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CURRICULUM GUIDE

FOR

THREE YEAR DIPLOMA IN TEACHING

Mathematics for Early Childhood

JOINT BOARD OF TEACHER EDUCATION

2004

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MATHEMATICS FOR EARLY CHILDHOOD

Revised under the aegis of

The Joint Board of Teacher Education

and

The ENACT Programme

(A joint initiative of the governments of Jamaica and Canada to promote sustainable development in Jamaica.)

2004

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Preface The Joint Board of Teacher Education (JBTE), in carrying out its mandate to ensure quality in the curriculum delivered by the consortium of teachers’ colleges which form its membership, must ensure that the curriculum responds to the dynamic nature of knowledge and reflects current trends and practices of the various subject disciplines. To this end, periodic curriculum reviews must be undertaken in order to incorporate new material and approaches and to ensure congruence with the national curricula of the relevant levels of the education system. The Sustainable Teacher Environmental Project funded by the ENACT Programme, a joint initiative of the Government of Jamaica and CIDA, has provided funding to enable such a review in a number of areas of the JBTE programme offerings. This has resulted in the redesign of the Secondary Science options of Biology, Chemistry and Physics, and the Early Childhood programme. The project has also provided for the development of a new elective course for the Secondary programme: Environmental Education for Secondary School Teachers, as well as the provision of some resource documents. The project also included activities to promote whole college strategies to make environmentally sustainable action a foundation of all teaching, research, operations and community outreach, strengthening the capacity for action research among college lecturers. The curriculum revision/development process has focused on a number of the expected outputs of the JBTE programme as outlined in the regulations, inter alia

The development of teachers with a thorough, accurate and appropriate knowledge and understanding of their areas of specialisation;

The transformation of the college programme from a teacher-centred, didactic mode of teaching to a collaborative, interactive and student-centred learning environment;

The development of a commitment, on the part of the teacher, to making the quality of life better for the children he/she teaches through an awareness of, and appreciation for, the importance of living in harmony with the environment.

The ENACT project formed important tiles in the mosaic of the JBTE activities, providing as it did

(a) A forum for students and staff at every level of JBTE member institutions to be exposed to the urgent and timely global issues related to environmental education and sustainable development,

(b) Revised curriculum documents which reflect current theories and practices, (c) Workshops for lecturers to develop and deliver new curricula.

The Project has therefore been a valuable component of the process of transformation of the classroom environment, curriculum, and assessment practices of the JBTE programmes.

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Introduction It is often stated that the teachers should be instructed in a manner similar to how they are expected to teach. A desirable aspect of teaching young children should be the use of the environment as a teaching tool. This Early Childhood Mathematics Syllabus has been drafted with this in mind so that the student teachers will be given the necessary exposure to methodology and strategies for teaching their young students. The suggested activities in this syllabus will give an initial exposure to the teacher in training who is expected to search for further knowledge. The student teacher, therefore, will seek to be proficient in the use of technology and the mathematics problem solving skills which would be used in the classroom and also would be applied to solving problems in every day life.

Rationale Society today expects all its children to have an opportunity to become mathematically literate in order for them to compete effectively in a global and technologically oriented society. Schools, therefore, have an obligation to provide and cultivate the medium or culture to meet and satisfy this need. Teachers in the early classroom are the vessels through which this development can be facilitated. Prospective teachers should be knowledgeable about the content which they teach and should always be able to handle content above the level of their charge. With increased usage of technology globally, the child in the early childhood mathematics classroom should be introduced to the use of the calculator and the computer as well as to learning the important cognitive skills for problem solving, mental computation and deductive reasoning.

Subject: Mathematics Title: Mathematics for

Early Childhood Teachers Programme: Early Childhood Years: 1 & 2 Duration: 165 Hours Credits: 11 Prerequisites: Grade 9 Mathematics

Formatted

Formatted

Formatted

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General Objectives To help students teachers to: 1. learn to value Mathematics through varied and inter-related situations – play, drama,

arts, dance and music.

2. become confident in their ability to do mathematics.

3. relate mathematical concepts to their everyday environment by using topics such as: creating patterns and designs, measuring, buying at the market, garbage disposal.

4. collect data and become a mathematical problem solver by

(i) engaging in independent exploration making conjectures, working on problems that involve many steps that may take hours, days, weeks and or months to get to the solution.

(ii) cultivating the habit of writing or formulating problems of the nature that will need time to arrive at the solution(s).

5. use the environment as a basis for mathematical discourse and interaction in the early childhood classroom.

