RANCANGAN PENGAJARAN DAN PEMBELAJARAN MI (1)

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PROGRAM: ____________________________________________________________________________ SEMESTER: ______ TAHUN: ______

Kursus: __________________________________________________________________________________________ Kod: ____________ Kredit: ____________

Minggu _KandunganTajuk dan _PembelajaranHasil Kuliah_(jam) Tutorial_(jam) Amali_(jam) _(jam)ISL Catatan

M1 Whole numbers To study early numbers development To explain number sense

 Pre-number concepts  Counting

strategies  Early

numbers

development and number sense

(2 hrs)

 Discuss: -what are some characteristics of numbers? - Illustrate with examples the meaning of number sense

(1 hr)

 Prepare a set of materials that can be helpful for

- counting - learning basic facts (eg. Ten- frame)

-writing and recording numbers - Try out the resources with your peers during micro teaching

(2 hrs)

Reading:

i.Reys, at. el(2004). Helping children learn Mathematics (7th_ed.) pp.137-163

ii. McIntosh,A.J.(1992). ’Two needed

revolutions’ from

Challenging Children to Think When They

Compute.QUT,

Brisbane (1 hr)

Note:

60hrs interaction will be done in 12 weeks. 1 week =(a+b)hours = 5 hours (a+b):

a represents lecture and tutorial hours b represents practical work

M2 Whole numbers To carry out counting strategies To represent place value in numbers

 Place value representation of numbers - Grouping or trading

-Developing place Value

-Regrouping and renaming

(2 hrs)

 Show

how 201 and 120 would be represented with three different place-value models.

 Exami

ne a primary mathematics text-book. How many different place-value models are illustrated? Which model is used the most? Comment if the textbook provides a good choice of models? Defend your answer.

(1 hr)

 Make a number expander (Reys, pp176) or arrow cards for use in reinforcing reading and writing numbers

 Make hundred number chart and carry out Lesson Idea 8-3 (Reys: pp 177) and Activity In the Classroom 8-3(reys:pp182)

 What have you learnt from these two activities?

(2 hrs)

Reading:

i. Reys, at.el(2004). Helping Children Learn Mathematics (7th_ed.) pp.166-192

(1 hr)

Reference: Booker,at.el.(1997) Teaching Primary Mathematics (2nd_Ed.). pp 53-92

Or refer Booker (2004)

Program Ijazah Sarjana Muda Perguruan (PISMP) dengan Kepujian 1 3

MTE3109 3 (2 + 1)

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M3 Number operations and

basic facts To construct models for addition and subtraction To construct models for multiplication and division

 Models for addition and subtraction  Models for

multiplication and division

 Basic facts

(1 hr)

 Read about basic facts from pp. 206-224 (Reys) and discuss questions 1-6 in page 224.

 Summarise all the strategies for teaching basic facts

(1 hr)

Task 1:

In pairs, choose and prepare only one card from Activity In the Classroom 9-5 to 9-9-8(Reys:pp210-212).

 Play with your peers.  Exchange the Activity

Cards with other groups so that you get a chance to play all the 4 types.

Task 2:

 In groups of 4, plan an activity with teaching material that can be used to reinforce basic facts.

Carry out micro-teaching using the models and aids prepared

(3 hrs)

Reading:

(1 hr)

Reference:

Cathcart, et al (2006). Learning Mathematics in Elementary and Middle Schools. A Learner-Centered Approach (4th Ed). pp. 145-162

M4 Operation sense and

computations To calculate by mental computations To make estimation in computations

 Mental computation -The role of mental computation  Computationa

l estimation - estimation skills

presentation of Activity 1: ‘How did you do it?’

 Make a

summary of the methods applied based on the data collected by the whole class.  Comment on the

findings regarding mental computation.

(2 hrs)

Activity 2:

Form groups and each group carry out one activity based on activity 2 to 6 in pp39(Groves).  -Record what happens

when you try out the activity and comment on what you have learnt .

 Submit your comments through weekly reflective log. Activity 3:

 Try activity 3.13 (Qs. A-M) listed in pp48 Reader ‘Computation Techniques and Number Sense.’

(2 hrs)

Reading:

Activity 1: For Tutorial W4

 In groups of three, interview at least 6 primary school children based on activity 1 : How did you do it?” ( pp. 38 of Groves).  Record

different methods and present to the class.

