- ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)
- (1) Results of the 2005 National Assessment of Educational Progress (NAEP) in Science
- (2) The Role of the National Science Foundation in K-12 Science and Math Education
- (3) “Early Development of Estimation Skills” by Robert S. Siegler and Geetha Ramani
- (4) “Learning From Symbolic Objects” by David H. Uttal and Judy S. DeLoache
- (5) Research in Mathematics Education Presentations at 2006 AERA Conference
- (6) “Some Worry About Potential Bias on the National Math Panel” by Sean Cavanagh
- (7) Results That Matter: 21st Century Skills and High School Reform
ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)
Source: National Center for Education Statistics and the California Department of Education
URL (NAEP-Science): http://nationsreportcard.gov/science_2005/
In 2005, a representative sample of more than 300,000 fourth, eighth and 12th-grade students nationwide participated in the science assessment of the National Assessment of Educational Progress (NAEP). The results of this study were released on Wednesday and indicate that science achievement in the United States has improved for elementary school students over the last decade, but has remained flat for middle school students and has declined among high schoolers.
The Nation’s Report Card Science 2005 details student achievement on the NAEP and includes state-by-state results for grades 4 and 8. Fourth-grade scores were higher in 2005 than in both 2000 and 1996, when previous science assessments were conducted. However, there was no overall improvement among eighth-graders, and average scores in grade 12–though not significantly different from the 2000 results–have decreased since 1996.
The 2005 results from The Nation’s Report Card for math and reading, released last October, showed similar trends: the fourth-grade math and reading scores have increased significantly since 2000, while since 2003, eighth-graders demonstrated modest improvement in math and a decline in reading.
“Policymakers and industry representatives are concerned about national competitiveness in an increasingly technical world,” said Darvin M. Winick, chair of the National Assessment Governing Board, the bipartisan group that sets policy for NAEP. “The lackluster achievement of our older students in science, as in math and reading, appears to confirm those concerns.”
Mary Frances Taymans, a member of the National Assessment Governing Board, noted that “The science assessment of the National Assessment of Educational Progress is not just a test of factual knowledge, though knowledge of science content is a crucial part of what NAEP tests. The NAEP science assessment framework also requires students to understand science concepts, to apply what they know to a new situation, and to use the skills and reasoning of scientific investigation. It is in these additional steps, I’m afraid, that too many of our students fall short of the scientific literacy they need.”
California’s Superintendent of Public Instruction Jack O’Connell issued the following statement about the NAEP results: “I am pleased to see that on this report card for science achievement, California’s fourth and eighth graders showed the largest increases in the nation. While this is encouraging, we have much work to do to improve student proficiency in science if California is to lead in an era that increasingly demands higher levels of scientific knowledge. We’ve taken steps to focus more strongly on science instruction by expanding standards-based professional development for teachers to include science, and by adding science to our California Standards Tests for students in grades five, eight, and ten. The state is also in the process of adopting new instructional materials in science. In addition, the California Mathematics and Science Grant Program funds several partnerships aimed at developing knowledge and instructional strategies of California teachers.
“While significant achievement gains were made by Hispanic and Asian students, there remains an unacceptable achievement gap that shows ethnic minorities, particularly African American students, and socio-economically disadvantaged students lagging behind. We must focus strongly on closing that gap while aiming to increase the achievement of all groups of California students.”
Copies of The Nation’s Report Card Science 2005 as well as additional data collected from the 2005 NAEP science assessment are available online at http://nationsreportcard.gov
Source: U.S. House Committee on Science
On March 30 and on May 3, the U.S. House Committee on Science held hearings on K-12 science and mathematics education. Webcasts of these hearings are available at the above Web site. (Real Player version 7 or higher is required to play the webcasts.)
(a) March 30, 2006 — “K-12 Science and Math Education Across the Federal Agencies”
(b) May 3, 2006 — “The Role of the National Science Foundation in K-12 Science and Math Education”
Source: Association of Psychological Science (APS); APS Observer – May 2006
The May issue of the APS Observer presents the second of a two-part series on “the role of cognitive sciences in improving educational instruction.” The articles in the May issue describe research funded by the Cognition and Student Learning (CASL) program of the Institute of Educational Sciences (IES). Below are excerpts from these two articles.
