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MATH IN FOCUS – SINGAPORE MATH GIRLS AND MATH Consistent gender differences have emerged around student beliefs about their abilities in math, their interest in math and their perceptions of the importance of math for their futures. In general, research- ers have found that girls have less confidence in their math abilities than boys have and that from early adolescence, girls show less interest in math careers. 1 As they move out of elementary school and into middle and high school and beyond, girls oſten underestimate their abilities in mathematics. However, not all girls have less confidence and interest in mathematics, and girls who have a strong self-concept regarding their abilities in math are more likely to choose and perform well in elective math courses and to select math-related college majors and careers. 2 THE POWER OF GROWTH MINDSET AND “YET!” At Laurel, we know that improving girls’ beliefs about their abilities can change their choices and performance. Research shows that students who have a growth mindset — who believe — that academic abilities can be expanded through effort and persistence — outperform fixed mindset students who believe that ability depends on innate talent. 3 We are a growth-mindset school! When a girl says, “I’m not good” at something, we say “You’re not good at it YET, but with hard work and persistence you can be.” In addition to boosting beliefs about ability with a growth-mindset approach, another way to encourage girls in math is to help them build the spatial skills that are crucial to success in many math-related fields. Research shows that even young children experience anxiety at the prospect of having to complete spatial reasoning tasks. is anxiety negatively impacts task performance, and girls experience more of this anxiety than boys do. 4 erefore, it is important to focus on spatial skills in early math instruction and for children to develop a sense of confidence in these skills, at a young age. WHY SINGAPORE MATH? Singapore has been a top-performing nation on international comparison stud- ies for 15 years. 5 “Singapore Math” refers to the math curriculum used in that country. “Attitude” is one of the five key components of the Singapore framework of mathematical instruction, and thus dovetails perfectly with Laurel School’s growth-mindset approach. Teachers at schools where Singapore Math has been introduced into the curriculum see the impact of its approach. As one noted, “[Aſter introducing Singapore Math strategies to my students] they became far more engaged in their math lessons. As a group they had an ‘I can solve anything’ attitude that I’d seen previously in only a small group of my students.” 6 What is the difference? Singapore Math emphasizes mastery of concepts, the development of spatial skills through a concrete–pictorial–abstract approach, metacognitive reasoning and the use of model drawing to solve and justify problems. Numbers and symbols can be confusing to a student who doesn’t have a grasp of what they actually mean. e National Math Advisory Panel Report (2008) recommends that students should develop immediate recall of arithmetic facts to free the “working memory” for solving more complex problems. Some research shows that while no gender differences exist in accuracy of completing arithmetic problems, boys show better fluency than girls on these tasks. 7 Singapore Math fosters strong number sense, excellent mental math skills and a deep understanding of place value at each grade level so that students understand how algorithms work. 8 WHAT IS MATH IN FOCUS? Math in Focus® 9 is the U.S. edition of Sin- gapore’s most widely used math program and follows the same scope, sequence and pedagogy but has been enhanced to include differentiation components and interactive technology. It also addresses the full spectrum of Common Core State Standards. In the Math in Focus curriculum, children develop math fluency through first gaining a deeper understanding of “why” basic math facts work. e progression from concrete to pictorial to abstract math provides frequent opportunities for practice with math facts. rough this repeated practice, students develop their math fluency while also learning broader math concepts. SINGAPORE MATH AT LAUREL SCHOOL

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At Laurel, we know that improving girls’ beliefs about their abilities can change their choices and performance. Singapore has been a top-performing nation on international comparison studies for 15 years. “Singapore Math” refers to the math curriculum used in that country. “Attitude” is one of the five key components of the Singapore framework of mathematical instruction, and thus dovetails perfectly with Laurel School’s growth-mindset approach.

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MATH IN FOCUS – SINGAPORE MATH

GIRLS AND MATH Consistent gender differences have emerged around student beliefs about their abilities in math, their interest in math and their perceptions of the importance of math for their futures. In general, research-ers have found that girls have less confidence in their math abilities than boys have and that from early adolescence, girls show less interest in math careers. 1 As they move out of elementary school and into middle and high school and beyond, girls often underestimate their abilities in mathematics. However, not all girls have less confidence and interest in mathematics, and girls who have a strong self-concept regarding their abilities in math are more likely to choose and perform well in elective math courses and to select math-related college majors and careers.2

THE POWER OF GROWTH MINDSET AND “YET!” At Laurel, we know that improving girls’ beliefs about their abilities can change their choices and performance. Research shows that students who have a growth mindset — who believe — that academic abilities can be expanded through effort and persistence — outperform fixed mindset students who believe that ability depends on innate talent. 3 We are a growth-mindset school! When a girl says, “I’m not good” at something, we say “You’re not good at it YET, but with hard work and persistence you can be.”

