Three exponential improvement of instructional design case

Abstract: The in-depth study and understand the basis of new curriculum, the paper discusses three cases of teaching instructional design during the exponential function, how to improve the introduction of new courses, multimedia use and the nature of the discovery process exponential function and the corresponding teaching.

Keywords:: exponential function; instructional design; teaching cases; multimedia; effective teaching


Exponential function is one of the key high school Mathematics, from the teaching requirements, first understand the definition of exponential function; the second is master of the exponential function and nature of the image. The following is the author of the open teaching of exponential improvement of three instructional design .


Case I: Improvement of the introduction of new courses

(A) original design
1. Over the old to know:
�� function y = x is the domain of
2. The introduction of new lesson: Teacher asks: function y = () with the function y = x, what is the difference from the formal point of view? Health A: From the formal point of view, the former index is the independent variable, the latter base is the independent variable. ( the introduction of topics)
(B) improve the design
1. The creation of situations: Some people say that the piece of paper folded 50 times since the thickness of the distance from Earth to the Moon more than you think possible? Set for each thickness of the White 0.01mm, the distance is known about the Earth to the Moon to 380000 km.

Fold the layers y and fold the number of x as a function of type that? Based paper's original area of 1, on the folded paper the size of z and fold the number of x what is the relationship? (Y = 2x, z = () x)
2. To ask questions: Teacher Q: Can you find y = 2x, z = () x in common?
Students to think a moment, the teacher prompts: from form, have in common? And marked with red chalk index x.

Health A: The index x is the independent variable, base is greater than 0 and not equal to a constant. (To introduce topics)
(C) Teaching Reflection
Kailov's "Five Steps" Teaching Theory: "over the old - into the new lessons - teaching a new lesson - consolidation - operation" is still deeply influence our teaching. But, if they so rigid, it becomes rigid and programmable. we always liked school, said: "Today we learned ... ...." teachers do not say, do not ask students and teachers how to say, the students how to learn. We know that Mathematics comes from life, but also used in practice. in the original design, the first grant of review with the new knowledge-related content, and then from the actual introduction of new courses, in line with the teaching schedule, so mathematical about Mathematics, seems boring, it is difficult to mobilize the students to learn. To this end, a sense from the students interested in starting an instance of life, causing students to pay attention and controversy, the teacher re-creation of the actual problem situation, to stimulate the students interest in learning, firmly attracted the attention of students and enhance the students desire for knowledge, and strengthen the students inside learning needs, skillfully into a new lesson.


Case II: Improved use of multimedia

(A) original design
1. Computer mapping: Teachers with a multimedia presentation y = 2x, y = () x of the mapping process.

2. Observation guess: Teachers guide students to observe y = 2x, y = () x of the image, the image y = 3x guess the shape.

3. Computer Validation: teachers make the Geometer's image y = 3x, validation conjecture.

4. Induction guess: from specific to general, given the exponential function of the image is divided into 01 categories, and with a multimedia presentation of their image features and properties.

(B) improve the design
1. Student drawing: under the guidance of teachers, students grouped by geometry as y = 2x, y = () x of the image. Then, on the Computer for students to y = 3x, y = 5x y = 10x, y = 0.2x, y = 0.7x and other functions of the image, and change the shape of the image to be observed and discussed.

2. Guess Shape: to enable students to guess the function y = 8x, y = 0.3x image shape, students discuss and list the relevant observation conclusions.

3. Group Inquiry 1: The general exponential function generally have several types of images (some movement)?
4. Group Inquiry 2: What were the conditions to meet the exponential function of the image is roughly in Figure 1, Figure 2?
5. Computer Validation: by geometry as y = ax (a> 0 and a �� 1) the image, any changes in the value of a to demonstrate the impact of the end of the image changes.

(C) Teaching Reflection
Original design, multimedia presentation on the suspect, the only play the role of a verification reflects the purpose of Computer-aided instruction can not be a bit superfluous, has become a superfluous.

