إرشادات دراسية ومبادئ تعلم الأطفال

Instructions for Studying this Course

• Pay attention to the subject before beginning to study for this course.
• Comments on previous semester results.
• Graduates, but be diligent, hardworking, and disciplined.
• Course description.
• Attendance and absence.
• Participation and interaction.
• Assignments (and matters related to uploading assignments to Blackboard).
• The course textbook.

Principles in Children's Learning

• A significant portion of a student's mathematical understanding is established in the early grades.
• Teaching plays an important role in young children's learning and understanding of mathematics.
• Factors that affect a child's learning: the student's direction and beliefs towards mathematics + parents' direction + teacher's knowledge and directions + background (economic, social conditions + social type, language, culture + special needs and prior mathematical knowledge).
• The child's cognitive, linguistic, physical, social, and emotional development.
• Students come to school with more prior mathematical knowledge and experience than we realize.
• Children develop a mathematical sense at a very young age.
• Children learn mathematics through intuitive thinking, learning from real-world, tangible examples.

Factors Teachers Should Consider

• Teachers should enable activities through direct handling of things, and reliance on the senses.
• Children learn from work, conversation, discussion and reflection, building their mathematical knowledge using their senses and natural situations.
• The teacher needs to assess pre-existing mathematical knowledge to guide subsequent teaching through interviews, meetings, and observing children as they work, speak, and discuss.
• Children's understanding improves when they face concepts in depth and logical sequence, allowing them to develop, construct, and reflect on their understanding.

Theories on Children's Learning and Concept Development

• Piaget: The ability to think verbally using tangible formats develops in children from the ages of seven or eight, approximately up to the age of twelve.
• Skills for reflection develop, meaning the ability to revert thought to the original starting point.
• Vygotsky mentioned that there is an area between Piaget's stages of intellectual development, which he called the zone of proximal development.
• The zone of proximal development is defined as the transition to the next intellectual stage facilitated by an experienced person.
• Bruner stated that learning in children should occur in 3 levels: the sensory level: learning through work, that is, direct experience. the iconic level (illustrative): the use of an image of the thing instead of the thing itself in teaching, that is, illustrated experience. the symbolic level: using abstract experience systems.

Elements of Mathematical Knowledge

• Mathematical Concepts
• Mathematical Generalizations
• Mathematical Skills
• Mathematical Problems

Mathematical Concepts

• The mental image that forms in the individual due to the generalization of common properties and characteristics among a group of elements.
• A collection of things, symbols, or special events that have been brought together based on shared characteristics that can be indicated by a name or a specific symbol.
• These things may be:
• Tangible or intangible.
• A word, symbol, or image.

Mathematical Generalizations

• A mathematical statement (informative sentence) that connects two or more concepts, has a universal quality, and the possibility of application to all similar cases, and is divided into 3 types:
• Axioms or truisms: a phrase we accept as true without proof.
• Theories: A generalization that is amenable to proof and affirmation.
• Laws and rules

Algorithms and Mathematical Skills

• Algorithms: The routine method and an organised flow to perform a task.
• Skills: The ability to perform work quickly, accurately, and with proficiency.

Mathematical Problems

• Note: Mathematical problems do not mean exercises.
• A mathematical problem is a new mathematical or life situation that a person encounters and does not have a ready-made solution at the time.
• One thinks about its solution and uses what he has learned previously to be able to solve it.

Question vs Exercise vs Problem

• Question: A position that requires the student to recall information from memory to answer it
• Exercise: a position that aims to acquire the learner to perform a skill or training based on known information.
• Problem: A new position requires the student to think about it, analyze it, and use what he has previously learned to reach a solution.

Examples Question, Exercise, Problem

• Question: Asking the student about multiplication facts
• Exercise: Find the product of the following: 265 + 324 = ?
• Problem: Ahmed has 67 riyals, bought a notebook for 22 riyals, how many riyals does he have left?

Using Manipulatives

• Using tangible materials provides students with experiences through touch.
• Physical manipulation helps students to model, describe, and explore mathematics.
• Instructions for Use of Manipulatives: Choose the manipulatives that support the concepts to be taught. Give students an initial opportunity to become familiar with the manipulatives. The teacher must use the manipulatives in the same way that the students will use them.
• Avoid activities that ask students to imitate the teacher. Give students an opportunity to discover the concept with a variety of manipulatives.
• Note: Manipulatives themselves do not carry mathematical understanding, but rather provide students with sensory ways to give meaning to new knowledge.
• Allowing them to describe mathematics, build a dialogue with the teacher, and make them more communicative.

Think about doing the following

• Discuss with your colleagues, under the guidance of the coordinator, some examples from mathematics courses on each of the above, based on your reading of the definitions.
• What is meant by content analysis?
• How is it used when teaching mathematics topics?

Lecture Three

• Mathematics in the World of the Child (Teaching Some Mathematical Concepts and Teaching Methods)

Introduction

• Intuitive Thinking: Learning through tangible, sensory things, direct experimentation and forming of experiences from embodied and diverse situations.
• Reliance on the senses and intuition, without relying on analytical thinking operations or steps, shapes.
• Child needs guidance, not traditional teaching in the traditional sense.
• The teacher needs to be a developmental teacher.

Teachers should encourage growth of the child

encourage the growth of the child's language and use words that are ingredients of the language of Mathematics like a lot small , long short , first ,after, inside outside ,before after , Today, yesterday, inside outside Accept the child as he is . . Accept his mistakes and guide him to the right way . Dont let him feel that mistake means failure and let him feel that he is able to succeed.. Let the child feel he is part of a group and encourage mutual activity. Focus on the strong traits that the students have Use motivation not intimidation Guide students and do not teach with dictation.

