Colorsampler_Final_Unpathed_Flattened.indd 3 21/3/14 3:44 PM ACHIEVEMENT IN INTERNATIONAL STUDIES Since 1995, Singapore’s outstanding performance has been highlighted across renowned international studies, such as Trends in International Mathematics and Science Study (TIMSS) and Programme for International Student Assessment (PISA). The latest results from these studies have shown that Singapore students are consistently improving and performing at a higher level. International BENCHMARk GRADE 4 TIMSS 2011 Mathematics PERfORMANCE 2011 94% Singapore emerged top in TIMSS 78% International Median for its achievement in mathematics Singapore Performance 69% in 2011. More than 75% of students in Singapore achieved high performance, compared to the 43% international median of 28%. 28% 4% Advanced High Intermediate Mathematics Literacy Skills PISA 2012 Countries Mean Score Singapore ranked among the top Shanghai - China 613 Singapore 573 countries for Mathematics Literacy Hong Kong - China 561 Skills, demonstrating that our Chinese Taipei 560 students are well able to think both Korea 554 critically and creatively when faced Average 494 with real-life situations. ABOUT MARSHALL CAVENDISH EDUCATION With more than 40 years of experience in educational publishing, Marshall Cavendish Education is the publisher of K–12 materials in Singapore. Our first Primary Mathematics series was adopted and used in Singapore from 1982 to 2001, contributing to the exceptional performance of our students in international studies and reports. Beyond Singapore, we have extended our success to over 50 countries through a holistic approach of curriculum, technology, and professional development. Colorsampler_Final_Unpathed_Flattened.indd 4 21/3/14 3:44 PM A MODEL Of Success backED By Research The Primary Mathematics series is based on sound research of effective approaches to teaching mathematics that have been tested successfully in classrooms both in Singapore and the United States. Research points to excellence of the curriculum as a contributing factor of Singapore’s success in mathematics. A study conducted by the American Institutes for Research (AIR) for the US Department of Education concluded, “What the United States needs overall are the sound features of the Singapore Mathematics system.” In studying several American school districts experimenting with the Singapore Mathematics Curriculum, including the Montgomery County Public Schools, AIR researchers found that “Singapore Mathematics textbooks can produce significant boost in achievement.” According to the AIR report, the Singapore Mathematics Curriculum “provides rich problem sets that give students many and varied opportunities to apply the concepts they have learned.” A 2009 study conducted by the Gabriella and Paul Rosenbaum Foundation supports this finding. Focusing on the effect of Singapore Mathematics Curriculum on student proficiency in a Massachusetts school district from 2002 to 2008, the study showed that significant improvement in student math performance correlated with the use of Singapore Mathematics Curriculum. According to the report’s summary, “for levels of Cumulative Singapore Mathematics experience (CSM), students’ scores increase with increasing CSM.”1 1 For a full copy of this study, send us an email at [email protected] Singapore’s students have consistently been high performers, ranking first in the world in mathematics in TIMSS in 2003. As a result, researchers have explored Singapore’s successful approach to mathematics instruction to identify features that could work in US schools. There are several “components that account for Singapore’s success, including “a highly logical national mathematics framework, mathematically rich problem-based textbooks, challenging mathematics assessments and highly qualified mathematics teachers”. Extracted from report by Achieve.org“ ABOUT SINGAPORE MATH INC® Singapore Math Inc® is the official US distributor of Primary Mathematics. Through a close relationship with Marshall Cavendish Education, it constantly monitors trends in the Singapore curriculum. Its mission is to bring quality educational books to schools and home educators in the US and Canada by offering only the best titles. Colorsampler_Final_Unpathed_Flattened.indd 5 21/3/14 3:44 PM THE SUCCESSfUL METHODOLOGy BEHIND Primary Mathematics (Common Core Edition) for Earlybird Kindergarten and Grades 1 to 5 contain the original content and methods that have been used and proven effective in Singapore since 1982, and in the United States since 1999. This series is updated to align with the Common Core State Standards. Districts that have successfully implemented this high quality series consistently show improved student performance. With an emphasis on