Motivating Student.ppt

8/14/2019 Motivating Student.ppt

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Motivating Students studying

high level Math

Shah Alam & Rawang

18 September 2013

Section 9, Shah Alam


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Agenda

1. Summary up to level F

2. Level G

3. Motivating Students


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3

D

C

B

8

72

14

136

4

1

3

1

6

12

2

1

8

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136

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8

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What skills are requiredfor smooth progress in Levels E and F?

1stskill: Mental calcu lat ion ski l l

2ndskill: Correct ion sk i l l

3rdskill: Comprehension ski l l

22

1

44

2

44

10

44

12

4

1

11

6

2

1

E

F


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1stskill Mental calculation skill

28

1

24

1

24x2=, x3=, x4=28x2=, x3=, x4=or

28+28+28+

Mental calculation

4) 28+28=

5) 56+28=

6) 84+28=

Written

calculation

1) 242=2) 243=

3) 24

4=

E Can you find L.C.Mimmediately?


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5

41

116

21

41

31

612

21 22

1

44

2

44

10

44

12

2nd skill Correction skill Can you find whichpart is wrong?

F

Improve correct ion Ski ll gradual ly

Erase everything without checking his answer.

And make mistakes many times.

Can locate and correct

mistakes immediately

Takes long time to

locate the mistakes

Develop the habit to check the

answer before erasing


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8

7

214

13

6 8

7

214

13

6 8

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14

136

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136

3rd skill Comprehension skill

E

Students have tocomprehend newrules by themselves

Develop self-learning attitude

Ask the staff without thinking by herself

Cannot comprehend by

herself or takes long time

Can comprehend by

herself

Improve comprehension Ski ll gradually

Teach them how to learn

from worksheets.


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Summary

Develop self-learning attitude , and teach studentshow to learn from worksheets.

Enable students to calculate without writingcarrying/borrowing by the end of eachsection, and then proceed to next section.

Develop the habit to check the answerbefore erasing

1stskill: Mental calculation skill

2nd

skill: Correction skill

3rdskill: Comprehension skill

*You need to explain the rules, if students still have

difficulty


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The state that the studentstry to think by themselvesfirst when encounteringthe NLF.

Attitude/skills to learn from

the examples

D151-F G H I

8

When giving instruction, aim

for students to develop the

attitude/skills to learn from

the examples at theintroductory parts.


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From Level J onwards, thenumber of the examplesincreases so that students

can proceed by selflearning.

Level Number of

examples

38 28 99 54 80 174 138 119

9

Attitude/skills to learnfrom the examples

EF GHI JKL

J57


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Have students try to grasp how to solve from the

examples

Mark in timely manner (adjust the timing of the

marking individually)

Have students carefully look at the examples again,and give instruction concisely in case they cannotcorrect by themselves.

11

Studying

Marking

Makingcorrections

Please keep thesepoints in mind!

Basic instruction at the introductory parts

Skills

Attitude


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Level H1

Basics for Level H11

21Literal equations

31

41 Simultaneous

equations

in 2 variables

51

6171

81

91 In 3 and 4

variables101

111 Applications

121 Inequalities131

141

Functions and

graphs

151

161

171

181Simplifyingmonomials/polynomials191

Level I1 Basics for Level I11

multiplication21

31

Factorization41

51

6171

81

Square roots91101

111Quadratic

equations121131

141 Graphs of

quadratic

functions

151

161

171The Pythagorean

theorem181191

Level G

1Basics for Level G

11

21 Positive /negativenumbers&

31

41

51

&

6171

Four operations8191

101 Value of algebraicexpressions111

121 Simplifyingalgebraic

expressions

131

141

151

Equations161

171

181191 Applications

Especially in Level G, since a lot of NFLs are introduced, such aspositive/negative numbers, Algebraic expressions, and Exponents,consider to mark in timely manner based on each students level.

12


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Basic instruction for Level G

As mentioned previously, a lot ofNLFs which are not familiar withare introduced in Level G.

So , the points above is important.13

Attitude/skills to learn from the

examples

(1) Have students write the intermediate

steps as shown in the examples

(2) Have students read the explanations andnotes carefully.

