- ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)
- (1) Educational Researcher Devotes December Issue to Report of the National Mathematics Advisory Panel
- (2) Results of the 2007 Trends in International Mathematics and Science Study (TIMSS)
- (3) “Algebra–Connect it to Students’ Priorities!” by Hank Kepner (NCTM President)
- (4) When 2 + 2 = Major Anxiety: Math Performance in Stressful Situations
ARTICLES & ANNOUNCEMENTS (NATIONAL FOCUS)
(1) Educational Researcher Devotes December Issue to Report of the National Mathematics Advisory Panel
Source: American Educational Research Association- 8 December 2008
URL (Special Issue): http://aera.net/publications/Default.aspx?menu_id=38&id=6562
The December 2008 issue of Educational Researcher (ER) provides a timely scholarly examination of Foundations for Success: The Final Report of the National Mathematics Advisory Panel. [The Panel’s report is available online at http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf] With peer-reviewed articles from leading education research experts, and under the guest editorship of Dr. Anthony E. Kelly of George Mason University, this ER issue presents diverse perspectives on substantive research in mathematics education and contributes to the discussion of valid methodological approaches.
The National Mathematics Advisory Panel (NMAP) was created in April 2006 by executive order of President George W. Bush to advise the U.S. Secretary of Education on ways to improve mathematics instruction across the nation. After two years of extensive research and hearings held around the United States, the panel prepared a final report that synthesized existing research and offered 45 recommendations on mathematics education.
The December ER picks up where the Foundations for Success report leaves off, by creating a forum for scientific dialogue and an exchange about broad strategies in the conduct of mathematics research. Eleven articles address a range of opportunities and challenges in preparing teachers and children to deal with critical 21st-century issues in mathematics education.
With an introduction by Guest Editor Anthony E. Kelly and rejoinder by Mathematics Panel Chairs Camilla Persson Benbow and Larry R. Faulkner, the special issue of ER is an invaluable resource for experts who seek to develop a coherent strategy for research and for policymakers who make critical decisions about mathematics education. According to Benbow and Faulkner, the dialogue presented in this ER issue “adds intellectual depth to what has become a national policy discussion.”
A majority of the contributing researchers took issue with the NMAP’s heavy reliance on quantitative studies. Hilda Borko and Jennifer A. Whitcomb, in their commentary on teaching and teacher education, summed up a common theme: “Different designs and methods are better for different purposes….multiple types of scientific inquiries and methods are required to generate the rich body of scientific knowledge needed to improve education.”
In addition to the panel’s narrow filter for research, scholars’ concerns included:
* lack of clear framing of measurement issues;
* focus on content knowledge to the exclusion of pedagogical content knowledge; and
* failure to address achievement disparities through improved mainstream instructional practices.
The researchers noted that the report, while summarizing each subpanel’s report, contained no integrative work. Patrick W. Thompson, in his commentary on curricula content, wrote that the panel’s “emphasis on proficiency with standard procedures in arithmetic and its lip service to ‘conceptual understanding’ will do little to address the fundamental problem of mathematics education in the United States–namely, the systematic inattention to students’ development of meanings that will support an interest in mathematics that results in taking more, and higher level, coursework.”
These articles in Educational Researcher “are intended to broaden the terms of the ongoing discussion of effective instruction as well as to draw sharp distinctions where there is disagreement,” concluded Kelly.
Following below are the article titles and the authors’ names and affiliations. To download the articles (PFD format), visit http://aera.net/publications/Default.aspx?menu_id=38&id=6562
Special December 2008 ER issue on Foundations for Success: The Final Report of the National Mathematics Advisory Panel.
