Tag Archives: Math Teaching

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©
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http://drwildareviews.wordpress.com/

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National Center for Education Statistics report: Algebra I means different things in different schools

12 Mar

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

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/

Sarah D. Sparks reports in the Education Week article, Algebra, Geometry Classes Vary in Rigor, Says Study:

The drive to get every student to take so-called college gateway courses has succeeded, a new federal study finds, but students taking Algebra I and Geometry classes are getting considerably less substance than their course titles would suggest.

Nearly all of the Class of 2005 graduated having taken Algebra I, according to the latest iteration of the National Assessment of Educational Progress’s high school transcript studyRequires Adobe Acrobat Reader, released this morning by the National Center for Education Statistics. Yet if their course materials are any indication, fewer than one in four of those students studied the kind of challenging topics needed to prepare them for college-level mathematics.

During the 2005 National Assessment of Educational Progress in mathematics, NCES researchers also collected course transcript data from a representative sample of 17,800 students who graduated with a regular or honors diploma that year. They also analyzed 120 Algebra I, Geometry, and integrated math textbooks used at the 550 public schools those students attended.

Education watchers hoping to close persistent achievement gaps among students of different racial and ethnic groups long have pushed for all students to take “college-ready” class schedules, including at least four years of high school math, including Algebra I and II, Geometry, and Calculus. Here, at least, the transcript study shows this push has paid off: Graduates in 2005 earned on average 3.8 credits in math, significantly more than the average of 3.2 credits earned by graduates in 1990. Moreover, from 1990 to 2005, black graduates closed a six-percentage-point gap with white graduates in the percentages of students earning at least three math credits, including in algebra and geometry.

What’s Covered in Algebra I?

While nearly all 2005 high school graduates had taken a course called Algebra I at some point, the content of those classes varied tremendously, according to a new analysis by the National Center on Education Statistics. The chart breaks down the types of topics actually covered in Algebra I courses that researchers classified as beginner-, intermediate-, and rigorous-level classes.

The study found that, on average, two thirds of Algebra I and Geometry courses covered core content topics in each of those subjects, while the other third covered topics in other math areas. Researchers also gauged the rigor of classes based on the topics and questions covered in each book. A course categorized by researchers as beginner-level algebra had more than 60 percent of its material on elementary and middle school math topics such as basic arithmetic and pre-algebra problems such as basic equations. By contrast, a rigorous Algebra I course includes more than 60 percent of material on advanced topics such as functions and advanced number theory, as well as other higher-level math subjects such as geometry, trigonometry, and precalculus.

We found that there is very little truth-in-labeling for high school Algebra I and Geometry courses,” said Sean P. “Jack” Buckley, the NCES commissioner, in a statement on the study.

What’s Covered in Algebra I?

While nearly all 2005 high school graduates had taken a course called Algebra I at some point, the content of those classes varied tremendously, according to a new analysis by the National Center on Education Statistics. The chart breaks down the types of topics actually covered in Algebra I courses that researchers classified as beginner-, intermediate-, and rigorous-level classes.

SOURCE: National Center for Education Statistics, High School Transcript

http://www.edweek.org/ew/articles/2013/03/12/26math.h32.html?tkn=YLOFKtLmOxgKmPV9bXJhz67yP%2Bl3YybnC81o&cmp=clp-edweek&intc=es

Citation:

 Algebra I and Geometry Curricula: Results from the 2005 High School Transcript Mathematics Curriculum Study
Description: The Mathematics Curriculum Study explores the relationship between student coursetaking and achievement by examining the content and challenge of two mathematics courses taught in the nation’s public high schools—algebra I and geometry. Conducted in conjunction with the 2005 National Assessment of Educational Progress (NAEP) High School Transcript Study (HSTS), the study uses textbooks as an indirect measure of what was taught in classrooms, but not how it was taught (i.e., classroom instruction). The study uses curriculum topics to describe the content of the mathematics courses and course levels to denote the content and complexity of the courses. The results are based on analyses of the curriculum topics and course levels developed from the textbook information, coursetaking data from the 2005 NAEP HSTS, and performance data from the twelfth-grade 2005 NAEP mathematics assessment.Highlights of the study findings show that about 65 percent of the material covered in high school graduates’ algebra I was devoted to algebra topics, while about 66 percent of the material covered in graduates’ geometry courses focused on geometry topics. School course titles often overstated course content and challenge. Approximately 73 percent of graduates in “honors” algebra I classes received a curriculum ranked as an intermediate algebra I course, while 62 percent of graduates who took a geometry course labeled “honors” by their school received a curriculum ranked as intermediate geometry. Graduates who took rigorous algebra I and geometry courses scored higher on NAEP than graduates who took beginner or intermediate courses.
Online Availability:

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Cover Date: March 2013
Web Release: March 12, 2013
Print Release: March 12, 2013
Publication #: NCES 2013451
General Ordering Information
Center/Program:

NCES

Authors: NCES
Type of Product: Statistical Analysis Report
Survey/Program Areas: High School Transcript Studies (HST)
National Assessment of Educational Progress (NAEP)
Keywords:
Questions: For questions about the content of this Statistical Analysis Report, please contact:
Janis Brown.

