IF YOU THINK WAEC MATHS IS HELL,HERE ARE 84 STEPS TO MATHS HEAVEN (3)

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CONCEPTS AND PRINCIPLES OF WAEC MATHS FOR EXAM SUCCESS

WAEC HAS ADVISED THAT UNDERSTANDING OF CONCEPTS IS  KEY TO OPENING MATHS DOORS

40.WAEC examiners year in, year out point out that understanding basic concepts and principles is crucial for unlocking the doors and windows of maths.

41.This is because concepts and principles constitute the vocabulary of maths. In English language, if we do not understand certain words we look for their meaning in dictionaries. This is applicable to maths too. At every stage from JSS 1 to SS 3, maths text books contain specific words which belong to the subject. Sometimes they are difficult to understand or define.

42.Almost  400  concepts and principles are to be found below

43.Concepts and principles have to be translated into mathematical questions or expressions or into diagrams and vice versa before maths can be made simple. But tutors will be useful for giving meanings which are down-to-earth, simple-to-understand and in many practical ways using real-life illustrations as examples.

44.Mathematical concepts actually explain what maths is about. Even the ape men understood them according to the needs of their period. But as their activities widened and they became more sophisticated, their maths concepts widened in scope too.. As long as we count, measure, estimate, calculate or describe shapes, objects etc, then we are performing maths operations. We therefore actually think maths, speak maths, and live maths without realizing it. The job of a school and its tutors should be to spend a great deal of time explaining  these concepts to  students.

45. Under step10, we mentioned that maths is a language. You may also be surprised to know that the roots and development of maths can be traced to music, fine-arts, games, poetry, astronomy, architecture, sculpting and later to engineering. All these art forms can be used to teach the concepts of maths. For examples, students can be given maths essays: students can also be asked to ACT a topic by being called to the board to summarize the way the topic has been taught or to demonstrate class understanding of the topic. Definitely, a student should be asked to express some understanding of “negative number” and inequalities” orally to his or her classmates! Students should also be given THINK ALOUD PROBLEM SOLVING (TAPS) concepts, and many word problems and logic, which will make them to reason. Students should be asked to state verbally how they will still solve a problem instead of writing the answer on  the board. Games such as CONCEPT BINGO ( to be explained by EDUPEDIA if you ask us through an e-mail) can also be used to make maths student-friendly. As mentioned earlier we also have what is known as SPEED (MENTAL) MATHS, KITCHEN MATHS, RECREATIONAL MATHS, MONEY MATHS AND LOGICAL PUZZLES which can be used to teach these concepts. Teachers should learn to teach “maths for humans” rather than for aliens as most of them presently do. But does the understanding of concepts alone bring the matter to a conclusion? No.
HOW MANY OF THESE CONCEPTS DO YOU REALLY UNDERSTAND MATHEMATICALLY?