= “Reflections on the National Mathematics Advisory Panel Final Report” by Anthony E. Kelly, George Mason University [Special Issue Overview] URL: http://aera.net/uploadedFiles/Publications/Journals/Educational_Researcher/3709/561-564_12EdR08.pdf
= “Teachers, Teaching, and Teacher Education: Comments on the National Mathematics Advisory Panel’s Report” by Hilda Borko, Stanford, and Jennifer A. Whitcomb, University of Colorado, Boulder
= “The Consequences of Experimentalism in Formulating Recommendations for Policy and Practice in Mathematics Education” by Paul Cobb and Kara Jackson, Vanderbilt University
= “On Professional Judgment and the National Mathematics Advisory Panel Report: Curricular Content” by Patrick W. Thompson, Arizona State University
= “When Politics Took the Place of Inquiry: A Response to the National Mathematics
Advisory Panel’s Review of Instructional Practices” by Jo Boaler, University of Sussex
= “On Learning Processes and the National Mathematics Advisory Panel Report” by Joanne Lobato, San Diego State University
= “Commentary on the National Mathematics Advisory Panel Recommendations on Assessment” by Lorrie A. Shepard, University of Colorado, Boulder
= “Mathematics Worth Knowing, Resources Worth Growing, Research Worth Noting: A Response to the National Mathematics Advisory Panel Report” by Jeremy Roschelle, Corinne Singleton, and Nora Sabelli, SRI International; Roy Pea, Stanford University; and John D. Bransford, University of Washington
= “Commentary on the Final Report of the National Mathematics Advisory Panel” by
James G. Greeno, University of Pittsburgh, and Allan Collins, Northwestern University
= “Randomized Trials in Mathematics Education: Recalibrating the Proposed High Watermark” by Finbarr C. Sloane, Arizona State University
= “Breaching the Conditions for Success for a National Advisory Panel” by Jere Confrey, Alan P. Maloney and Kenny H. Nguyen, North Carolina State University
= “Policy, Politics, and the National Mathematics Advisory Panel Report: Topology, Functions, and Limits” by James P. Spillane, Northwestern University
= “Rejoinder to the Critiques of the National Mathematics Advisory Panel Final Report” by Camilla Persson Benbow, Vanderbilt, and Larry R. Faulkner, Houston Endowment
Source: Stuart Kerachsk, Acting Commissioner, National Center for Education Statistics (NCES)
URL (NCES Statement): http://nces.ed.gov/whatsnew/commissioner/remarks2008/12_9_2008.asp
URL (Highlights): http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001
URL (Full Report): http://nces.ed.gov/pubs2009/2009001.pdf
On Tuesday, December 9, the National Center for Education Statistics released results on the performance of students in the United States on the Trends in International Mathematics and Science Study (TIMSS). The 2007 TIMSS is the fourth administration since 1995 of this cross-national comparative study. Developed through the auspices of the International Association for the Evaluation of Educational Achievement (IEA), TIMSS assesses the mathematics and science knowledge and skills of fourth- and eighth-graders.
TIMSS is designed to align broadly with mathematics and science curricula in the participating countries. The results, therefore, suggest the degree to which students have learned mathematics and science concepts and skills likely taught in school. TIMSS also collects background information on students, teachers, and schools to allow cross-national comparison of educational contexts that may be related to student achievement.
TIMSS is open to countries, as well as large subnational education systems. For example, Hong Kong, which also participated in TIMSS 1995, is now a Special Administrative Region (SAR) of the People’s Republic of China. For convenience, however, the term “country” or “nation” is used in the report to refer to all participating entities. In 2007, mathematics and science assessments and associated questionnaires were administered in 36 countries at the fourth-grade level and 48 countries at the eighth-grade level.
The TIMSS fourth-grade assessment was implemented in 1995, 2003, and 2007, while the eighth-grade assessment was implemented in 1995, 1999, 2003, and 2007. For a number of participating countries, including the United States, changes in achievement can be documented over the last 12 years, from 1995 to 2007.
The results presented here focus on the performance of U.S. fourth-and eighth- grade students in mathematics and science relative to that of their peers in other countries in 2007 and since 1995.
How TIMSS was Conducted
In the United States, TIMSS was administered in spring 2007. The U.S. sample is representative of both public and private school students at 4th and 8th grades nationally. In total, 257 schools and 10,350 students participated at grade four, and 239 schools and 9,723 students participated at grade eight. More information about how the assessment was developed and conducted is included in the technical notes of the U.S. report on TIMSS (http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009001).
How TIMSS Results are Reported
Like other large-scale assessments, TIMSS was not designed to provide individual student scores, but rather national and group estimates of performance. Achievement results from TIMSS are reported on a scale from 0 to 1,000. In order to compare performance over time, each TIMSS administration is placed on the same scale, which has a mean of 500 and standard deviation of 100. The TIMSS scale average (500) is the mean score of the original TIMSS 1995 countries (including the United States). Countries can compare their scores over time to this standardized TIMSS scale average, as well as compare their scores directly with other countries…
In addition to numerical scale results, TIMSS includes international benchmarks at four points on the mathematics and science scales—advanced international benchmark (625), high international benchmark (550), intermediate international benchmark (475), and low international benchmark (400).
