Tag Archives: Math Curriculum

Michigan State University study: Young children can understand large numbers

21 Dec

Mary Niederberger of the Pittsburgh Post-Gazette writes in the article, Formula written for math success:

Mastery of fractions and early division is a predictor of students’ later success with algebra and other higher-level mathematics, based on a study done by a team of researchers led by a Carnegie Mellon University professor.
That means more effective teaching of the concepts is needed to improve math scores among U.S. high school students, which have remained stagnant for more than 30 years….
The study said a likely reason for U.S. students’ weakness in fractions and division could be linked to their teachers’ “lack of a firm conceptual understanding” of the concepts, citing several other studies in which many American teachers were unable to explain the reasons behind mathematical solutions, while most teachers in Japan and China were able to offer two or three explanations. http://www.post-gazette.com/stories/news/education/formula-written-for-math-success-640962/#ixzz1ym9qos5j

Citation:

Early Predictors of High School Mathematics Achievement
1. Robert S. Siegler1,
2. Greg J. Duncan2,
3. Pamela E. Davis-Kean3,4,
4. Kathryn Duckworth5,
5. Amy Claessens6,
6. Mimi Engel7,
7. Maria Ines Susperreguy3,4 and
8. Meichu Chen4Abstract
Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.
1.Published online before print June 14, 2012, doi: 10.1177/0956797612440101 Psychological Science June 14, 2012 0956797612440101

Math is important for a number of reasons.

Michigan State University’s Office of Supportive Services succinctly states why math is important:
Why is math important?

All four year Universities have a math requirement
Math improves your skills:
◦Critical Thinking Skills
◦Deductive Logic and Reasoning Skills
◦Problem Solving Skills
A good knowledge of math and statistics can expand your career options
Physical Sciences – Chemistry, Engineering, Physics
Life and Health Sciences – Biology, Psychology, Pharmacy, Nursing, Optometry
Social Sciences – Anthropology, Communications, Economics, Linquistics, Education, Geography
Technical Sciences – Computer Science, Networking, Software Development
Business and Commerce
Actuarial Sciences
Medicine
http://oss.msu.edu/academic-assistance/why-is-math-important

Young children have the ability to grasp large numbers.

Science Daily reported in the article, Kids Grasp Large Numbers Remarkably Young:

Children as young as 3 understand multi-digit numbers more than previously believed and may be ready for more direct math instruction when they enter school, according to research led by a Michigan State University education scholar.
The study, online in the journal Child Development and funded by the U.S. Department of Education’s Institute of Education Sciences, has implications for U.S. students who continue losing ground internationally in mathematics performance.
“Contrary to the view that young children do not understand place value and multi-digit numbers, we found that they actually know quite a lot about it,” said Kelly Mix, MSU professor of educational psychology and co-author of the study. “They are more ready than we think when they enter kindergarten.”
Understanding place value is the gateway to higher math skills such as addition with carrying, and there is a strong tie between place value skills in early elementary grades and problem-solving ability later on.
“In short, children who fail to master place value face chronic low achievement in mathematics,” the study states.
In several experiments, Mix and Richard Prather and Linda Smith, both from Indiana University, tested children ages 3 to 7 on their ability to identify and compare two- and three-digit numbers.
In one task, for example, children were shown two quantities (such as 128 and 812) and asked to point out which was larger. “There was significant improvement in interpreting place value from age 3 to 7,” Mix said, “but it was remarkable that even the youngest children showed at least some understanding of multi-digit numbers.”
Mix said the surprising findings are likely due to the fact that children in today’s society are bombarded with multi-digit numbers — from phone numbers to street addresses to price tags.
Interestingly, children may be developing partial knowledge of the place value system at least partly from language, she explained. Children often hear multi-digit numbers named while also seeing them in print, such as when parents comment on a calendar, ask their child to push the elevator buttons or look for a room number in an office building.
http://www.sciencedaily.com/releases/2013/12/131218112914.htm#.UrVMao_ZKxU.email

Citation:

Journal Reference:
1.Kelly S. Mix, Richard W. Prather, Linda B. Smith, Jerri DaSha Stockton. Young Children’s Interpretation of Multidigit Number Names: From Emerging Competence to Mastery. Child Development, 2013; DOI: 10.1111/cdev.12197
Michigan State University (2013, December 18). Kids grasp large numbers remarkably young. ScienceDaily. Retrieved December 21, 2013,

Jonathan Cohn reported about an unprecedented experiment which occurred in Romanian orphanages in the New Republic article, The Two Year Window. There are very few experiments involving humans because of ethical considerations.

