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CHAPTER TWO
Curriculum of Mathematics
Why we Learn
Math? What we
Teach in Math?
How we Measure
Learning
Outcomes?
Why we teach mathematics? The answer to this question is
to define the objectives of teaching mathematics.
What we teach in mathematics? The answer means select
the content.
To whom we teach math? The answer to this question is to
identify the methods and strategies of teaching.
The modern definition of the math curriculum: includes all
the educational experiences (inside classroom or outside
classroom) which the school is planning, supervising and
evaluating.
1) Principles for writing the curriculum
Mathematics curriculum must take into consideration these principles
A) Basic Needs:
There are basic needs to consider when choosing the objectives of
teaching mathematics:
The individual's need to understand the natural phenomena,
and how mathematics contributes to this understanding.
The individual's need to use mathematical methods in research,
analysis, interpretation and decision-making.
Section 2.2: Contents of Curriculum
Section 2.1: The New Definition of
Curriculum
To know how mathematics contributes as a science and art to the
cultural and civilizational heritage of the nation and human
society.
Preparation of members of the community of different
professions that need or benefit from mathematics.
The use of the language of mathematics in intellectual and
cultural communication and the need to send concepts and
mathematical ideas to others accurately and clearly through
mathematics.
B) The construction of mathematics: consists of concepts,
terminology, generalizations, principles, theories, skills, algorithms, and
mathematical questions.
C) Teaching and learning mathematics: There are many modern
theories of education in the learning and teaching of mathematics, which
in turn influenced the construction and re-organization of the
mathematics curriculum.
Among the principles to be observed are:
1. Introduce pre-learning as a
basis and a prelude to new
learning.
2. Use different teaching
strategies based on discovery
and participation and away from
indoctrination.
3. Introducing the topic in more than one way or method. Education
is a developing process and the student is not expected to fully
understand the topic from for the first time.
4. Taking into consideration individual differences among students.
5. Encouraging students to self-study inside and outside the school.
6. Focus on training to help learning concepts and getting skills.
D) Uses of Mathematics:
Mathematics is divided into two main areas: abstract mathematics
and applied mathematics, and it is important to attach the various
mathematics classes to the applied-practical aspect in order to
consolidate the concepts, theories and principles in the students' minds.
Applications of mathematics appear within one subject, for
example the derivation of functions; applications appear in the
maximum and minimum values and the graph of function. The
application of derivatives outside mathematics appears in practical life
or equations related to time
or mechanics.
The ways of solving
the problems in the form of
discovery or conclusion can
be generalized to solve
problems in everyday life.
The steps to solve the
mathematical problems are
considered as the basis for
addressing the human life
situations.
2) Objectives of teaching mathematics
A) General Objectives:
These objectives are for all levels from elementary to university.
For example, a mathematical concept can be taught in more than
one row of consecutive classes. It may extend to more than one
stage, but its processing in the higher grades is more profound.
The concept of inductive thinking and the concept of deductive
thinking at the primary stage through the examples of each and
then studying the same concepts then in the following stages in
some detail and more accurate and comprehensive.
The most important general objectives of teaching mathematics can be
identified as follows:
Provide the opportunity to practice comprehensive
thinking
The student uses different thinking methods, such as inductive,
deductive, and meditative methods
Know the limits of confidence in the results obtained by one of
the methods of thinking
Defines the difference between absolute issues of generalization
and those of limited circulation
Tries to ascertain the validity of the issues on which the decision
is based
Tries to review the steps of his thinking in the light of the issues
given and reliable
Acquisition of skill in solving mathematical problems
Determines the meanings of
the words and symbols in
the problem text and
identifies the relationships
involved.
Determines what is needed
in the problem and what
information will be used in the solution.
Translate the problem into relationships or geometric shapes.
Sets possible assumptions for the solution.
Identify missing information that may solve the problem.
Reaches to the solution in a logical scientific formulation and
supports its steps further.
Review the solution and make sure it is correct.
Trying to find more than one way to solve the problem.
Better articulate the problem that is best given.
Trying to take advantage of solving a similar problem.
He proposes a problem of his creativity or develops the
problem that he solved.
Recognize the influence of
mathematics and its importance in the
development of society
Recognizes the most important aspects of the history of math
thought, especially among Muslims.
Recognizes the most important aspects of the interaction of
mathematics with human civilization.
Recognizes the most important areas of mathematics application
in its local environment.
Recognize math contributions in the service of other sciences
Knows the most important purposes of mathematics in scientific
progress
Tries to use mathematics in his public life
Acquire the necessary skills to discover
new relations
Fluent to read the problem and explain
the words and symbols.
