Teacher recruitment

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Key topics in the recruitment of primary school mathematics teachers in Xiamen, Fujian Province can be found in official website, Fujian Province. You can refer to the 20 15 Fujian Xiamen teacher recruitment examination outline for primary school mathematics examination for review and preparation.

First, the nature of the examination.

The open recruitment examination for new teachers in primary and secondary schools in Fujian Province is a unified selection examination for candidates who meet the recruitment requirements. The examination results will be used as the basis for the open recruitment interview of new teachers in primary and secondary schools in Fujian Province. The recruitment examination should comprehensively assess the candidates from the aspects of teachers' professional quality and teaching ability, and select the best candidates. The recruitment examination should have high reliability, validity, necessary discrimination and appropriate difficulty.

Second, the examination objectives and requirements

This paper focuses on the examination of candidates' mathematical professional knowledge and teaching skills, and requires candidates to systematically understand and master primary school mathematical professional knowledge, teaching skills and teaching theory. While examining mathematical professional knowledge, we should pay attention to examining professional ability and highlight the ability to use mathematical professional knowledge flexibly to solve practical problems.

1. The requirements of mathematical professional knowledge are divided into three levels: understanding, understanding and mastering.

⑴ Understanding: It is required to have a preliminary perceptual understanding of the meaning and background of the listed knowledge, know what this knowledge content is, and identify it in related issues.

⑵ Understanding: It is required to have a deep understanding of the listed knowledge, be able to explain, give examples, deform and infer, and use knowledge to solve related problems.

⑶ Mastery: It requires the system to master the internal relations of knowledge, and be able to use the listed knowledge to analyze and solve more complex or comprehensive problems.

2. Professional abilities include thinking ability, computing ability, spatial imagination ability, practical ability and innovation ability.

(1) Thinking ability: the ability to observe, compare, analyze, synthesize, abstract and summarize problems or data; Able to use analogy, induction and deduction for reasoning; Can be expressed logically and accurately.

⑵ Operation ability: can perform correct operation, deformation and data processing according to laws and formulas; According to the conditions and objectives of the problem, find and design a reasonable and simple operation mode; Can estimate and approximate data as needed.

⑶ Space imagination: We can make correct graphics according to conditions and imagine intuitive images according to the graphics; Can correctly analyze graphic elements and their relationships; Can decompose, combine and transform graphics; Can use graphics and charts to reveal the essence of the problem vividly.

⑷ Practical ability: Being able to comprehensively apply the learned mathematical knowledge, ideas and methods to solve problems, including solving simple mathematical problems in related disciplines, production and life; Be able to understand the materials stated in the question, summarize, sort out and classify the information provided, abstract the actual problem into a mathematical problem and establish a mathematical model; Be able to use relevant mathematical methods to solve problems and verify them; Be able to express and explain correctly in mathematical language.

5. Innovative ability: being able to choose effective teaching methods and means and analyze teaching information and teaching situation; Being able to comprehensively apply the learned mathematics knowledge, ideas and methods, make independent thinking, exploration and research, put forward new problems in primary school mathematics teaching, find ways, methods and means to solve problems, and creatively solve teaching problems.

3. Teaching skill requirements.

Candidates are required to use these knowledge theories to analyze teaching materials, formulate reasonable education and teaching plans, make rational use of teaching resources, scientifically compile teaching plans, flexibly use heuristic, inquiry, discussion and participatory teaching methods, infiltrate modern educational technology into teaching and evaluate teaching cases.

Third, the scope and content of the examination.

Professional knowledge of mathematics

Understanding of 1 figure

Examination content: integer, fraction, decimal, percentage, rational number and real number.

Examination requirements:

(1) Grasp the meanings of integers, fractions, decimals and percentages, and rewrite and reduce as required; Master the order, name and relationship of counting units of numbers and levels; Use flexible methods to compare fractions, decimals and percentages.

⑵ Understand the nature of decimals and the basic nature of fractions, and use the basic nature of fractions for division and division; Understand the relationship among fractions, decimals and percentages, and use flexible methods to realize mutual transformation.

⑶ Understand the meaning of rational numbers; Understand the concepts of irrational numbers and real numbers.

⑷ Understand the concepts of square root, arithmetic square root and cubic root.

2. Digital operation

Exam content: four operations, root and power operations, divisibility, prime and composite numbers, greatest common divisor and least common multiple, and fundamental theorem of arithmetic.

Examination requirements:

(1) Understand the meaning of the four operations; Master the algorithm; Understand the relationship between addition, subtraction, multiplication and division; Master the basic methods of oral calculation, written calculation and estimation, and understand the corresponding arithmetic.

⑵ Understand the changing law of product, the invariable property of quotient and the changing law caused by the movement of decimal point position; Master the laws of addition, multiplication and related operations, use them flexibly, and perform simple operations on integers, decimals and fractions.

(3) To master the names and relationships of ratios and proportions, and to understand the significance of positive ratios and inverse ratios; Understand the meaning and basic properties of ratio and proportion, and solve problems related to ratio, simplification and solution.