In addition to boosting beliefs about ability with a growth-mindset approach, another way to encourage girls in math is to help them build the spatial skills that are crucial to success in many math-related fields. Research shows that even young children experience anxiety at the prospect of having to complete spatial reasoning tasks. This anxiety negatively impacts task performance, and girls experience more of this anxiety than boys do.4 Therefore, it is important to focus on spatial skills in early math instruction and for children to develop a sense of confidence in these skills, at a young age.

WHY SINGAPORE MATH? Singapore has been a top-performing nation on international comparison stud-ies for 15 years.5 “Singapore Math” refers to the math curriculum used in that country. “Attitude” is one of the five key components of the Singapore framework of mathematical instruction, and thus dovetails perfectly with Laurel School’s growth-mindset approach. Teachers at schools where Singapore Math has been introduced into the curriculum see the impact of its approach. As one noted, “[After introducing Singapore Math strategies to my students] they became far more engaged in their math lessons. As a group they had an ‘I can solve anything’ attitude that I’d seen previously in only a small group of my students.”6

What is the difference? Singapore Math emphasizes mastery of concepts, the development of spatial skills through a concrete–pictorial–abstract approach, metacognitive reasoning and the use of model drawing to solve and justify problems. Numbers and symbols can be confusing to a student who doesn’t have a grasp of what they actually mean. The National Math Advisory Panel Report (2008) recommends that students should develop immediate recall of arithmetic facts to free the “working memory” for solving more complex problems. Some research shows that while no gender differences exist in accuracy of completing arithmetic problems, boys show better fluency than girls on these tasks.7 Singapore Math fosters strong number sense, excellent mental math skills and a deep understanding of place value at each grade level so that students understand how algorithms work.8

WHAT IS MATH IN FOCUS? Math in Focus® 9 is the U.S. edition of Sin-gapore’s most widely used math program and follows the same scope, sequence and pedagogy but has been enhanced to include differentiation components and interactive technology. It also addresses the full spectrum of Common Core State Standards. In the Math in Focus curriculum, children develop math fluency through first gaining a deeper understanding of “why” basic math facts work. The progression from concrete to pictorial to abstract math provides frequent opportunities for practice with math facts. Through this repeated practice, students develop their math fluency while also learning broader math concepts.

Laurel School One Lyman Circle

Shaker Heights, Ohio 44122216.464.1441

www.LaurelSchool.org

[ ENDNOTES ]1 Andre, T., Whigham, M., Hendrickson, A., and Chambers, S. (1999). Competency beliefs, positive affect, and gender stereotypes of elementary students and their

parents about science versus other school subjects. Journal of Research in Science Teaching, 36, 719-747.

Herbert, J., and Stipek, D. (2005). The emergence of gender differences in children’s perceptions of their academic competence. Applied Developmental Psychology, 26, 276–295.

Jacobs, J.E., Lanza, S., Osgood, D.W., Eccles, J.S., and Wigfield, A. (2002). Changes in children’s self-competence and values: Gender and domain differences across grades one through twelve. Child Development, 73, 509–527.

Wigfield, A., Eccles, J.S., Mac Iver, D., Reuman, D.A., and Midgley, C. (1991). Transitions during early adolescence: Changes in children’s domain-specific self-percep-tions and general self-esteem across the transition to junior high school. Developmental Psychology, 27, 552–565.

2 Simpkins, S.D., and Davis-Kean, P.E. (2005). The intersection between self-concept and values: Links between beliefs and choices in high school. New Directions for Child and Adolescent Development, 110, 31–47.

Updegraff, K.A., and Eccles, J.S. (1996). Course enrollment as self-regulatory behavior: Who takes optional high school math courses? Learning and Individual Differ-ences, 8, 239–259.

3 Henderson, V. & Dweck, C.S. (1991). “Adolescence and achievement,” in S. Feldman & G. Elliott eds., At the threshold: Adolescent development (Cambridge, MA: Harvard University Press: 197-216.

4 Ramirez, G., Gunderson, E.A., Levine, S.C., & Beilcok, S.L. (2012). Spatial anxiety relates to spatial abilities as a function of working memory in children. The Quarterly Journal of Experimental Psychology, 65, 474-487.

