Singapore Math Research And Efficacy - (Mi) 2
Singapore MathResearch and EfficacyOverview
Table of ContentsWhat is Singapore Math?.1Common Core Connection. 6–7Foundational Research . 2–4U.S. Results.8–11International Results.5Testimonials.12–13
What is Singapore Math?Math in Focus : Singapore Math by Marshall Cavendish, for Grades K–8, is the U.S. editionof Singapore’s most widely used curriculum, bringing Singapore’s effective approach to mathematicsto U.S. classrooms.Singapore math emphasizes problem solving and positive attitudes toward mathematics, while focusing on studentdevelopment of skills, concepts, processes, and metacognition. Students are encouraged to reflect on their thinkingand learn how to self-regulate so that they can apply these skills to varied problem-solving activities. The SingaporeMinistry of Education uses a pentagon with problem solving in the center to represent its curriculum framework.Singapore Mathematics kilNumerical calculationAlgebraic manipulationSpatial visualizationData analysisMeasurementUse of mathematical toolsEstimationMonitoring ofone’s own thinkingetSelf-regulationacof enceuttiPerseveranceAtReasoning,communicationand connectionsThinking skillsand heuristicsApplications andmodelingConceptsNumerical, Algebraic, GeometricalStatistical, Probabilistic, AnalyticalFrom the Singapore Ministry of EducationThis framework aligns with a strong base of foundational research and has also been proven to produce exceptionalresults both internationally and within the United States.3AS ingapore math’s resounding success can be traced toits unique pedagogy which helps students master theconcrete, pictorial, and abstract. What we have learned fromSingapore has enabled us to form a program that has beenproven to improve math score wherever it is implemented.—Marshall Cavendish, Singaporehmheducation.com/singaporemath1
Singapore math is built upon keyresearch-based principlesProblem SolvingPRINCIPLES FROM RESE ARCHGrade 3“Problem solving is a fundamental part of mathematics—and everydaylife. The ability to solve problems is both a goal of mathematics—and atool within mathematics. As such, problem solving should be integratedinto all mathematical learning situations.”C R ITIC AL TH INKING S KIL L SPut On Your Thinking Cap!PRO B L E M S O LVINGRita wrote three 4-digit numbers on a sheet of paper.She accidentally spilled some ink on the paper.Some digits were covered by the ink.Using the clues given, help Rita find the digits covered by the ink.—National Council of Teachers of Mathematics, 2000TURNING PRINCIPLES INTO SUCCESSWITH MATH IN FOCUSESCLUProblem solving is at the heart of the Singapore math curriculum. Eachchapter contains numerous embedded problem-solving situations sothat students learn to flexibly apply their mathematical knowledge.Additionally, Put On Your Thinking Cap! problems require studentsto extend the concepts they have learned to non-routine situations todemonstrate mastery.The sum of all the ones is 17.The ones digit of the first number is the greatest 1-digit number.The digit in the tens place of the second number is one more thanthe digit in the tens place of the first number.The tens digit of the third number is 4 less than the tens digit ofthe second number.ON YOUR OWNGo to Workbook A:Put on Your Thinking Cap!pages 17–18Conceptual Understanding321G3A TB Ch 01.indd 32PRINCIPLES FROM RESE ARCHMaking Number BondsLesson Objectivespartwholenumber bond Find differentnumber bonds for numbers to 10.Grade1arn You can make number bonds with12/17/08 6:51:10 PMVocabulary Use connecting cubes or a math balance tofind number bonds.le“This concrete to pictorial to abstract approach benefitsall students but has been shown to be particularly effectivewith students who have mathematics difficulties, mainlybecause it moves gradually from actual objects throughpictures and then to symbols.” —Jordan, Miller, & Mercer, 1998Chapter 1 Numbers to 10,000ssoNle.You can use a number train to make number bonds.into two parts.Sam putpartTURNING PRINCIPLES INTO SUCCESSWITH MATH IN FOCUSSingapore math emphasizes a concrete to pictorial to abstract pedagogy.Students are first introduced to concepts with concrete manipulatives,which allow them to experience and understand the math they arelearning. They then learn to visually represent concepts using models,including number bonds and bar models. Finally, once students have astrong understanding of the concept, they move to the abstract stagewhere they use symbols, such as numbers and equations, to representmathematical situations.2Math in Focus: Singapore Math by Marshall CavendishpartHow many are in each part?part34whole13 and 1 make 4.This picture shows a number bond.part30Gr1 TB A Ch 2.indd 30Chapter 2Number Bonds8/19/08 4:32:56 PM