(4) Grasp the quantitative relationship of mathematical problems required by primary schools, and focus on understanding engineering problems, travel problems, scores and percentages, geometry problems, etc. In practical problems, the comprehensive application of knowledge and methods to solve practical problems reflects the thinking method of using mathematics to solve problems.

5] Master the addition, subtraction, multiplication, division, multiplication and simple mixed operations of rational numbers, and use rational number operations to solve simple problems.

[6] Understand the concept of quadratic root and its laws of addition, subtraction, multiplication, division and Divison, and use it to perform four simple operations on real numbers.

⑺ Understand the closure of the operation of addition, subtraction, multiplication and division of integer pairs, and discuss the problem by using the closure of the operation of addition, subtraction, multiplication and division of integer pairs.

Master the definitions of divisibility, divisor and multiple, and prove the problem of divisibility with definitions.

I have mastered the definition and expression of division with remainder (dividend, divisor, incomplete quotient and remainder).

⑽ Master the definitions of odd and even numbers; Master "odd number ≠ even number" and use this property and "parity analysis method" to analyze problems.

⑾ Grasp the characteristics that numbers can be divisible by 2, 3, 4, 5, 8, 9, 1 1.

⑿ Understand the concepts of factor (divisor), multiple, odd number, even number, prime number, composite number, prime factor, greatest common factor (greatest common factor), least common multiple and prime number; Find the greatest common factor and the least common multiple of several integers; Using the greatest common factor and the least common multiple to solve simple practical problems.

[13] Understand fundamental theorem of arithmetic, decompose natural numbers into prime factors, and write the standard decomposition formula of natural numbers.

3. Ordinary quantity

Examination content: unit of measurement, input rate and conversion rate.

Examination requirements:

(1) Understand the commonly used time units, length units, mass units, area units, volumes, unit of volume and their rates.

⑵ Skillfully use the ratio between units for conversion.

4. Formulas and equations

Exam content: algebraic formula, algebraic expression and score, equation.

Examination requirements:

⑴ Understand the meaning of numbers expressed by letters, analyze the quantitative relationship of simple problems and express them by algebra, so as to find the value of algebra.

⑵ Understand the meaning and basic properties of integer exponential power; Understand the concept of algebra, and do simple algebra addition, subtraction, multiplication and division.

⑶ Understand the concept of fractions, and use their basic properties to add, subtract, multiply and divide fractions and Divison.

(4) Understand the properties of the equation; Understand the concepts of equation, equation solution and equation solution.

5] According to the quantitative relationship in specific problems, list the equations; Cleverly solve linear equations of one variable, quadratic equations of one variable, two-dimensional linear equations and fractional equations that can be transformed into linear equations of one variable; According to the practical significance of specific problems, whether the test results are reasonable or not.

5. Inequalities

Examination content: inequality, basic properties, proof, solution, inequality with absolute value.

Examination requirements:

⑴ Understand the nature of inequality and its proof.

⑵ Master the theorem that the arithmetic mean of two (not three) positive numbers is not less than its geometric mean and simply apply it.

⑶ Prove simple inequalities by analysis, synthesis and comparison.

⑷ Master the solution of simple inequalities, and list linear inequalities of one variable and linear inequalities of one variable according to the quantitative relationship in specific problems, so as to solve simple problems.

put together

Examination content: set, interval and neighborhood.

Examination requirements:

(1) Understand the meaning of set; Master the relationship between elements and sets; Master the representation of a set.

⑵ Understand the relationship between sets.

⑶ Understand the meaning of complete works and empty sets; Understand the meaning of union, intersection and complement of two sets and perform simple set operations.

(4) Understand the definition of interval and neighborhood; Master the representation of interval and neighborhood.

7. Function

Examination contents: mapping, concept and representation of function, basic properties of function, inverse function and compound function, images and properties of basic elementary function, operation and properties of rational exponential power, operation and properties of logarithm, basic relationship of trigonometric function with the same angle, inductive formula of trigonometric function, sine, cosine, tangent formula of sum and difference of two angles, double angle and elementary function.

Examination requirements:

(1) Understand the concept of mapping; Master the definition of function and its three elements; Find the definition domain and value domain of simple function; Find the inverse function of a simple function.

⑵ Understand the meaning of constants and variables and the concepts of linear function, proportional function, inverse proportional function and quadratic function; Use the knowledge of linear function, proportional function, inverse proportional function and quadratic function to solve some simple practical problems.

⑶ Understand the concepts of parity, monotonicity, boundedness, periodicity and concavity of functions; Judge the parity, monotonicity, boundedness, periodicity and concavity of simple functions.

⑷ Understand the concept of compound function and decompose it into simple functions; On the contrary, simple functions are combined into composite functions.

5] Understand the concept of fractional exponential power; Master the operation and properties of rational exponential power; Understand the concept of logarithm; Master the operation and properties of logarithm.

[6] Understand the concept of elementary function; Master the definition, properties and images of power function, exponential function, logarithmic function and trigonometric function.

Once you master the basic relationship of trigonometric functions with the same angle, the inductive formulas of sine and cosine, and the sine, cosine and tangent formulas of two angles and the sum of two angles. Master sine theorem and cosine theorem, and use them to solve oblique triangles.

