# K-12 Math Courses under TEKS Standards

The USA has been the leading country in medical research, healthcare, technological innovation, artificial intelligence, and much more. This can be attributed to highly educated foreign immigrants who have strong STEM backgrounds. Moreover, math scores of Asian Americans, often representing skilled immigrants and their offspring, rank among the best in the OECD. The United States as a whole ranks eighth among 27 participating OECD countries on the TIMSS math test for fourth-graders while the U.S. Asians have the second-highest score in the OECD; the country ranks fifth on the TIMSS math test for eighth-graders while the U.S. Asians have the third-highest score in OECD. Unfortunately, the American K-12 math education has not seen the same results since 2003 as the US immigrants from other leading countries in STEM are demonstrating.

In the most recent 2018 PISA results, China (the provinces of Beijing, Shanghai, Jiangsu, and Zhejiang) and Singapore once again came out on the top, ranking first and second in all three subjects, respectively. In fact, China scored 113 points higher and Singapore scored 91 points higher than the US in math. Therefore, one of the main factors that caused this huge difference includes the math curriculum.

## K-12 Math Courses under TEKS standards

### K-8 math courses in Texas teach about the following topics:

• Grade K: understanding counting and cardinality, understanding addition as joining and subtraction as separating, and comparing objects by measurable attributes.
• Grade 1: understanding and applying place value, solving problems involving addition and subtraction, and composing and decomposing two-dimensional shapes and three-dimensional solids.
• Grade 2: making comparisons within the base-10 place value system, solving problems with addition and subtraction within 1,000, and building foundations for multiplication.
• Grade 3: place value, operations of whole numbers, and understanding fractional units.
• Grade 4: use of operations, fractions, and decimals and describing and analyzing geometry and measurement
• Grade 5: solving problems involving all four operations with positive rational numbers, determine and generate formulas and solutions to expressions, and extending measurement to area and volume.
• Grade 6: number operations; proportionality; expressions, equations, and relationships; and measurement and data.
• Grade 7: number and operations; proportionality; expressions, equations, and relationships; and measurement and data
• Grade 8: proportionality; expressions, equations, relationships, and foundations of functions; and measurement and data.

## K-12 Chinese Math Curriculum

School is mandatory for nine years in China – six of primary and three of junior secondary. At the primary level, students are taught in nine subject areas, but must pass exams in Chinese and math to graduate. At the end of junior secondary school, students must pass several educational examinations and meet specific physical education standards. If they choose to continue their education, there are two paths for senior secondary school: general and vocational. Additionally, to gain entrance to the general education program, students must pass entrance exams in subjects similar to the graduation exams from junior secondary school. This path is meant to prepare students for college, and they must pass the National Higher Education Entrance Exam in order to enroll in universities/colleges. Lastly, Should a student choose the vocational path, they are offered a trade-centered education that prepares them to get a job following completion.

### K-12 math courses in China teach about the following topics:

• Grade K: using and applying number from numbers 0 to 20; understanding and counting the ordinal number system from numbers 1 to 9; reasoning and calculating simple addition and subtraction up to number 10; understanding the concept of time (days of the week and duration)
• Grade 1: reasoning and calculating addition and subtraction up to number 20 and beyond; calculating multiplication using equal groups and repeated addition; understanding multiplication sign and strategies for division; comparing length by using informal units of measurement; introducing the concept of mass; understanding the concept of time (months, seasons of the year, quarter past and quarter to, and o’clock and half past on the analogue clock)
• Grade 2: understanding multiples of 10 up to 100; calculating addition and subtraction up to number 99; describing position (lines and angles); introducing data pictograms and bar charts, using the metre as a formal unit to measure perimeter; using the formal unit of centimetre to measure length and perimeter; introducing the volume using the cubic centimetre as a standard unit, introducing the concept of mass

