Vietnam: What is the expression of the third identity? What are the regulations on assessing educational results for Mathematics in general education?

What is the expression of the third identity?

The third identity is one of the important mathematical formulas, widely used in transforming and simplifying algebraic expressions.

Identity number 3: Difference of squares.

Formula:

(a - b)² = a² - 2ab + b²

*Significance:

The square of a difference equals the square of the first term minus twice the product of the first term and the second term, plus the square of the second term.

Example:

(x - 3)² = x² - 2*x*3 + 3² = x² - 6x + 9

(2a - b)² = (2a)² - 2*2a*b + b² = 4a² - 4ab + b²

*Application:

Factorizing polynomials:

When encountering an expression in the form a² - b², it can be factored into (a - b)(a + b).

Simplifying expressions:

Use the identity to transform complex expressions into a simpler form.

Solving equations:

Apply the identity to bring equations into a factorized form to find solutions.

*Other notable identities:

Square of a sum: (a + b)² = a² + 2ab + b²

Cube of a sum: (a + b)³ = a³ + 3a²b + 3ab² + b³

Cube of a difference: (a - b)³ = a³ - 3a²b + 3ab² - b³

Sum of cubes: a³ + b³ = (a + b)(a² - ab + b²)

Difference of cubes: a³ - b³ = (a - b)(a² + ab + b²)

*Note: Information is only for reference purposes./.

What is the expression of the third identity? What are the regulations on assessing educational results for Mathematics in general education in Vietnam? (Image from the Internet)

What is the duration of the Mathematics curriculum by grade in Vietnam?

Under sub-section 2, section 8 of the Mathematics General Education Program issued with Circular 32/2018/TT-BGDDT, the duration of the Mathematics curriculum by grade is as follows:

Specifically, at the upper secondary level, each grade has an additional 35 lessons/year for elective academic topics.

What are the regulations on assessing educational results for Mathematics in general education in Vietnam?

According to section 7 of the General Education Program for Mathematics issued with Circular 32/2018/TT-BGDDT:

-  Assessment of the educational results in Mathematics aims to provide accurate, prompt, and valuable information about the development of abilities and progress of students based on the required achievements for each grade and education level;

Adjust teaching activities to ensure the progress of each student and improve the quality of Mathematics education in particular and education quality in general.

- Employ a combination of multiple forms of assessment (process assessment, periodic assessment), and multiple assessment methods (observation, recording the implementation process, verbal interview, objective tests, essays, written tests, practice exercises, projects/products assignments, real-world tasks,...) and at appropriate times.

- Process assessment (or continuous assessment) is conducted by the subject teacher, combined with assessments from teachers of other subjects, self-assessment by the assessed student, and other students in the group, class or assessment by the student's parents.

Process assessment is linked to students' learning activities, avoiding a disconnection between teaching and assessment processes, and ensuring assessment objectives for students' progress in learning.

- Periodic assessment (or summative assessment) primarily aims to assess the achievement of learning objectives.

Results from periodic and summative assessments are used to certify learning levels and recognize students' achievements.

Periodic assessment is conducted by educational institutions or through national testing and assessment.

- Periodic assessment is also used to serve the management of teaching activities, ensuring quality at educational institutions and serving the development of the Mathematics program.

- Assess students' abilities through evidence reflecting achievements during the execution of students' actions.

The assessment process includes basic steps: determining assessment purposes; identifying necessary evidence; selecting appropriate assessment methods and tools; collecting evidence; interpreting evidence and making comments.

- Focus on selecting methods and tools for evaluating the components of mathematical competencies. To be specific:

+ Assess the ability to think and reason mathematically: it may involve some methods and tools like questions (oral, written), and exercises,... requiring students to present, compare, analyze, aggregate, and systematize knowledge;

Must apply mathematical knowledge to explain and justify reasoning.

+ Assess the ability to model mathematically: select real-world situations that prompt mathematical problems.

From this, students are required to identify a mathematical model (including formulas, equations, tables, graphs,...) for situations presented in real-world problems;

Resolve mathematical issues within the established model; present and assess solutions in a practical context and improve the model if the solutions are not appropriate.

+ Assess the ability to solve mathematical problems: methods such as requiring learners to identify situations, recognize and present issues to be solved;

Describe and explain initial information, objectives, and expectations of the current problem situation; collect, select, organize information and connect with existing knowledge;

Use questions (may require spoken or written responses) that demand learners to apply knowledge to solve issues, especially practical ones; use observation methods (such as checklists based on established criteria), and observe learners during problem-solving;

Essess through learners' practice products (such as results from learning projects); reasonably consider integrated assessment tasks.

+ Assess the ability to communicate mathematically: methods such as requiring learners to understand verbally, read, record (summarize), analyze, select, and extract essential core mathematical information in spoken or written texts;

Use mathematical language combined with regular language to present, express, question, discuss, debate mathematical content, ideas, solutions in interaction with others.

+ Assess the ability to use mathematical tools and means: methods such as requiring learners to recognize the name, function, usage specifications, method of preservation, advantages, and limitations of mathematical tools and means;

Present the method (appropriately) of using tools and means for performing learning tasks or to express mathematical reasoning and proof.

When teachers plan lessons, it is necessary to establish criteria and methods of assessment to ensure that by the end of each lesson, students meet basic requirements based on set criteria before proceeding with subsequent learning activities.