(S) MEANS CONCEPT IS MEANT FOR SENIOR SCHOOL ONLY

ACUTE ANGLE	BREADTH	COMPLETING THE SQUARE(S)	DEVIATION
ACUTE BISECTOR	BREAK – EVEN POINT (S)	COMPONENT	DIAGONAL
A.C.F	BROKER	COMPOUND/SIMPLE INTEREST	DISJOINT SET
ALMIGHTY FORMULA	BUTUT	CONCAVE	DISTRIBUTION
ALTITUDE	CALENDAR YEAR	CONCENTRIC	DIVERGENCE
ANGLE OF DEPRESSION	CAPITAL	CONCENTRIC ARCS	DIVISOR
ANGLE OF ELEVATION	CARDINAL NUMBER	CONCURRENCE (S)	DOMAIN (S)
ANGULAR DISTANCE (S)	CARDINAL NUMBER	CONE	DUMMY
ANGLE OF INCIDENCE	CEDI/PASEWA	CONFIGURATION	DUODECIMAL
ANGLE OF INCLINATION (S)	CENTRAL TENDENCY	CONGRUENT (S)	EAST(E)
ANNUAL (S)	CENTRE OF GRAVITY	CONSECUTIVE	ECHELON
ANNULUS	CENTRIFUGAL	CONSTANT	EDGE
ANNUITY	CENTRIPETAL	CONSTRUCT	EIGEN VALUE (S)
ANTI – CLOCKWISE	CENTROID	CONSTANT TERM	ELASTICITY
ANTI-LOGARITHM	CENTRE OF PARALLEL	CONTINUUM	ELIMINATE
APEX	CHANGE	CONTOUR LINE/MAP	ELLIPSE(S)
APPROXIMATION	CHARGEABLE INCOME	CONSTRUCTION	ELLIPSOID
ARC	CHART	CONVERGENCE	EMPIRICAL
AREA/VOLUME	CHANGE OF SUBJECT	CONVERSE	EMPTY SET
ARITHMETIC SEQUENCE	CHORD	CONVERSION	ENDOWMENT POLICY (S)
ARITHMETIC PROGRESSION (S)	CIRCLE	CONVEX	ENLARGEMENT
ARRAY	CLOSE SOLID	COORDINATE	ENUMERATE
ASCENDING ORDER	CIRCULAR MOTION	CORRECT TO	ENUMERATOR
EXTERIOR/INTERIOR  ANGLE	INCLINED	HEPTAHEDRON (S)	IRREGULAR FIGURE
EXTERIOR ANGLE	INCLUSIVE	HEXAGON	ISOGONAL
EXTRAPOLATION (S)	INCOME	HEXAHEDRON (S)	ISOMETRICAL
FACE OF A SOLID	INCOME TAX	HISTOGRAM	ISOSCELES
FACTOR	INCOMPATIBLE	HISTOGRAM	INTEGRATE(S)
FACTORISATION	INCREMENT	HOLLOW SPHERE	INTERDEPENDENT
FINITE SET	INCOSAHEDRON(S)	HORIZONTAL	INTEREST
FRUSTUM(S)	% INCREASE	HYPERBOLA (S)	INTER-QUARTILE(S)
GEOMETRICAL MEAN (S)	IN DESCENDING POWER	HYPOTENUSE	INTERSECTION
GOLDEN MEAN (S)	INDEMNITY	HYPOTHETICAL	INVERSE
GRAPHICAL	INDETERMINATE	IDEAL POINT	INVERT
GRAVITATIONAL	INDEPENDENT	IF AND ONLY IF (S)	INVERSE RATIO
GRID	INDICES(S)	IMAGE	INVERSE OPERATION
GROSS	INELASTIC	IMAGINARY POINT	KILOGRAM
HECTARE	INEQUALITIES	IMAGINARY QUANTITIES	KILOMETER
HECTOMETRE	INFERENCE	IMPROPER FRACTION	KILOWATT
HECTOGRAM	INFINITE	IN ASCENDING POWER	KINETICS (S)
HELIX(S)	INITIAL	IN CENTER
HEMISPHERE(S)	INSTALLMENT	INCLINATION
HEMISPHERAL TANK	INTEGERS	IRRATIONAL
HEPTAGON	INTERCEPT (S)	IRRATIONAL NUMBER