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Scheme of Assessment YEAR 1 Course Work: 50% Written Examination: 50% Duration: 3 hrs Written Examination Section 1 20 Multiple choice 20 marks 10 True-False 10 marks 10 Matching 10 marks 10 Short Answer 10 marks

Section 2 5 Methodology 5 marks each 25 marks 5 Content 5 marks each 25 marks

Total 100 marks

YEAR 2 Course Work: 50% Written Examination: 50% Duration: 21/2 hrs Written Examination Section 1 20 Multiple choice (10 Content, 10 Methods) 20 marks 10 Short-answer (5 Content, 5 Methods) 10 marks Section 2 5 Methodology 5 marks each 25 marks 5 Content 5 marks each 25 marks Total 80 marks

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GRID FOR COMBINING COURSE WORK AND EXAMINATION GRADES

WHERE A WEIGHTING OF

FIFTY PERCENT (50%) HAS BEEN GIVEN TO COURSE WORK

AND FIFTY PERCENT (50%) TO EXAMINATIONS

THREE-YEAR INTRA-MURAL PROGRAMME

Note: Exam grades are weighted at 50% and Course Work is weighted at 50%.

COURSE WORK GRADES Examination

Grades 9 A

8 B+

7 B

6 B-

5 C+

4 C

3 C-

2 D

1 E

80 – 100 A 9

A A B+ B B B- B- B- C+

70 – 79 B+ 8

B+ B+ B+ B B- B- C+ C+ C+

65 – 69 B 7

B+ B B B B- B- C+ C+ C

60 – 64 B- 6

B B B- B- B- C+ C+ C C

55 – 59 C+ 5

B B- B- C+ C+ C+ C C C-

50 – 54 C 4

B- B- C+ C+ C C C C- C-

45 – 49 C- 3

B- C+ C+ C C C- C- D D

40 – 44 D 2

C+ C+ C C C- D D D D

0 – 39 E 1

D D D D E E E E E

Note: Scheme of Assessment for Course Work should be followed.

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YEAR 1, SEMESTER 1

Number of Hours: 4 Instructional Objectives: Student teachers should be able to: 1. examine the varying concepts of what is mathematics.

2. give their own understanding of what is mathematics.

3. give reasons for including mathematics as a subject in the early childhood curriculum.

4. state the aspects of psychological theories that have influenced children’s learning of mathematics.

5. make the link(s) between procedural and conceptual knowledge.

6. examine and explain stages of argumentative development/readiness, pupils and teachers’ attitudes, motivation, learning styles, teaching processes that affect the teaching/learning of mathematics.

CONTENT SUGGESTED ACTIVITIES

1. What is Mathematics? Why learn Mathematics?

Research and discussion on topic. Debate: “How will the varying views

on mathematics impact on mathematics for Early Childhood?”

2. How children learn Mathematics. Support from learning theorists: Piaget, Dienes, Vygotsky, Bruner, Gagne, Ausubel, etc.

Research presentations: “The constructivist view of learning”

Select a readiness concept for teaching at EC level for which this approach could be used. Develop a sequence of steps using this approach for teaching this concept. Include questions and activities that the teacher might ask to help students develop an understanding of the concept

Research essay: Piaget’s cognitive development in children. Practice the task on conservation of numbers with your peers. Record results

Research and use David Ausubel’s advanced organisers to design lessons for readiness activities

Children’s Mathematical DevelopmentUNIT 1A

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3. Conceptual and procedural knowledge.

Research and class debate: “Procedural and conceptual understanding are necessary elements of the mathematics classroom.”

4. Motivation and the Learning Process: Maslow’s Hierarchy of Learning.

Research presentations: The impact of Marlow’s learning hierarchy on Early Childhood Education

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Number of Hours: 5

Instructional Objectives: Student teachers should be able to: 1. identify the major factors that influence the mathematics curriculum.

2. use the Ministry of Education, Youth and Culture’s Early Childhood Curriculum to plan for teaching.

3. create mathematical learning environments in the early years that are child centered.

4. examine and explain processes involved in the mathematics curriculum: problem solving, use of manipulatives, use of technology, using the child’s environment.

5. develop materials that could be used to teach readiness activities and topics in the curriculum of the early childhood.

6. use the environment and materials found in the environment in the teaching/learning of mathematics.

7. use the language of mathematics to express mathematical ideas precisely.

8. Integrate mathematics and language through the language communication skills.


1. The Mathematics curriculum - Content of the M.O.E. Y & C.

Early Childhood Curriculum. - Processes involved in teaching

the curriculum. - Materials in the Early Childhood

physical environment.