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

A huge part of the math equation is attracting talented math majors and providing them with the training to teach math.

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/

Study: Elementary school teachers have an impact on girls math learning                                                                           https://drwilda.com/2013/01/31/study-elementary-school-teachers-have-an-impact-on-girls-math-learning/

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

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Study: Elementary school teachers have an impact on girls math learning

31 Jan

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.

But the stereotype that girls don’t do math was odd to lead author Dario Cvencek, who was born and raised in the former Yugoslavia. “We didn’t have that stereotype where I grew up,” said Cvencek, a postdoctoral fellow at the UW Institute for Learning & Brain Sciences. “People there thought that math went with girls just as much as it did with boys.”

Cvencek and his co-authors wanted to examine whether American children have adopted the cultural stereotype that math is for boys during elementary-school years, and if so, whether they apply that stereotype to themselves….

Math self-concept — how much youngsters identify themselves with math, as in “math is for me” — has been left out of previous studies of the math-gender stereotype. Even though other studies using self-report measures show that boys and girls alike make the “math is for boys” linkage, the studies don’t distinguish between whether girls simply know about the math-gender stereotype but aren’t fazed by it, or are instead applying it to themselves so that it affects their identity, interests and actions….

In the math-gender stereotype test, for example, children sorted four kinds of words: boy names, girl names, math words and reading words. Children expressing the math-gender stereotype should be faster to sort words when boy names are paired with math words and girl names are paired with reading words. Similarly, they should be slower to respond when math words are paired with girl names and reading words are paired with boy names.

As early as second grade, the children demonstrated the American cultural stereotype for math: boys associated math with their own gender while girls associated math with boys. In the self-concept test, boys identified themselves with math more than girls did.

The researchers also used self-report tests and on all three concepts found similar responses to the Implicit Association Test.

“Our results show that cultural stereotypes about math are absorbed strikingly early in development, prior to ages at which there are gender differences in math achievement,” said co-author Andrew Meltzoff, a UW psychology professor and co-director of the UW Institute for Learning & Brain Sciences. Meltzoff holds the Job and Gertrud Tamaki Endowed Chair at UW.

Parental and educational practices aimed at enhancing girls’ self-concepts for math might be beneficial as early as elementary school, when the youngsters are already beginning to develop ideas about who does math, 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:

Sarah D. Sparks writes in the Education Week article, For Girls, Teachers’ Gender Matters, Study Says:

Female elementary school teachers’ comfort with mathematics has an outsize effect on the girls they teach, according to new research.

Girls taught by a female teacher got a learning boost if that teacher had a strong math background, but had consistently lower math performance by the end of the school year if she didn’t, according to a study presented at the American Economic Association’s annual conference here.

By contrast, boys’ math scores were not affected by having a female math teacher, regardless of the teacher’s background in that subject, and there were no differences in math performance among male and female students of male teachers of different math backgrounds. The study adds to growing evidence that children’s gender biases can significantly affect their own ability.

“Children’s perceptions of gender start emerging between the ages of 7 and 12,” said study coauthor I. Serkan Ozbeklik, an assistant economics professor at Claremont McKenna College in Claremont, Calif. “Positive or negative, the primary school experiences may shape the academic course of students, leading to long-term consequences like choice of study, choice of major, and occupation.”

Scope of Research

Researchers led by Heather Antecol, an economics professor at Claremont McKenna, analyzed the mathematics performance of more than 1,600 1st through 5th grade students under 94 teachers in 17 high-poverty, high-minority schools in Baltimore, Chicago, Los Angeles, Houston, New Orleans, and the Mississippi Delta region between the 2001-02 and 2002-03 school years.

On average, the teachers had more than six years of experience, but only 11.5 percent of the study’s students had a teacher with a bachelor’s degree in math or a related field like engineering, economics, or accounting. Nearly a third of the teachers were men, far above the national average of only one-tenth of primary school teachers.

Ms. Antecol and her colleagues found that girls taught by a female teacher, as opposed to a male teacher, saw their math test scores drop by 4.7 percenage points by the end of the school year. Moreover, those girls performed on average 1.9 percentage points lower than their male classmates, about 10 percent of a standard deviation. The researchers characterized both effects as strong.

By contrast, boys saw no drop in math performance under the same teachers.