Drury, Nelson, and their collaborators are still learning about the orphans. But one upshot of their work is already clear. Childhood adversity can damage the brain as surely as inhaling toxic substances or absorbing a blow to the head can. And after the age of two, much of that damage can be difficult to repair, even for children who go on to receive the nurturing they were denied in their early years. This is a revelation with profound implication—and not just for the Romanian orphans.
APPROXIMATELY SEVEN MILLION American infants, toddlers, and preschoolers get care from somebody other than a relative, whether through organized day care centers or more informal arrangements, according to the Census Bureau. And much of that care is not very good. One widely cited study of child care in four states, by researchers in Colorado, found that only 8 percent of infant care centers were of “good” or “excellent” quality, while 40 percent were “poor.” The National Institute of Child Health and Human Development has found that three in four infant caregivers provide only minimal cognitive and language stimulation—and that more than half of young children in non-maternal care receive “only some” or “hardly any” positive caregiving. http://www.tnr.com/article/economy/magazine/97268/the-two-year-window?page=0,0&passthru=YzBlNDJmMmRkZTliNDgwZDY4MDhhYmIwMjYyYzhlMjg

Because the ranks of poor children are growing in the U.S., this study portends some grave challenges not only for particular children, but this society and this country. Adequate early learning opportunities and adequate early parenting is essential for proper development in children. https://drwilda.wordpress.com/2011/12/18/jonathan-cohns-the-two-year-window/

Related:

Study: Gender behavior differences lead to higher grades for girls
https://drwilda.com/2013/01/07/study-gender-behavior-differences-lead-to-higher-grades-for-girls/

Girls and math phobia https://drwilda.com/2012/01/20/girls-and-math-phobia/

University of Missouri study: Counting ability predicts future math ability of preschoolers
https://drwilda.com/2012/11/15/university-of-missouri-study-counting-ability-predicts-future-math-ability-of-preschoolers/

Is an individualized program more effective in math learning?
https://drwilda.com/2012/10/10/is-an-individualized-program-more-effective-in-math-learning/

Where information leads to Hope. © Dr. Wilda.com

Dr. Wilda says this about that ©

Blogs by Dr. Wilda:

COMMENTS FROM AN OLD FART©
http://drwildaoldfart.wordpress.com/

Dr. Wilda Reviews ©
http://drwildareviews.wordpress.com/

Dr. Wilda ©
https://drwilda.com/

Tags: , , , , , , , , , , , , , , , , , , , , , , , , , , ,

University of Missouri study: Counting ability predicts future math ability of preschoolers

15 Nov

Jacob Vigdor wrote the interesting Education Next article, Solving America’s Math Problem:

American public schools have made a clear trade-off over the past few decades. With the twin goals of improving the math performance of the average student and promoting equality, it has made the curriculum more accessible. The drawback to exclusive use of this more accessible curriculum can be observed among the nation’s top-performing students, who are either less willing or less able than their predecessors or their high-achieving global peers to follow the career paths in math, science, and engineering that are the key to innovation and job creation. In the name of preparing more of the workforce to take those jobs, we have harmed the skills of those who might have created them. Although there is some evidence of a payoff from this sacrifice, in the form of marginally better performance among average students, some of the strategies used to help these students have in fact backfired…

Not all children are equally prepared to embark on a rigorous math curriculum on the first day of kindergarten, and there are no realistic policy alternatives to change this simple fact. Rather than wish differences among students away, a rational policy for the 21st century will respond to those variations, tailoring lessons to children’s needs. This strategy promises to provide the next generation of prospective scientists and engineers with the training they need to create jobs, and the next generation of workers with the skills they need to qualify for them. http://educationnext.org/solving-america%E2%80%99s-math-problem/#.UG25FCk_6rE.email

One way of looking at Vigdor’s conclusions is to ask whether high performance preschool programs and early intervention can affect student achievement?

Science Daily reports about a University of Missouri study about the effect of counting ability in preschoolers in the article, Preschoolers’ Counting Abilities Relate to Future Math Performance, Researcher Says:

Along with reciting the days of the week and the alphabet, adults often practice reciting numbers with young children. Now, new research from the University of Missouri suggests reciting numbers is not enough to prepare children for math success in elementary school. The research indicates that counting, which requires assigning numerical values to objects in chronological order, is more important for helping preschoolers acquire math skills.

“Reciting means saying the numbers from memory in chronological order, whereas counting involves understanding that each item in the set is counted once and that the last number stated is the amount for the entire set,” said Louis Manfra, an assistant professor in MU’s Department of Human Development and Family Studies. “When children are just reciting, they’re basically repeating what seems like a memorized sentence. When they’re counting, they’re performing a more cognitive activity in which they’re associating a one-to-one correspondence with the object and the number to represent a quantity.”

Manfra analyzed data from more than 3,000 children from low-income households in order to determine if the children’s reciting and counting abilities in preschool affected their first-grade math scores. He found that students who could recite and count to 20 in preschool had the highest math scores in first grade; however, less than 10 percent of the children in the study could count and recite to 20.

“Counting gives children stronger foundations when they start school,” Manfra said. “The skills children have when they start kindergarten affect their trajectories through early elementary school; therefore, it’s important that children start with as many skills as possible.” http://www.sciencedaily.com/releases/2012/11/121108142808.htm

Here is the press release from the University of Missouri:

News Bureau

University of Missouri

Preschoolers’ Counting Abilities Relate to Future Math Performance, MU Researcher Says

Counting, in addition to reciting, should be emphasized in early childhood education to establish foundation for future academic success

Nov. 08, 2012

Story Contact(s):
Jesslyn Chew, ChewJ@missouri.edu, (573) 882-8353

COLUMBIA, Mo. – Along with reciting the days of the week and the alphabet, adults often practice reciting numbers with young children. Now, new research from the University of Missouri suggests reciting numbers is not enough to prepare children for math success in elementary school. The research indicates that counting, which requires assigning numerical values to objects in chronological order, is more important for helping preschoolers acquire math skills.

