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Teaching of Mathematics (EDU510)
Assignment I
Total Marks: 20
Lesson: 1-12 (Topics 1-78)
1. As a teacher responsible for teaching Mathematics to Elementary school children (ages between 10 to 12 years old), it is important to ensure that the teaching should be carried out in an interesting way. By using various instructional resources (Audio, Visual Aids), prepare a lesson plan to teach Algebra to 7th class students. (10)
Ans:
1. Subject: Math
2. Topic: Introduction of algebra
3. Grade level: 7th
4. Instructional objectives (use an action verb in a description of a measurable outcome)
Student will able to define a constant as a symbol having a fixed numerical value.
Student will able to recall a literal as an unknown number represented by a letter of an alphabet. To develop thinking and reasoning power in the students
5. Rationale: Algebra is one of the useful tools in mathematics .It is also use in mathematical statement to describe the variables relationship. Many problems of arithmetic simplified for the learner. It induces the power of analysis and a good instrument for mental training.
6. Resources: ICT for seeing the video, White board , white board marker , text book ,copy book where student write their notes, algebra worksheet for assessment to check their understanding
7. Procedure:
Focusing event: Teacher will write the word ALGEBRA on board and ask student. Have you ever listen this word before?
Teaching procedures: (Teacher will use discussion method and deductive method for this topic) after starter teacher will discuss lesson by asking questions what you know about this word. After asking question about the topic she will wait for their reply then she will explain ‘what is algebra?’ ‘Where this word comes from?’ She will give brief introduction of algebra with examples. Teacher will also discuss that arithmetic and alphabet is the combination of algebra by giving them examples: +, −, ×, ÷ .
1+3=--- , 5-2= , 7 × ----= 56
1+3= x , 5-2= y, 7 × a=56
She will also tell them that unknown variable is also use as alphabets.
Formative check: she will ask questions during the lesson to check their understanding. What is algebra? Where this word comes from? What is the use of algebra? Why we use algebra in math? What is Arithmetic? What are arithmetic operators? What is the relation of algebra and arithmetic and alphabets?
Student Participation: students will participate in discussion and also teacher will ask them randomly to solve questions
Closure: Teacher will summarize the entire lesson by asking different questions and ask students to write some examples on the board.
8. Assignment or Homework:
Find the value x, y and a
1. x = 2 +4 2. a × 3 =3 3. a + x + x=12 find the value of a
y = 6 -5 y =3 ÷ 4
9. Assessment: Teacher will give them worksheet for their assessment to check their understanding during the lesson.
10. Time allotted:45 minutes
2. When you work to teach a mathematical problem, would you prefer to have one teaching method which works or many methods which work for the problem? Explain in the light of teaching methods with some practical examples.
Ans: As a teacher will use many methods when teaching Mathematical problem. Because the demand of her job is to develop different methods or use different ways of teaching which benefit her students and make them successful. There are different methods that teacher use in different problem solving.
Lecture Method: It is the method of presenting the word picture of an idea; or the method of imparting information through a speech. Example: Teachers prepare the topic at home and just explain it in the class learners are the listeners only. Teacher solve all the question on board student just copy it.
Dogmatic Method: This method of mathematical knowledge observes a high standard of exactness. Example:find the area of square= l x b=?
L=5 b=9
Area of square=5 x 9 =45 ans
Inductive Method: It deals from concrete to abstract, particular to general and from examples to general rule. Example:
Deductive Method: It is opposite to inductive method. Here the learner proceeds from general to particular, abstract to concrete and formula to examples. Example:
perimeter of square=2(l+w)
2(3m+3m)=12m
Analytical method: It proceeds from unknown to known, ’Analysis’ means ‘breaking up’ of the problem in hand so that it ultimately gets connected with something obvious or already known. It is the process of unfolding of the problem. Example: If a/b = c/d, prove that ac −2b2 /b = c2 – 2bd/d
The analysis will start from the unknown part of the statement.
ac −2b2 /b = c2 – 2bd/d is to be proved true.
ac −2b2 /b = c2 – 2bd/d will be true
If acd−2b2 d = bc2 – 2b2 d
(Cancelling −2b2 d, which exists on both sides of the equation).
:. acd – 2b2d = bc2 – 2b2d will be true
If acd = bc2
:. acd = bc2 will be true if ad = bc
ad = bc will be true if a/b = c/d, which is known and true.
ac −2b2 /b = c2 – 2bd/d is also true.