(3) Consider assigning the marking in timely

manner for some students

Level G

1Basics for Level G

11

21 Positive /negativenumbers&

31

41

51

&

6171

Four operations8191



expressions

131

141

151

Equations161

171

181191 Applications


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16.010016

254

G1-G20: Basic of Level G

G7b: Q8 and Q9


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176

11

6

72

21

5

1

9

5

2

21)

20

13

20

17(

9

52

21)

100

65

20

17(

9

5

21

2)65.0

20

17(

9

5

Convert immediately

Ability to judge 100 or 20

Examples of step in fraction

G1-G20: Basic of Level G


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7

31

7

107

6

3

5

7

6)

15

101(

7

6)

15

71

15

3(

7

6)

15

71

5

1(

6

7)

15

712.0(

6

11)

15

712.14.1(

Steps can be skipped

Must use decimals when

both are decimals

Need to convert improper

fraction immediately

If follow is + or -, and

denominator is multiples

of 15, no need to reduce


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G21-G70: Positive/Negative Numbers

Level G

1 Basics for Level G11

21Positive /negative numbers

& 31

41

51&

6171

Four operations8191


121

Simplifying algebraicexpressions

131

141

151

Equations161

171

181

191 Applications

NLF for Advance

students

Basic rules of adding

and subtracting positiveand negative numbers

More Additional Notes

e.g. G21a&b, G25b.

More examples, from

G21 -30 got 10

examples.


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Level G1 Basics for Level

G11

21 Positive /negative

numbers

&

31

41

51&

61

71Four operations81

91

G21-

30

G31-

40

G41-

50

Rules for the signs +&-

Removing brackets

Including different

denominator

20

Please fill in the blanksand think about the

reason why we shouldbe careful in G41-50.


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2121

(2) Have students read the explanations

and notes carefully.(3) Consider assigning the marking in

timely manner for some students

G41a

G41 is better to assignas CW in case of firsttrial and have students

read the note carefully.



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Level G1 Basics for Level

G11

21 positive /negative

numbers

&

31

41

51&

61

71Four operations81

91

G51-

54

G55-

60

G61-

70

Rules for the multiplication

Including exponents

Rules for the division

22

Next point is G55-60.Please fill in theblanks and thinkabout the reason.


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It is not necessary to teach law of exponentialbecause the major difficulty is in getting the result.

If we teach law of exponential students may getconfused.

Write Intermediate step as shown in the example

Keep it simple!


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Four operations of

negative number.

G74To remind the

example used in G50bTo check whether

student are writing the

intermediate steps and

can correct theirmistakes.

G71-G100: Four Operation

Level G



& 31

41

51&

6171

Four operations8191


121


131

141

151

Equations161

171

181

191 Applications


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G71-100

G176-200

Level G1

Basics for Level

G1121 Positive /

Negative

numbers

31

41

51

&

6171

Four operations8191

101 Value of algebraic

expressions111


expressions

131

141

151

Equations161

171

181191 Applications

Attitude/skills to calculate accurately

(1) Have students develop the attitude to

verify their answers

(2) Have students write the appropriate

intermediate steps

It is better to be careful here todevelop these 2 attitude.

25

G71-G100: Four Operation


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NLF for Advancestudents

Students to first write

out the expressions bysubstituting the variable(s)

with its assigned

numerical value.

The expressions are

grouped by equivalent

expressions.

G101-G120: Values of Algebraic Expressions

Level G



& 31

41

51&

6171

Four operations8191


121


131

141

151

Equations161

171

181

191 Applications


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When substituting positivenumbers, no parenthesis isneeded except G104b, Q1

When substitute a fractioninto index, some students

may not need to addparenthesis as the step will belonger

22

)2

1(b

G101 is better to assignas CW in case of firsttrial and have studentsread the examplecarefully.