“Reciting means saying the numbers from memory in chronological order, whereas counting involves understanding that each item in the set is counted once and that the last number stated is the amount for the entire set,” said Louis Manfra, an assistant professor in MU’s Department of Human Development and Family Studies. “When children are just reciting, they’re basically repeating what seems like a memorized sentence. When they’re counting, they’re performing a more cognitive activity in which they’re associating a one-to-one correspondence with the object and the number to represent a quantity.”

Manfra analyzed data from more than 3,000 children from low-income households in order to determine if the children’s reciting and counting abilities in preschool affected their first-grade math scores. He found that students who could recite and count to 20 in preschool had the highest math scores in first grade; however, less than 10 percent of the children in the study could count and recite to 20.

“Counting gives children stronger foundations when they start school,” Manfra said. “The skills children have when they start kindergarten affect their trajectories through early elementary school; therefore, it’s important that children start with as many skills as possible.”

Previous research has shown that, in low-income families, parents often think children’s educations are the responsibility of teachers, while teachers expect parents to teach some essential skills at home, Manfra said.

“These low-income children aren’t learning math skills anywhere because parents think the children are learning them at school, and teachers think they’re learning them at home,” Manfra said. “This is a problem because it gives parents and teachers the idea that it’s not their responsibility to educate the children, when it’s everyone’s responsibility. This is problematic because, when the children enter kindergarten and are at lower math levels, they don’t have the foundational skills needed to set them on paths for future success.”

Parents and teachers should integrate counting into all aspects of children’s daily activities so they can master the skill, Manfra said.

“You can learn anything anywhere, and this is very true for counting,” Manfra said. “When adults read books with children, they can count the ducks on the page. They might count the leaves that fall to the ground outside or the number of carrots at lunchtime.”

The Department of Human Development and Family Studies is part of the MU College of Human Environmental Sciences. The study, “Associations between Counting Ability in Preschool and Mathematic Performance in First Grade among a Sample of Ethnically Diverse, Low-Income Children,” will be published in an upcoming issue of the Journal of Research in Childhood Education.

There will continue to be battles between those who favor a more traditional education and those who are open to the latest education fad. These battles will be fought out in school board meetings, PTSAs, and the courts.

There is one way to, as Susan Powder says, “Stop the Insanity.” Genuine school choice allows parents or guardians to select the best educational setting for their child. Many policy wonks would like to believe that only one type of family seeks genuine school choice, the right wing wacko who makes regular visits on the “tea party” circuit. That is not true. Many parents favor a back-to-the basics traditional approach to education.

A one-size-fits-all approach does not work in education

Related:

Study: Early mastery of fractions is a predictor of math success                                                                                  https://drwilda.com/tag/formula-written-for-math-success/

Dr. Wilda says this about that ©

Blogs by Dr. Wilda:

COMMENTS FROM AN OLD FART © http://drwildaoldfart.wordpress.com/

Dr. Wilda Reviews ©                                 http://drwildareviews.wordpress.com/

Dr. Wilda ©                                                                                   https://drwilda.com/

Tags: , , , , , , , , , ,

Is an individualized program more effective in math learning?

10 Oct

Moi wrote in Study: Early mastery of fractions is a predictor of math success:

Math is important for a number of reasons.

Michigan State University’s Office of Supportive Services succinctly states why math is important:

Why is math important?

All four year Universities have a math requirement

Math improves your skills:

  • Critical Thinking Skills

  • Deductive Logic and Reasoning Skills

  • Problem Solving Skills

A good knowledge of math and statistics can expand your career options

Physical Sciences – Chemistry, Engineering, Physics

Life and Health Sciences – Biology, Psychology, Pharmacy, Nursing, Optometry

Social Sciences – Anthropology, Communications, Economics, Linquistics, Education, Geography

Technical Sciences – Computer Science, Networking, Software Development

Business and Commerce

Actuarial Sciences

Medicine

http://oss.msu.edu/academic-assistance/why-is-math-important

In Perhaps the biggest math challenge is how to teach math, moi said:

There will continue to be battles between those who favor a more traditional education and those who are open to the latest education fad. These battles will be fought out in school board meetings, PTSAs, and the courts.

There is one way to, as Susan Powder says, “Stop the Insanity.” Genuine school choice allows parents or guardians to select the best educational setting for their child. Many policy wonks would like to believe that only one type of family seeks genuine school choice, the right wing wacko who makes regular visits on the “tea party” circuit. That is not true. Many parents favor a back-to-the basics traditional approach to education.

A one-size-fits-all approach does not work in education https://drwilda.wordpress.com/2012/02/01/perhaps-the-biggest-math-challenge-is-how-to-teach-math/

https://drwilda.com/2012/06/26/study-early-mastery-of-fractions-is-a-predictor-of-math-success/

Jacob Vigdor wrote the interesting Education Next article, Solving America’s Math Problem:

American public schools have made a clear trade-off over the past few decades. With the twin goals of improving the math performance of the average student and promoting equality, it has made the curriculum more accessible. The drawback to exclusive use of this more accessible curriculum can be observed among the nation’s top-performing students, who are either less willing or less able than their predecessors or their high-achieving global peers to follow the career paths in math, science, and engineering that are the key to innovation and job creation. In the name of preparing more of the workforce to take those jobs, we have harmed the skills of those who might have created them. Although there is some evidence of a payoff from this sacrifice, in the form of marginally better performance among average students, some of the strategies used to help these students have in fact backfired.