KITE	MIXED NUMBERS/FRACTIONS	ORDERED PAIR	PROFIT	SECANT VALUE	VENN DIAGRAM (S)
KNOT (SPEED)	MODE	ORIENT	PROPORTIONAL	SEGMENT (S)	VERIFY
LAMINA	MODULUS	ORTHOGONAL	POPULATION	SELLING PRICE	VERTEX
LATITUDE (S)	MOMENTUM	OSCILATE	POLYNOMIAL EQUATIONS (S)	SEMI CIRCLE	VERTICAL
LATERAL	MONOTONE	OUTCOME	PROJECTION	SEQUENTIAL	VERTICAL ANGLES
L.C.M	MONOMIAL	OUTCOME TABLE	PYRAMID	SET NOTATION (S)	VOLUME
LEAP YEAR	MULTIPLICAND (S)	OUTLINE	PYTHAGORAS THEOREM	SIGNIFICANT FIGURE	VULGAR FRACTION (S)
LENGTH OF CHAIN	MUTUALLY EXCLUSIVE (S)	OUTPUT	QUADRATIC EQUATION	SIMILAR	WEEKLY
LESS THAN	NANO	OVAL	QUADRATIC FORMULA	SINE	WHOLESALE
LEONE	NATURAL NUMBERS	OVERDRAWN	QUADRATIC MEAN (S)	SKEWED	WORD PROBLEM
LINEAR	NAUTICAL MILE	OVERHEADS	QUADRANT	SOUTH EAST(SE)	YEAR
LOAD	NEGATIVE ANGLE	OVERTIME	RADIUS	SOUTH WEST (SW)	YEARLY
LOGARITHM (S)	NONAGON	PARABOLA(S)	RADIANS (S)	SPAN	YIELD
LONGITUDINAL	NORTH EAST (NE)	PARALLELOGRAM	RANGE	SPEED	ZERO HOUR
LOOP (S)	NORTH WEST (NW)	PARAMETER	RATIO	SPHERE
LOCUS/LOCI	NOTATION	PARTIAL	RECIPROCAL	SPIRAL
LUNAR	NOT LESS THAN	PARALLEL	RECTANGLE	SQUARE ROOT
LUNAR DISTANCE	NOT MORE THAN	PASCAL’S TRIANGLE	REFLECTION	STANDARD DEVIATION (S)
LUNAR MONTH	NTH TERM	PATH	REFLEX ANGLE	STANDARD ERROR
LUNAR YEAR	NUCLEUS	PENDULUM	REGION	STANDARD FORM
MAGNIFY	NULL	PENTAGON	REMAINDER	STATIONARY
MAGNITUDE	NULL SET	PERFECT NOS	REMITTANCE	STATISTICS (S)
MAGIC SQUARE	NUMERAL	PERRANUM	RESIDUAL	STOCK
MAGNETIC EQUATOR (S)	NUMERATOR	PERCENTILE (S)	RESULTANT	TANGENT
MAJOR ARC	NUMBER LINE	PERPENDICULAR	RETAIL	TETRAHEDRON (S)
MAJOR AXIS	OBLIQUE	PERIMETER	REVERSE	TRAPEZIUM
MANTISSA (S)	OBTUSE	PERIODIC	REVOLUTION	TREE DIAGRAM
MAPPING	OBTUSE ANGLE	PERFECT SQUARE	RHOMBUS	TRIAL AND ERROR
MARGINAL DISTRIBUTION	OCTAHEDRON	PERPENDICULAR HEIGHT	RIGHT ANGLE	TRIANGLE
MARK-UP-PRICE	ODD NUMBER	PIE CHART	RING	TRIGONOMETRICAL
MATURITY	OGIVE (S)	PIVOT	ROOT	UNEQUAL
MAXIMUM	ONE TO MANY	PICTOGRAM	ROOTS OF AN  EQUATION (S)	UNIT
MAXIMA	ONE TO ONE	PREMIUM	RULE	UNIVERSAL
MEAN	ONE AND ONLY ONE	POLYGON	SALES TAX	UNIVERSAL SET
MEDIAN	OPEN SOLID	POSITIVE NUMBER	SAMPLE	UNKNOWN/UNLIKE TERMS
MENSURATION	OPEN AT ONE END	PRIME FACTOR	SAMPLING	VANISHING POINT (S)
MID POINT	OPTIMUM (S)	PRIME NUMBERS	SCALAR PRODUCT (S)	VARIABLE
MINIMUM	ORBIT	PRISM	SCATTER DIAGRAMS (S)	VARIANCE (S)
MINIMA	ORDER	PROBABILITY	SCORE	VARIATION
MINUEND	ORDINATE	PRODUCT OF	SECTOR (S)	VELOCITY

 

MATHS FEVER!.....STOP SHIVERING,HERE IS HOW TO PASS WAEC/NECO MATHEMATICS

 HOW YOU CAN BEAT WAEC MATHEMATICS

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 A. EVERYTHING STARTS FROM SELF-BELIEF AND CONVICTION

1. Most students wonder whether maths is real or just a torturing spirit of the air whose form or goal can neither be “seen” nor understood. Sometimes they understand a bit of it but most of the time they wonder what it is really all about.

