Math Standards Research Articles

Shining a Light or Fumbling in the Dark? The Effects of NCLB’s Subgroup-Specific Accountability on Student Achievement

The theory of action behind the No Child Left Behind Act of 2001 is that “shining a light” on subgroup performance will increase reading and math test scores for minority and disadvantaged students. Using a panel of all students in Grades 3 through 8 in North Carolina from 2000 to 2008 ( N = 1.7 million students in 1,800 schools), the authors estimate double- and triple-differenced models with school fixed effects to examine whether subgroup-specific accountability threats increase high-stakes test scores. These sanctions are found to have positive effects for minority and disadvantaged students. Larger positive effects emerge for the lowest achieving schools rather than schools near the margin of passing. Some evidence of adverse effects is also found for low and high achievers in math, but not in reading, a finding attributed to the combination of increases in the rigor of state standards in math and responses to an accountability metric based on test score status rather than growth. The implications of the findings for the design of educational accountability systems are discussed.

Constrained Curriculum in High Schools: The Changing Math Standards and Student Achievement, High School Graduation and College Continuation

Mathematics education is a critical public policy issue in the U.S. and the pressures facing students and schools are compounded by increasing expectations for college attendance after high school. In this study, we examine whether policy efforts to constrain the high school curriculum in terms of course requirements and mandatory exit exams affects three educational outcomes – test scores on SAT math, high school completion, and college continuation rates. We employ two complementary analytic methods – fixed effects and difference in differences (DID) – on panel data for all 50 states from 1990 to 2008. Our findings suggest that within states both policies may prevent some students from completing high school, particularly in the near term, but both policies appear to increase the proportion of students who continue on to college if they do graduate from high school. The DID analyses provide more support for math course requirement policies than mandatory exit exams, but the effects are modest. Both the DID and fixed effects analyses confirm the importance of school funding in the improvement of high school graduation rates and test scores.

Too Much Too Soon? Common Core Math Standards in the Early Years

The author expresses concern about the math standards of the Common Core Curriculum in relation to young children. The editorial cites others who share concerns about how the global community uses standards. She suggests caution in implementation because the overemphasis on the standards may overlook the investment needed in effective curriculum development and professional development for teachers. The editorial concludes with the revisions will be neccesary to the current version of the Common Core Standards given the concern.

Real-Life Problem Solving: Examining the Effects of Alcohol Within a Community on the Navajo Nation

TASC, DISCOVER, PBL, and Prism models were integrated and applied in a Community Awareness Unit designed for sixth grade. The students listed different problems they considered important in their community and then selected a theme that was of the greatest interest to them: The effects of alcohol on the community. The teacher wrote a problem based scenario to explain the theme and the students divided into six stakeholder groups to investigate and gather information on the essential question from their stakeholder group's viewpoint. At the end they presented their results to their peers and the community. The students developed realistic solutions to a community problem that affected all of them. The students gained valuable skills from the required curriculum as outlined in the Arizona State Standards in language arts, science, math, and technology. They applied these skills and concepts in an integrated way and exercised their creative problem solving abilities to propose innovative solutions to persistent problems.

A reflection framework for teaching math

Evaluate the quality of your instruction by using the eight dimensions of M-Scan, an observation tool that links math standards with day-to-day practice.

Teaching Mathematics and Science Standards to Students With Moderate and Severe Developmental Disabilities

This study evaluated strategies to teach secondary math and science content to students with moderate and severe developmental disabilities in a quasiexperimental group design with special education teachers randomly assigned to either the math or the science treatment group. Teachers in the math group implemented four math units representing four of the five national math standards. The science teachers implemented four science units representing three of eight national science content standards. A fourth standard, science as inquiry, was embedded within each of the units. Results showed students made gains in respective content areas. Students who received instruction in math scored higher than students who received instruction in science on the posttest of math skills. Likewise, students who received instruction in science scored higher than students who received instruction in math on the posttest of science vocabulary skills. Limitations and suggestions for future research and practice are discussed.

Common U.S. Math Standards

The United States has never had national standards or curricula for mathematics. Instead, each state decides, for example, what version of high-school algebra should be taught and how to assess whether students have learned it. In March 2010, the National Governors Association and the Council of Chief State School Officers released Common Core State Standards (CCSS) for English language arts and mathematics ( www.corestandards.org ). The goal is to have all states adopt these as their standards, making more uniform the knowledge and skills expectations for students in preparation for success in college and careers.