Represent relationships with geometric
shapes or other teaching aids.
Remember the information quickly To assign all steps of the
solution to its mathematical bases.
Conclude new relationships to employ find a correct idea of the
answer either by guessing or intuition.
Get the answer in as little time as possible.
Use Different methods to solve the problem.
Establishing positive attitudes toward
mathematics
Encourage attendance at mathematics
classes and respect teachers.
Perform all duties properly and on time.
He frequently asks about the new mathematical ideas and
deduces some of them.
He tries to find more than one solution to the problem.
He expands on mathematics subjects and other sources other
than the curriculum.
He tries to explain some phenomena and learn about the
influence of mathematics of them and in the development of
human thought.
Self-dependence in the
achievement of mathematics
Listen carefully to the
discussions and record the key ideas of
the lesson.
Summarize every point about mathematics.
Prepare a plan to organize his time to memorize the various
articles.
Skill formation in writing logical and organizational solutions
logically.
Identify sources of information from outside textbooks. Tries to
discuss what he cannot solve with others.
Solve exercises without the help.
Discuss a lot of exercises outside the textbook with the teacher.
Create positive habits and
accept criticism
Exchange information with
other students and help those
who need it.
Keeps the integrity and
cleanliness of his books and tools
and organizes writing in the mathematics book.
Does not interrupt his colleague through discussions and accepts
criticism from the mathematics teacher and his colleagues.
Draw geometric shapes precisely and express symbols.
Accepts collective or voluntary work.
B) Objectives of teaching mathematics in the primary and
secondary stages
Objectives of teaching mathematics in
primary stage (1-6).
Understand the basic concepts of
arithmetic and some applications of
these concepts in life.
Recognition of simple geometric shapes and familiarity with
their properties.
Gain skill in each of the following: Read and write numbers to
at least nine digits.
Perform the four basic processes.
Perform operations for calculating the percentage, proportion,
proportionality.
Use geometric tools, and precision in drawing shapes.
Objectives of teaching mathematics in the intermediate stage
(7-9).
Organizing previous mathematical experiences, and facilitating
the learning of subsequent mathematics, by studying common
concepts such as groups and relations.
Understanding the nature of numbers, by having the concepts,
relations and skills of number systems.
Understanding the nature of variables, apply their concepts and
symbols, and have the ability to use them in mathematical
expressions and sentences, and to use them in solving equations
and inequalities.
Expanding the base taught at the elementary level for the
Euclidean level study, and thus to infer the characteristics of the
geometric shapes at the level by logical conclusion, showing the
characteristics and role of the geometric transformations.
Understanding analytical geometry and its role in linking
geometry to numbers.
Development of measurement and control it.
Practicing different patterns.
Objectives of Teaching Mathematics in Secondary stage (10-
12)
Students in this stage must be able to:
Develop the ability to conclude, generalize and use their own
logic.
Understand some mathematical concepts. Such as: relations,
functions, trigonometric functions, differentiation, integration,
probability.
Understand the mathematical proof and its logical basis.
Understand some mathematical systems such as: group,
matrices.
Love mathematics, and learn about its most important
applications in life.
3) Curriculum Content
Educational experiences include information, skills and attitudes,
whether descriptive or non-descriptive, that will achieve the objectives
of the curriculum. Educational experience is an educational situation in
which the individual interacts with the surrounding educational
environment.
Count
Algebra
Engineering
Measurement
Statistics and
Probability
Triangles
The mathematics curriculum consists of the following
basic criteria:
1. Count and operations include:
Understanding numbers and methods of
representation and relationships between numbers
and numerical systems.
Understanding the meaning of operations and how
they relate to one another.
Doing the calculations easily and make reasonable estimations.
2. Algebra includes:
Understanding patterns, relations and functions
Representing and analyzing mathematical equations using
algebraic symbols.
Using mathematical models to represent and understand
quantitative relationships.
Analyzing the variable in different contexts.
3. Engineering include:
Analyzing of the properties and characteristics of 2D and 3D
geometric shapes.
Describing functions and equations using coordinate geometry
and other representation systems.
Applying transformations and use the symmetry to analyze
mathematical graphs.
Using graphs and engineering modeling to solve problems.
4. Measurement includes:
Understanding the measurable characteristics of objects, as well
as units, systems and processes.
Using methods, tools, equations and laws to determine
measurements.
5. Statistics and Probability includes:
Reading and understanding charts.
Organizing information in frequency table.
Find the measures of central tendency and the measurement of
variations.