(“Early Development of Estimation Skills”)
Approximately how much is 192 times 12? About how much will each teammate have to pay to buy a $50 present for the coach? Roughly how many marbles are in this jar?
Learning how to estimate is important, not only because estimating is something we need to do all the time, but also because proficiency at estimation is substantially correlated with many aspects of numerical understanding and with overall math-achievement-test scores…
Yet little is known about the development of estimation skills. To obtain a more detailed understanding, we conducted a series of studies on number-line estimation. Children are presented a blank line, on which only a zero is printed at the left end and the number 10, 100, or 1,000 is printed at the right end. Children estimate the positions of various numbers, one number per line. This number-line task lets us see how children of various ages make estimates independent of specific entities (such as marbles or dollars) whose qualities are being estimated. It also allows us to examine any range of numbers, and allows for the examination of relations between actual and estimated numerical magnitudes.
The research has revealed that children progress through a consistent developmental sequence. Young children generate logarithmic patterns of estimates, in which estimated magnitudes rise more quickly than actual magnitudes (e.g., the number 15 is estimated as being around where the number 60 should be on a zero-100 number line). Older children generate linear functions (e.g., the number 15 is estimated as being around where 15 should be.) The same logarithmic to-linear sequence has been observed among kindergartners through second graders for zero – 100 number lines and for second through sixth graders for zero-1,000 lines… The linearity of estimates has also proven to be highly correlated with overall math-achievement scores among students in kindergarten through fourth grade…
IES’s emphasis on translating educationally relevant research into evidence-based curricula encouraged us to apply these findings to help low-income preschoolers improve their numerical understanding. Large discrepancies in numerical knowledge between children from lower- and middle-income families are already present before children enter school. Consistent with this general finding, Siegler and Ramani (2005) found that on zero–10 number lines, the estimates of 4-year-olds from lower-income backgrounds were only weakly correlated with the actual magnitudes of the numbers, whereas the estimates of peers from middle income backgrounds were substantially correlated with the actual magnitudes and fit a linear function quite well.
These differences between the numerical knowledge of preschoolers from different socioeconomic backgrounds seem likely to reflect their differing experiences with informal number-related activities in the home environment. Board games with linearly arranged sequences of numbers seem likely to play an especially important role in promoting numerical understanding, because they provide multiple cues to numerical magnitudes…
Therefore, we randomly assigned children from urban Head Start centers to play a board game four times over a two-week period, 15 minutes per session, either with 10 consecutively numbered squares or with 10 differently colored squares. On each turn, the child would spin a spinner, obtain a “one” or a “two,” and then move the token one or two squares forward, saying either (for example) “four, five” or “red, blue.” Before the first session and after the last session, children were presented the number-line estimation task.
Children who used the numbered boards made substantial progress. By the posttest, their number-line estimates were as accurate and as linear as those of middle-income children who had not played the game. By contrast, children whose boards varied in color rather than number showed no improvement in numerical knowledge.
With the support of IES, we are following up these findings to determine whether they are stable over a three-month period and to determine whether they generalize to other numerical tasks. If so, we plan to determine whether such instruction is effective at the level of entire classes as well as in one-on-one interactions. Through encouraging such research, IES is helping to bridge the gap between educationally relevant research and classroom practices.
Source: Association of Psychological Science (APS); APS Observer – May 2006
Perhaps the most important challenge of early-childhood education is helping children to master a variety of symbol systems. Within a few short years, children must learn to understand and use letters, numbers, mathematical symbols, maps, and other symbol systems. Parents, educators, and researchers naturally want to find the most effective educational techniques and tools to help them learn.
A variety of objects have been designed to help young children learn letters and numbers. For example, letter and number magnets and blocks are found in the homes of many American preschoolers. In the classroom, teachers sometimes use more formal manipulative systems composed of concrete symbolic objects, such as Cuisenaire Rods or Digi-Blocks, that have been explicitly designed to help young children learn mathematics.
The design and use of these concrete symbolic objects is motivated by the assumption that young children’s thinking is concrete (rather than abstract) by nature. Based on the writings of scholars such as Piaget, Bruner, and Montessori, educators have suggested that young children learn best through the use of highly concrete objects. However, our prior research on a variety of symbol systems (e.g., scale models, pictures, and maps) leads us to think twice about the value of having young children play with objects that are intended to be used as symbols.