FoundationalResearchVisualization / RepresentationLEPRINCIPLES FROM RESE ARCHSSON1Using Part-Part-Whole inAddition and SubtractionLe“For students to understand such mathematical formalisms,we must help them connect these formalisms with otherLesson Objectivesforms of knowledge, including everyday experience, Use bar models to solve addition and subtraction problems. Apply the inverse operations of addition and subtraction.concrete examples, and visual representations.Grade 2Such connections form a conceptual frameworkarn You can use bar models to help you add.that holds mathematical knowledge together andMandy makes 10 granola bars.facilitates its retrieval and application.”Aida makes 12 granola bars.How many granola bars do they make in all?—Donovan & Bransford, 2005, p. 364TURNING PRINCIPLES INTO SUCCESSWITH MATH IN FOCUS10“Many students who have difficulty grasping abstractmathematical concepts would benefit from visualrepresentations of mathematical ideas. As part of thisapproach, the Singapore illustrations demonstrate how tographically decompose, represent, and solve complicatedmulti-step problems.”12?10 12 22They make 22 granola bars in all.Check!22 – 10 1222 – 12 10The answer is correct.—Ginsburg, et al., 2005, p. xii.96Math in Focus teaches students several consistent visualmodels they can use to make sense of mathematicalrelationships and solve problems. They include barmodels, place-value charts, number bonds, arraymodels, and more. Each model is fully integratedinto the program and carried across grade levels,allowing students to build upon them and understandincreasingly complex concepts.MS Gr2A unit04.indd 96Chapter 4Using Bar Models: Addition and Subtraction8/26/08 4:37:43 PMManipulatives play a key role in theconcrete to pictorial to abstractdevelopment of Singapore math.hmheducation.com/singaporemath3
Differentiated InstructionPRINCIPLES FROM RESE ARCH“Differentiated instruction is an instructional process that hasexcellent potential to positively impact learning by offeringteachers a means to provide instruction to a range of students intoday’s classroom situations.”—Hall, Strangman, & Meyer, 2003TURNING PRINCIPLES INTO SUCCESSWITH MATH IN FOCUSMath in Focus supports mathematical instruction at a variety oflevels to target all learners, from struggling to gifted. Teachershave access to online and print resources including Reteach, ExtraPractice, and Enrichment. Students also benefit from colorful,engaging online Interactivities. Additional support is included inthe Teacher’s Edition to further differentiate instruction and ensuresuccess for all learners.Online Student Interactivities bring Singapore math to lifewith fun, interactive tutorials, activities, and quizzes.4Math in Focus: Singapore Math by Marshall Cavendish
International resultsStrong research-based foundationslead to exceptional international resultsTIMSS 2007* Grade 4Hong Kong607Singapore599Japan586Chinese Taipei576Kazakhstan549Russian Federation544England541Latvia537PISA Mathematics Scale 2009* *1 Shanghai-China6002 Singapore5623 Hong Kong-China5554 Korea5465 Chinese Taipei5436 Finland5417 Liechtenstein5368 Switzerland5349 Japan52910 Canada52711 Netherlands52612 Macao-China52513 New Zealand51914 Belgium51515 Australia514Netherlands53516 Germany513Lithuania53017 Estonia512United States52918 Iceland507Germany52519 Denmark503Denmark52320 Slovenia501Australia51621 Norway498Hungary51022 France49723 Slovak Republic49724 Austria49625 Poland49526 Sweden49427 Czech Republic49328 United Kingdom49229 Hungary49030 Luxembourg48931 United States487Data from international studies has shown that the United States hasbeen surpassed in its mathematics performance. Meanwhile, Singapore’sstudents have consistently been top performers in internationalassessments. This is evidenced in Singapore’s consistent top performanceon the TIMSS and PISA studies.Trends in International Math andScience Study (TIMSS)Since the Trends in InternationalMath and Science Study (TIMSS)began in 1995, Singapore hasconsistently ranked at the top.The graph displayed here showsthe top 15 countries from the2007 report, with Singaporeoutperforming the United Statesby 70 points.*http://nces.ed.gov/timssOECD Programme for International StudentAssessment (PISA)In 2009, Singapore participated in the PISA study,which assesses 15-year-olds in industrialized countries.Singapore was a top-performing nation in math, andwhile Singapore students scored significantly abovethe international average, the United States scoredbelow the average, ranking #31 out of 66.5
Singapore’s international success pavesthe way for the Common Core StandardsBecause of its consistent success in achieving exceptional student achievement and its foundationon key research-based principles, Singapore math was one of the key models for the CommonCore State Standards. According to Achieve, an independent, nonprofit educational foundation:Overall, the Common Core State Standards (CCSS) are wellaligned to Singapore’s Mathematics Syllabus. Policymakerscan be assured that in adopting the CCSS, they will be settinglearning expectations for students that are similar to those setby Singapore in terms of rigor, coherence and focus.—Achieve* (achieve.org/CCSSandSingapore)The key ideas in the Common Core State Standards parallel theSingapore Mathematics Framework.PRINCIPLES FROM THE COMMON CORE“For over a decade, research studies of mathematics educationin high-performing countries have pointed to the conclusion thatthe mathematics curriculum in the United States must becomesubstantially more focused and coherent in order to improvemathematics achievement in this country.”Table of ContentsNumbers to 10,000Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1ADifferentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1BAssessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1CChapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1DChapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Recall Prior Knowledge and Quick Check Counting Place value . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–3—Common Core State Standards, corestandards.org1.1Counting2DAYLesson. 5Learn Use base-ten blocks to show numbers Express a number in different forms Count to tenthousand Count on by ones Count on by tens Count on by hundreds Count on by thousandsLet’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . 10–111.2TURNING PRINCIPLES INTO SUCCESSWITH MATH IN FOCUSPlace Value2DAYLesson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Learn Use a place-value chart and place-value strips to find the value of each digit in a numberGame Roll and Show!Learn Use a place-value chart and base-ten blocks to show greater numbersLet’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . 18–191.3One of the key high-performing countries that the creators of theCommon Core State Standards looked at was Singapore, whosemathematics curriculum truly embodies the notion of focused andcoherent. Through multi-day lessons and minimal repetition fromyear to year, students learn concepts in depth to mastery.Comparing and Ordering Numbers2DAYLesson. . . . . . . . . . . . . . 20Learn Use base-ten blocks to compare and order numbers Use base-ten blocks to compare andorder numbers place value to compare numbers Use place value to order numbersHands-On Activity Use clues on place values to guess a numberLearn Look for patterns on a number lineLet’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . . . 29Let’s Explore! Make 4-digit numbers with leading digits of specific value then find their differenceMath Journal Reading and Writing Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30–31Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . 32Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33–34Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33–34Assessments Book Test Prep 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Table of ContentsMIF 3ATE TOC(Path).indd 39* Achieve is a bipartisan, nonprofit educational reform organization that partnered with NGA and CCSSO on the Common Core State Standards Initiative.6Math in Focus: Singapore Math by Marshall CavendishT393/9/09 11:28:46 PM
Common CoreConnectionPRINCIPLES FROM THE COMMON CORE“The composite standards [of Hong Kong, Korea, and Singapore] havea number of features that can inform an international benchmarkingprocess for the development of K–6 mathematics standards inthe U.S. First, the composite standards concentrate the earlylearning of mathematics on the number, measurement, andgeometry strands with less emphasis on data analysis and littleexposure to algebra.”5A5A—Common Core State Standards, corestandards.orgTURNING PRINCIPLES INTO SUCCESSWITH MATH IN FOCUSMath in Focus emphasizes number and operations in everygrade. The textbook is divided into two books, roughly a semestereach. Book A focuses on number and operations while Book B focuseson geometry and measurement, where number concepts are practiced,connected, and applied.PRINCIPLES FROM THE COMMON CORE“One hallmark of mathematical understanding is the ability to justify,in a way appropriate to the student’s mathematical maturity, why aparticular mathematical statement is true or where a mathematical rulecomes from.”Grade 4R e a D iN G a N D W R i T i N G M aT HMath JournalBoth Andy and Rita think that 0.23 is greater than 0.3.—Common Core State Standards, corestandards.org23 is greater than 3,so 0.23 is greater than 0.3.TURNING PRINCIPLES INTO SUCCESSWITH MATH IN FOCUSThe Singapore Mathematics Framework and pedagogy emphasize deepunderstanding, which is demonstrated through consistent opportunitiesto explain why mathematical concepts work. This is modeled for studentsthroughout Math in Focus with thought bubbles, which display picturesof students expressing their understanding. Students then have theopportunity to justify their own understanding through activities such asMath Journals.23 tenths is greaterthan 3 tenths, so 0.23is greater than 0.3.Do you agree? Why or why not? Explain your answer.Lesson 7.3 Comparing Decimalshmheducation.com/singaporemath337
United States students experienceexceptional results with Math in FocusOld Bridge, New Jersey3xgreater gainsState Test Score AnalysisAn analysis of 2010 state test scores in Old Bridge,NJ sought to determine if Math in Focus studentsexperienced greater gains on the state mathematicstest (NJ ASK).Results4th-Grade Student Performance on NJ ASKMath in Focus students improved an average of12.4 points, more than three times the averageimprovement that occurred across the remainingstudents in the district in the comparison group.Gains on the NJ ASK State Testwith Math in Focus!14.0Grade 412.012.48.06.04.03.52.00.0Control GroupMath in FocusMore students reachNJ ASK gains at the AdvancedProficient LevelThe percentage of 4th-grade students scoring atthe highest level, advanced proficient, increased by22% for the Math in Focus group, while thecontrol group increased by only 4%.NJ ASK gains at theAdvanced Proficient Leveladvanced levelswith Math in Focus!3025Grade 422%201510504%Control GroupFor full reports, please contact your local Account Manager.8Math in Focus: Singapore Math by Marshall CavendishMath in Focus
