Tag: Math
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Is A Head Start Helpful in Geometric Proof and Deductive Reasoning?
In the competitive exam-oriented educational system, it is common for Chinese students to dedicate their summer and winter breaks to advance their understanding of upcoming semester’s subject matter, aiming to maintain their advantageous position. Students who have already delved into algebra may enjoy certain benefits over their counterparts who have not done so. For instance,…
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Intuition Can Be Cultivated, But Is There A Limit? — Insights from Chinese School Geometry Education
Drawing from my decade-long experience as a math teacher, I’ve observed that the introduction of geometric proof often marks a fresh beginning for middle school students. Interestingly, students who are good at algebra may not necessarily excel in geometry, while those under performers in elementry school may surprisingly develop a fondness for geometry. In contrast…
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A Journey of Self-growth in Learning Mathematics
After receiving the mid-term exam paper, J.L., a student in my math class, cried to me, “I’ve tried my best to learn geometric proofs, but I just don’t know when and where to add auxiliary lines. I’m not as smart as D.G. (D.G. is the best performer in the class). Mathematics frustrates me”. J.L. is…
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Area Model: from Distributive Property to Calculus
“Mommy, do you know how many bars of chocolate are there?”, Shawn asked when he opened the pack of chocolate.“Hmm, there are 24 bars”, I replied in about 2 seconds.Shawn, “how can you count the total numbers so quickly? I didn’t count but tried to add 6 bars four times, yet I’m still slow, much…
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Square Numbers and Odd Numbers
When we were having dinner, Shawn’s dad casually tested his calculation.Dad: 1 plus 3 is?Shawn: 4Dad: How about 1 plus 3 plus 5?Shawn: 9Dad: Add the next odd number 7?Shawn: Well, it is 9 plus 7, and it equals 16. Shawn’s dad suddenly realized that square numbers could be formed by adding consecutive odd numbers…
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Explore: use subtraction to get the area
Given that P is a point in parallelogram ABCD, line GF passes through point P and is parallel to AB, line EH passes through point P and is parallel to AD. If the area of BFPE =3，the area of PHDG = 5, find the area of ▵APC. Area of a triangle? Formula: Area=1/2 base∙heightIt is quite hard to get the length of the three bases. It is even more…
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Explore: sides and interior angles of a polygon
Question: Suppose a convex polygon has exactly 4 obtuse interior angles. What is the maximum number of the sides of such a polygon? Hints behind the information Convex polygon？A polygon with all its interior angles less than 180° exactly 4 obtuse interior angles: 90°<obtuse angle<180° (Hint: the other interior anlges ≤ 90°) maximum number of the sides? What’s the relationship between sides and interior angles? Let’s use regular…
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Build a Math Brain Through Deliberate Training
My son could say numbers from 1 to 10 in both Chinese and English at age 3. However, numbers to him were nearly the same as Peppa Pig to him, which were merely words with distinct pronunciation. He couldn’t count the number of toy cars he owned due to a lack of sense on numbers…
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Chinese Students TOP PISA 2018
Why are Chinese students always top in International Mathematics Olympiad? Most people would argue that China has the most population and therefore more intelligent people can be selected, the same theory as the Olympic Games. However, some other countries with similar population sizes are not as outstanding as China in math competitions. People also believe…