5 National Center for Education Statistics. (2012). Highlights From TIMSS 2011: Mathematics and Science Achievement of U.S. Fourth- and Eighth-Grade Students in an International Context (NCES Publication No. 2013009). Retrieved from http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2013009.

6 Hazecamp, J (2011). Why Before How, 1. 7 Carr, M., Steiner, H.H., Kyser, B., & Biddlecomb, B. (2008). A comparison of predictors of early emerging gender differences in mathematics competency.

Learning and Individual Differences, 18, 61-75.

8 Kanter, P.F. Singapore Math: Place value in Math in Focus. Retrieved from http://www.hmheducation.com/assets/pdf/singaporemath/MathInFocus_PlaceValue.pdf

9 http://www.hmheducation.com/singaporemath/index.php

10 Clark, A. Singapore Math: A visual approach to word problems. http://www.hmheducation.com/assets/pdf/singaporemath/MathInFocus_ModelDrawing.pdf SIN

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GRADES K–5 SCOPE AND SEQUENCE Math in Focus answers the call for a coherent sequence of topics that gives students time to fully master foundational math skills. Since each grade level covers fewer topics—but in more depth—little repetition is required the following year. This means that a great deal of attention is paid to the order in which math concepts are taught at each grade and the time spent on each.

HIGHLY SCAFFOLDED CURRICULUM Math in Focus adapts instruction to the needs of individual learners through scaffolding, the systematic sequencing of prompted content, and supports optimize learning. The ultimate goal of scaffolding is to remove gradually the supports as the learner masters the task.

Math in Focus uses this approach to introduce new concepts and increasingly difficult problems. Scaffolding is apparent in the concrete–pictorial–abstract approach that appears throughout the program and in the sequencing of the word problems that go from one step to two steps to multistep.

VISUAL REPRESENTATIONS Math in Focus uses the bar modeling method as a problem-solving tool that is taught explicitly beginning in Grade 2. Students become familiar with this systematic way to translate complex word problems into mathematical equations and avoid the common issue of not knowing where to begin. Word problems grow in complexity from one step to two steps to multistep, which enhances students’ ability to think critically in a systematic process.

With Model Drawing (Bar Modeling), students organize their thoughts, create a visual model of the problem and focus on the question being asked. Students are taught to visualize and construct “pictures” to help them make sense of word problems.

Model drawing equips students with a strong conceptual understanding to solve even the most challenging problems.10 It serves as a link to algebra. Symbolic representation of unknowns, a key to success in algebra, is simply a natural extension of the model-drawing method.

In early grades, students create math stories by matching number bonds to illustrations.

NUMBER BOND EXAMPLE

1-0=1

2-1=1

3-1=2

1

1 0

2

1 1

3

1 2

MODEL DRAWING EXAMPLE

Greta played in three basketball games during winter vacation. She scored 24 points in the first game, 18 points in the second game, and 27 points in the third game. On average, how many points did she score each game?

Greta scored an average of 23 points each game.

24 + 18 + 27 = 69

69 ÷ 3 = 23

24 18 27

23 23 23

DIFFERENTIATION RESOURCES

Extra Practice and Re-teach opportunities are provided for every lesson. These can be implemented on a whole-class basis, in a small-group, or in individual settings. Enrichment exercises of varying complexity provide advanced students opportunities to extend learning.RE

SOU

RCES

RESOURCES FOR PARENTS— LEARN MORE ABOUT SINGAPORE MATH http://www.hmheducation.com/singaporemath/what-is-singapore-math.php

http://www.hmheducation.com/singaporemath/helping-your-child.php

http://www.sde.com/singapore-math/faq.asp

http://www.sde.com/singapore-math/what.asp

+CONCRETE

PICTORIAL

2 + 1 = 3

ABSTRACT

Concepts are introduced through hands-on

experiences with manipulatives.

Students visualize the concept and represent it pictorially

through models such as number bonds and bar models.

Students only use abstract numbers and symbols when they

have enough context to understand what they mean.

VIS

UA

L RE

PRES

ENTA

TIO

NS

SINGAPORE MATH AT LAUREL SCHOOL

GRADES K–5 SCOPE AND SEQUENCE Math in Focus answers the call for a coherent sequence of topics that gives students time to fully master foundational math skills. Since each grade level covers fewer topics—but in more depth—little repetition is required the following year. This means that a great deal of attention is paid to the order in which math concepts are taught at each grade and the time spent on each.