Heuristic Method: The method involves finding out by the student, instead of merely telling of everything by the teacher. In this method the child is put in the place of a discoverer.
Synthetic Method: It is the opposite of the analytic method. In this method one proceeds from known to unknown. It starts with something already known and connects that with the known part of the statement. Example: If a/b = c/d, prove that ac −2b2 /b = c2 – 2bd/d
Synthetic Proof
a/b = c/d a/b – 2b/c = c/d – 2b/c
or ac −2b2 /bc = c2 – 2bd/cd
or ac −2b2 /b = c2 – 2bd/d
Hence the identity is proved.
Laboratory Method: Mathematics is a subject which has to be learnt by doing rather than by reading. Example:
The project Method: It is method of spontaneous and incidental teaching. This is learning by doing method. Students can learn by collaboration and association. Example: Providing a situation , Choosing and purposing , Planning of the project , Executing the project , Judging the project
Concentric Method: The method implies widening of knowledge just as concentric circles go on extending and widening.
Topical Method: It is the opposite of concentric method. Concentric method involves the breaking up of a topic into suitable portions, whereas topical method aims at keeping it intact
Math teacher always use different method for teaching math as every problem have different demand of teaching method some are simple and easy so teacher use deductive method or if problem if little lengthy and need more details to make student understand clear so she will use analytical method. Actually it’s depending on the problem that which method will use to solve it.
1:Deductive method example:
If the length and width of a rectangle is 8m & 6m respectively then find out the perimeter of rectangle?
Solution: learner will use the formula for solving this problem
Perimeter of rectangle =2(l + w)
= 2(8m + 6m)
= 28m
.
2:Analytic Method Example:
if a/b = c/d then prove that ac =3b2 / bc = c2 + 3bd / dc
Solution: Proving for this quotation we will do analysis to unknown
Unknown is ac+3b2/bc = c2+3bd/dc
ac+3b2/b =c2 +3bd/d
d(ac+3b2)= b(c2+3bd)
dac +3bd2 =bc2+3b2d
dac = bc2
da =bc
a/b = c/d
Reason :In this method student learn by doing and it is also helpful for learner because this leaves no doubt in mind of learners .It might be lengthy but each step has justification and reason.
Resources: with the help of handouts and internet
https://algebra.nipissingu.ca/tutorials/induction.html
Assignment I
Total Marks: 20
Lesson: 1-12 (Topics 1-78)
1. As a teacher responsible for teaching Mathematics to Elementary school children (ages between 10 to 12 years old), it is important to ensure that the teaching should be carried out in an interesting way. By using various instructional resources (Audio, Visual Aids), prepare a lesson plan to teach Algebra to 7th class students. (10)
Ans:
1. Subject: Math
2. Topic: Introduction of algebra
3. Grade level: 7th
4. Instructional objectives (use an action verb in a description of a measurable outcome)
Student will able to define a constant as a symbol having a fixed numerical value.
Student will able to recall a literal as an unknown number represented by a letter of an alphabet. To develop thinking and reasoning power in the students
5. Rationale: Algebra is one of the useful tools in mathematics .It is also use in mathematical statement to describe the variables relationship. Many problems of arithmetic simplified for the learner. It induces the power of analysis and a good instrument for mental training.
6. Resources: ICT for seeing the video, White board , white board marker , text book ,copy book where student write their notes, algebra worksheet for assessment to check their understanding
7. Procedure:
Focusing event: Teacher will write the word ALGEBRA on board and ask student. Have you ever listen this word before?
Teaching procedures: (Teacher will use discussion method and deductive method for this topic) after starter teacher will discuss lesson by asking questions what you know about this word. After asking question about the topic she will wait for their reply then she will explain ‘what is algebra?’ ‘Where this word comes from?’ She will give brief introduction of algebra with examples. Teacher will also discuss that arithmetic and alphabet is the combination of algebra by giving them examples: +, −, ×, ÷ .
1+3=--- , 5-2= , 7 × ----= 56
1+3= x , 5-2= y, 7 × a=56
She will also tell them that unknown variable is also use as alphabets.
Formative check: she will ask questions during the lesson to check their understanding. What is algebra? Where this word comes from? What is the use of algebra? Why we use algebra in math? What is Arithmetic? What are arithmetic operators? What is the relation of algebra and arithmetic and alphabets?
Student Participation: students will participate in discussion and also teacher will ask them randomly to solve questions
Closure: Teacher will summarize the entire lesson by asking different questions and ask students to write some examples on the board.
