whole number values so that or just become calculated values. This then helps to justify the values of , why logarithms of numbers smaller than are negative and why it is not possible to find the logarithm of a negative number. Familiarity with the exponential graph helps to avoid students believing that can be have a negative value. If reduction to linear form is not clearly related to the equation of a straight line then the connection is not properly made and this becomes an incomprehensible process. The last section is not very different to growth and decay taught at GCSE and if this link is again made then it is not a difficult topic; it is not one that should ever stand alone as an add-on to the main course but as a culmination of all the previous skills.
Thinking Conceptually General approaches The initial approach to this should be a recap of the work on indices. This forms the foundation of understanding of the work on logarithms. The work on the introduction of the exponential function should be done graphically so that it is clear how this function works. This graphical process can also be used to show the inverse function through its reflection in the line . This helps justify the impossibility of a negative value within the logarithm. With the work on indices reviewed, proving and demonstrating the laws of logarithms becomes a more natural process. There are a multitude of examples of modelling with exponential functions within many other subject areas, including physics, chemistry, biology, economics, geography, psychology. This is not an area that will ever run dry and provides a depth of applications to stimulate interest. Common misconceptions or difficulties learners may have The failure to link this work to indices often means that there is a failure to see the whole number values so that or just become calculated values. This then helps to justify the values of , why logarithms of numbers smaller than are negative and why it is not possible to find the logarithm of a negative number. Familiarity with the exponential graph helps to avoid students believing that can be have a negative value. If reduction to linear form is not clearly related to the equation of a straight line then the connection is not properly made and this becomes an incomprehensible process. The last section is not very different to growth and decay taught at GCSE and if this link is again made then it is not a difficult topic; it is not one that should ever stand alone as an add-on to the main course but as a culmination of all the previous skills.
416786-section-1.06-exponential-and-logarithms-delivery-guide.docx