2. But the worst cases are those who have psychologically accepted that in them maths is dead  and buried. This group also believes that nothing can be woken up from within to change their attitude towards maths.

3. Our message today is that if you are one of such students you are very mistaken. There is no magic to understanding maths or to unlocking its doors than overcoming your anxiety or hatred for the subject. You might have been led astray by your beliefs, convictions and perhaps backgrounds. But the good news is that you can come to love maths like many others who eventually shed their togas of unbelief through our schools, Mason College and PASS Tutorial College both in Festac.

4. Each of you must understand that God planted maths in everyone. There is no one with a special maths mind or brain. It is your attitudes and beliefs that determine   performance. Each human being is a mathematical end-product of the almighty God. Nothing shows this more than when the left-hand side of our bodies is compared to the right-hand side and you get an exact match. Every hair, vein, artery or muscle in our bodies including all the cells are mathematically numbered and programmed by God. Maths is therefore not a spirit and definitely not as far away from you as you think.

5. There is maths every where around you even in your rooms, kitchens, toilets, beds, and television. The balls you play and the plates you use to eat food are all basedon maths. As long as you have a cylindrical, spherical, cubical, or any object of any shape you are directly or indirectly using objects made or produced through maths. And there is none of them you cannot calculate its length, radius, circumference, arc, area or volume by the use of a simple string or meter rule.

 B. BE PREPARED TO FORGIVE TUTORS WHO ARE/WERE NOT HELPFUL TO YOU

6. Lack of good teachers might also have killed   enthusiasm for minimum effort on the part of many students. And in others the gates to maths understanding were closed and padlocked by tutors’ attitudes and teaching methods. The classrooms of such tutors are usually torture chambers during maths periods. And today you still remember how much relieved you usually are when maths periods are over. But do you know that there is no need for such antagonism? Are you aware that your relationship with maths was not supposed to be that bad?

7. Are you aware the write-up titled “84 Steps To Maths Heaven” was purposely written to help improve  your attitude towards maths in case your teachers failed to deliever? Please allow us suggest you forgive such teachers as their mistakes are usually that of omission and not commission?

C. SCHOOLS ALSO HAVE MANY CLOSE AND PERSONAL CONTRIBUTIONS TO MAKE

8. In Mason College, weak maths students had to go through at least 2 of 4 maths remedial programs depending on individual performances,evaluations and categorization. These programmes were called MATHS CLINIC, MATHS CONTINUOUS EXERCISES, MATHS FOUNDATION CLASSES and MATHS PRACTICALS. Edupedia shall be willing to be consulted on these for implementation in schools.

9. Students tend to think maths is made up of calculations only.That is far from the truth. A good school can direct the minds of its students to more humane maths-related activities such as MATHS POETRY/SONGS, MATHS ESSAYS, MATHS DEBATES, MATHS DIALOGUE, MATHS RADIO, MATHS LOGIC GAMES, MATHS PUZZLES, WORD PROBLEMS, QUICK MATHS, KITCHEN MATHS, ROAD MATHS, MONEY MATHS, BUSINESS MATHS, MATHS NEWS, MATHS MILESTONES and a host of other related activities to take the anxiety out of learning and applying maths practically to life.. The aim must be to instill confidence in students by proving that maths is just a series of very simple steps from every day living and that it is not a ghost.

D.  INTRODUCTION TO “84 STEPS TO MATHS HEAVEN”

This is a write-up divided into 84 paragraphs and 6 appendices. Its proposals are as follows:

BRANCHES OF MATHEMATICS

10. THAT TO UNDERSTAND MATHS EACH STUDENT SHOULD KNOW ITS BRANCHES.MATHS IS SAID TO HAVE 7 DIVISIONS NAMELY: ARITHMETIC, ALGEBRA, TRIGONOMETRY, GEOMETRY, PROBABILITY, STATISTICS AND STRUCTURE. BUT IT IS EASIER FOR A NIGERIAN STUDENT TO THINK OF MATHS AS A COUNTRY WITH 7 STATES WITH EACH  HAVING A SET OF RULES AND REGULATIONS TO BE STUDIED AND REMEMBERED BY THE STUDENT. THIS IS BECAUSE CLASS WORK,  HOME ASSIGNMENTS AND EXAMINATION QUESTIONS CAN BE EASILY RECOGNIZED FOR APPROPRIATE SOLUTION METHODS. ON THE OTHER HAND OUR STUDENTS CAN IMAGINE MATHS AS A HOUSE WITH SEVEN BEDROOMS WHICH ARE INTERCONNECTED.