HIGHLY SCAFFOLDED CURRICULUM Math in Focus adapts instruction to the needs of individual learners through scaffolding, the systematic sequencing of prompted content, and supports optimize learning. The ultimate goal of scaffolding is to remove gradually the supports as the learner masters the task.

Math in Focus uses this approach to introduce new concepts and increasingly difficult problems. Scaffolding is apparent in the concrete–pictorial–abstract approach that appears throughout the program and in the sequencing of the word problems that go from one step to two steps to multistep.

VISUAL REPRESENTATIONS Math in Focus uses the bar modeling method as a problem-solving tool that is taught explicitly beginning in Grade 2. Students become familiar with this systematic way to translate complex word problems into mathematical equations and avoid the common issue of not knowing where to begin. Word problems grow in complexity from one step to two steps to multistep, which enhances students’ ability to think critically in a systematic process.

With Model Drawing (Bar Modeling), students organize their thoughts, create a visual model of the problem and focus on the question being asked. Students are taught to visualize and construct “pictures” to help them make sense of word problems.

Model drawing equips students with a strong conceptual understanding to solve even the most challenging problems.10 It serves as a link to algebra. Symbolic representation of unknowns, a key to success in algebra, is simply a natural extension of the model-drawing method.

In early grades, students create math stories by matching number bonds to illustrations.

NUMBER BOND EXAMPLE

1-0=1

2-1=1

3-1=2

1

1 0

2

1 1

3

1 2

MODEL DRAWING EXAMPLE

Greta played in three basketball games during winter vacation. She scored 24 points in the first game, 18 points in the second game, and 27 points in the third game. On average, how many points did she score each game?

Greta scored an average of 23 points each game.

24 + 18 + 27 = 69

69 ÷ 3 = 23

24 18 27

23 23 23

DIFFERENTIATION RESOURCES

Extra Practice and Re-teach opportunities are provided for every lesson. These can be implemented on a whole-class basis, in a small-group, or in individual settings. Enrichment exercises of varying complexity provide advanced students opportunities to extend learning.RE

SOU

RCES

RESOURCES FOR PARENTS— LEARN MORE ABOUT SINGAPORE MATH http://www.hmheducation.com/singaporemath/what-is-singapore-math.php

http://www.hmheducation.com/singaporemath/helping-your-child.php

http://www.sde.com/singapore-math/faq.asp

http://www.sde.com/singapore-math/what.asp

+CONCRETE

PICTORIAL

2 + 1 = 3

ABSTRACT

Concepts are introduced through hands-on

experiences with manipulatives.

Students visualize the concept and represent it pictorially

through models such as number bonds and bar models.

Students only use abstract numbers and symbols when they

have enough context to understand what they mean.

VIS

UA

L RE

PRES

ENTA

TIO

NS

SINGAPORE MATH AT LAUREL SCHOOL

MATH IN FOCUS – SINGAPORE MATH

GIRLS AND MATH Consistent gender differences have emerged around student beliefs about their abilities in math, their interest in math and their perceptions of the importance of math for their futures. In general, research-ers have found that girls have less confidence in their math abilities than boys have and that from early adolescence, girls show less interest in math careers. 1 As they move out of elementary school and into middle and high school and beyond, girls often underestimate their abilities in mathematics. However, not all girls have less confidence and interest in mathematics, and girls who have a strong self-concept regarding their abilities in math are more likely to choose and perform well in elective math courses and to select math-related college majors and careers.2

THE POWER OF GROWTH MINDSET AND “YET!” At Laurel, we know that improving girls’ beliefs about their abilities can change their choices and performance. Research shows that students who have a growth mindset — who believe — that academic abilities can be expanded through effort and persistence — outperform fixed mindset students who believe that ability depends on innate talent. 3 We are a growth-mindset school! When a girl says, “I’m not good” at something, we say “You’re not good at it YET, but with hard work and persistence you can be.”

In addition to boosting beliefs about ability with a growth-mindset approach, another way to encourage girls in math is to help them build the spatial skills that are crucial to success in many math-related fields. Research shows that even young children experience anxiety at the prospect of having to complete spatial reasoning tasks. This anxiety negatively impacts task performance, and girls experience more of this anxiety than boys do.4 Therefore, it is important to focus on spatial skills in early math instruction and for children to develop a sense of confidence in these skills, at a young age.