(1 hr)

Reference: i.Groves, S. (2006) ‘Computation Techniques and Number Sense (In Week 5)

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pp.228-249

M5

Operation sense and

computations

To use

calculators and abacus in computations To construct teaching aids for numbers

 The

role of algorithms - Children’s use

and understanding of

algorithm in whole number operations

 Calculators and abacus

(1 hr)

 Make a list of the standard written algorithm for the whole numbers which you believe should be included in the primary mathematics curriculum.

 Comment about your list compare with the views put forward by Plunkett’ in his article.

(2 hrs)

 In about half a page, summarise and present your views on whether or not children in primary school should use calculators and the way in which they could be used.  In groups of suitable size, design an exercise or games where you can use abacus/calculators to teach operations of numbers.  How far abacus is used

in teaching whole numbers in Malaysian primary schools? Discuss with examples

(2 hrs)

Reading:

ii. Plunkett, S.(1979). ‘Decomposition and all that rot’, Mathematics in School, Vol 8 No. 3.pp. 2-5

(prepare Tutorial W5)

(1 hr)

References: iii. Groves, S. (2006) Computation

techniques and number sense.

pp 32-35 iv. Groves,S & Cheeseman, J(1995).’ Beyond expectations: Using calculators with young children’

v. Metallo. (undated)The abacus: Its history and applications” M6 Key issues in

teaching whole numbers

To discuss issues in knowing basics facts

To make

recommendations in the teaching of place value To debate the mathematics knowledge of teachers

 Issues in teaching whole number

- Kno

wing basic fact

- Teac

hing of place value

- Math

ematics knowledge of teachers

(1 hr)

 Read article X and summarise the issues raised in the teaching of

mathematics in primary school.

(2 hrs)

Acyivity 1:In groups, discuss the issues related to the teaching of numbers that exist in our local school context.

 Present your issues and make recommendations on how they can be

overcome. Support your presentation with references. Activity 2: Debate

 Training a

mathematics generalist or a specialist in handling primary mathematics in school: Its impact on children’s learning of mathematics.

(2 hrs)

Reading: Article X:

i. Review: Knowing and Teaching Mathematics by Roger Howe

http://www.ams.org/n otices/199908/rev.ho we.pdf

(1 hr)

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-M7 Fractions, decimals and percentages

Fractions

To explain the meaning of fraction and equivalent To relate mixed number and improper fraction

 Conceptual development of fractions and equivalent fractions

 Mixed

number and improper fraction

(2 hrs)

 Based on Reys (2004) Helping Children Learn Mathematics 7th_{ed. pg 282 –} 296, discuss and do activities, “In the classroom 12-1, 12-2, 12-3”.

(1 hr)

In groups:

 prepare suitable models for introducing fractions, including word and symbol cards(Refer Reys: pp. 289)  prepare suitable models for teaching equivalent fractions, mixed numbers & improper fractions

 plan a teaching activity and carry out micro-teaching using the models and aids prepared

(2 hrs)

Readings:.

(Compulsory) (1 hr)

Reference:

ii. Cathcart, et al (2006). Learning Mathematics in Elementary and Middle Schools. A Learner-Centered Approach (4th_Ed) Pg 201-225 iii.Booker,at.el. (1997).Teaching Primary Mathematics (2nd ed.). pp 97-117 iv. Kennedy et al. (2004). Guiding Children’s Learning of Mathematics (10th_ed) pg 401 – 420

M8 Fractions

To carry out fraction operations (+,-,x,/)

 Fractions operations - addition of fractions - subtraction of fractions

(1 hr)

 Design an

assessment task or a game [refer Kennedy et al (2004) page 474] that will help you understand whether or not your students understand operations with fractions.

 Discuss with

your peers the effectiveness or suitability of your

assessment task /game (1 hr)

In groups:

 Make

teaching aids suitable for addition and subtraction of fraction

 Plan and carry out teaching steps using the aids you have prepared and use the assessment task you have designed in your tutorial

(3 hrs)

Reading:

iii. Kennedy et al. (2004). Guiding Children’s Learning of Mathematics (10th_Ed) pg 457 - 477

(1 hr)

Reference:

ii.Cathcart, et al (2006). Learning Mathematics in Elementary and Middle Schools. A Learner-Centered Approach (4th_Ed) Pg 227-238

M9 Fractions

To construct teaching aids for fraction

 Fractions operations – multiplication of fractions - division of

 Discuss the following questions:

o How is multiplication of fractions different from multiplication of whole

In groups create four story problems that involve:

 multiplication of fraction with:

- whole numbers

Reading:

i. (Refer to Week 17)

Askey, R. (1999).