Examine the structure of the National Early Childhood curriculum and make lists of the specific mathematics concepts and skills it contains

Research and discuss some issues that surround its development

2. Child centeredness. Lecture/discussion: Features of

child-centeredness and its impact on the development of the whole child

3. Use of environment in teaching Mathematics.

Research and report: Design a series of lessons with related aids using the child’s home environment for teaching readiness skills and concepts in the Early Childhood syllabus

4. Communicating mathematically. The teacher’s role in developing

communication skills in the Early Childhood classroom

Integrating mathematics and language

UNIT 1B Principles in Teaching Mathematics to Young Children

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Number of Hours: 21

Instructional Objectives: Student teachers should be able to: 1. state the importance of pre-number activities.

2. develop and describe appropriate activities to help children develop their pre-number skills.

3. use counting principles to help them to understand errors children make while counting.

4. distinguish between rote and rational counting.

5. identify and use the different counting strategies.

6. plan appropriate activities for use in teaching children the counting strategies.

7. use a collection of integrated relationships to develop number sense.

8. distinguish between cardinality and ordinality.

9. use and describe different techniques to teach children how to read, form and use numerals.

10. plan appropriate activities to help children understand number relationships. 11. integrate mathematics with art, music and movement and science concepts/aspects. (a) PRE-NUMBER ACTIVITIES


1. Classification.

Make collection on an outdoor walk. Classify collection and define classification (oral or written) communicating why each object belongs/does not belong

2. Matching.

Make scrapbook of sets of matching objects proportionally, e.g., sets of balls of varying sizes to sets of bats; size of heaps of to size of containers, size of greeting cards to size of envelopes, etc.

3. Patterns.

Use letters of the alphabet or numbers to form a pattern, e.g., AB AB AAB AA, AB AB AAB AA then integrate with music and movement, e.g., clap, step, etc.

4. One–to–one correspondence.

Distribute materials and ask questions to find out if there are enough for the class. Have class make statements about the situation, e.g., there are enough sheets of

UNIT 2 Developing Early Number Concepts, Number Sense and Counting

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paper for the class, there are fewer sheets of paper than students, the number of sheets of paper is the same as the number of students, etc.

5. Comparison.

Fit shapes alongside one another to make judgments of “more” or “less” or to develop creativity and problem solving skills involved in representational constructions (e.g., use of set of solids distributed by MOEYC in representational construction)

(b) COUNTING


6. Principles of counting.

Use the calculator to answer the question “one more!” to develop counting principles

7. Stages of counting. Integrate inquiry skill by letting students

use the environment (indoor/outdoor) to answer the question “How many do you see?”

Integrate counting with the their environment, e.g., count number of objects/persons in classroom/canteen, number of teachers in their school, number of straws or pieces of scrap paper seen on the classroom floor, etc.

Integrate counting with language arts and science, e.g., write story about numbers in health area, the number of scrap papers, straws, bits of garbage found on floor of class room and relate it to sanitation and healthy living

8. Counting strategies: counting all, counting on, counting back, skip counting.

Use of the calculator, of song “Ten Green Bottles” or question “What is one fewer?” to aid counting backwards

Use the idea of collecting in one location followed by another, e.g., bottles for recycle bin to encourage counting on

Use the idea of position/location to develop counting on

Use of pairs in pictures or other groupings and the calculator to develop skip counting

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(c) EARLY NUMBER DEVELOPMENT: NUMBER RELATIONSHIPS CONTENT SUGGESTED ACTIVITIES

9. More and less. Compare pictorial representation of number quantities and describe the findings (one is more than the other, etc.)

10. Cardinality and ordinality. Use line/queuing to map counts Align objects onto a number line. Use of game in identifying positions up to

20 in a linear arrangement/ in a queue, e.g., select card for next position, card will have the ordinal numbers

11. Part – part whole. Draw pictures/objects to represent

number quantity given

12. Relative size.

Use the calculator to find missing symbol in a sequence

13. Bench marks.

Use materials from the environment to make number combinations 1 to 5, 5 to 9 and 10 to 20, etc.

14. Reading, writing and using numerals.

Match number symbol to pictorial representation of number quantities and vice versa

Use play dough/clay to form number symbols

Use of flash card or calculator for students to call number name matching the displayed symbol

Writing and calling number name that matches quantity

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Number of Hours: 21

Instructional Objectives: Student teachers should be able to: 1. use specified set notation throughout this unit.

2. classify objects and ideas according to identifying properties.

3. use friendly plane shapes to develop the concept.

4. draw Venn Diagrams to represent groupings or classification of objects.

5. list the elements of a set.

6. classify sets as finite, infinite or empty.

7. distinguish between equal and equivalent sets.

8. identify universal sets.

9. use diagrams to show the relationships between intersecting sets or disjoint sets.

10. discover and write the formula for the number of subsets in a given set.

11. describe new sets formed as a result of set operations of union, intersection, and complementation.