To some extent, the nation has reduced the costs of this movement through immigration. Foreign students account for more than half of all doctorate recipients in science and engineering, two-thirds of those in engineering. Many of these degree recipients leave the country when they finish, however, limiting their potential benefit to native-born Americans. Immigration policy reform that emphasizes skills over traditional family reunification criteria, much like the policies in place in Australia, Canada, and other developed nations, could change this pattern.

A second possible policy option would be to implement a curricular reform more radical than tinkering with the timing of already existing courses. Many schools have adopted the so-called “Singapore math” model, which emphasizes in-depth coverage of a limited set of topics. There are concerns, however, regarding whether a curriculum developed in a different cultural and educational context could produce similar results here. Singapore’s public schools, for example, use a year-round calendar, obviating the need to review basic subjects after a summer spent out of the classroom. Evidence also indicates that Singapore’s teachers have a firmer grasp of math than their American counterparts.

The United States need not import its science and engineering innovators, however. It need not borrow a faddish curriculum from a foreign context. And it need not sacrifice the math achievement of the average student in order to cater to superstars. It need only recognize that equalizing the curriculum for all students cannot be accomplished without imposing significant lifelong costs on some and perhaps all students.

Curricular differentiation might, for its part, exacerbate test-score gaps between moderate and high performers, if high performers move ahead more quickly. A narrow-minded focus on the magnitude of the gap, however, can lead to scenarios where the gap is closed primarily by worsening the performance of high-achieving students—bringing the top down—without raising the performance of low-achieving students. Society’s goal should be to improve the status of low-performing students in absolute terms, not just relative to that of their higher-performing peers. A growing body of evidence suggests that this type of improvement is best achieved by sorting students, even at a young age, into relatively homogenous groups, to better enable curricular specialization. Recent results from Chicago, cited above, provide evidence that differentiating the high school mathematics curriculum can have long-run benefits, even for students assigned to remedial coursework.

Not all children are equally prepared to embark on a rigorous math curriculum on the first day of kindergarten, and there are no realistic policy alternatives to change this simple fact. Rather than wish differences among students away, a rational policy for the 21st century will respond to those variations, tailoring lessons to children’s needs. This strategy promises to provide the next generation of prospective scientists and engineers with the training they need to create jobs, and the next generation of workers with the skills they need to qualify for them. http://educationnext.org/solving-america%E2%80%99s-math-problem/#.UG25FCk_6rE.email

One way of looking at Vigdor’s conclusions is to ask whether high performance preschool programs and early intervention can affect student achievement?

Moi wrote in Oregon State University study: Ability to pay attention in preschool may predict college success:

In Early learning standards and the K-12 continuum, moi said:

Preschool is a portal to the continuum of life long learning. A good preschool stimulates the learning process and prompts the child into asking questions about their world and environment. Baby Center offers advice about how to find a good preschool and general advice to expectant parents. At the core of why education is important is the goal of equipping every child with the knowledge and skills to pursue THEIR dream, whatever that dream is. Christine Armario and Dorie Turner are reporting in the AP article, AP News Break: Nearly 1 in 4 Fails Military Exam which appeared in the Seattle Times:

Nearly one-fourth of the students who try to join the U.S. Army fail its entrance exam, painting a grim picture of an education system that produces graduates who can’t answer basic math, science and reading questions, according to a new study released Tuesday.

Many children begin their first day of school behind their more advantaged peers. Early childhood learning is an important tool is bridging the education deficit. https://drwilda.wordpress.com/2012/01/03/early-learning-standards-and-the-k-12-contiuum/

Jonathan Cohn’s study about the value of early learning is described in Jonathan Cohn’s ‘The Two Year Window’:

Jonathan Cohn reports about an unprecedented experiment which occurred in Romanian orphanages in the Nw Republic article, The Two Year Window. There are very few experiments involving humans because of ethical considerations.

Drury, Nelson, and their collaborators are still learning about the orphans. But one upshot of their work is already clear. Childhood adversity can damage the brain as surely as inhaling toxic substances or absorbing a blow to the head can. And after the age of two, much of that damage can be difficult to repair, even for children who go on to receive the nurturing they were denied in their early years. This is a revelation with profound implication—and not just for the Romanian orphans.

APPROXIMATELY SEVEN MILLION American infants, toddlers, and preschoolers get care from somebody other than a relative, whether through organized day care centers or more informal arrangements, according to the Census Bureau. And much of that care is not very good. One widely cited study of child care in four states, by researchers in Colorado, found that only 8 percent of infant care centers were of “good” or “excellent” quality, while 40 percent were “poor.” The National Institute of Child Health and Human Development has found that three in four infant caregivers provide only minimal cognitive and language stimulation—and that more than half of young children in non-maternal care receive “only some” or “hardly any” positive caregiving. http://www.tnr.com/article/economy/magazine/97268/the-two-year-window?page=0,0&passthru=YzBlNDJmMmRkZTliNDgwZDY4MDhhYmIwMjYyYzhlMjg

Because the ranks of poor children are growing in the U.S., this study portends some grave challenges not only for particular children, but this society and this country. Adequate early learning opportunities and adequate early parenting is essential for proper development in children. https://drwilda.wordpress.com/2011/12/18/jonathan-cohns-the-two-year-window/

https://drwilda.com/2012/08/08/oregon-state-university-study-ability-to-pay-attention-in-preschool-may-predict-college-success/