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Some students may forget usingparenthesis when substitutingfraction into square (review G104b)

3

1,

2

1 yxWhen

substitutes into 232 yx


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G121-

130

G131-

140

G141-

150

Combining like terms

using the distributive law to

remove the bracket.

removing the brackets

Level G


expressions111

121 Simplifying

algebraicexpressions

131

141

151

Equations161

171

181

191 Applications

29

G121-G150: Simplifying Algebraic Expressions


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yxyx

baba

34)4

1

3

1(12

126)42(3

Why 6a and (-4x)?

Why 12b and (-3y)?

For some students, G 141(expansion) might need to

assign as class work. Praising

is needed to increase

motivation.



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G122, Starting using

improper fraction

For some students, be strict to the format of answer;

ax + y (not y + ax)

x + a (not a + x)

For some students, G 141 (expansion) might need to

assign as class work.


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G151-

160

Level G


expressions111121Simplifying algebraic

expressions131

141

151

Equations161

171181

191 Applications

32

G161-

170

Introduction of equations

equations by using transpose

G151-G190: Equations

G171


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G171-

175removing the brackets

G176-

190

Equation with fractional

terms

33

Level G


expressions111

121Simplifying algebraic

expressions131

141

151

Equations161

171

181

191 Applications

G153 is better to assign

as CW in case of first

trial and have students

read the example carefully.

May need to explain thenotes.

S mmar of Le el G

Summary of level G


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G71-100

G176-200

Summary of Level G

Level G1

Basics for Level

G1121 Positive / Negative

numbers

31

41

51&

61

71Four operations81

91


expressions111

121Simplifying algebraic

expressions131141

151

Equations161

171

181

191 Applications


(1) Have students develop the attitude to verifytheir answers

(2) Have students write the appropriateintermediate steps

Have them write

the intermediatesteps neatly here.

34

Summary of level G


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Todays Sharing

Motivating Student Studying High Levels

Mathematics


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Math Literacy = Numeracy

Mathematics is the only language shared by all human beings

regardless of culture, religion, or gender.

Pi 3.14159

Adding up the cost of a basket full of groceries involves the

same math process regardless of whether the total is

expressed in dollars, Ringgit, or yen.

With this universal language, all of us, no matter what our unit

of exchange, are likely to arrive at math results the same way.


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Simple Number Trick

1. Pick a two digit number

2. Add the digits

3. Subtract the sum from the original number

4. Then, add the digits of the result


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Answer

A two digit integer can be written as nm

(eg in 23, n=2 and m=3)

Then nm=10n+m

And the sum of the 2-digits is n+m

Original integersum of the 2-digits:

nm-(n+m)=10n+m-n-m=9n

Thus, the result of subtracting the sum of the digitsfrom the original integer is a multiple of nine

Wh d d t t d hi h l l


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Why do we need to study high level

Mathematics?

Level J Level K Level L

Level M Level N Level O

Level XT Level XV Level XM

Level XP Level XS


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Algebra(Level 7AJ, XV, XM)


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Essenceoflgebra

Arithmetic Variable Expression Equation

NumberFour

Operations

Inequality

SolvingEquation

Simplifying

EquationCombiningLike Term

Rational&

IrrationalNumber

ComplexNumber

Vector&

Matrix

Monomial&

Polynomial

Factorization

Algebra


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CalculusA small stone used for counting

(Level KO, XT)

C l l


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EssenceofCalculus

Sequences&

Series

Limit&

ContinuityDifferentiation Integration

Finite Infinite

GeometricArithmetic

DivergenceConvergence

DefiniteIntegral

IndefiniteIntegral

Derivative

Maxima,Minima

&Point of Inflection

Concavity

Trigonometry

Calculus


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Statistics

(Level XP & XS)


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Why is Mathematics useful?

What Is The Application Of


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What Is The Application Of

Mathematics In Daily Life?