12. draw Venn Diagrams to illustrate set relations and set operations.

13. model word problems using knowledge of sets.

14. model settings in the environment.

15. use their knowledge of sets to solve problems modelled.

16. state the significance of set theory in developing early number concepts.

17. integrate mathematics concepts with those of their subject area.

SETS AND NUMBER CONCEPTS


1. Classification of objects into groups/sets and naming.

Sort and classify objects in the surrounding environment into defined and well-defined groupings/sets

Use different media to display sets, e.g., a rod abacus to display sets of beads, etc.

2. Set notation. Students to do pictorial representation of

how objects are kept together Use construction skills in putting together

sets of objects to build farmyard, classroom, bedroom, village/community, etc.

3. Describe elements in a set.

Sort and find sets within a large collection, then write stories or give oral description of the sets

UNIT 3 Early Number Concepts and Sets

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4. Types of sets: finite, infinite, empty, equal, equivalent, Universal set, subset complement.

Sort and find sets within a large collection, then write stories or give oral description of the sets, e.g., the same as, larger than, not any of, the remainder of and contained in

Build groups of objects from farmyard, health care facility, their home village or community and indicate groups and sub groupings

5. Pictorial representation. Use friendly/Venn diagrams to represent

data from social studies, religious studies and science

6. Solve simple word problems using sets and Venn Diagrams.

Solve problems using drama/pictorial/ diagrammatic representation, e.g., Venn Diagram

Research and debate: “The place of set theory in early number concepts.”

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YEAR 1, SEMESTER 2

Number of Hours: 18 Instructional Objectives: Student teachers should be able to: 1. compare and contrast decimal system with other systems of numeration.

2. list the essential characteristics of a number system.

3. use the terms face value, true value, place value, digits, numbers and numeral symbols appropriately.

4. identify different types of addition and subtraction word problems.

5. compare different types of strategies children use to solve word problems involving addition and subtraction.

6. identify different types of multiplication and division word problems.

7. identify different strategies children use to solve word problems involving multiplication and division.

8. plan activities to help children to develop the strategies for solving word problems.

9. use activities to introduce children to symbols (+, -, x and ÷) at the appropriate time.

10. explain the differences between measurement, partitive and division.

11. write number sentences for addition and subtraction, multiplication and division.

12. identify basic facts.

13. identify different thinking strategies children use to solve basic facts.

14. plan activities to help children develop their thinking strategies.

15. use the calculator to perform operations.


1. Systems of numeration: Babylonian, Egyptian, Roman, Mayan, Hindu- Arabic, Decimal Systems.

Make concept map/web of concepts and issues related to place value, the four basic operations, fractions, decimals

Write rules, symbols and operations for developing an original number system

2. Introducing operations with word problems:

- Addition and subtraction: join, separate, part, whole, compare

- Multiplication and division: partitive division, measurement division, multiplication

Use the flannel board, counters, etc., and represent “less than ten”, “ten” and “more than ten”. Separate set into ten and more, i.e., ten + more or 10 +

Making the various models for each of the four basic operations, e.g., two missing number problems for addition

Number Concepts, Systems and Operations UNIT 4

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3. Concepts of whole numbers: numbers, numerals, digits, face value, place value.

4. Basic facts: strategies used for solving basic facts.

5. Use of the calculator in exploring whole numbers, integers - estimating, rounding.

Construct and use basic fact table along with the calculator to verify solutions and encourage correct use of calculator

6. Properties of the set of whole numbers.

7. Writing mathematical sentences.

8. Problem solving.

Modelling of word problems writing mathematics sentences, making pictorial representation, miming, acting, etc.

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Number of Hours: 12 Instructional Objectives: Student teachers should be able to: 1. create and represent images from spatial objects.

2. describe the difference between spatial visualisation and spatial orientations.

3. explore and describe space in terms of proximity or relative position- near, far, close to, next to, beside, up, down, under, below, above.

4. explore and describe space in terms of separation, distinguishing an object or part of from another.

5. explore and describe space in terms of order – before, in front of, behind.

6. explore and describe space in terms of enclosure - linear and two and three dimensional.

7. describe objects or shapes as larger than, smaller than, the same as.

8. use paper folding and measurement by comparison to determine and describe the properties/forms/generalisations of named plane shapes.

9. integrate mathematics with writing in language arts.


1. Spatial awareness, proximity, (near, far, close by, up, down, beside, next to separation, order and enclosure).

In groups examine sets of physical objects according to proximity to another object interchanging the reference point, etc.