Activities for a Child's World

Teacher to facilitate children to gain knowledge Create an environment and an opportunity to discover themselves. Students will be presented things that they can describe and identify their properties with comparison.

Example Activities

Describe this object Identify the object by touching it. Complete the task Pattern shape look....etc Sort objects by length , size or contents . According to Piaget, the child's constructs with concrete experiences build the time and shape dimensions. The child needs to interact with objects and connect the concept with his brain

Pigaet's Stages of Development

• Sensory Motor Phase (0-2): Pre-verbal and pre-symbolic stage. Development takes place from spontaneous movements to acquired habits, and the child performs actions that indicate intelligence.
• Pre-Operations (2-7): The ability to use words that express things grows, and they begin to deal with symbols and representations of the world around them, and there is nothing to indicate logical thinking.
• Tangible operations 7-12: Logical thinking grows partially based on tangible interaction with things. Skill of reversion grows with them.
• Abstract operations 12 and beyond: They learn deduction in deductive ways and using abstract ideas, and thinking operations are not related to

The Constructivist Theory

• an educational psychology concept.
• focus of this is the concept that learning is an active precess in which the learner builds knowledge on past experiences
• the study of knowledge
• current curricula were built according to the theory.
• previous curricula were used according to behavioral theory

The number and its presentation

• number is a natural thing in the life of a child .

the meaning of the number will be learned by

• Playing with group of physical object .
• used of images , shapes ..
• symbol of the object
• words to describe what those object are

Follows

what we said required a Sense the number in the student by using many objects, with mentioning the name for the child to read . Present group of objects physical with mentioning the name for the child to read . Ask the students to mention some physical object that make two objects .

Problems that May Occur During Teaching Numbers

• Rote counting and counting on fingers leads to confusion between the rank of the number and the size (how many) of the number, which is known as the cardinal number.
• Lack of control when counting, in the sense of not being able to control the things that are being counted.
• Can count the same thing more than once.
• Shuffle the order while counting.

Awareness of place

• Thinking in place begins with the child's transition from the topographical stage to traditional thinking, which begins around the age of 5-7. That means that the child is able to draw shapes whose properties do not change/ sides and measurements . This shift doesn't happen suddenly, it takes time. The child begins with the ability to use correct names for shapes: . line, square, triangle دائرة

Topological concept

• study of features and spatial relation that continue with no change.
• when the shape changes because of tension the length the mess , size may change but some features continue, such as location of all shapes points stay the same,
• EX If we drew a shape on a elastic then that changes with out cutting them.

Aclsidee concept

• the features stay the same, the area point and all points inside and the relation ship from the inside and out stay the same and don changes at all by transition or rotate.

The teacher can

• ask students to build a house or a car using cubes and what they will pt in place.
• provide them with plastic , dollls , cube ...etc
• put the students into circles to communicate
• rank the objects to a special point like being close to each other.
• let the student daw the shapes .

Awareness in time

• the thought of what happen first takes over and start to remember.
• the event or happening starts together and the child is able to determine the relation and speed .

activities to develop understanding

• kinetic activities link movement with time.
• less or less time
• comparison
• depend on the story what they present

Test questions

• everything mention is a conceots besides Problem
• angels in side a quadrille . equal 360 this Is
• read a number contain 3 numbers

Learning

• take objects that are share

Lecture Four: Methods and Approaches in Teaching and Learning Mathematics

• What is meant by effective teaching?
• Thinking: Try to relate the pictures to the subject of the lecture

Effective Teaching

• Are there methods that are suitable for teaching mathematics and helping students to gain the most from it?
• Is there a single method suitable for all students?
• Is there a single method suitable for all mathematics topics? The answer to all of the above questions is: No

How to Preparation for a successful teaching method

• Determine the mathematical tasks that will be presented, and the conditions that will facilitate their learning. How? Preparation, short presentation, activities and work papers
• Use of e-learning materials .
• Determine the teacher's and students' roles.
• Determine the learning resources Textbook, mathematics laboratory, learning resource center, visits and field trips, video clips,
• Conscious preparation that the teaching method includes: dialogues - work performed by students - direct presentations - summaries of what some students say - investigative work - summaries at the end of the lesson of what was closed the lesson) - varied evaluation

General Teaching Skills

• You must possess general teaching skills in addition to mastering your scientific material, which is divided into: Skills are non-verbal such, Skills are verbal such.

First Organized Learning

• what do we mean ص 112
• some guidace of the how it can be improved
• there can be many examples to learn this way

Second education with small group

• What is meant by cooperative ?116
• charteris of cooperative s 117
• How it can be divided and what should we do before we begin .

Third Strategy think pair chair

What are steps of this ? What characteriz it ? create a time of thinking help cooperation the main aim is for everyone to learn.

the four ? strategy

know its name step of this it will br there in pictures coming

Method ? jigsaw

to all the student of the task of special group the student will be with groups with shared task

Method ?Jigsaw

Everyone learn there group Each students shows what he had learned.

Method Direct introduction

The teacher control and dominated the subject

Method discover in

Discover 116

Method Free discover :

give the students a way to what they can discover

Guided :

the teacher helps student to reach

Strategies of discovery

A -inductive use to introduce what it is known

Strategies of discovery

B - deductive use the logical the concepts The mathematical way of number

In mathematics way of number

A number odd a number Even ; A . inductive way : introduce tangible materials with different objects

In mathematics way of number

B - deductive ; introduce an even and odd number by division ,