8. Assignment or Homework:
Find the value x, y and a
1. x = 2 +4 2. a × 3 =3 3. a + x + x=12 find the value of a
y = 6 -5 y =3 ÷ 4
9. Assessment: Teacher will give them worksheet for their assessment to check their understanding during the lesson.
10. Time allotted:45 minutes
2. When you work to teach a mathematical problem, would you prefer to have one teaching method which works or many methods which work for the problem? Explain in the light of teaching methods with some practical examples.
Ans: As a teacher will use many methods when teaching Mathematical problem. Because the demand of her job is to develop different methods or use different ways of teaching which benefit her students and make them successful. There are different methods that teacher use in different problem solving.
Lecture Method: It is the method of presenting the word picture of an idea; or the method of imparting information through a speech. Example: Teachers prepare the topic at home and just explain it in the class learners are the listeners only. Teacher solve all the question on board student just copy it.
Dogmatic Method: This method of mathematical knowledge observes a high standard of exactness. Example:find the area of square= l x b=?
L=5 b=9
Area of square=5 x 9 =45 ans
Inductive Method: It deals from concrete to abstract, particular to general and from examples to general rule. Example:
Deductive Method: It is opposite to inductive method. Here the learner proceeds from general to particular, abstract to concrete and formula to examples. Example:
perimeter of square=2(l+w)
2(3m+3m)=12m
Analytical method: It proceeds from unknown to known, ’Analysis’ means ‘breaking up’ of the problem in hand so that it ultimately gets connected with something obvious or already known. It is the process of unfolding of the problem. Example: If a/b = c/d, prove that ac −2b2 /b = c2 – 2bd/d
The analysis will start from the unknown part of the statement.
ac −2b2 /b = c2 – 2bd/d is to be proved true.
ac −2b2 /b = c2 – 2bd/d will be true
If acd−2b2 d = bc2 – 2b2 d
(Cancelling −2b2 d, which exists on both sides of the equation).
:. acd – 2b2d = bc2 – 2b2d will be true
If acd = bc2
:. acd = bc2 will be true if ad = bc
ad = bc will be true if a/b = c/d, which is known and true.
ac −2b2 /b = c2 – 2bd/d is also true.
Heuristic Method: The method involves finding out by the student, instead of merely telling of everything by the teacher. In this method the child is put in the place of a discoverer.
Synthetic Method: It is the opposite of the analytic method. In this method one proceeds from known to unknown. It starts with something already known and connects that with the known part of the statement. Example: If a/b = c/d, prove that ac −2b2 /b = c2 – 2bd/d
Synthetic Proof
a/b = c/d a/b – 2b/c = c/d – 2b/c
or ac −2b2 /bc = c2 – 2bd/cd
or ac −2b2 /b = c2 – 2bd/d
Hence the identity is proved.
Laboratory Method: Mathematics is a subject which has to be learnt by doing rather than by reading. Example:
The project Method: It is method of spontaneous and incidental teaching. This is learning by doing method. Students can learn by collaboration and association. Example: Providing a situation , Choosing and purposing , Planning of the project , Executing the project , Judging the project
Concentric Method: The method implies widening of knowledge just as concentric circles go on extending and widening.
Topical Method: It is the opposite of concentric method. Concentric method involves the breaking up of a topic into suitable portions, whereas topical method aims at keeping it intact
Math teacher always use different method for teaching math as every problem have different demand of teaching method some are simple and easy so teacher use deductive method or if problem if little lengthy and need more details to make student understand clear so she will use analytical method. Actually it’s depending on the problem that which method will use to solve it.
1:Deductive method example:
If the length and width of a rectangle is 8m & 6m respectively then find out the perimeter of rectangle?
Solution: learner will use the formula for solving this problem
Perimeter of rectangle =2(l + w)
= 2(8m + 6m)
= 28m
.
2:Analytic Method Example:
if a/b = c/d then prove that ac =3b2 / bc = c2 + 3bd / dc
Solution: Proving for this quotation we will do analysis to unknown
Unknown is ac+3b2/bc = c2+3bd/dc
ac+3b2/b =c2 +3bd/d
d(ac+3b2)= b(c2+3bd)
dac +3bd2 =bc2+3b2d
dac = bc2
da =bc
a/b = c/d
Reason :In this method student learn by doing and it is also helpful for learner because this leaves no doubt in mind of learners .It might be lengthy but each step has justification and reason.
Resources: with the help of handouts and internet
https://algebra.nipissingu.ca/tutorials/induction.html
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