1. Calculate, then explain the method
Question: What is 8 + 7? Can you explain why?
One solution: 15. Split 7 into 2 and 5: 8 + 2 + 5 = 10 + 5 = 15. A single task can explore both the answer and a way of thinking about how numbers can be split.
Arithmetic and thinking maths: how do they compare?
Arithmetic practice focuses attention on numbers and calculation methods; reasoning-focused maths emphasises finding relationships and explaining solutions. In actual lessons, these activities overlap. Arithmetic involves thought and understanding, and problem solving can involve calculation. Compare the tasks and teaching rather than assuming one label means better education.
What do these Korean terms mean?
Yeonsan (연산) means arithmetic operations such as addition and subtraction. We use sagoryeok suhak (사고력 수학) here for activities emphasising relationships, strategy and explanation. This comparison is not a division of Korea’s national curriculum into two courses, and providers do not necessarily use the labels identically.
Our explanatory English terms are arithmetic practice and reasoning-focused maths. A product name such as Critical Thinking Math needs to be read alongside that provider’s actual syllabus.
The US National Research Council’s 2001 report treats conceptual understanding, procedural fluency, problem-solving strategies and reasoning as interconnected. Dividing maths into “arithmetic without thinking” and “thinking maths” is therefore misleading. Read the educational framework
What should parents compare?
An editorial comparison of emphasis, not mutually exclusive subjects.
| Look at | Arithmetic emphasis | Reasoning and problem-solving emphasis |
|---|---|---|
| Question | What calculation is needed, and why use that method? | What conditions or relationships matter, and how can the problem be solved? |
| Example activities | Split and combine numbers; explain a calculation | Find possible cases; explain a pattern; represent it with a drawing |
| What to examine | The answer and understanding of the calculation | A valid solution, checked conditions and explanation |
| Where they overlap | Choosing and explaining a method involves reasoning | Checking a condition or finding an answer can involve calculation |
Three examples: different questions about maths
These tasks and worked answers were created by Babyroum to explain the comparison. They are not copied from provider worksheets, age benchmarks, entrance tests or giftedness assessments. There is no time limit.
2. Find a grouping that meets a condition
Question: Use cards numbered 1, 2, 3 and 4 exactly once to make two pairs. How can both pairs have the same sum?
One solution: Pair (1, 4) and (2, 3); each sums to 5. Another explanation starts with the total, 10: two equal sums must each be 5. Both checking the condition and calculating matter.
3. State a rule clearly and explain it
Question: Repeat the group “circle, circle, triangle”. What is the seventh shape?
One solution: A circle. Positions 1–3 and 4–6 contain the same group; a new group starts at position 7. An explanation can use words or a drawing. The repeating rule is explicit rather than inferred from just a few shapes.
How does a public programme example organise this?
In Eye Level UK’s public curriculum PDF, page 1 places number writing and making 10 in Basic Thinking Math; page 5 includes repeating patterns and shape and size comparisons in Critical Thinking Math. This illustrates one provider’s organisation of two areas. See the official sample document
The document is published on the UK website. Do not assume the materials or sequence match related Korean products or branches in other countries. A provider’s account of lesson content is also different from independent evidence of educational results.
Questions to ask about a course
These are Babyroum’s comparison prompts. Check official samples and the instructor’s explanation rather than relying on a course name.
- Can children explain a method with words or drawings as well as give an answer?
- How does the instructor explain an unfamiliar task and give feedback?
- How are repeated practice, unfamiliar problems and discussion organised?
- What work happens between lessons, and what must a parent help with?
- What school stage and prior concepts are expected? How is an unsuitable level adjusted?
- Does the sample match the level of the materials the child would actually receive?
This guide does not prescribe a starting age, daily question count or ratio between activities. The comparison helps parents examine programmes; it does not assess an individual child’s level.
Additional checks for families outside Korea
Check the languages of the materials, teaching and parent instructions separately. Understanding the maths and reading instructions in an unfamiliar language can present different demands, so look at the sample instructions too.
Ask the provider which courses are actually available in your country, the time zone for online classes, delivery areas, and whether materials and tuition are charged separately. This guide is not a verified listing of current prices or country-specific availability. Labels such as “Korean”, “thinking” or “gifted” do not establish effectiveness.
Common questions
Is arithmetic or thinking maths better?
The labels alone do not establish a ranking. Understanding calculation methods and explaining how to solve a problem are connected activities. Compare actual tasks and feedback.
Must children finish arithmetic before starting thinking maths?
This guide does not prescribe that fixed sequence. Calculating 8 + 7 and explaining the method shows how the activities can coexist. Ask each provider about the course’s prerequisites and intended learners.
Does thinking maths mean gifted education or an intelligence test?
Here, thinking maths describes activities emphasising reasoning and problem solving. The label does not make a course an official gifted-education programme or an intelligence test. Our examples are not assessment tools.
Sources and review scope
Sources checked: . We compared the educational framework with the provider’s public sample. No education-specialist or native-English human review has been completed.
- National Research Council · Adding It Up (2001), Chapter 4 ↗
An educational framework linking understanding, procedural fluency and reasoning. It does not evaluate Korean academies or individual products.
- Eye Level UK · Maths Curriculum Chart (PDF) ↗
A public UK provider document: examples on PDF pages 1 and 5. It does not establish equivalence to Korean courses, current fees, overseas enrolment or effectiveness.
No paid placement or affiliate links. Corrections: support@babyroum.com. Send the page URL and a source, not private information about a child.