While education-watchers have voiced similar concerns about gender stereotyping of boys’ reading ability, the study found no differences between boys’ and girls’ reading performance based on having a male or female teacher. http://www.edweek.org/ew/articles/2013/01/16/17gender.h32.html?tkn=TQQF4ViNm%2F1xKCaioCNY6Pqekt2d6g3I1Bbu&cmp=clp-edweek&intc=es

Citation:

The Effect of Teacher Gender on Student Achievement in Primary School: Evidence from a Randomized Experiment

Author Info

  • Antecol, Heather

(hantecol@cmc.edu) (Claremont McKenna College)

  • Eren, Ozkan

(ozkan.eren@unlv.edu) (University of Nevada, Las Vegas)

  • Ozbeklik, Serkan

(serkan.ozbeklik@cmc.edu) (Claremont McKenna College)

Registered author(s):

Abstract

This paper attempts to reconcile the contradictory results found in the economics literature and the educational psychology literature with respect to the academic impact of gender dynamics in the classroom. Specifically, using data from a randomized experiment, we look at the effects of having a female teacher on the math test scores of students in primary school. We find that female students who were assigned to a female teacher without a strong math background suffered from lower math test scores at the end of the academic year. This negative effect however not only seems to disappear but it becomes (marginally) positive for female students who were assigned to a female teacher with a strong math background. Finally, we do not find any effect of having a female teacher on male students’ test scores (math or reading) or female students’ reading test scores. Taken together, our results tentatively suggest that the findings in these two streams of the literature are in fact consistent if one takes into account a teacher’s academic background in math.

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Moi has written about the importance of motivation in student learning. In Research papers: Student Motivation: An Overlooked Piece of School Reform, moi wrote:

Moi often says education is a partnership between the student, the teacher(s) and parent(s). All parties in the partnership must share the load. The student has to arrive at school ready to learn. The parent has to set boundaries, encourage, and provide support. Teachers must be knowledgeable in their subject area and proficient in transmitting that knowledge to students. All must participate and fulfill their role in the education process. A series of papers about student motivation by the Center on Education Policy (CEP) follows the Council on Foreign Relations report by Condoleezza Rice and Joel Klein.  https://drwilda.com/2012/05/30/research-papers-student-motivation-an-overlooked-piece-of-school-reform/

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/

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/

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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 ©

Who says Black children can’t learn? Some schools get it

22 Mar

People want an education for a variety of reasons. Some have a love of learning. Others want to attend a good college or vocational school. Still others, see an education as a ticket to a good job. Increasingly for schools, the goal is to prepare kids with the skills to attend and succeed at college. In order to give children the skills to succeed, schools need teachers who are effective at educating their population of kids. There are many themes in the attempt to answer the question, what will prepare kids for what comes after high school. What will prepare kids for what comes after high school is a good basic education. The schools that provide a good basic education are relentless about the basics.

Sharon Otterman has a good news story in the New York Times about how a relentless focus on the basics can yield results. In Brooklyn School Scores High Despite Poverty Otterman reports:     

To ace the state standardized tests, which begin on Monday, Public School 172 in Sunset Park, Brooklyn, finds money for coaches in writing, reading and math. Teachers keep detailed notes on each child, writing down weaknesses and encouraging them to repeat tasks. There is after-school help and Saturday school.

But at the start of this school year, seven or eight students were still falling behind. So the school hired a speech therapist who could analyze why they and other students stumbled in language. A psychologist produced detailed assessments and recommendations. A dental clinic staffed by Lutheran Medical Center opened an office just off the fourth-grade classrooms, diagnosing toothaches, a possible source of distraction, and providing free cleanings.

Perfection may seem a quixotic goal in New York City, where children enter school from every imaginable background and ability level. But on the tests, P.S. 172, also called the Beacon School of Excellence, is coming close — even though 80 percent of its students are poor enough to qualify for free lunch, nearly a quarter receive special education services, and many among its predominately Hispanic population do not speak English at home.

In 2009, the 580-student primary school, tucked between fast-food restaurants and gas stations in a semi-industrial strip of Fourth Avenue, topped the city with its fourth-grade math scores, with all students passing, all but one with a mark of “advanced,” or Level 4. In English, all but one of 75 fourth graders passed, earning a Level 3 or 4, placing it among the city’s top dozen schools.

On average, at schools with the same poverty rate, only 66 percent of the students pass the English test, and 29 percent score at an advanced level in math, according to a New York Times analysis of Department of Education statistics. And though it is less well known, P.S. 172 regularly outperforms its neighbors in Park Slope and Carroll Gardens, where parents raise hundreds of thousands a year for extra aides and enrichment.

The school’s approach, while impressive in its attention to detail, starts with a simple formula: “Teach, assess, teach, assess,” said Jack Spatola, its principal since 1984.