Determining the sample space, elements and probability of event.
Using the properties of probability
6. Triangles:
Applying Pythagorean's theorem.
Finding the trigonometric ratios of the angle.
Solving the right angle triangle.
4) Methods and Activities
These include methods of teaching the curriculum, using the
teaching aids, and using the different types of activity accompanying
the curriculum. When choosing a teaching strategy, it is important to
be appropriate for the educational objects, and the diversity of
teaching strategies used to achieve the objectives must be taken into
consideration.
5) Evaluations
The aim of the evaluations is to identify strengths to
emphasize them and weaknesses to avoid them. The evaluation
strategies are chosen to be as diverse as observation, testing or
performance evaluation in order to know the extent to which the
goals achieve information and skills of the students.
Section 2.3: Guidance for
Teaching Mathematics
1) The modern methods are concerned with the following
Discovery learning: This means that the
student has the opportunity to reach some of the
concepts and relations that he will learn through the
preparation of organized activities in the textbook.
The importance of learning discovery is that it
provides an opportunity for students to reach solutions and
answers, which leads to the development of high level of mental
processes.
Diversity of experiences in which the student participates,
which helps to facilitate the concepts and remove boredom from
the student.
Linking the scientific material, including concepts, skills and
generalizations in real life.
Taking into account the order in teaching the scientific
material, the current information is based on previous
information, for example, multiplication come after addition, and
division comes after multiplication
2) Directions for evaluations:
The evaluation is used to measure the achievement of mental goals or
skills. Therefore, the assessment deals with concepts, algorithms and
problems whether arithmetic, algebraic or geometric.
The assessment includes three dimensions:
Evaluate the progress of the students towards the achievement
of educational objects.
Evaluate teachers through the teaching strategies used.
Evaluate the educational experiences in terms of achieving the
general and special objectives.
Section 2.4: Methods of
Applying the Curriculum
Among the aids that support the teacher and
facilitate his work are the following:
A) Textbook: It takes into account in the
textbook what follows:
It consists of two separate parts,
each part taught in a semester.
Take into consideration the order of
the course content.
Develop a set of exercises in each
lesson.
Develop a set of exercises and a test at the end of each
unit.
Start each lesson with a problem or an interesting
question.
View images and graphics in an exciting way.
Include lessons some activities.
Highlight concepts and theories in a unique color.
B) Teacher's manual: The manual should include the following:
Number of proposed lessons of the units.
The mathematical content of the unit with depth.
The answers of the exercises and tests.
Pre-learning activities.
Horizontal and vertical integration.
Improvement questions and questions to address errors.
The teaching plan of the unit, including the objectives
and strategies of teaching and evaluation strategies.
Unit test and proposed worksheets.
C) Educational aids:
It is an essential part in teaching mathematics and the
characteristics of the aids are accuracy, simplicity and their
association with the objectives.
Chapter Activities
Search for different definitions for curriculum, what are
the common elements of it?
Answer these basic questions (Why we teach
mathematics? What we teach in mathematics? How we
measure learning objectives?)
Look for one of the mathematics textbooks for the ninth
grade published before 1970, and compare it with the
ninth grade mathematics textbooks in 2020, in terms of
similarities and differences in content and teaching
methods...
Meet one of the teachers who taught old curriculum and
other one who taught modern curriculum of
mathematics. Ask them about their opinions in old and
modern curriculum. You can ask the following questions:
o Which one do you prefer, the old or modern
curriculum? Why?
o Do you think that modern curriculum is better than
old curriculum? Why?
o Do you think students are learning better using old
curriculum? Why?
o What are the differences between old curriculum
and modern curriculum?
o Do you think that old curriculum made students
love math more than modern curriculum?
If you can develop a new mathematics curriculum, what
topics will you delete or what topics you will add to the
curriculum?
Why do you think there are many different views on
modern mathematics curriculum?
Why Teach Mathematics? By Mathew
Felton
Source: National Council of Teachers Mathematics
https://www.nctm.org/
In this article, the author mentions some interesting reasons for
teaching mathematics in school, the main reasons as he decides are:
It is a beautiful and amazing human accomplishment.
For college and future careers, especially in science,
technology, engineering, and mathematics.
In addition to the goals listed above, he believes that
students should study mathematics to:
Learn about and appreciate diversity in human thinking
and accomplishments throughout history and around the
world.
See the role of mathematics in their daily lives, their
community practices, and their cultural backgrounds.
Understand, analyze, critique, and take action regarding
important social and political issues in our world,
especially issues of injustice.