Solving Word Problems


In 1977, Australian educator Anne Newma discussed five steps that students need to work through in order to solve a word problem successfully.  Her research showed that over 50% of errors that children make occur in the first three steps- before they even begin to solve the problem!

  1. reading the problem
  2. comprehending what was read
  3. transforming the words into a mathematical strategy
  4. applying a mathematical procedure and
  5. writing the answer.
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An in-person American view of Singapore education, especially math

Bill Jackson travels to Singapore

The Singapore Chinese Girls’ School (SCGS) was founded 111 years ago by Singapore-born Chinese businessmen to educate Chinese girls because only Chinese boys were able to attend school at that time. Today, about 2400 girls attend the school in the primary (grades 1-6) and secondary (grades 7-10) levels. (After secondary school Singaporean students attend Junior College and then either university or trade school.) Although begun for Chinese girls, the school now serves girls from many ethnic backgrounds, principally Chinese, Malay, and Indian.

The SCGS consistently scores among the top schools in Singapore on the PSLE and O-Level exams – extremely high stakes tests that students take at the end of grades 6 and 10 respectively. The school seeks to develop both academic competency and character.

Link to Day 1 – Part 1 – “Singapore: Five Surprises in Education”
Link to Day 1 – Part 2 – “The Professional Lives of Teachers in Singapore”
Link to Day 2 – “The Teacher Model In Singapore: What Matters Most”
Link to Day 3 – “The Creativity & Critical Thinking Initiative”

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Readings/analysis of Singapore Math

Singapore Math: Can It Help Solve Our Country’s Math-phobia?

Singapore bar model problem solving strategy

Beyond Singapore’s Mathematics Textbooks:
Focused and Flexible Supports for Teaching & Learning
(American Educator, Winter 2009-2010).

Great exposition of the SG educational system

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NYT 10/2 “Singapore Math” article

Source: NYT Oct 2nd article

The slower pace is a cornerstone of the district’s new approach to teaching math, which is based on the national math system of Singapore and aims to emulate that country’s success by promoting a deeper understanding of numbers and math concepts. Students in Singapore have repeatedly ranked at or near the top on international math exams since the mid-1990s.

Singapore math may well be a fad, too, but supporters say it seems to address one of the difficulties in teaching math: all children learn differently. In contrast to the most common math programs in the United States, Singapore math devotes more time to fewer topics, to ensure that children master the material through detailed instruction, questions, problem solving, and visual and hands-on aids like blocks, cards and bar charts. Ideally, they do not move on until they have thoroughly learned a topic.

Singapore math’s added appeal is that it has largely skirted the math wars of recent decades over whether to teach traditional math or reform math. Indeed, Singapore math has often been described by educators and parents as a more balanced approach between the two, melding old-fashioned algorithms with visual representations and critical thinking.

Singapore math was developed by the country’s Ministry of Education nearly 30 years ago, and the textbooks have been imported for more than a decade. The earliest adopters in the United States were home-school parents and a small number of schools that had heard about it through word of mouth.

Today it can be found in neighborhood schools like P.S. 132, which serves mostly poor students, as well as elite schools, including Hunter College Elementary School, a public school for gifted children in Manhattan, and the Sidwell Friends School in Washington, a private school attended by President Obama’s daughters.

Interesting Comments

From a Singaporean now in the US

A substantial portion of the education that students receive is typically from private tuition. This relatively unregulated and untaxed part of our economy is a major pillar in supporting the educational success and progress of our school going citizenry.

Comment #60

I’ve read that in Singapore, parents and students are extremely competitive. There’s a different culture – one of shame if you don’t do well especially in math. Many parents pay for private classes in addition to the public classes for their kids, if they can afford it.

parent of a son in the Singapore school system

The real reason Singapore kids score well in Maths and other subjects is the huge amount of private tuition that almost every Singapore school child receives.

Good background on Singapore math

Singapore is a highly ethnically diverse, formerly impoverished country. Until the implementation of its current curriculum, Singapore’s international test scores were terrible. Up until the 1970s, Singapore’s Mathematics instruction was a hodge-podge (just like here). Books were imported from other nations, there was no standardization of curricula or national educational leadership.

As a part of the plan to modernize the country, a national Mathematics curriculum was developed using best practices from throughout Asia. The program called “My Pals are Here” was implemented in over 90% of schools. Several years after the implementation, their test scores rocketed to the top of the international community. The demographics of the students did not change – it’s approach to instruction did.

There is no reason to think this approach could not be implemented with success here in the US. In fact, many of the elements of our new Common Core standards (to be implemented in 2013 in NYS) were pulled from Singapore Math and other SouthEast Asian approaches.

Comment #108

Finally, if our students are going to be prepared to succeed in the contemporary global economy, they will need more mathematics and mathematical thinking than perhaps was required in the past. The daunting challenge for all teachers is how to enable all students to meet these standards.

Comment #116

arithmetic being the manipulation of numbers in various algorithms while mathematics is being able to apply the arithmetic to solve problems. In the earlier grades I always stressed more arithmetic and in the later grades I would emphasize mathematics more.

Singaporean in the USA

I am from Singapore, and I lived through the Singapore school system from 6 years of age to 18 years. For those unfamiliar with the Singapore system, as a benchmark, I scored 800 for the US mathematics SAT at age 18 – based on my opinion then, it was probably set at the level of an average Singapore college-track students aged 16 or l5. In terms of mathematics, I have to say that SingaporeMath is most likely a fad – you are comparing a country whose students have several hours of homework daily, with no extended summer break. Parents in Singapore are obsessed with education for their children. … In education, there is no substitute for hard work, discipline and parental motivation, all of which are found in spades in Singapore schools.

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FL 5th Grade Math Standards

Sunshine State Standards Grade Level Expectations
Fifth Grade

Sunshine State Standards Grade Level ExpectationsMathematicsFifth Grade

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