U.S. Performance in Mathematics
Average scores in 2007
In 2007, the average mathematics scores of both U.S. fourth-graders (529) and eighth-graders (508) were higher than the TIMSS scale average.
The average U.S. fourth-grade mathematics score was higher than those of students in 23 of the 35 other countries, lower than those in 8 countries (located in Asia or Europe), and not measurably different from those in the remaining 4 countries. Fourth-graders from Hong Kong SAR had the highest estimated mathematics score in TIMSS 2007.
At eighth grade, the average U.S. mathematics score was higher than those of students in 37 of the 47 other countries, lower than those in 5 countries (located in Asia), and not measurably different than those in the other 5 countries. Eighth-graders from Chinese Taipei had the highest estimated mathematics score in TIMSS 2007.
Trends in scores since 1995
Compared with 1995, the average mathematics scores for both U.S. fourth- and eighth-grade students were higher in 2007. At fourth grade, the U.S. average score in 2007 was 529, 11 points higher than its 1995 average. At eighth grade, the U.S. average mathematics score in 2007 was 508, 16 points higher than its 1995 average score…
Performance on the TIMSS international benchmarks
In 2007, …10 percent of U.S. fourth-graders performed at or above the advanced benchmark (625) compared to the international median of 5 percent. These students demonstrated an ability to apply their understanding and knowledge to a variety of relatively complex mathematical situations and explain their reasoning.
Similar to their fourth-grade counterparts, …6 percent of U.S. eighth-graders performed at or above the advanced benchmark (625) compared to the international median of 2 percent. These students demonstrated an ability to organize and draw conclusions from information, make generalizations, and solve nonroutine problems.
Differences in mathematics performance by selected student characteristics
Scores of lower and higher performing students
In 2007, the highest-performing U.S. fourth-graders (those performing at or above the 90th percentile) scored 625 or higher in mathematics. This was higher than the 90th percentile scores for fourth-graders in 23 countries and lower than the 90th percentile score for students in 7 countries: Singapore, Hong Kong SAR, Japan, Chinese Taipei, Kazakhstan, England, and the Russian Federation…
At grade eight, the highest-performing U.S. students in mathematics scored 607 or higher in 2007. The U.S. 90th percentile score was higher than that of 34 countries and lower than the 90th percentile score in 6 countries: Chinese Taipei, Korea, Singapore, Hong Kong SAR, Japan, and Hungary…
Performance by race/ethnicity
In the United States, students were asked whether they were of Hispanic origin and their race. Students who identified themselves as being of Hispanic origin were classified as Hispanic, regardless of race.
In 2007, U.S. White, Asian, and multiracial (non-Hispanic students who identified with two or more races) fourth-graders all scored higher, on average, in mathematics than the TIMSS scale average, while Black fourth-graders scored lower, on average. Hispanic fourth-graders’ average score showed no measurable difference from the TIMSS scale average.
At grade eight, the average scores of U.S. White, and Asian students were higher than the TIMSS scale average in mathematics. On the other hand, the average scores of Black and Hispanic eighth-graders were lower than the TIMSS scale average. The average score of multiracial eighth-graders was not measurably different from the TIMSS scale average.
Examination of performance over the 12-year period, from 1995 to 2007 in the United States, shows that White, Black, and Asian students in both fourth and eighth grades, as well as Hispanic students in grade eight, have mostly improved in mathematics. Hispanic fourth graders have improved over a shorter period, between 2003 and 2007.
Performance by school poverty level
The U.S. results are also arrayed by the concentration of low-income enrollment in the public schools, as measured by eligibility for free or reduced-price lunch, and shown in relation to the TIMSS scale average and the U.S. national average.
In comparison to the TIMSS scale average, the average mathematics score of U.S. fourth-graders in the highest poverty public schools (at least 75 percent of students eligible for free or reduced-price lunch) in 2007 was lower; the average scores of fourth-graders in each of the other categories of school poverty was higher than the TIMSS scale average.
