Lesson proposition
Lesson plan for Grade Six
Lecture Hall [Red 301]
Teacher : Hosomizu Yasuhiro
Research Theme

Feel For the New Way of Teaching Mathematics – Proposition forDeveloping Lessons As Drama Serial

1. Subject : the mystery of numbers and figures
2. About the research theme
Is problem solving learning becoming a mere shell? The problem solving learning thatshould be completed by only one lesson, the learning which must have a “goal” at thebeginning, and a “summary” at the end. Under the situation of a growing attainment
gap happens in the classroom, saying “must do” is nothing else but a sign of mere
shell.
In recent years, big value has been putted on making students “able to do” and“understood”, and researches are focused on the teaching method for that. There are
only a few lessons seeking for the “essential interest of mathematics”. And as
everyone is aiming at developing lessons after the manual, lessons which can impress
the students are becoming fewer and fewer. Now is the time to change the concept ofteaching from developing “able to do” and “understood” lessons to developing “lessonsfor appreciating the merit and beauty of mathematics, the pleasure of thinking andexpressing”(1) Proposition for a new way of developing the problem solving learning
When making a lesson plan, first of all I will reveal the “objective”. Then I will thinkof the “summary” which could match that objective. That is to say, reveal the ability
that you would like to be acquired by the students in this lesson and set up the“summary”. The “summary” is not only about the knowledge, understanding and skill,
but also about the way of thinking and the attitude. (Make clear that what is thefoundation and what is the objective.) Then, think of the teaching materials which
could lead the students to do that “summary”. Of course we should develop teachingmaterials which are close in the objective, but we should also devise the way ofpresenting the materials in order to make students willing to tackle the problems bythemselves. (Develop the teaching materials, problems and devise the way ofpresenting them.) After that, think of how to develop the lesson from presenting theteaching materials to the summary. Think about the “introduction, development, turnand conclusion” so as to create lessons which could appreciate “the merit and beautyof mathematics, the pleasure of thinking”. (Devise the way of developing the lesson.)
The foundation of these ways of developing lessons is the problem solving learning.
However, to meet the actual condition of students and the situation, the ways ofdeveloping lessons is always being devised and changed. As a result, several effective
ways of developing lessons have been recognized.

・develop learning completed by only one problem
・develop learning like a drama serial
・develop learning for concept acquisition
・develop learning for proficiency
・develop learning for bringing up the ability of application
Mathematics is interesting. Its true nature is full of mystery and beautiful. To makestudents appreciate it, I am willing to develop the way of teaching and spread toothers. This lesson is based on the way of developing lessons like drama serial.
Following are the points I kept in mind when developing this lesson.
(2) Treat the development of a lesson which could raise inductive thought, deductive
thought and the thought of analogy as one packLet the students to find the sum of three consecutive numbers on the calendar. Thenthe rule will come into view (inductive thought). Make them think why the rule exists(deductive thought). And use “if, …” to extend the problem and solve it(thought ofanalogy). I wish the students would feel enjoyable during these activities of thinking.
(3) Let students appreciate the delight of inquiry while developing the lesson likedrama serial
After solving one problem, finish the first lesson just at the point that extended stage
has been showed. With the summary of this problem, next problems come into being,
so we could finish the lesson with the students’ willingness to continue. Students
could appreciate the delight of inquiry which is difficult to appreciate in the learningcompleted by only one lesson.
(4) Attach importance to the activities of writing, reading and transforming
mathematical expressions
If students could explain clearly by using figures, symbol, expression, and the rules ofcalculation, along with the knowledge which has been learned, they would be able
perceive and appreciate the merit and beauty of mathematics. Moreover, as thisperiod of time is connected with secondary school, I would like to pay attention to thefollowing abilities of students.
・ability to write, read and transform mathematical expressions
・ability to use symbol・ability to apply the rules of calculation
・ability to explain deductively(5) Create situation for extension, make students able to appreciate the delight ofapplication
I would like to make sure how the students would extend the situation, whether they
could apply what they have learned to solve the problem, and whether the students
feel enjoyable through these activities.
3. Lesson plan
Although I can also design a special unit with several lessons like “expression andcalculation”, “symbol and expression”, I set the topic as “the mystery of numbers andfigures” for this special situation.

4. Learning for this lesson(1) Objective
・Through the activity for finding the rule of calendar problem and thinking of thereason of its existence, develop students’ abilities to think inductively and deductively,
and make them able to enjoy the activities of thinking and inquiring.
(2) Development
learning activities
1. have a clear grasp of the problem
What is the sum of three horizontallyconsecutive numbers on the calendar?
2+3+4=9
10 + 11 + 12 = 33
the answer is the multiples of three-“Really?”-“Absolutely?”notes of teaching
・Make the students grasp the problem byhiding the three numbers on thecalendar.
・ Let the students to write down thethings that they realize. Make sure they
use the right words.
・ Usequestions
like“really?”,“absolutely?” to bring out the deductive
thought like “because, …”.

2. think of the reason that the answer is ・If various expressions are created by thestudents such as using symbol or using
multiples of threemathematical expression, display them to-“if the first number is n, …”
the hole class.
n + (n + 1) + (n + 2) = n × 3 + 3
・Pick up the mathematical expression,-“if the second number is n, …”
make the students able to realize the(n - 1) + n + (n + 1) = n × 3
merit in explaining with mathematicalexpression, and develop the ability toapply it through the activity of reading
mathematical expression.
3. review what has been learned in thislesson and create new problem bychanging some conditions①three → four consecutive numbers②horizontally → vertically consecutive
numbers③calendar→
numbertable,
multiplication table

・Review activity 1 and 2
find the rule → think of its reason
write, read and transform mathematicalexpressions
・ Set up a activity of creating new
problem by changing some conditions of
the original problem, using “if, …”.
・ Make the students have theirperspective of new problems and solve
them in next class.