Mr. Spatola attributed the coaches and other extra help to careful budgeting and fighting for every dollar from the Department of Education; the school’s cost per pupil, in fact, is lower than the city’s average. [Emphasis Added]

What this school does well is know its student population and design assessments and interventions targeted at its population of kids. It is an example of the think small not small minded philosophy.    

Betsy Hammond has penned The Oregonian story, Predominantly African American AP calculus class is exceptionally rare, marked by camaraderie and success:

The mood is cheerful as seniors in this small calculus class at De La Salle North Catholic High begin a warm-up exercise. They’re seeking the integral of x divided by x-squared minus four.

They work fast, cranking out steps that rely on u-substitution and the anti-differentiation rule. Clearly, they find this a cinch.

Teacher Scott Reis asks for a volunteer to show the answer on the board, and Alex Faison-Donahoe jumps up: “Mr. Reis, let me do it!”

The eagerness and camaraderie in the room at the private North Portland school are not what you might expect in a tough Advanced Placement calculus class, but they’re genuine.

Even more unusual: Two-thirds of the students, including Faison-Donahoe, are African American; only one of the 15 students is white. .

That’s a sharp contrast with other advanced high school math classes in Oregon. Among the state’s 42 public schools that enroll at least 25 African Americans and offer calculus, just five had even a single black student in calculus, according to recently released federal civil rights data from 2009-10. No school had more than five black students in the course.

Schools that enrolled substantial numbers of African Americans but none in calculus included Beaverton’s Westview High, Portland’s Grant and Madison high schools, and David Douglas High in outer Southeast Portland, the federal data show.

Only Roosevelt High, also in North Portland, has come close to matching private De La Salle’s track record. It has 31 students in AP calculus this year, including 10 African Americans and five Latinos….

De La Salle, a low-cost Catholic high school that enrolls promising students from low-income backgrounds, didn’t end up with a predominantly black calculus class easily or by design.

Students admitted to De La Salle as freshmen arrive, on average, a year and a half behind academically. They come from schools including Portsmouth, Ockley Green and H.B. Lee middle schools — high-poverty schools with low test scores.

But they also are hungry — to learn, to work hard, to get to college. “This is a tough place with a high bar,” says Principal Tim Joy. “The primary thing we look for (in applicants) is desire….”
A culture of success

Lisa Delpit, author of the new book “‘Multiplication is for White People’; Raising Expectations for Other People’s Children,” says widespread underestimation of black students’ abilities to succeed at rigorous academics is societal and begins before African American children start school.

She says Reis and De La Salle have overcome the problem in exactly the right way — by assembling a big group of black students, not just a handful, to take a demanding class, then helping the students form a sense of community.

http://www.oregonlive.com/education/index.ssf/2012/03/predominantly_african_american.html

Another example of a school that is relentless about the basics.

There are certain elements that successful schools share. The Wisconsin Department of Education has a good guide about successful schools. Chapter One, Characteristics of Successful Schools, lists key elements:

VISION

Definition

A vision represents clearly articulated statements of goals, principles, and expectations for the entire learning community. A common unifying vision is achieved when the administration, teachers, support staff, students, families, and demographically representative community members are able to clearly communicate that vision through the daily operation of the school district. A vision becomes a guiding force when all educational decisions are based on its framework and goals.

Rationale

A clear vision is like a good road map. Without a good map it is difficult to determine where you are going and, impossible to know when you arrive. A dynamic vision engages and represents the whole community and outlines a path to follow. The vision allows school leaders to create a compelling view that excites and engages other constituents to join in the educational journey.

Key Ideas

  1. Effective schools have a clearly defined vision for the improvement of learning for each and every student.
  2. Emphasis is on the achievement of a broadly defined set of standards that includes academic knowledge, skill, development, and standards of the heart.
  3. Goals are framed in a way that can be benchmarked through the school year and measured at year’s end. Progress is recorded and used for improvement efforts.
  4. Communication about the goals as well as progress toward them is a regular part of school activities among all constituents.

Successful Schools Have a Vision That:

  1. is accompanied by other strategic planning. Strategic planning is a data-driven process that guides decision making, as well as program implementation components such as:
    • goal statements
    • means to accomplish the goals
    • timelines
  2. links education standards to teacher expectations and student performance
  3. fosters district wide expectations and experiences that result in all students mastering challenging standards at proficient or above levels
  4. engages the entire learning community to take responsibility for all students’ learning
  5. includes carefully defined terms that are known and supported by all constituents
  6. is developed with representation from a wide variety of publics and demographic groups
  7. drives resource allocation in the learning as well as the broader community
  8. allows the societal, academic, and organizational components of education to operate in a seamless manner
  9. articulates the learning community’s commitment to both excellence and equity in the organization
  10. embraces the dual mission of creating in each student solid and rigorous academic achievement and civic caring and responsibility

Note, De La Salle North Catholic High is one example of what is possible with school choice.

Dr. Wilda says this about that ©

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 ©