• Grade 3: subtraction with borrowing; subtraction of two-digit numbers involving comparison; introducing the square centimetre; comparing and ordering areas, constructing models; using the cubic cm and displacement to measure volume and capacity; understanding the unit kilogram; using the prefix to determine polygons; introducing Spatial properties of quadrilaterals; comparing analogue and digital time; using fractions 1/2, 1/4, 1/8 to describe part of a whole, a group or collection
• Grade 4: placing value, adding and subtracting numbers 100 to 9,999; measure and classify angles; recognise and name triangles and pyramids; understanding the common units of capacity; understanding AM and PM time; adding and subtracting decimals to two decimal places; understanding the relationship between percentages, decimals and fractions
• Grade 5: counting numbers from 10,000 to 99,999; adding to 9,999 and beyond; multiplying by 2, 3 and 4 digits; understanding time zones; recognise nets for prisms, pyramids, cubes and cones; understanding informal coordinate system; calculating area, capacity, volume, weight, decimals and fractions; solving word problem by recognizing sign words
• Grade 6: repeated subtraction with and without remainders; problem solving strategies; problems with numbers, length, mass, area and volume/capacity; problems involving money
• Grade 7: adding and subtracting fractions with same or different denominators; using Order of Operation procedures (BIDMAS) with fractions; introducing the rules for finding the area of a rectangle and a parallelogram; finding the area of a triangle and other composite shapes; introducing the formula for volume; algebraic expressions
• Grade 8: multiplying mixed numbers; expanding and simplifying algebraic expressions; finding highest common factor; solving equations containing addition, subtraction, multiplication and division; solving two step equations; solving equations containing binomial expressions; understanding exterior angle theorem; understanding geometric constructions; introducing Pythagorean triples; understanding the definitions of range, mode, mean and median; calculating probability of simple events

• Grade 9: understanding the rules for indices/exponents; understanding trigonometric ratios; using calculators; understanding angles of elevation and depressions
• Grade 10: using scientific notation;solving problems involving overlapping triangles; coordinating geometry (distance, mid-point and gradient formulas; lines through the origin; slope intercept; point slope form); calculating cumulative frequency; calculating the median from a frequency distribution; understanding tree diagrams
• Grade 11: Topics include Stem and Leaf Plots, Box and Whisker Plots, algebraic fraction simplification, finding equations from coordinates, probability with dice, experimental and complementary probability, mutually exclusive events, and compound interest.
• Grade 12: calculating mean, mode and median from grouped data; standard deviation applications; normal distribution; Scatter Diagrams; the cosine and sine rules to find an unknown side and angle; the area formula; understanding permutations and combinations

## K-12 Singaporean Math Curriculum

In Singapore’s Mathematics Curriculum Framework, students from primary to pre-university levels focus on developing mathematical abilities, especially problem-solving. Teachers employ the Concrete-Pictorial-Abstract (C-P-A) method to help students understand abstract math concepts through real-life experiences and visual aids.

#### Lower Secondary Mathematics (Grades 7-8)

##### Number and Algebra
• Whole numbers, fractions, and decimals, and the four arithmetic operations (addition, subtraction, multiplication, and division)
• Calculation with calculators
• Factors and multiples
• Ordering of numbers
• Approximation and estimation
• Percentage
• Ratio
• Speed
• Algebraic expressions in one variable
• Negative numbers, integers, rational numbers, and real numbers, and the four arithmetic operations (addition, subtraction, multiplication, and division)
• Calculation with calculators
• Prime numbers, highest common factor, and lowest common multiple
• Ordering of numbers
• Use of symbols including <, >, ≤, ≥
• Approximation and estimation
• Percentage
• Ratio, and direct and inverse proportion
• Map scales
• Rate and speed
• Algebraic expressions and formulas
• Algebraic manipulation (linear and quadratic)
• Functions and graphs (linear and quadratic)
• Linear equations with one unknown
• Simultaneous linear equations with two unknowns
• Linear inequalities with one unknown
##### Geometry and Measurement
• Measurement of length, mass, volume, time, and angle
• Area and perimeter of triangles, squares, and rectangles, area and circumference of circles, and volume of cubes and cuboids
• Properties of simple geometric figures
• Nets of simple solids
• Line symmetry
• Ideas of tessellation
• Properties and construction of simple geometric figures
• Angles associated with parallel lines
• Angles of polygons
• Congruence and similarity
• Area of plane figures, volume and surface area of three-dimensional solids
• The Pythagorean Theorem
• Trigonometric ratios of acute angles in a right-angled triangle
##### Statistics and Probability
• Picture graphs, bar graphs, tables, line graphs, and pie charts (including interpretation and use of information to solve problems)
• Average
• Data analysis (including interpretation and analysis of various statistical representations)
• Probability

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#### Citations:

U.S. Immigrant Performance on International Tests – cis.org
The things America leads the world in – lovemoney.com
What 2018 PISA international rankings tell us about U.S. schools – hechingerreport.org
Chinese Curriculum – futureschool.com
The Mathematics Curriculum in Primary and Lower Secondary Grades – timssandpirls.bc.edu