Reference:

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fractions (1 hr)

numbers?

o How do you illustrate the multiplication and division of:

 fractio

n with a whole number, e.g.





2

5

3

,

5

4

3 x

=

 fractio

n with a fraction, e.g.





2

1

4

3

,

2

1

4

3 x

=

(1 hr)

and fractions;

 division of fraction with: - whole numbers

and fraction

 Prepare a relevant lesson plan, the required models and teaching aids and carry out micro-teaching using the four story problems above

(3 hrs)

Knowing and Teaching Elementary

Mathematics, American Educator, American Federation of Teachers, retrieved from:

http://www.aft.org/pubs

-reports/american_educ ator/fall99/amed1.pdf

(1 hr)

iii. Cathcart, et al (2006). Learning Mathematics in Elementary and Middle Schools. A Learner-Centered Approach (4th Ed)

pp 238-249 iv. Kennedy et al. (2004). Guiding Children’s Learning of Mathematics (10th_Ed) pg 478 - 502

M10 Decimals To relate and convert fractions and decimals To represent place value in decimals

 Common

fractions and decimals :relationship and conversion  Place value,

ordering and rounding

(1 hr)

Briefly outline the steps that explain the meaning of the commonly used rule ‘divide the numerator by the denominator’

 Discuss how rounding the divisor can assist in making an initial estimate in division with larger numbers.

(1 hr)

 Prepare teaching materials to introduce children to decimal notation of tenths , hundredths and

thousandths. (3 hrs)

Readiing: i. Booker G. at el (1997)

Teaching Primary Mathematics (2nd_Ed) pg 247 – 249, 250-252

(2 hrs)

Reference:

ii. Reys, at.el(2004). Helping Children Learn Mathematics (7th_ed.) pp.303-309

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M11 Decimals To arrange decimals in order To round up decimals To construct teaching aids for decimals

 Decimal operations

 Discuss the use of place value chart to help children understand decimal computation.

(1 hr)

 Write a lesson plan to introduce decimal computation (for an operation of your choice) by linking this topic to fraction computation.

(1 hr)

Readings: i. Cathcart, et al (2006). Learning Mathematics in Elementary and Middle Schools. A Learner-Centered Approach (4th_Ed)

Pg 261-269

Refer to article week 10 pg 261 – 269

(1 hr)

Percentage To find the relationship between fraction, decimals To construct teaching aids for percentages

 Percentage - Relationship

between fractions, decimals and percentages

(1 hr)

 Construct models that can be used to help children understand percentages.  Try out the model with

your peers.

 Discuss with examples the use of percentages in daily lives.

(2 hrs)

Reading: . iii. Cathcart, et al (2006). Learning Mathematics in Elementary and Middle Schools. A Learner-Centered Approach (4th_{ed) pp. 271-281} iv. Kennedy et al. (2004). Guiding Children’s Learning of Mathematics (10th_Ed) pp. 443-450, 508-513

(1 hr)

Reference:

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M12 Key issues in teaching fractions, decimals and percentages

To discuss key issues in

teaching, fraction, decimals, and percentages

 Key issues in teaching of fractions, decimals and percentage :

 Stud

ent related  Teacher

related  Environmenta

lly related (Social-economic demands) (1 hr)

 Discuss the differences between pedagogical issues & content pedagogical issues  Discuss why teachers’

content pedagogical knowledge is crucial to effective and meaningful teaching of elementary mathematics [Read: Askey, R. (1999). Knowing and Teaching Elementary Mathematics]

(1 hr)

 Refer to

Askey, R. (1999). Knowing and Teaching Elementary Mathematics

 In groups:

Create real-life stories related to the practical applications of the concepts and operations learned in Fractions, Decimals & Percentages.

 Share the

stories with peers and discuss the merits of these stories.

 Comment and

discuss how the stories can be used in class instructions.

(3 hrs)

Reading:

i. Askey, R. (1999). Knowing and Teaching Elementary

Mathematics

http://www.aft.org/pubs

-reports/american_educ ator/fall99/amed1.pdf

(2 hrs)

M13 _Revision

M14 _Revision