teaching math reasoning and logical thinking, this series encourages students to visualize problems and develop their mental math capabilities. The hallmarks of this remarkable series include: Concrete Pictorial Abstract approach to encourage students to encounter, translate, understand, and apply concepts Model drawing method to help students visualize, see connections, and solve problems Teaching to mastery for deep understanding Spiral progression to aid students to review and expand strong mathematics foundation Metacognition to promote logical thinking, reflection, and communication The impact of this program on test scores, students’ engagement and teachers’ confidence were noticeable in the first year. Now we’re in our third year of use and our test scores continue to “show significant growth. Teachers praise the intentionality of the material’s scope and sequence, the way the lessons allow for a variety of entry points for learners and, most importantly, that the students are developing a strong number sense. Cathy D’Alessandro Mathematics Department Head Harvest Christian Academy“ Colorsampler_Final_Unpathed_Flattened.indd 6 21/3/14 3:44 PM CTEONCRE Pictorial Abstract ApproacH To encounter, translate, understand, and apply concepts The Concrete Pictorial Abstract approach enables students to encounter Mathematics in a meaningful way and translate mathematical concepts from the concrete to the abstract. This approach allows students to understand mathematical concepts before learning the “rules” or formulaic expressions. 9. 2. How many stamps are there? Tens Ones 6 5 sixty-fi ve Students first encounter the mathematical concepts through the use of visual manipulatives. 5 more than 60 is 65. 2 hundreds 3 tens 6 ones (a) What number is 1 more than 65? Hundreds Tens Ones 236 (b) What number is 1 less than 65? 2 3 6 (c) What number is 10 more than 65? 2 0 0 3 0 (d) What number is 10 less than 65? 6 10. (a) What number is 2 more than 65? two hundred thirty-six (b) What number is 2 less than 65? 3. (a) (c) What number is 20 more than 65? Students move on to the pictorial stage in which (d) What number is 20 less than 65? pictures are used to model problems. 2 hundreds 5 tens 8 ones 11. (a) 50 + 1 = (b) 50 + 2 = (c) 50 + 10 = (d) 50 + 20 = Hundreds Tens Ones (e) 50 – 1 = (f) 50 – 2 = When students are familiar with the ideas taught, 2 5 8 (g) 50 – 10 = (h) 50 – 20 = they progress to a more advanced or abstract 200 + 50 + 8 = stage in which only numbers, notation and (b) 400 + 70 = (c) 800 + 9 = 12 Exercise 3, pages xx–xx symbols are used. 17 Exercise 5, pages xx–xx G2_TB A_1proof_U1_21Feb.indd 12 22/02/14 3:52 pm G2_TB A_1proof_U1_21Feb.indd 17 22/02/14 3:53 pm Primary Mathematics’ concrete-pictorial-abstract methodology allows students to develop deep understanding of new ideas and gradually transfer this understanding to more complex situations. “It is a carefully designed program that emphasizes depth over breadth. Nancy Pavia — Math Helping Teacher, Scarsdale Public Schools, Scarsdale,“ NY From students working with numbers for the first time to children exploring bar modeling with fractions, Singapore Math gives each and every one of my second graders a well-structured “Concrete Pictorial Abstract approach to Mathematics. Nathan Havner, Maury Elementary School, Washington,“ D.C. Colorsampler_Final_Unpathed_Flattened.indd 7 21/3/14 3:44 PM MODEL DRAWING To visualize, see connections, and solve problems Model drawing is an ingenious problem solving strategy built into the Primary Mathematics curriculum. Students are taught to visualize and construct bar models to help them make sense of word problems. The model drawing method requires students to understand the mathematical concepts underlying word problems and equips them with a strong conceptual foundation in mathematics to solve even the most challenging problems. The model drawing technique not only provides a powerful method for solving problems but also serves as a link to algebra. Symbolic representation of the problems, the mainstay of algebra, emerges as a logical extension of the model drawing technique. 4 Word Problems Mary made 686 paper fl owers. She sold some of them. If 298 were left, how many paper fl owers did she sell? number made 686 When students encounter a word problem, they ? 298 are taught to use bar models to organize the Model drawing transforms number sold number left necessary information. To fi nd the number sold, words into recognizable we subtract the number left from the whole. The use of a visual tool enables students to 686 – 298 = quickly identify the mathematical concepts She sold paper fl owers. pictures for young minds. required and solve problems efficiently. 134 girls and 119 boys took part in an art competition.