Dr. Wilda says this about that ©

Blogs by Dr. Wilda:

COMMENTS FROM AN OLD FART© http://drwildaoldfart.wordpress.com/

Dr. Wilda Reviews ©                                     http://drwildareviews.wordpress.com/

Dr. Wilda ©                                                                                                 https://drwilda.com/

Tags: , , , , , , , , , , ,

Study: Early mastery of fractions is a predictor of math success

26 Jun

Joy Resmovits has an interesting article at Huffington Post. In U.S. Students’ Low Math Test Proficiency Could Have Consequences For GDP Resmovits reports:

U.S. students rank poorly in proficiency on both domestic and international math exams, a problem that could cost the country $75 trillion over 80 years, according to a new study.

U.S. students fall behind 31 countries in math proficiency and behind 16 countries in reading proficiency, according to the report released Wednesday, titled “Globally Challenged: Are U.S. Students Ready to Compete?“

Resmovits is reporting about the report, Globally Challenged: Are U. S. Students Ready to Compete? The latest on each state’s international standing in math and reading by Paul E. Peterson, Ludger Woessmann, Eric A. Hanushek and Carlos X. Lastra-Anadón. Here is a portion of the Executive Summary:

Proficiency in Mathematics

U.S. students in the Class of 2011, with a 32 percent proficiency rate in mathematics, came in 32nd among the nations that participated in PISA. Although performance levels among the countries ranked 23rd to 31st are not significantly different from that of the United States, 22 countries do significantly outperform the United States in the share of students reaching the proficient level in math. In six countries plus Shanghai and Hong Kong, a majority of students performed at the proficient level, while in the United States less than one-third did. For example, 58 percent of Korean students and 56 percent of Finnish students were proficient. Other countries in which a majority—or near majority—of students performed at or above the proficient level included Switzerland, Japan, Canada, and the Netherlands. Many other nations also had math proficiency rates well above that of the United States, including Germany (45 percent), Australia (44 percent), and France (39 percent). Shanghai topped the list with a 75 percent math proficiency rate, well over twice the 32 percent rate of the United States. However, Shanghai students are from a prosperous metropolitan area within China, with over three times the GDP per capita of the rest of that country, so their performance is more appropriately compared to Massachusetts and Minnesota, which are similarly favored and are the top performers among the U.S. states. When this comparison is made, Shanghai still performs at a distinctly higher level. Only a little more than half (51 percent) of Massachusetts students are proficient in math, while Minnesota, the runner-up state, has a math proficiency rate of just 43 percent. Only four additional states—Vermont, North Dakota, New Jersey, and Kansas—have a math proficiency rate above 40 percent. Some of the country’s largest and richest states score below the average for the United States as a whole, including New York (30 percent), Missouri (30 percent), Michigan (29 percent), Florida (27 percent), and California (24 percent)….

Performance of U.S. Ethnic and Racial Groups

The percentage proficient in the United States varies considerably across students from different racial and ethnic backgrounds. While 42 percent of white students were identified as proficient in math, only 11 percent of African American students, 15 percent of Hispanic students, and 16 percent of Native Americans were so identified. Fifty percent of students with an ethnic background from Asia and the Pacific Islands, however, were proficient in math. In reading, 40 percent of white students and 41 percent of those from Asia and the Pacific Islands were identified as proficient. Only 13 percent of African American students, 5 percent of Hispanic students, and 18 percent of Native American students were so identified….

Here is the citation:

http://www.hks.harvard.edu/pepg/PDF/Papers/PEPG11-03_GloballyChallenged.pdf

Mary Niederberger of the Pittsburgh Post-Gazette writes in the article, Formula written for math success:

Mastery of fractions and early division is a predictor of students’ later success with algebra and other higher-level mathematics, based on a study done by a team of researchers led by a Carnegie Mellon University professor.

That means more effective teaching of the concepts is needed to improve math scores among U.S. high school students, which have remained stagnant for more than 30 years….

The study said a likely reason for U.S. students’ weakness in fractions and division could be linked to their teachers’ “lack of a firm conceptual understanding” of the concepts, citing several other studies in which many American teachers were unable to explain the reasons behind mathematical solutions, while most teachers in Japan and China were able to offer two or three explanations.
http://www.post-gazette.com/stories/news/education/formula-written-for-math-success-640962/#ixzz1ym9qos5j

Citation:

Early Predictors of High School Mathematics Achievement

  1. Robert S. Siegler1,
  2. Greg J. Duncan2,
  3. Pamela E. Davis-Kean3,4,
  4. Kathryn Duckworth5,
  5. Amy Claessens6,
  6. Mimi Engel7,
  7. Maria Ines Susperreguy3,4 and
  8. Meichu Chen4Abstract

Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.

  1. Published online before print June 14, 2012, doi: 10.1177/0956797612440101 Psychological Science June 14, 2012 0956797612440101
  1. » AbstractFree
  2. Full Text
  3. Full Text (PDF)
  4. Supplemental Material

Math is important for a number of reasons.

Michigan State University’s Office of Supportive Services succinctly states why math is important:

Why is math important?