WHY SINGAPORE MATH? Singapore has been a top-performing nation on international comparison stud-ies for 15 years.5 “Singapore Math” refers to the math curriculum used in that country. “Attitude” is one of the five key components of the Singapore framework of mathematical instruction, and thus dovetails perfectly with Laurel School’s growth-mindset approach. Teachers at schools where Singapore Math has been introduced into the curriculum see the impact of its approach. As one noted, “[After introducing Singapore Math strategies to my students] they became far more engaged in their math lessons. As a group they had an ‘I can solve anything’ attitude that I’d seen previously in only a small group of my students.”6

What is the difference? Singapore Math emphasizes mastery of concepts, the development of spatial skills through a concrete–pictorial–abstract approach, metacognitive reasoning and the use of model drawing to solve and justify problems. Numbers and symbols can be confusing to a student who doesn’t have a grasp of what they actually mean. The National Math Advisory Panel Report (2008) recommends that students should develop immediate recall of arithmetic facts to free the “working memory” for solving more complex problems. Some research shows that while no gender differences exist in accuracy of completing arithmetic problems, boys show better fluency than girls on these tasks.7 Singapore Math fosters strong number sense, excellent mental math skills and a deep understanding of place value at each grade level so that students understand how algorithms work.8

WHAT IS MATH IN FOCUS? Math in Focus® 9 is the U.S. edition of Sin-gapore’s most widely used math program and follows the same scope, sequence and pedagogy but has been enhanced to include differentiation components and interactive technology. It also addresses the full spectrum of Common Core State Standards. In the Math in Focus curriculum, children develop math fluency through first gaining a deeper understanding of “why” basic math facts work. The progression from concrete to pictorial to abstract math provides frequent opportunities for practice with math facts. Through this repeated practice, students develop their math fluency while also learning broader math concepts.

Laurel School One Lyman Circle

Shaker Heights, Ohio 44122216.464.1441

www.LaurelSchool.org

[ ENDNOTES ]1 Andre, T., Whigham, M., Hendrickson, A., and Chambers, S. (1999). Competency beliefs, positive affect, and gender stereotypes of elementary students and their

parents about science versus other school subjects. Journal of Research in Science Teaching, 36, 719-747.

Herbert, J., and Stipek, D. (2005). The emergence of gender differences in children’s perceptions of their academic competence. Applied Developmental Psychology, 26, 276–295.

Jacobs, J.E., Lanza, S., Osgood, D.W., Eccles, J.S., and Wigfield, A. (2002). Changes in children’s self-competence and values: Gender and domain differences across grades one through twelve. Child Development, 73, 509–527.

Wigfield, A., Eccles, J.S., Mac Iver, D., Reuman, D.A., and Midgley, C. (1991). Transitions during early adolescence: Changes in children’s domain-specific self-percep-tions and general self-esteem across the transition to junior high school. Developmental Psychology, 27, 552–565.

2 Simpkins, S.D., and Davis-Kean, P.E. (2005). The intersection between self-concept and values: Links between beliefs and choices in high school. New Directions for Child and Adolescent Development, 110, 31–47.

Updegraff, K.A., and Eccles, J.S. (1996). Course enrollment as self-regulatory behavior: Who takes optional high school math courses? Learning and Individual Differ-ences, 8, 239–259.

3 Henderson, V. & Dweck, C.S. (1991). “Adolescence and achievement,” in S. Feldman & G. Elliott eds., At the threshold: Adolescent development (Cambridge, MA: Harvard University Press: 197-216.

4 Ramirez, G., Gunderson, E.A., Levine, S.C., & Beilcok, S.L. (2012). Spatial anxiety relates to spatial abilities as a function of working memory in children. The Quarterly Journal of Experimental Psychology, 65, 474-487.

5 National Center for Education Statistics. (2012). Highlights From TIMSS 2011: Mathematics and Science Achievement of U.S. Fourth- and Eighth-Grade Students in an International Context (NCES Publication No. 2013009). Retrieved from http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2013009.

6 Hazecamp, J (2011). Why Before How, 1. 7 Carr, M., Steiner, H.H., Kyser, B., & Biddlecomb, B. (2008). A comparison of predictors of early emerging gender differences in mathematics competency.

Learning and Individual Differences, 18, 61-75.

8 Kanter, P.F. Singapore Math: Place value in Math in Focus. Retrieved from http://www.hmheducation.com/assets/pdf/singaporemath/MathInFocus_PlaceValue.pdf

9 http://www.hmheducation.com/singaporemath/index.php

10 Clark, A. Singapore Math: A visual approach to word problems. http://www.hmheducation.com/assets/pdf/singaporemath/MathInFocus_ModelDrawing.pdf SIN

GA

PORE

MAT

H A

T LA

URE

L SC

HO

OL