All symbolic objects have a dual nature: They are both objects in their own right and representations of something else. Therefore, to use a symbol as a representation of something else, one must focus more on what it represents and less on the symbol as an object. We suggest that using letter and number toys as representations may have just the opposite effect than what is intended: making children focus more on them as objects and less on what they stand for.
This theoretical perspective has motivated a line of IES funded research on the effects of using concrete objects… We investigated the effectiveness of concrete symbolic objects, known as manipulatives, in helping young elementary-school children learn the procedures associated with two-digit subtraction. We taught children using either using the traditional written method or a commercially available manipulatives set, per the manufactures instructions. This set was composed of small individual blocks that could be assembled into larger units of ten to represent both the tens and ones units of a quantity. Children could physically remove blocks from this quantity to concretely carry out the process of double-digit subtraction.
We found that children initially performed equally well in both training conditions. However, those children who learned with the manipulatives had trouble transferring knowledge to written versions of the math problems; they did not use what they had learned using the manipulatives to solve written versions of the same or similar problems. Moreover, learning with the manipulatives took almost three times as long as learning with the written method. This result does not mean that manipulatives are never useful, but it does challenge the typical assumption that they are more effective than other teaching tools in all contexts.
Our work shows that the theories and methods of developmental psychology are highly relevant to issues of concern in education. Evidence-based research both challenges traditional assumptions regarding the education of young children and points to exciting and promising new directions.
Source: Karen Hollebrands, Webmaster for the Research in Mathematics Education Special Interest Group (SIG/RME) of the American Educational Research
A listing of 2006 AERA conference sessions sponsored by SIG/RME is now available on the SIG Web site at http://www.sigrme.org/aera/aera06.htm
Dr. John Bruer provided the SIG/RME Invited Address at the AERA conference. His article, “Education and the Brain: A Bridge Too Far” (Educational Researcher, November 1997) still stimulates discussion. This article is available for download at http://www.jsmf.org/about/j/education_and_brain.htm Bruer’s PowerPoint presentation for his AERA address (“Spanning Disciplines: ‘Bridge’ Revisited”) can be viewed at http://www.sigrme.org/bruer.htm or downloaded from http://www.sigrme.org/bruerppt.ppt
Source: Education Week – 24 May 2006
Supporters of a new expert panel on mathematics are confident it will help identify national strategies for improving student learning in that subject–even as critics ask whether its members have the classroom teaching experience, and the objectivity, needed to accomplish that mission.
The National Mathematics Advisory Panel, whose 17 voting members President Bush named last week, includes a number of mathematicians and cognitive and developmental psychologists from across the country.
But the advisory group, which [met] for the first time May 22 in Washington, has only one member who currently teaches in a K-12 school, a lack of representation that some observers find puzzling, given the panel’s stated purpose of exploring math teaching and learning from basic math through subjects such as calculus.
Others worry that the panelists’ backgrounds suggest they will favor a particular approach to teaching math–generally speaking, one that stresses the need for drill and practice in basic computation at early grade levels, at the expense of problem solving.
“It does not represent a balanced view of mathematics,” contended Steven Leinwand, a principal research analyst at the American Institutes for Research, a private research organization in Washington that studies behavior and social-science issues. He believes that teachers should cultivate students’ skills in understanding broader math concepts, along with basic skills.
The panel needs a stronger voice from “the excellent classroom teachers working with students day in, day out,” Mr. Leinwand added. “We instead have experts on teaching mathematics at the college level.”
Similar charges of bias dogged the National Reading Panel, formed in 1997, which Bush administration officials have said is a model for the math group.
The reading panel ended up recommending a strong emphasis on teaching phonics, a classroom strategy using a basic-skills approach that critics say the administration tends to favor in the awarding of billions of dollars in federal reading grants.
Others, however, say worries about a biased math panel are overblown. Tom Loveless, a senior scholar at the Brookings Institution who was selected for the panel, has written about American students’ weaknesses in arithmetic, and he acknowledges that some skeptics are likely to question his objectivity. But Mr. Loveless, a former 6th grade public school teacher, said he favors building a range of student math skills, and he believes other panelists are similarly broad-minded.