All four year Universities have a math requirement

Math improves your skills:

  • Critical Thinking Skills
  • Deductive Logic and Reasoning Skills
  • Problem Solving Skills

A good knowledge of math and statistics can expand your career options

Physical Sciences – Chemistry, Engineering, Physics

Life and Health Sciences – Biology, Psychology, Pharmacy, Nursing, Optometry

Social Sciences – Anthropology, Communications, Economics, Linquistics, Education, Geography

Technical Sciences – Computer Science, Networking, Software Development

Business and Commerce

Actuarial Sciences

Medicine

http://oss.msu.edu/academic-assistance/why-is-math-important

In Perhaps the biggest math challenge is how to teach math, moi said:

There will continue to be battles between those who favor a more traditional education and those who are open to the latest education fad. These battles will be fought out in school board meetings, PTSAs, and the courts.

There is one way to, as Susan Powder says, “Stop the Insanity.” Genuine school choice allows parents or guardians to select the best educational setting for their child. Many policy wonks would like to believe that only one type of family seeks genuine school choice, the right wing wacko who makes regular visits on the “tea party” circuit. That is not true. Many parents favor a back-to-the basics traditional approach to education.

A one-size-fits-all approach does not work in education https://drwilda.wordpress.com/2012/02/01/perhaps-the-biggest-math-challenge-is-how-to-teach-math/

Dr. Wilda says this about that ©

Tags: , , , , , , , ,

Perhaps the biggest math challenge is how to teach math

1 Feb

Joy Resmovits has an interesting article at Huffington Post. In U.S. Students’ Low Math Test Proficiency Could Have Consequences For GDP Resmovits reports:

U.S. students rank poorly in proficiency on both domestic and international math exams, a problem that could cost the country $75 trillion over 80 years, according to a new study.

U.S. students fall behind 31 countries in math proficiency and behind 16 countries in reading proficiency, according to the report released Wednesday, titled “Globally Challenged: Are U.S. Students Ready to Compete?”

The report looked at the performance of students who graduated high school in 2011 on two tests: the 2009 Programme for International Student Assessment (PISA), the exam administered by the Organization for Economic Cooperation and Development, and the 2007 National Assessment for Educational Progress (NAEP), a national exam considered the gold standard in testing.

The analysis focused on mathematics, Peterson said, because “math skills are the most significant for economic growth.”

Resvoits is reporting about the report, Globally Challenged: Are U. S. Students Ready to Compete? The latest on each state’s international standing in math and reading by Paul E. Peterson, Ludger Woessmann, Eric A. Hanushek and Carlos X. Lastra-Anadón.

Here is a portion of the Executive Summary:

Proficiency in Mathematics

U.S. students in the Class of 2011, with a 32 percent proficiency rate in mathematics, came in 32nd among the nations that participated in PISA. Although performance levels among the countries ranked 23rd to 31st are not significantly different from that of the United States, 22 countries do significantly outperform the United States in the share of students reaching the proficient level in math. In six countries plus Shanghai and Hong Kong, a majority of students performed at the proficient level, while in the United States less than one-third did. For example, 58 percent of Korean students and 56 percent of Finnish students were proficient. Other countries in which a majority—or near majority—of students performed at or above the proficient level included Switzerland, Japan, Canada, and the Netherlands. Many other nations also had math proficiency rates well above that of the United States, including Germany (45 percent), Australia (44 percent), and France (39 percent). Shanghai topped the list with a 75 percent math proficiency rate, well over twice the 32 percent rate of the United States. However, Shanghai students are from a prosperous metropolitan area within China, with over three times the GDP per capita of the rest of that country, so their performance is more appropriately compared to Massachusetts and Minnesota, which are similarly favored and are the top performers among the U.S. states. When this comparison is made, Shanghai still performs at a distinctly higher level. Only a little more than half (51 percent) of Massachusetts students are proficient in math, while Minnesota, the runner-up state, has a math proficiency rate of just 43 percent. Only four additional states—Vermont, North Dakota, New Jersey, and Kansas—have a math proficiency rate above 40 percent. Some of the country’s largest and richest states score below the average for the United States as a whole, including New York (30 percent), Missouri (30 percent), Michigan (29 percent), Florida (27 percent), and California (24 percent).

Here is the citation:

http://www.hks.harvard.edu/pepg/PDF/Papers/PEPG11-03_GloballyChallenged.pdf

Sarah D. Sparks reports in the Education Week article, Study Helps Pinpont Math Disability about a study regarding how students learn math .

Burgeoning research into students’ difficulties with mathematics is starting to tease out cognitive differences between students who sometimes struggle with math and those who have dyscalculia, a severe, persistent learning disability in math.

A new, decade-long longitudinal study by researchers at the Kennedy Krieger Institute in Baltimore, published Friday in the journal Child Development, finds that 9th-graders considered dyscalculic—those who performed in the bottom 10 percent of math ability on multiple tests—had substantially lower ability to grasp and compare basic number quantities than average students or even other struggling math students.

“Formal math requires some effort, and it requires effort to different degrees for different children,” said Michèle M. M. Mazzocco, the director of the Math Skills Development Project at Kennedy Krieger. “Just because someone is having difficulty with math doesn’t necessarily mean they have a math learning disability. This study points to a core marker” of true dyscalculia.

The study, she said, may help researchers and educators understand the underlying causes of persistent math problems and identify the students who need the most intensive instructional support.