U.S. REsultsInstructional Effectiveness Study OverviewAn independent research firm conducted a yearlong study that examined 2nd-grade achievement inMath in Focus compared to a control group.ResultsAt Grade 2, the Math in Focus group of studentsmade significant and greater academic gains frompretest to posttest.2nd-Grade SAT-9 Score Improvement(improvement from pretest to posttest)60Grade 256.250403042.220100Comparison GroupGains compared to other typesof mathematics programsMath in Focus student performance on the NJ ASKtest was also compared to comparison groups usingconstructivist and explicit mathematics programs.The three programs were taught in the same schoolsby similar teachers. The analysis showed that theMath in Focus, a program that utilizes a balancedapproach, outperformed the students in thealternative programs.Gains in % of Students Scoringat the Advanced Proficient LevelMath in FocusProveneffective pedagogyin U.S. classrooms!4035Grade 434%302523%20151016%50Constructivist Program Explicit ProgramBalanced ProgramMath in Focushmheducation.com/singaporemath9
KentuckyA longitudinal analysis of Math in Focus in Lexington, KYLongitudinal data analysis was conducted to investigate student mathachievement over the course of two consecutive years. The samplewas comprised of 272 students from Title 1-eligible schools. Studentmath performance was measured using the Measures of AcademicProgress (MAP).MAP Scores for 2009 Academic Year225Grade 5220215210205200209214.5In addition to showing growth in thelongitudinal analysis, Lexington studentsusing Math in Focusalso showed exceptional resultson the Kentucky state test.Highlights include:Gains in Proficient and Distinguishedratings for African-American students:219.6 Deep Springs Elementary –26% gain at 3rd grade195 Breckenridge Elementary –25% gain at 5th grade190185Fall 2009Winter 2009Spring 2010Gains in Proficient and Distinguishedratings for Hispanic students:ResultsStatistical analysis indicated that using Math in Focus was associatedwith increased student math performance. This improvement wasstatistically significant even after controlling for student level variables.Thinklink Benchmark Test Improvementin Marshall County, KYThe Thinklink benchmark test ranks students onfour levels: Novice, Apprentice, Proficient, andDistinguished. After using Math in Focus in Grade3 from 2010 to 2011, the Thinklink benchmark testscores showed a significant improvement for Math inFocus students, rising from 57% to 91% of studentsat the Distinguished level for Algebra
Math in Focus : Singapore Math by Marshall Cavendish, for Grades K–8, is the U.S. edition of Singapore’s most widely used curriculum, bringing Singapore’s effective approach to mathematics to U.S. classrooms. Singapore math emphasizes problem solving and positive attitudes towar
of the Singapore Constitution (London: RoutledgeCurzon, 2009). Thio Li-ann, A Treatise on Singapore Constitutional Law (Singapore: Academy Publishing, 2012). Kevin YL Tan (ed), Essays in Singapore Legal History (Singapore: Singapore Academy of Law & Marshall
Singapore 3rd Grade Math Worksheet: 7 Mass, Length, Volume, Money and Time Name:_ Date:_ Question 1 Einstein and my math teacher took part in a tough Singapore math quiz. My smart math teacher took 1 h 26 min to complete the quiz. Einstein had great difficult
Singapore Math : Place Value in Math in Focus Singapore Math is a trademark owned by Singapore Math Inc. and Marshall Cavendish Education Pte. Ltd. There are several skills that are critical to mathematics success in the elementary grades. Among them are an understanding of number, number sense, and place value.
Singapore Strategies Below is a list of strategies taken from various Singapore Math Trainings. Click on the name of the strategy to view a video explanation and example. 1) Math Talks (Look & Talks) Math Talks are guided math discussions using pictures to help students develo
Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra 1/2 Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra ½ form a series of courses to move students from primary grades to algebra. Each course contains a series of daily lessons covering all areas of general math. Each lesson
In Singapore Math written by Andy Clark Ever since Singapore scored first in both 4th and 8th grades in the Trends in International Math and Science Study (TIMSS) comparison assessments in 1995, 1999, and 2003, and in the top three in 2007, math educators have been interest
Singapore Math Using the bar model approach, Singapore textbooks enable students to solve difficult math problems—and learn how to think symbolically. John Hoven and Barry Garelick H ere is a math problem you can solve easily: A man sold 230 balloons at a fun fair in
orientations/briefings before any 3-day weekend. The training must include a review of local driving laws/regulations, motor vehicle safety inspections, the effects of fatigue or alcohol on a driver’s capabilities, and review of any local driving hazards. Commanders will ensure POVs of all military personnel are given a safety inspection prior to holidays as required by AR 385-10, at a .