Build and use peg-board as a one-dimensional space to show linear enclosure and “between-ness”

Use ring games such as “Farmer in the Dell” and “Bull in the Pen” to introduce the concept of enclosure

Model a farmyard of animals and crops or a cow pasture with cows in and out of the pasture. Discuss the relative positions of the animals in and out of their enclosures in relationship to their impact on environment/effect of environment on them, etc.

2. Exploring three dimensional figures, faces, vertices, sides, parallel and perpendicular edges, corners.

Construct symbol(s) and place named feature in appropriate locations (as in pasting the tail on a donkey) stating the reason for selection of location

UNIT 5 Geometric Concepts I

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3. Exploring two-dimensional and three-dimensional enclosures.

Field trip to the bauxite plant rail yard to observe a full-length freight train, re: arrangement of the engine and the different types of cars and caboose

Make a scrapbook on field trip to rail yard Make a collage of a train using solid

shapes and explain their reason for the arrangement of each section

4. Symmetry of plane shapes.

Field trip to examine shapes in environment that are symmetrical, e.g., traffic signs, houses, cars, butterflies

5. Circle, triangles and

quadrilaterals.

Integrate the properties of shapes with language arts, poetry or story/essay. “What make(s) me what I am?” and “Who am I?”

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Number of Hours: 15 Instructional Objectives: Student teachers should be able to: 1. describe ways in which they can help children use arbitrary units to measure.

2. justify the need for standard units.

3. measure lengths and demonstrate proper usage of a ruler.

4. estimate the measures of different attributes by using standard units.

5. state simple relationships, e.g., 1 meter = 100 centimeter in units.

6. develop activities to help children identify the two time attributes of events: time of occurrence and duration.

7. develop strategies for teaching children the different skills and ideas that are involved in interpreting the markings on a clock face.

8. develop activities to help students to identify various temperatures.

9. describe and use of a clinical thermometer, laboratory thermometer and wet/dry bulb thermometer to measure temperature and relative humidity.

10. integrate the attribute temperature with concepts of health, wellness, weather and weather conditions.

11. identify terminologies used to describe weight, e.g., heavy/light.

12. read scales and balances.

13. develop activities that children can use to develop estimation skills.

14. weigh objects using a scale and ascertain mass of objects by using a balance.

15. research and state the importance/value of a collection of coins.

16. state the importance of coins of lower denomination.

17. establish equal values of different combinations of coins of varying denominations.

18. develop appropriate activities to introduce length terminologies to children.

19. develop strategies for using different body units to measure length.


1. Comparing lengths using the following terminologies: as long as, longer than, shorter than.

In groups examine sets of physical objects according to length, making relative comparisons such as longer than, etc., interchanging the reference point

UNIT 6 Measurement, Part I

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2. Use of non-standard units: - Body units. - Span, width of finger, foot length,

etc. - Arbitrary units (paper clips, cord

lengths, pencil lengths).

Use body units and arbitrary units, to measure how far along a straight line and how far around.

Children in groups use span to measure lengths; generate debate on their findings and make rule for consistency

3. Standard units: (centimeters, meters using rulers/straight edge).

Use lengths of string cord, straight edge to measure distance/length; compare (longer than, shorter than, etc.)

4. Time: - Sequencing of events. - Concept of early, late, before,

after, now and then, etc. - Concept of morning, midday,

evening, night, a.m., p.m. - Salutations involving time. - Comparison and estimation. - Non-standard units of time. - Calendar – months, days, year,

decade, century, era. - Seasons and events. - Standard units of time, the clock.

Make word list of attributes in every day life that are linked to time

Draw or make collage relating to the attributes that are linked to a time of day or year (changes due to rain, sunshine, cooler temperatures, etc.)

Write sentences as it relates to the relative position of time of the day

Sequence order of information and/or order of action in solving of mathematics problems

5. Temperature: - Direct comparison. - Hot, cold, luke-warm, warm,

freezing, etc. - Standard units of temperature. - Different types of thermometers. - Measures of other attributes

linked with the weather – rain, wind, sunshine and snow.

Measure and describe different attributes by comparison, to generate terms such as “hot”, “hotter than”, “cold”, “colder than”

Draw pictures of evidence of temperature change/weather patterns

Role play: radio/television announcing of weather report and students dressing accordingly. Integrate weather by linking to: - literacy skills, e.g., listening

to, writing on, story telling, (weather report on quantity of rain in different communities)

- representing information by bar chart built from congruent rectangular cut -outs

- social activities-farming, washday, playing, going to work/school/party

- artwork - charts showing

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activities associated to day’s weather

- nature walk – observations on a rainy day, sunny day, etc.

6. Mass and weight: - Types of scales (bathroom,

market) and balances (post office, laboratory).

- Read scales and balances. - Estimate mass of given objects. - Find the mass of given objects.