CONCEPTS OF MATHEMATICS

11. THAT TO UNDERSTAND MATHS EACH STUDENT  MUST REMEMBER THAT MATHS IS A LANGUAGE LIKE FRENCH WHOSE WORDS AND MEANINGS HOLD THE KEY TO THE HOUSE REFERRED TO ABOVE. MATHS CONCEPTS MUST BE STUDIED AND INTERPRETED LIKE YORUBA, IGBO, HAUSA OR ANY SECOND LANGUAGE. UNFORTUNATELY, BECAUSE ITS CONCEPTS ARE IN ENGLISH, MANY STUDENTS TEND TO THINK THEY KNOW WHAT THESE CONCEPTS ARE. WHAT MANY  FAIL TO REALIZE  IS THAT MATHS CONCEPTS ARE THE ENGINES FOR SETTING MATHS QUESTIONS AND THAT THE IMPORTANCE OF BEING WELL- GROUNDED IN THESE CONCEPTS CAN NEVER BE OVEREMPHASIZED. CONCEPTS CONSTITUTE A VOCABULARY WHOSE MEANINGS MUST BE CONTINUOUSLY CHECKED TO UNDERSTAND MATHS.

IMAGINATION/VISUALIZATION

12. THAT TO TRULY UNDERSTAND MATHS THERE IS NO BETTER WAY  THAN THROUGH IMAGINATION AND LOGIC.YOU ALSO NEED TO VISUALIZE MATHS PROBLEMS  WITH YOUR 3^RD EYE (YOUR MIND) BEFORE YOU CAN SOLVE THEM.


FORMULAE,HINTS,SIGNS,NOTATIONS AND SYMBOLS

13 THAT YOU NEED TO GET USED TO MATHS FORMULAE, HINTS, SIGNS, NOTATIONS AND SYMBOLS.

OTHER COMMON SENSE FACTS RELATING TO MATHS (SEE DETAILED NOTES IN THE “84-STEPS” WRITE-UP)

 14. READ THE NEXT  MATHS TOPIC  BEFORE YOUR CLASS MATHS LECTURES.

15. WHEN WRITING CLASS NOTES OR ANSWERING QUESTIONS WRITE ONE STEP BELOW THE OTHER RATHER TO THE LEFT THAN TO THE RIGHT OF THE PAGE OF YOUR NOTEBOOK.

16. ALWAYS WORK AS MANY PROBLEMS AS POSSIBLE AT THE END OF EACH CHAPTER IN YOUR TEXTBOOK. THIS IS WHAT MATHS CONTINUOUS PRACTICE IS ALL ABOUT. UNFORTUNATELY THIS  SEEMS TO BE THE ONLY  EMPHASIS BY MOST TUTORS.

17. OBEY ALL MATHS ETIQUETTES WHEN PRACTISING SOLUTIONS.

18. IF A PROBLEM CANNOT BE SOLVED IMMEDIATELY DURING CLASS LECTURES OR STUDIES, DON’T BE DISCOURAGED. READ LATER OR RE-READ YOUR TEXT BOOK OR READ ANOTHER ONE FOR MORE IDEAS. AND THEN RE-ATTEMPT ITS SOLUTION.

WE HAVE JUST LAUNCHED THE FIRST MISSILE ON YOUR FEAR OF MATHS...TO BE CONTINUED UNDER 84 STEPS TO MATHS HEAVEN

ACKNOWLEDGEMENT FOR THIS AND  SUBSEQUENT POSTS UNDER 84 STEPS TO WAEC MATHS HEAVEN

1.STUDENTS’ DICTIONARY OF MATHEMATICS BY B.O SOYEMI (EDUCARE FOUNDATION)

2. MR O OWOLABI (EX-MATHS TUTOR,MASON COLLEGE FESTAC)