In comparison to the U.S. national average score, fourth-graders in schools with 50 percent or more students eligible for free or reduced-price lunch scored lower, on average, while those in schools with lower proportions of poor students scored higher, on average, than the U.S. national average.
On average, U.S. eighth-graders in public schools with at least 50 percent eligible for free and reduced price lunch scored lower than the TIMSS scale average in 2007. U.S. eighth-graders attending public schools with fewer than 50 percent of students eligible for the free or reduced-price lunch program scored higher than the TIMSS scale average in mathematics.
In comparison to the U.S. national average, U.S. eighth-graders in public schools with fewer than 25 percent of students eligible scored higher in mathematics, on average, while students in public schools with at least 50 percent eligible scored lower, on average.
U.S. Performance in Science
Average scores in 2007
In 2007, the average science scores of both U.S. fourth-graders (539) and eighth-graders (520) were higher than the TIMSS scale average (500 at both grades).
The average U.S. fourth-grade science score was higher than those of students in 25 of the 35 other countries, lower than those in 4 countries (located in Asia), and not measurably different from those in the remaining 6 countries. Fourth-graders from Singapore had the highest estimated science score in TIMSS 2007.
At eighth grade, the average U.S. science score was higher than the average scores of students in 35 of the 47 other countries, lower than those in 9 countries (located in Asia or Europe), and not measurably different from those in the other 3 countries. Again, Singapore had the highest estimated science score.
Trends in scores since 1995
Compared with 1995, the average science scores for both U.S. fourth- and eighth-grade students were not measurably different from 2007. The U.S. fourth-grade average science score in 2007 was 539 and in 1995 was 542. The U.S. eighth-grade average science score in 2007 was 520 and in 1995 was 513…[Please visit http://nces.ed.gov/whatsnew/commissioner/remarks2008/12_9_2008.asp for more details.]
For More Information
* The statement above covers some of the major findings from the TIMSS 2007 highlights report from the U.S. perspective available on the NCES website. For more information on TIMSS, please visit the TIMSS website at http://nces.ed.gov/timss/
* Acting Commissioner Stuart Kerachsky’s Presentation: Highlights From TIMSS 2007 is available for download from http://nces.ed.gov/whatsnew/commissioner/remarks2008/pdf/TIMSS_12_9_2008.pdf
Source: NCTM [(National Council of Teachers of Mathematics)] News Bulletin – December 2008
When you hear the word algebra, what comes to mind? A one- or two-year course focusing on manipulating symbols? Well, algebra is much more than that! One of the biggest challenges facing us as mathematics teachers is to show all students–and their parents–that algebra is a tool for understanding and describing relationships in widely varied settings. Making connections from descriptions in words, graphs, or tables to symbolic representations brings insight to students. Seeing these links strengthens students’ ability to move back and forth between the concrete and the abstract and boosts their confidence in using symbols that they understand to be firmly based on mathematical properties and connected to the world.
Algebra and algebraic reasoning have recently received considerable attention. NCTM’s Principles and Standards for School Mathematics (published in 2000) and Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics (2006) provide guidance and a broad vision of algebra in mathematics curricula. A new NCTM position statement on algebra–“Algebra: What, When, and for Whom?” (see http://www.nctm.org/about/content.aspx?id=16229)–gives a concise statement of this vision. All these documents call for building conceptual understanding, procedural skills, and problem-solving simultaneously.
Successful problem solving, in both purely mathematical and real-world contexts, is critical to students’ motivation throughout their school years. Problem statements and solution strategies take different forms at different levels. Consider, for example, the following story problem: “Tanya has 5 marbles. Her brother gives her some more. Then she has 12. How many marbles does Tanya receive from her brother?” Students in grade 1 might use objects, tallies, and counting strategies such as “counting on” from 5 to 12. Then children learn to make the statement, “5 + what = 12?” Later, every Algebra 1 textbook includes a corresponding exercise: “5 + x = 12.”
All students need ongoing experiences that assist them in making connections by requiring them to produce multiple representations. As students advance in school, they must have many opportunities to model real-world problems and contexts with appropriate mathematical representations, including algebraic expressions, functions, and equations or inequalities. Not only does this work help students progress to skillful use of symbols but also gives a motivating reason for doing so. The tasks that we pose are critical in motivating students! In working with spreadsheets, for example, students discover that algebraic expressions define the values in many cells, demonstrating that algebra carries beyond the mathematics classroom to other areas of their lives.