Measure and describe different items by comparison to generate terms such as “heavy, heavier than”, “light (not heavy), lighter”

7. Money: - Use of money. - Denominations. - Making change.

Role play at the store, shop, making change

Field trip to the super market to observe or to gather data on size and related cost of same commodity of different brands. NB: Use data to draw graph and possibly make decisions on the best buy

Make models of instruments for measuring different attributes

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YEAR 2, SEMESTER 1

Number of Hours: 18 Instructional Objectives: Student teachers should be able to: 1. establish and explain the need for and importance of planning for the mathematics

class.

2. apply and describe different patterns of instructions in teaching.

3. acquire planning for teaching skills and apply them in the early childhood mathematics classroom.

4. teach problem solving skills.

5. teach math via problem solving.

6. use the Ministry of Education, Youth and Culture’s revised curriculum to organise and write chunks of content for daily, weekly or monthly usage in the mathematics classroom.

7. examine alternative assessment procedures and explain their uses in the mathematics classroom.

8. develop rubrics for different types of assessment and patterns of instructions.

9. make and use a wide variety of manipulatives suitable for teaching in the early childhood classroom.

10. use the environment to teach topics in mathematics in the early childhood classroom.


1. Patterns of instruction: - Direct Instruction – play modeling,

drama, and singing, miming, drawing.

- Discovering – exploration, inquiry. - Problem solving and investigation.- Using the environment to teach

topics in math. - Making connections in

mathematics across the curriculum – yhematic approach, interdisciplinary, intra-disciplinary.

- Questioning.

Model story problems Write story problem from models Collect and represent data from the

environment, e.g.: i. for connection with Social Studies-

size of household according to bedrooms and number of persons in house, male, female, relationship of occupants

ii. for connection with – Science number of ants around piece of food, size of leaves on plant inside classroom, heights of classmates

Keep scrapbook/journal of mathematics field trips

Use topological experiences with objects in their environment (furniture, plants, strings, rubber bands, pictures) to refine understanding of relative

Planning to TeachUNIT 7

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positions, order separation, proximity and enclosure

Make the link with language experiences of opposites, i.e., - over/under - open/closed - inside/outside

2. Types of plan: monthly, unit, daily. Discuss the processes involved in

planning: monthly, weekly, daily, unit, lesson

Identifying: - the important aspects of this

process - the aspects which are recorded - how these aspects are recorded

Review and critique successful lessons. - How can you tell to what extent

objectives have been met? Presenting of parts of a lesson (a self-

contained part). Discuss the plan for the lesson segment

Obtain feedback for different stated segments of the lesson and discuss improvements/changes where necessary

3. Instructional materials: - Numbers corner. - Making, using, storing of

instructional materials. - Using the calculator and the

computer-logo the computer turtle.

Make math corner/math lab for classroom for appropriate age group

Build mathematics corner by preparing activities and materials for named topic or concept being studied

Use the calculator for estimating solutions

Use computer software such as logo for simple geometrical operations and construction

4. Assessing mathematical abilities of the young child:

- Why assess. - Ways to assess: observation,

listening, written test, portfolio, journal, interview.

- Rubrics for different types of assessment and patterns of instruction.

Research and present on the following topics: - Mathematical tasks - Alternative assessment in

mathematics, process/product - Journal keeping as a tool for

assessment - Assessment recording systems

Write rubrics for assessing the processes and the products of the mathematics classroom

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Number of Hours: 12 Instructional Objectives: Student teachers should be able to: 1. design and use instrument, interview schedule, questionnaire and direct observation

to gather data relating to any familiar experiences.

2. gather data by counting and tallying.

3. sort and classify data (sets of objects or situations according to similar stated attributes).

4. collect, sort, classify, display, analyse and interpret data when given situations involving factors within their environment.

5. collect, sort, classify, display, analyse and interpret data by using a variety of graphical methods.

6. display data using circle graph, pictograph, stem and leaf plot and box and whiskers plot.

7. solve problems using information given in table or pictorial display.

8. solve problems involving the three measures of central tendency, mean, mode and median.

9. create a problem statement involving probability based on information from a given problem situation.

10. solve problems involving the probability of single events.

11. construct sample space and simple tree diagram that represents all possible results.

12. model situations by devising and carrying out simple experiments or simulations to determine probabilities.

13. model situations by constructing sample space to determine probabilities.

14. conduct probability experiments and record outcomes.

15. predict the outcomes of experiments.

16. compare predictions with outcomes of experiment.

17. use appropriately the terms used in probability theory.

18. interpret probability from sample space graph or table.

19. link the concept of data collection and management with its usefulness in science and social studies.

20. link the concept of probability with science and social studies.