Math-learning disability affects about 5 percent to 8 percent of school-age children nationwide, about as many people nationwide as are affected by dyslexia. Yet experts say research on the reading problem has for decades dwarfed studies of math difficulties by 20 to one…

“We know that basic numeracy skills are a greater predictor of later success in life than basic literacy skills,” said Daniel Ansari, one of the pioneers in the neuroscience of dyscalculia, speaking at a research forum on the disability held in Chicago last month, who is unconnected to the Kennedy Krieger study.

See, Girls and math phobia  https://drwilda.wordpress.com/2012/01/20/girls-and-math-phobia/

Barry Garelick has written an interesting article, Mathematics Education: Being Outwitted by Stupidity which appears at Education News:

While there has been a good amount of research and effort into early interventions in reading and decoding instruction, extremely little research of equivalent quality on the learning of mathematics exists. Given the education establishment’s resistance to the idea that traditional math teaching methods are effective, this research is very much needed to draw such a definitive conclusion about the effect of instruction on the diagnosis of learning disabilities.1

Some Background

Over the past several decades, math education in the United States has shifted from the traditional model of math instruction to “reform math”. The traditional model has been criticized for relying on rote memorization rather than conceptual understanding. Calling the traditional approach “skills based”, math reformers deride it and claim that it teaches students only how to follow the teacher’s direction in solving routine problems, but does not teach students how to think critically or to solve non-routine problems. Traditional/skills-based teaching, the argument goes, doesn’t meet the demands of our 21st century world.

As I’ve discussed elsewhere, the criticism of traditional math teaching is based largely on a mischaracterization of how it is/has been taught, and misrepresented as having failed thousands of students in math education despite evidence of its effectiveness in the 1940’s, 50’s and 60’s. Reacting to this characterization of the traditional model, math reformers promote a teaching approach in which understanding and process dominate over content. In lower grades, mental math and number sense are emphasized before students are fluent with procedures and number facts. Procedural fluency is seldom achieved. In lieu of the standard methods for adding/subtracting, multiplying and dividing, in some programs students are taught strategies and alternative methods. Whole class and teacher-led explicit instruction (and even teacher-led discovery) has given way to what the education establishment believes is superior: students working in groups in a collaborative learning environment. Classrooms have become student-centered and inquiry-based. The grouping of students by ability has almost entirely disappeared in the lower grades—full inclusion has become the norm. Reformers dismiss the possibility that understanding and discovery can be achieved by students working on sets of math problems individually and that procedural fluency is a prerequisite to understanding. Much of the education establishment now believes it is the other way around; if students have the understanding, then the need to work many problems (which they term “drill and kill”) can be avoided…..

Having seen the results of ineffective math curricula and pedagogy as well as having worked with the casualties of such educational experiments, I have no difficulty assuming that RtI plays a significant role in reducing the identification of students with learning disabilities. In my opinion it is only a matter of time before high-quality research and the best professional judgment and experience of accomplished classroom teachers verify it. Such research should include 1) the effect of collaborative/group work compared to individual work, including the effect of grouping on students who may have difficulty socially; 2) the degree to which students on the autistic spectrum (as well as those with other learning disabilities) may depend on direct, structured, systematic instruction; 3) the effect of explicit and systematic instruction of procedures, skills and problem solving, compared with inquiry-based approaches; 4) the effect of sequential and logical presentation of topics that require mastery of specific skills, compared with a spiral approaches to topics that do not lead to closure and 5) Identifying which conditions result in student-led/teacher-facilitated discovery, inquiry-based, and problem-based learning having a positive effect, compared with teacher-led discovery, inquiry-based and problem-based learning. Would such research show that the use of RtI is higher in schools that use o-based math programs and teaching? If so, shouldn’t we be doing more of the RtI style of teaching in the first place instead of waiting to heal reform math’s casualties?

Until any such research is in, the educational establishment will continue to resist recognizing the merits of traditional math teaching. One education professor with whom I spoke stated that the RtI model fits mathematics for the 1960s, when “skills throughout the K-8 spectrum were the main focus of instruction and is seriously out of date.” Another reformer argued that reform curricula require a good deal of conceptual understanding and that students have to do more than solve word problems. These confident statements assume that traditional methods—and the methods used in RtI—do not provide this understanding. In their view, students who respond to more explicit instruction constitute a group who may simply learn better on a superficial level. Based on these views, I fear that RtI will incorporate the pedagogical features of reform math that has resulted in the use of RtI in the first place.

While the criticism of traditional methods may have merit for those occasions when it has been taught poorly, the fact that traditional math has been taught badly doesn’t mean we should give up on teaching it properly. Without sufficient skills, critical thinking doesn’t amount to much more than a sound bite. If in fact there is an increasing trend toward effective math instruction, it will have to be stealth enough to fly underneath the radar of the dominant edu-reformers. Unless and until this happens, the thoughtworld of the well-intentioned educational establishment will prevail. Parents and professionals who benefitted from traditional teaching techniques and environments will remain on the outside — and the public will continue to be outwitted by stupidity.                                                           http://www.educationnews.org/education-policy-and-politics/barry-garelick-math-education-being-outwitted-by-stupidity/

There will continue to be battles between those who favor a more traditional education and those who are open to the latest education fad. These battles will be fought out in school board meetings, PTSAs, and the courts.