“It’s very clear that our jobs here are not to go in with any kind of an agenda,” he said. “It’s an opportunity to cut through a lot of the noise surrounding math.”
President Bush established the panel as part of a broader, $380 million proposal aimed at improving student performance in math and science and making the United States more competitive internationally. A second piece of that proposal would have the federal government take a stronger role in promoting instructional strategies in that subject that are backed up by research.
For years, disputes over how to teach math, known as the “math wars,” have pitted those who say students need more grounding in basic skills against those who argue that more attention should be paid to building their problem-solving abilities.
Many educators and researchers who once fought those battles have called for détente. While disagreements remain, they say, educators generally agree that students need a balance between knowing number facts and basic procedures and having a broad understanding of math concepts.
Various factions of math educators have long accused the National Council of Teachers of Mathematics, an influential, 100,000-member organization in Reston, Va., of placing too little emphasis on the basics.
But NCTM President Francis M. “Skip” Fennell, who was named to the panel, said he is willing to believe the commission could work past disagreements. “I’m certainly going into it with an open mind,” he said. “I have to be positive.”
One panelist and past critic of the NCTM, Harvard University mathematics professor Wilfried Schmid, reiterated his view that students should be “computationally fluent.” But he also believes that advocates from different camps are working more cooperatively today. He noted that he had joined other scholars and business representatives in identifying skills that individuals on different sides of past “math wars” would regard as crucial–from students’ understanding of fractions and algorithms to their proper use of calculators and their ability to do problems in real-world contexts. “We can see some consensus emerging,” he said.
Several panelists and outside observers said they believe far less research is available on effective K-12 math teaching than in subjects such as reading. A major charge of the panel will be to identify the existing research and where more study is needed.
Vern S. Williams, a math teacher at Longfellow Middle School in the 164,000-student Fairfax County, Va., school system, is the only panelist who is now a K-12 teacher. On a Web site he set up on math topics, Mr. Williams has criticized the NCTM for promoting what he sees as “fuzzy” math standards. In an interview, he suggested the panel could encourage schools to require more demanding math lessons of elementary and middle school students. Many educators today, he said, wrongly assume that children cannot handle that work.
“We’ve been focusing for so long on pedagogy and teaching methods,” Mr. Williams said. “We need to focus on what to teach.”
Source: The Partnership for 21st Century Skills
The Partnership for 21st Century Skills and 20 leading advocacy groups, companies and education organizations have endorsed a powerful set of principles for guiding high school redesign initiatives focused on a framework for 21st century learning. The “Principles for Connecting High School Reform and 21st Century Skills” outlines the beliefs that are critical to high school redesign that focuses on preparing students to be effective citizens in the new global economy. For an overview, see http://www.21stcenturyskills.org/index.php?option=com_content&task=view&id=205&Itemid=115
The Partnership has issued a national report, “Results That Matter: 21st Century Skills and High School Reform,” which is available to download from http://www.21stcenturyskills.org/documents/RTM2006.pdf
This report presents three fundamental ideas about high schools…
* There are results that matter for high school graduates in the 21st century and these results are different from and go beyond traditional metrics. Even if every student in the country satisfied traditional metrics, they still would remain woefully under-prepared for 21st century success beyond high school.
* Improving high schools requires the nation to redefine “rigor” to encompass not just mastery of core academic subjects, but also mastery of 21st century skills and content. Rigor must reflect all the results that matter for all high school graduates today. Today’s graduates need to be critical thinkers, problem solvers and effective communicators who are proficient in both core subjects and new, 21st century content and skills. These 21st century skills include learning and thinking skills, information and communications technology literacy skills, and life skills. Twenty-first century skills are in demand for all students, no matter what their future plans–and they will have an enormous impact on students’ prospects.
* The results that matter–21st century skills integrated with core academic subjects–should be the “design outcomes” for creating high schools that prepare students for success in the 21st century. Only by setting clear goals that incorporate 21st century skills can high schools truly prepare students to succeed in postsecondary education, workplaces and community life.
“Redefining ‘Rigor’ for a New Century: Results that matter for today’s high schools go beyond core subjects” by Ken Kay & G. Thomas Houlihan