1. Classifying and sorting information/ data.

Gather and display data from familiar experiences. Going shopping, favourite food, favourite brand, voting for class monitor or class trip, etc.

Managing DataUNIT 8

26

2. Representing data/graphical methods: - Bar charts, pictograph, line graph,

tables. - Stem and leaf plot, box and

whiskers plot. - Circle graph/pie- chart to include

only halves, quarters and eights.

Record heights of each member of class by lining up against a class room wall; use information in another class for comparison

Use the concept of fractions and the fraction circle to represent information on the circle graph/pie chart

3. Read and interpret diagrammatic representation:

- Collecting data. - Questionnaire interviews,

schedule, counting, tally marks, tables, etc.

Use students’ display of data from familiar situations, e.g., voting for class monitor or class trip to analyse, interpret and make decisions from data collected

4. Measures of central tendency – mean, mode and median.

Rearrange by re-recording individual heights in sequence (tallest to shortest or vice versa) to display the middle height (median)

Estimating and leveling off heights to find another average (the mean)

Line up against recorded heights to determine the most popular height (mode)

CONCEPTS OF PROBABILITY


5. Terms used in probability: chance, event prediction, odd, outcome, like, unlike, sample arrangement.

Listen to weather forecast for a month and record the frequency of the usage of the words “chance” and “probability” in reporting

With the help of dictionary and other research tools determine the meaning of the listed words

6. Representing sample space as a fraction, by using tree diagrams or from lists/tables.

Interpret probability from sample space, graph or table

7. Conduct probability experiments and record outcomes.

Compare predictions with outcomes of experiments and make connections

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Number of Hours: 18 Instructional Objectives: Student teachers should be able to: 1. explain how to develop the child’s concept of a fraction through a variety of methods

in relation to completeness and entirety.

2. develop the concept of equivalent factions.

3. employ and describe a variety of strategies that will enable children to acquire skills and concepts of:

a. Adding fractions.

b. Subtracting fractions.

c. Multiplying fractions.

d. Dividing fractions.

4. state to what extent children’s knowledge of the place value system relates to the decimal fraction system.

5. identify strategies for teaching the four basic operations of decimals.

6. plan strategies to help children estimate their answer and check for the “reasonableness” of their answers.

7. express decimals in expanded notations.

8. approximate with respect to:

a. Decimal units.

b. Decimal places.

c. Significant figures.

9. arrange decimals and numbers in order of magnitude.

10. estimate calculations involving decimals.

11. use calculators for speedy calculations, for checking calculations and to reinforce mathematical concepts.

12. relate percentage to common fractions and decimals.

Exploring Further Number ConceptsUNIT 9

28


1. The conceptual knowledge of fractions: - Real objects. - Concrete models for fractions. - Diagrams for fractions. - Fraction symbols. - Oral fraction names.

- Comparisons of fractions. - Equivalent fractions.

Use: i. Shaded area of geometric

shapes to represent fractions ii. Chalkboard diagrams or

pictures of articles (chocolate bars of varying sizes) to talk about fractions, number of partitions, quantity of portions

iii. Fraction board to compare number of parts to whole

Superimpose fraction wheels to

compare and find equivalent fractions

Use the calculator Math Explorer to compare fractions

2. The four basic operations on fractions:

- Develop problems involving the four basic operations on common fractions.

Make and use place value pockets Use fraction bars and/or families to

combine or separate fractions (addition and subtraction)

Superimpose congruent rectangular region line shaded in different directions to develop the concept of multiplication of fractions

3. Conceptual knowledge of decimals:

- Models and oral language for lengths.

- Symbols for length. - Tenths and hundredths. - Ordering and comparing decimals. - Four basic operations on decimals.- Estimating with decimals. - Writing fractions as decimals. - Scientific notation.

Use metric distances on the number line and/or real money (dollars and cents) to represent decimals

Use a floor number line to order, compare and estimate decimals

Superimpose pairs of fraction wheels -one family of tenths and common fraction such as ½,1/4

,1/5,1/8,

1/10 . Compare and find equivalent decimals

4. The concepts of ratio and proportion: - Relationships to common factors

or rates. - Part to part and part of whole. - Use of ratio in solving story word

problems.

Integrate math and science, “willingness to observe health rules”: mime, skit “at the doctor” or “at the clinic”; pharmacist mixing and dispensing medicine according to a proportion - 4 tablets per day or two teaspoonfuls

5. The concept of percentage: - Percentage relationship to rates,

e.g., Method of savings (partner), Why save.

Mime, skit, acting out “saving at home” in various locations, e.g., under bed, in box, and losing savings because of …

29

- Banking and interest rate. - Profit and loss and consumer

arithmetic.