8. Series

Exam content: series, arithmetic progression and its general formula, arithmetic progression's first n sum formulas, geometric progression and its general formula, infinite recursive sum formula of equal proportion series.

Examination requirements:

(1) Understand the concept of sequence; Understand the meaning of the general term formula of sequence; Knowing the recursive formula is a way to give a series and write the first few items of the series according to the recursive formula.

(2) Understand the concept of arithmetic progression; Master arithmetic progression's general formula and the first n summation formulas, and solve related simple practical problems.

⑶ Understand the concept of geometric series, master the general formula of geometric series and the summation formula of infinite recursive proportional series, and solve related simple practical problems.

9. restrictions

Examination content: limit of sequence, limit of function, four operations of limit and two important limit and continuous functions.

Examination requirements:

(1) Understand the definitions of sequence limit and function limit.

⑵ Master the four operations and two important limits of limit, and find the limit of sequence and the limit of function.

⑶ Grasp the definition of function continuity, and correctly judge the position of continuous interval or discontinuous point of function, especially the continuity of piecewise function at piecewise point.

⑷ Understand the properties and applications of continuous functions on closed intervals.

5] Master the definitions of infinitesimal and infinitesimal, and compare the order of infinitesimal.

10. derivative

Examination content: the concept of derivative, the derivation rules of sum, difference, product and quotient of functions, the derivation rules of compound functions, the second derivative, the differentiation of functions and the simple application of derivatives.

Examination requirements:

(1) Master the definition and geometric meaning of derivative.

⑵ Master the basic derivative formula and skillfully use the four operation rules of derivative, the derivative rule of compound function and the derivative rule of elementary function.

⑶ Understand the definition and solution of the second derivative.

(4) Understand the definition of differential; Differential formula and differential algorithm of basic elementary function.

5. Understand the relationship between differentiability and continuity.

[6] Understand the necessary and sufficient conditions for the derivative function to obtain the extreme value at a certain point; Find the maximum and minimum of some practical problems (generally referring to unimodal functions).

1 1. integral

Examination content: the concepts and properties of indefinite integral, definite integral, Newton-Leibniz formula and double integral.

Examination requirements:

(1) Understand the definition and properties of indefinite integral. Master the basic integral table, and use the properties of indefinite integral and the basic integral formula to find the indefinite integral of unary function.

⑵ Understand the definition, properties and geometric significance of definite integral; Master Newton-Leibniz formula and use the properties of definite integral and Newton-Leibniz formula to find the definite integral of unary function.

⑶ Understand the definition and geometric meaning of double integral.

⑷ Understand the thinking method of definite integral and double integral to find the area of curved trapezoid and the volume of curved cylinder.

12. Vector Algebra

Examination contents: space rectangular coordinate system, vector and its addition and subtraction, multiplication of vector and number, coordinate representation of vector, product and cross product of quantity.

Examination requirements:

(1) Master the spatial rectangular coordinate system and the distance formula between two points in space.

⑵ Master the concepts of vector, geometric representation and coordinate representation.

⑶ Master the definitions, properties and operation rules of addition and subtraction of vectors, multiplication of vectors and numbers, quantitative product of two vectors and cross product of two vectors.

13. Equations of lines and circles

Examination contents: inclination angle and slope of straight line, formula of point inclination and two points of straight line equation, general formula of straight line equation, parallel and vertical conditions of two straight lines, intersection angle of two straight lines, distance from point to straight line, concept of curve and equation, listing curve equation, standard equation and general equation of circle from known conditions.

Examination requirements:

(1) Understand the concepts of inclination angle and slope of a straight line; Master the slope formula of a straight line passing through two points; Master the point-oblique formula, two-point formula and general formula of one-dimensional linear equation and skillfully solve one-dimensional linear equation according to conditions.

⑵ Master the condition that two straight lines are parallel and vertical, the angle formed by two straight lines and the distance formula from point to straight line, and judge the positional relationship of two straight lines according to the equation of straight lines.

⑶ Understand the basic ideas of analytic geometry and coordinate method.

⑷ Master the standard equation and general equation of a circle.

14. Conic curve equation

Examination contents: ellipse and its standard equation, simple geometric properties of ellipse, hyperbola and its standard equation, simple geometric properties of hyperbola, parabola and its standard equation, simple geometric properties of parabola.

Examination requirements:

(1) Master the definition, standard equation and simple geometric properties of ellipse.

⑵ Master the definition, standard equation and simple geometric properties of hyperbola.

⑶ Master the definition, standard equation and simple geometric properties of parabola.

⑷ Understand the preliminary application of conic curve.

15. Straight line, plane geometry and simple geometry

Examination contents: plane geometry and its basic properties, direct-view drawing of plane graphics, the positional relationship between two straight lines, two planes, straight lines and planes in space, polyhedron, regular polyhedron, prism, pyramid and sphere.

Please click /Item-3960.aspx for details of the outline of primary school mathematics examination. For more information about Fujian teacher recruitment examination and download of real questions, please visit Fujian Education official website.