Improvements, in accordance with the "hands-on - the creation of situations - Observation guess - verified proof of" the idea of design, the first computer mapping, for students to observe, exchange the creation of situations; and then guide the students in-depth and meticulous observation of the image, students in each debate, discussion democratic process of sharing, listening to others, sharing of Research results, the image at the two suspect cases; the end, and then verify the conjecture of multimedia. This rule designed to meet the student's knowledge and habits of mind, stimulate the intellectual curiosity of students, enhance the learning of self-confidence, assertive personality of students, successfully solved the difficulty of teaching.

We use computer-aided teaching, do not forget to "assist" the word, assisted in no difficulty at the multimedia teaching, supporting the idea, while not for use with multimedia and multimedia. Reposted elsewhere in the Research Papers Download http: / / www.hi138.com Case III: the nature of exponential improvements in the discovery process

(A) original design
1. Student mapping: Teachers for the y = 2x image for demonstration. And then the students imitate as y = () x of the image, to consolidate the mapping method.

2. Computer presentations: Teacher's multimedia presentation y = 2x, y = () x of the mapping process.

3. Observed characteristics: teachers guide the students to observe the characteristics of the two images, and extended to the general case.

4. Inductive nature: According to the image features and write their properties.

(B) improve the design
Use of multimedia in front of students into groups to make y = 2x, y = () x, y = 3x, y = 5x, y = 10x, y = 0.2x, y = 0.7x and other functions on the basis of the image, teachers guide students to observe discussion, the nature of induction obtained.

1. Self-observation: the general exponential function, which features the image?
2. Group Discussion: Students group discussion, show the results of the discussion. In addition to the general characteristics of the image is obtained, it is worth mentioning is that some students also speak of the function y = 2x and y = () x in the image on the y axial symmetry and other features.

3. Inductive nature: According to the image features and write their properties.

4. For the diagram: According to the nature of exponential function, teachers allow students to y = 8x, y = 0.6x diagram of the image such functions.

Teacher: a perceptual observation and conjecture does not mean that conclusions be correct, but also a rational proof of ... ...

(C) Teaching Reflection
New curriculum standards that: too much emphasis on curriculum implementation should be changed to accept learning, rote, mechanical training of the phenomenon, promote active learning, willing to explore, eager hands, to develop students the ability to collect and process information, acquire new knowledge, analysis problem-solving skills and the ability to exchange and cooperation. Therefore, teachers should study the process of discovery, exploration, Research and other cognitive activities exposed, the learning process become more of the students identify problems, Research questions and problem-solving process.

Focus on these two designs for students to engage in meaningful mathematical activities are related to exploration activities and the students frequently used methods, such as from specific to general, and then from the general to the specific, analog, Lenovo, guess so.

Original design in actual teaching, activities, lack of internal connections and constraints of teachers, activities, single, students draw two types of images seem more rigid, and then study the general case seems to come "suddenly" from the exception to the general situation and not play a bridging role for extradition, the formation of a cognitive difficulty. This design does not really play the main role of students, is still the teacher dominates the classroom, holding students to take, or teaching knowledge, teaching materials, is a dominant teaching mode.

Improvements, changes in teaching methods, teachers gave up full-led initiative to learn to students, by their own to observe, to find, in the student exchange, seminars, interactive process, the students to observe in-depth and active thinking , creative. the role of teachers was students partners in student cognitive learning, interaction with students to guide students, and actively concerned about, listen to student exchanges. This rule designed to meet the student's cognitive and thinking habits, for students to create a safe psychological environment, students learn very well the nature of the exponential function, and the students feel that these ways of thinking is very natural, you can Xuedao Shou and to be able to apply, for the future study made the necessary groundwork This is a typical teaching guide.

Students are masters of learning, independent learning is their natural right to enforce any rigid indoctrination and training of students are violated sovereignty.


References:

[1] Luo Wenjie. Exponential function of the instructional design [J]. Guangdong Education, 2007, (7) :205-207.

[2] Gao. Patterns of Modern Teaching [M]. Jinan: Shandong Education Press, 2003.

[3] Zhen Zhang. On some measures for improving classroom teaching [J]. School Mathematics, 2001, (8). Links http://www.hi138.com Research Papers Download