Debate on strengths and weaknesses of banking systems

Visit super market: calculate unit price, comparison to find the best price

30

Number of Hours: 15 Instructional Objectives: Student teachers should be able to: 1. identify different movements observed in nature and in the built environment.

2. identify the four main types of transformations: turn slide (translation), flip reflection, turn sized enlargement/reduction.

3. use the concept of rotation to introduce concepts of circle, semicircle and quarter circle.

4. use circular movement to introduce the concept of angles.

5. construct accurately triangles of 300, 600, 900, 450 and their composites.

6. make two congruent shapes coincide to show that every occurrence of this is through a turning point.

7. accurately construct triangles and quadrilateral.

8. write the formula for the sum of the angles in a polygon.

9. identify the different types of triangles according to sides and according to angles.

10. show that every turning motion is about a point (the center).

11. identify figures with line symmetry.

12. determine number of lines of symmetry.

13. use the concept of symmetry to write the properties of triangles and quadrilaterals.

14. use the concept of line and rotational symmetry to draw pictures and create designs.

15. translate shapes on the plane in the given directions – north, south, east and west.

16. use concept of translation to create patterns.

17. apply the concept of perspective drawing to develop the concept of enlargement.

18. make enlargement/reduction of plane shapes by construction.

19. write the properties of the plane shapes under the four transforms studied.

20. use the transforms to determine similarity and congruency of plane shapes.

21. use the concept of tessellation to develop or reinforce the area concept.

22. apply the concept of tessellation to design and pattern making.

Geometric Concepts IIUNIT 10

31


1. Movement: Relation – Revolution – Circle – Semicircle, ¼ Circle.

Use of varying sized rubber bands to construct closed curves on Geo-board. Tracing of shape to define simple and complex closed curves, inside/outside of curves and their shapes

2. Angles: Types of angles Construction of Angles: 30, 60, 90, 45 and their composites.

Use of the corner angle/right angle to make estimates of acute angles

3. Constructions of triangles and quadrilaterals. Use of the protractor.

Making of models of protractors Use these models to draw angles

of varying sizes

4. Sum of angles in a polygon. Types of triangles according to sides and angles.

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Number of Hours: 12 Instructional Objectives: Student teachers should be able to: 1. develop and describe activities for teaching children the concept of perimeter.

2. teach young children the concept of area using various activities.

3. find the area of plane shapes.

4. use the concept of area to formulate problems relating to real life situations.

5. develop and describe activities for teaching children the following concepts: volume and capacity.

6. calculate the volume of solids, e.g., cuboids, cylinders, cones, and pyramids.


1. Perimeter: concept of perimeter, perimeter plane shapes.

Use various implements to measure the length of the boundary line of plane shapes.

Use trundle wheel to measure given distances/ lengths in the school environment

2. Area: concept of area:

- Area of plane shapes – quadrilaterals, triangles, circle and their composites.

Use different plane shapes to cover and fit the surface within the boundary line of given plane shapes

Investigate and report on places in the environment where other shapes or objects are used to cover (considering to the effect, the material used, why this is used, quantity used, etc.)

Investigate the covering of circular regions by non-circular regions

Write the findings/explanations in math journal

Use square tiles or squared sheets or the computer to investigate area/perimeter relationship of a shape (rectangular)

3. Volume and capacity: - Concept of volume and capacity. - Direct measurement. - Filling, packing and stacking. - Volume of cuboids/cylinders,

cones and pyramids.

Research and explain concepts of volume/capacity/differences between them

Use methods of stacking/packing/ filling to develop the concepts of capacity and volume

Measurement, Part IIUNIT 11

33

References

Copley, Juanita V. (2000). Th eYoung Child and Mathematics. Washington, DC:National Association for the Education of Young Children (NAEYC).

Haddens, James W. Today’s Mathematics (6th Edition). Concepts and Methods in

Elementary School Mathematics

Kennedy, Leonard M., Tipps, Steve. (2000). Guiding Children’s Learning of Mathematics (9th Edition)

National Council for Teachers of Mathematics. (2000). Principles and Standards for School Mathematics

Payne, Joseph N. (Ed). (1999).Mathematics for the Young Child. National Council of Teachers of Mathematics

Reys, Robert E., Suydam, Marilyn N, Lindquist, Mary M., Smiyh Nancy L. (1995). Helping Children Learn Mathematics (5th Edition)

Robinson, Eugena. (1994). Understanding Mathematics in the Early Childhood Curriculum. Publication of the UWI Bernard van Leer Foundation North Coast Project, Port Antonio.

mathematics for early childhood - jbte.edu.jm syllabus/mathematic… · piaget, dienes, vygotsky,...

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