There is one way to, as Susan Powder says, “Stop the Insanity.” Genuine school choice allows parents or guardians to select the best educational setting for their child. Many policy wonks would like to believe that only one type of family seeks genuine school choice, the right wing wacko who makes regular visits on the “tea party” circuit. That is not true. Many parents favor a back-to-the basics traditional approach to education.

A one-size-fits-all approach does not work in education.

Dr. Wilda says this about that ©

Tags: , , , , ,

Girls and math phobia

20 Jan

Many students have difficulty with math. Sarah D. Sparks reported in the Education Week article, Study Helps Pinpont Math Disability

Burgeoning research into students’ difficulties with mathematics is starting to tease out cognitive differences between students who sometimes struggle with math and those who have dyscalculia, a severe, persistent learning disability in math.

A new, decade-long longitudinal study by researchers at the Kennedy Krieger Institute in Baltimore, published Friday in the journal Child Development, finds that 9th-graders considered dyscalculic—those who performed in the bottom 10 percent of math ability on multiple tests—had substantially lower ability to grasp and compare basic number quantities than average students or even other struggling math students….

There is a persistent myth that girls have difficulty with math because of self-esteem issues regarding the study of math.

The University of Missouri is reporting about a new study which examines past research regrading women and math. Here is an excerpt from the press release:

A University of Missouri researcher and his colleague have conducted a review that casts doubt on the accuracy of a popular theory that attempted to explain why there are more men than women in top levels of mathematic fields. The researchers found that numerous studies claiming that the stereotype, “men are better at math” – believed to undermine women’s math performance – had major methodological flaws, utilized improper statistical techniques, and many studies had no scientific evidence of this stereotype.

This theory, called stereotype threat, was first published in 1999 in the Journal of Experimental Social Psychology. Essentially, the theory is that due to the stereotype that women are worse than men in math skills, females develop a poor self-image in this area, which leads to mathematics underachievement.

“The stereotype theory really was adopted by psychologists and policy makers around the world as the final word, with the idea that eliminating the stereotype could eliminate the gender gap,” said David Geary, Curators Professor of Psychological Sciences in the MU College of Arts and Science. “However, even with many programs established to address the issue, the problem continued. We now believe the wrong problem is being addressed.”

In the study, Geary and Gijsbert Stoet, from the University of Leeds in the United Kingdom, examined 20 influential replications of the original stereotype theory study. The researchers found that many subsequent studies had serious scientific flaws, including a lack of a male control group and improperly applied statistical techniques….

The researchers believe that basing interventions on the stereotype threat is actually doing more harm than good, as vital resources are being dedicated to a problem that does not exist.

“These findings really irritate me, as a psychologist, because this is a science where we are really trying to discover what the issues are,” Geary said. “The fact is there are still a disproportionate number of men in top levels of science, technology, engineering and mathematics. We need more women to succeed in these fields for our economy and for our future.”

See, Math Gender Gap Not Result of Girls’ Low Self-Esteem, Researchers Say http://www.huffingtonpost.com/2012/01/18/gender-gap-in-math_n_1214517.html?ref=email_share

Other studies have looked at the influence of gender on math performance.

Science Daily reported in the March 14, 2011 article, Gender Stereotypes About Math Develop As Early As the Second Grade

Children express the stereotype that mathematics is for boys, not for girls, as early as second grade, according to a new study by University of Washington researchers. And the children applied the stereotype to themselves: boys identified themselves with math whereas girls did not.

The “math is for boys” stereotype has been used as part of the explanation for why so few women pursue science, mathematics and engineering careers. The cultural stereotype may nudge girls to think that “math is not for me,” which can affect what activities they engage in and their career aspirations.

The new study, published in the March/April issue of Child Development, suggests that, for girls, lack of interest in mathematics may come from culturally-communicated messages about math being more appropriate for boys than for girls, the researchers said.

Here is the study citation:

Dario Cvencek, Andrew N. Meltzoff, Anthony G. Greenwald. Math-Gender Stereotypes in Elementary School Children. Child Development, 2011; DOI: 10.1111/j.1467-8624.2010.01529.x

John ChildUp has an excellent synopsis of the math study, Math Gender Stereotypes Start As Early As Second Grade at his ChildUp blog:

Some sobering news for parental foes of sex stereotypes: A new study reinforces the devastating impact stereotypes can have on girls when it comes to math.

Little boys may love their trains and toys, but as early as second grade they’re already showing prowess on the mathematical front, sending a subliminal message to their female classmates about expectations for math test scores and even potential career paths, according to a new study, “Today” reports.

Researchers at the Institute for Learning & Brain Sciences at the University of Washington studied 247 American children between the ages of 6 and 10 and found that second grade boys identified with math more strongly than girls. The study was published in Wiley’s Child Development.

See, U.S. Teens Trail Peers Around World on Math-Science Test http://www.washingtonpost.com/wp-dyn/content/article/2007/12/04/AR2007120400730.html

It is important both for an individual student and the national competitiveness to have trained teachers and curriculum to advance the math education of all populations of students.

Not everything that counts can be counted. Not everything that can be counted counts.

– Albert Einstein

Contact information:

The study, “Can stereotype threat explain the sex gap in mathematics performance and achievement?” will be published in the journal Review of General Psychology.

Story Contact:
Steven Adams, AdamsST@missouri.edu, 573 882-8353

 

Dr. Wilda says this about that ©

 

Tags: , , , , , ,