Lesson Plan for Logarithms

Booppps Lesson Plan for a class in exponentials and logarithms

This is what I have in mind for presentation day:

1. Bridge (the hook) – The history that Ralph wrote

2. Teaching Objectives – Cover the laws of exponentials and logarithms and then as a class work through a problem together. If there is time have them work on another similar problem with less guidance from the teacher.

3. Learning Objectives – Have the students apply various log rules to solve two questions, displaying their understanding.

4. Pretest – Go over the rules of exponentials and logarithms which Ralph wrote down. Have them answer a few simple questions. Show that graph comparing log base 10, 2 and e noting key points and why they are important.

5. Participatory Acitivity – Work through one of those 2 questions I sent out.

6. Post Test – Have them solve the second of the 2 questions, time permitting.

7. Summary

Citizenship Education Math

CITIZENSHIP EDUCATION IN THE CONTEXT OF SCHOOL MATHEMATICS

by Elaine Simmt, UA

This paper suggests that the math classroom and the teacher has a role in citizenship education.

Mathematics teaches us The Art of Problem Posing*1 that can be applied to any field not just that of mathematics. So then the student of mathematics needs to see how this learned questioning can be used to make them better citizens by questioning events in their communities, provinces and nation. Every student questions the need to study mathematics which is answered by Keith Devlin with the quote "the study of mathematics is ultimately the study of humanity itself" (Devlin, 1998, 9).

Mathematics teachers have always tried to show the relevance of mathematics to the participation in students' everyday world. The NCTM articulates their position for the goals of mathematics education first for life, second for cultural heritage, thirdly for the workplace and fourth for scientific advancement.

"When students are occasioned by such prompts to act mathematically they specify and negotiate the problems they seek and the resolutions they come to. Because most problems that arise in our day to day living are not pre-specified but arise in our actions and interactions, active and critical participation in society requires citizens to specify and negotiate problems that are important and to evaluate resolutions."(ibid)

Unlike much of mathematics which when it is applied the correct answer is required, in citizenship there can be many answers that meet with the "truth" that mathematics teaches us to seek out and find.

Teaching students to identify and pose problems, to explain themselves in terms others can understand and to question the invisible structures of mathematics is key to developing informed, active and critical citizens. Mathematics has a role in citizenship education because it has the potential to help us understand our society and our role in shaping it. (ibid)

Mathematics should encourage all participants in our society to think and solve any problems that arise by questioning and conversation with which others can understand, and solutions that are fair to all.

The mathematics teacher has a new role that dates back to the ancient Greeks and that is to teach our students how to think and solve problems on both human and academic levels.


1. The Art of Problem Posing by Stephen Brown and Marion Walter, Routledge 2005

References

Devlin, Keith. 1998. The language of mathematics: making the invisible visible New York: W. H. Freeman and Company.

The Art of Problem Posing

This book presents some very interesting views that could be used to gain insight into any problem by starting out with Level zero with an hypothesis of What If?

This level should be able to be used by all levels of mathematics students from K - 12 and beyond.

The next stage is to list all the attributes that make up level zero, the given hypothesis. Attributes
are simply a thorough listing of what is given in detail, such as powers,+,-,=,>,<, and what some people might say is obvious.

Level 2 is to review all the attributes and ask, What If Not?, that is what if this were not true. As you ask this question things may open up and change the view of your original problem. This level may require higher thinking and would be excellent to pose to all your students K-12 to see how they are thinking. You may find some wonderful insight from the younger grades as they do not find a predisposition in their thinking.

This whole new way of looking at the problem from a different perspective may now cycle into some new attributes for each what-if-not question asked about the previous level attributes. This expansion and cycling will expand the future avenues of investigation that you may wish to pursue. To pursue these may require higher level mathematics and challenge even the brightest students.

This explosion in questions can take you off track so it is important to go to level 2 and then to return to solve the original question and then to pursue the other avenues. This procedure can be cycled over again into level three questioning of ,what -if and what -if not until you see no further sensible questioning.

Now all your questions need to be analyzed and answered to see the many possibilities that you have created for you to investigate which is level 4.

Your hypothesis started out so simple and manifested itself into a network of possibilities. Choose carefully the pursuit of these addition direction to analyze as you must not loose site of your original objective.

This method of what if and what if not can be very powerful in uncovering new ideas, but it can also be a huge consumer of your time. Choose wisely and prioritize those additional directions that you may wish to analyze, so that they do not distract you from the current work at hand.

The Art of Posing Problems

Why did you not look at x^2 +y^2 = z^2 for z = to discrete values starting at 1, then this is the formula for what geometric shape other than a triangle? Unit circle is on what axis?

Can this be the formula for any other conic shapes? On what axes?

Should the domain be divided into various groups to get discrete, continuous, less than zero, greater than zero, equal to zero for each of the x, y, and z axies?

Can we assume things based on our audiences level of mathematics?

Looking back to this being Pythagorean then should it be grouped as above?

Could this lead into Trigonometry?

Can the solver be correct if they only solve part of the possibilities, the ones which they specified?

Similarly if one solves more than what they think was asked is this a bonus?

We are mathematicians not lawyers, can we still have fun?

Baker at Best is Best

I never thought that I would be writing to you ten years after having helped me through Math 11, but a dream of mine has come true and I wanted to say thank you.

You were relentless in helping me to solve why mathematics seemed so difficult to me and yet you discovered the many bits and pieces that I did not understand and made the pieces fit together like a jigsaw puzzle to create a whole understanding that stayed with me throughout the rest of my schooling.

Think and you will solve, stuck in my mind and your constant questioning how things worked and were there other ways to get to the other side of a problem, kept popping up in my mind these past years as I continued my educational journey.

The day has come where I would like to share the joy of this day with you and invite you to be there with me when I graduate with my PhD. Thank you for believing that I could do math by thinking through the challenges and getting to the other side of every problem, you were the greatest math teacher that I ever had!


Today I have to write to you to tell you how much work you have made me do these past ten years, checking and double checking recalling the relationships, functions, sines, and cosines. Making me work hard at those logarithms and exponents and drawing those endless graphs that you found meanings in and your making me try to visualize. Today all those boring details that I hated in grade 11 that made me hate you so, have helped me to land the first manned mission on Mars.

Students may love you or hate you for making them work hard and set their standards of achievement high, but later in life they will see that it will pay off.