Liberal Arts Blog — Singapore Math, Russian Math, Direct Instruction

John Muresianu
3 min readSep 14, 2020


Liberal Arts Blog — Monday is the Joy of Math, Statistics, and Numbers Day

Today’s Topic — Singapore Math, Russian Math, Direct Instruction

What’s the best way to teach math? Does it depend on the student? Is there one way that should be standard for students of average intelligence another for the gifted? One for the disadvantaged? Another for the privileged? What do the data say? Are there good data? What methods were you subjected to? Or your children? Or your grandchildren? Pros and cons of each? Best article on the subject? Is Khan Academy really the best mouse trap out there? Does it get less attention than it deserves because it’s free? Experts — please chime in. Correct, elaborate, elucidate.

SINGAPORE MATH — developed in the 1980s, inspired by American psychologist Jerome Bruner

1. Three-stage learning process: from concrete objects to diagrams to numbers.

2. “Bar modeling” (above) is a way of learning arithmetic with simple diagrams.

3. Students start with objects: chips, dice, paper clips.

NB: Singapore’s international ranking in mathematics apparently skyrocketed after its implementation. But I haven’t found the data to verify this claim. Can anybody help?

RUSSIAN MATH — “derivation and visualization” — not memorization

1. In 1997, Russian immigrant Irina Khavinson set up the Russian School of Mathematics in Newton, MA. She now has 40,000 students in 53 locations in 22 states. Online versions have customers in 24 countries.

2. The pitch is that the program teaches students to “derive” not “memorize.” As in Singapore math, visualization is a key theme.

3. Critics say that the reality is that any increase in performance is a result of two other factors: a.) four or more extra hours per week spent on math, b.) extremely motivated parents with plenty of resources.

DIRECT INSTRUCTION — old-fashioned, drill based, memorization works

1. Many have argued that this is the only way to close the black-white achievement gap in math.

2. Focus on “fun” activities and “concept-based learning” just does not work.

3. Three characteristics: a.) only 10% of material is new while the remaining 90% of material is a review of previously taught content b.) Students are grouped based on their skill levels that are determined by assessments administered before commencing the Direct Instruction program, c.) emphasis on student’s pace by either slowing down, reteaching, or accelerating through easily understood material.

NB: This is how I learned math back in the 1950s and 1960s. Has anything really improved since then? And how effective is Khan Academy? Should every school use it?

Russian School of Mathematics

Should Your Kid Be Taking Russian Math?

Direct instruction

Study: Struggling Math Students Need Direct Instruction, Not ‘Fun’ Activities

Khan Academy


So what are your personal favorite magic numbers? What do they stand for? Please share the coolest thing you learned this week related to math, statistics, or numbers in general. Or, even better, the coolest or most important thing you learned in your life related to math.

This is your chance to make someone else’s day. And to consolidate in your memory something you might otherwise forget. Or to think more deeply than otherwise about something dear to your heart. Continuity is key to depth of thought.



John Muresianu

Passionate about education, thinking citizenship, art, and passing bits on of wisdom of a long lifetime.