Cooking

Grocery shopping

Budgeting household

expenses

Paying bills

Measuring space

Games


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Games

Sudoku

Tic-Tac-Toe

Reversi


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Functions & Graphs


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Sleep & Death Rate

Studies on the relationship

between the death rate of

men and an average number

of sleep hours per day

showed to fit quadratic function


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Brain, Muscle & Body Weight

The weight of the humans brain and muscle

are directly proportional to a persons body

weight


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Estimating Heights

An anthropologist can

use certain linear

functions to estimate

the height of a male or

female, given the length

of certain bones


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DifferentiationRate of Change = Derivative


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Production

Number of items produced over time


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Territorial Area, W T

It has been hypothesized

in statistical studies that

the area of the region canbe approximated by a

function that involves the

animals weight, 0dW

dT


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Application of DifferentiationMaxima & Minima


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Light Maximizing

V l M i i i


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Volume Maximizing

Pg253, 264

Eff ti f Ad ti i


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Effectiveness of Advertising

Rate of change of the number of units soldwith respect to the amount spent on advertising


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Medication in The Bloodstream

After injection, the amount of a medication in

the bloodstream will decrease after time


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Smart Phones

Usage of hand

phones over time:

Prediction of market in

terms of the demand

and potential revenue

Elasticity of Demand


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Elasticity of Demand

Responsiveness in the quantity demanded as aresult of change in price


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Movie Box-Office Revenue

Using the results of the before/ current movies

to predict the revenue of the upcoming movie

Population Growth


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Population Growth

What will the world human population be in 2014?

How about population growth in this island?

Solving Crime


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Solving Crime

Cooling of body for coroner to check when

was a murder committed taking the room

temperature into consideration


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Integration

Efficiency of A Machine Operator


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Efficiency of A Machine Operator

The rate at which a machine operators

efficiency changes with respect to time


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Bowling Scores

Find the probability of a range of scores

using normal distributed function


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Transportation Planning

Transportation planningis the field involved with the

sitting of transportation facilities (generally streets, highways,

sidewalks, bike lanes and public transport lines).

Transportation planner can determine the probabilities that

cars are certain distances apart.


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Trigonometry

Astronomy


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Astronomy

Measure the distance to nearby star

Mercury, Venus, Mars, Jupiter,

Saturn, the moon, and the sun

Geography


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Geography

Measure distances between landmarks, and

in satellite navigation systems on the oceans,

in aircraft, and in space


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Matrix

Business Analysis


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Business Analysis

Identify business needs and determine

solutions to business problems by solving

systems of linear equations

Computer Programming


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Computer Programming

Manipulate arrays of numbers for either

spreadsheets programs or graphics programs

How to study high level Math?


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How to study high level Math?

Make small notes using own words Copy formulas and examples into a book for easy

reference

Put marks on tough questions indicatingquestions that require more attention

Learn from example and simpler problems/

methods

Form smart table or chart for easy understanding

Copy formulas and examples into a book


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for easy reference

Put marks on tough questions indicatingti th t i tt ti


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questions that require more attention

Form smart table or chart for easy understanding


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Minimum

Value

b> 0

Method A1

b< 0

Method B2

Maximum

Value

b> 0

Method B1

b< 0

Method A2

b> 0 b< 0

Maximum Method B Method A

Minimum Method A Method B

Write them at an easy visible place in order to

k l f h d


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take a glance of them everyday

How to memorise and understand


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How to memorise and understand

formulas?

Write them at an easy visible place in order to take a

glance of them everyday

Say them out using the parrot fashion

Link it with the easier formula that is learnt before

Know how the formula came about ~ the derivation

of formula

Practice, practice, practice

Li k it ith th i f l


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Lets try this!

FBIMCAISAUOBAB

CCan you memorise this?

Link it with the easier formula


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FBIMCAISAUOBAB

C

If we can find a strategy to link allthe alphabets to a familiar pattern,we will be able to memorise it.

FBI MCA ISA UOB - ABC. When a strategy is able to ease ones

work, we shall learn!

Able to self-learn


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The role of the Instructorsis not to simply teach howto solve the problems.

Our mission as Instructor isto achieve the ideal statewhich enable students toself-learn from Level J

onwards with the attitude/skills shown on the left, andthis should be theinstruction we give to thestudents.

from Levels JKL

(1) Have students write the intermediatesteps as shown in the examples

(2) Have students read the explanationsand notes carefully.

(3) Consider assigning the marking intimely manner for some students

(1) Have students develop the attitudeto verify their answers

Attitude/skills to learn from the

examples


Motivating Student.ppt

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