Students do not acquire an understanding of algebraic concepts or the skill to use them in a single mathematics course or year. Developing algebraic reasoning should be a focus of mathematics instruction, extending from work with describing patterns in preschool and continuing through justifying procedures and solving problems by using whole numbers, fractions, decimals, and integers and performing advanced work with functions in high school and beyond.
As adults, we recognize algebra and its applications as important gateways to expanded opportunities. Our challenge is to give all students the necessary preparation and opportunities to make learning algebra a successful experience.
Excerpt–NCTM Position Statement on Algebra: “Algebra: What, When, and for Whom?”
URL (PDF version): http://www.nctm.org/uploadedFiles/About_NCTM/Position_Statements/Algebra%20final%2092908.pdf
NCTM Position: Algebra is a way of thinking and a set of concepts and skills that enable students to generalize, model, and analyze mathematical situations. Algebra provides a systematic way to investigate relationships, helping to describe, organize, and understand the world. Although learning to use algebra makes students powerful problem solvers, these important concepts and skills take time to develop. Its development begins early and should be a focus of mathematics instruction from pre-K through grade 12. Knowing algebra opens doors and expands opportunities, instilling a broad range of mathematical ideas that are useful in many professions and careers. All students should have access to algebra and support for learning it.
Visit the Web site above for details regarding the following key tenets of the position statement:
– Algebra is more than a set of procedures for manipulating symbols…
– Algebraic concepts and skills should be a focus across the pre-K–12 curriculum…
– Algebra when ready…
– All students should have opportunities to develop algebraic reasoning…
Source: University of Chicago – 9 December 2008
Imagine you are sitting in the back of a classroom, daydreaming about the weekend. Then, out of nowhere, the teacher calls upon you to come to the front the room and solve a math problem. In front of everyone. If just reading this scenario has given you sweaty palms and an increased heart rate, you are not alone. Many of us have experienced math anxiety and in a new report in Current Directions in Psychological Science, a journal of the Association for Psychological Science, University of Chicago psychologist Sian L. Beilock examines some recent research looking at why being stressed about math can result in poor performance in solving problems.
Much of Beilock’s work suggests that working memory is a key component of math anxiety. Working memory (also known as short term memory), helps us to maintain a limited amount of information at one time, just what is necessary to solve the problem at hand. Beilock’s findings suggest that worrying about a situation (such as solving an arithmetic problem in front of a group of people) takes up the working memory that is available for figuring out the math problem.
The type of working memory involved in solving math problems may be affected by the way the problems are presented. When arithmetic problems are written horizontally, more working memory resources related to language are used (solvers usually maintain problem steps by repeating them in their head). However, when problems are written vertically, visuospatial (or where things are located) resources of working memory are used. Individuals who solve vertical problems tend to solve them in a way similar to how they solve problems on paper. Beilock wanted to know if stereotype-induced stress (i.e., reminding women of the stereotype that “girls can’t do math”) would result in different results for solving vertical versus horizontal math problems. The findings showed that the women who had been exposed to the negative stereotype performed poorly, although only on the horizontal problems (which rely on verbal working memory). Beilock suggests that the stereotype creates an inner monologue of worries, which relies heavily on verbal working memory. Thus, there is insufficient verbal working memory available to solve the horizontal math problems.
It has generally been shown that the more working memory capacity a person has, the better their performance on academic tasks such as problem solving and reasoning. To further explore this, Beilock and her colleagues compared math test scores in individuals who had higher levels of working memory with those who had less. The subjects took a math test either in a high pressure situation or low pressure situation. It turns out that the subjects with higher working memory levels performed very poorly during the high pressure testing situation–that is, the subjects with the greatest capacity for success were the most likely to “choke under pressure.”
Beilock surmises that individuals with higher levels of working memory have superior memory and computational capacity, which they use on a regular basis to excel in the classroom. “However, if these resources are compromised, for example, by worries about the situation and its consequences, high working memory individuals’ advantage disappears,” Beilock explains…
These studies [are] relevant and important for the development of exams and training regimens that will ensure optimal performance, especially by the most promising students.