China and U.S. Can Swap Ideas about Math and Science

In an era when technology and the rapid flow of information dominate every major area of economic growth, innovation and excellence in math and science are integral to any nation's long-term success. So there is a strong interest in every country in learning about best practices in math and science education. The rising economies of Asia admire U.S. scientific research and innovation and send their students to train in America's graduate schools. Yet the United States, dominant in science for most of the second half of the 20th century, is concerned that its long-term scientific capacity may be eroding; international comparisons of student achievement show that performance of American K-12 students continues to be mediocre compared with students in other countries, including East Asia. Take China as an example of an East Asian system. What can the United States learn from the Chinese system about how to produce scientific competence on a broad scale across the population? And what can China learn from the United States about producing innovation? Learning from China There are several key ways in which China, and East Asia more broadly, have been successful in producing higher student achievement in math and science. These include: National standards and aligned instruction. China has national standards in math and science that drive coherent textbook content, teacher preparation, and professional development, whereas in the United States, there is a great deal of variation in the rigor and quality of standards across educational jurisdictions. Strong core curriculum. In China, biology, chemistry, and physics, as well as algebra and geometry, are mandatory for completion of high school. In the United States, students are allowed to choose among different levels of learning, and many opt out of more advanced courses. Rigorous teacher preparation. In China, far higher proportions of science and math teachers have degrees in their discipline than their U.S. counterparts. And specialist math and science teachers are employed in the elementary schools, unlike in the United States, where most primary teachers are generalists, typically responsible for all subjects. Examinations focus students. China's education system is exam-driven. Math and science play a major role in the highly competitive entrance examinations for universities. U.S. college entry requirements are broader and do not require as much math and science competence. Time on task. Chinese schools and learning time after school are intense and focused on academics. The Chinese school year is a full month longer at the secondary level than American schools and, overall, Chinese students spend twice as many hours studying as their U.S. peers. Learning from the United States Curriculum. The Chinese curriculum, while rigorous, is overloaded with scientific facts and weak in teaching inquiry. A major curriculum reform is now attempting to remedy that, informed in part by U.S. traditions of curriculum design. …

National Standards Closer to Reality

Twenty years after President George H.W. Bush and the nation's governors ventured a cautious challenge to the long tradition of local control in public education--establishing a national goal that students demonstrate competency in core subjects--we're headed toward voluntary national standards and testing in public education. There's been so much momentum in that direction in Washington recently that what would amount to a sweeping shift in policy has hardly rated a headline. The President and Secretary of Education Duncan have publicly praised the idea. Having 50 different goalposts is absolutely ridiculous, Duncan said of the state standards required by the No Child Left Behind Act in an address to the American Council on Education. And he has signaled that there's hundreds of millions of dollars in federal stimulus money waiting for state leaders who step forward to craft common tests built on higher standards. Duncan is working closely with two organizations representing key stakeholders--the Council of Chief State School Officers (CCSSO) and the education policy arm of the National Governors Association (NGA). They've called on states to demand more from their schools in the name of a stronger workforce and greater economic competitiveness by voluntarily adopting a common core of internationally benchmarked standards in math and language arts for grades K-12. An astonishing 49 states and territories already have signed onto the initiative. Leaders in the philanthropic community, including the Bill & Melinda Gates Foundation and the Eli and Edythe Broad Foundation, also have joined the common standards campaign, as have influential civil rights groups like the Education Trust and education policy voices on both the left (the Center for American Progress) and the right (the Thomas B. Fordham Foundation). And a key congressional player, George Miller, the California Democrat who chairs the House Committee on Education and Labor, signaled his support earlier this year when he held a hearing titled Strengthening America's Competitiveness Through Common Academic Standards, where witnesses called for fewer, tougher standards over the vast and vague expectation of many states today. Logic of National Standards The logic of national public school standards and tests is compelling. The reading, writing, and math skills students need don't vary a whole lot from California to Kansas, particularly when many of today's increasingly global employers are able to tap digitally into talent wherever they find it. Even with the inevitable fights over evolution and creationism and over some parts of the cultural canon, the same is mostly true for some subjects, such as science and history. And how schools teach would be left to them. On the testing side of the equation, the inefficiency of 51 redundant state testing systems is obvious. The nation's testing infrastructure suffers from a severe lack of funding and expertise, and moving to common standards and assessments would permit the creation of a smaller number of higher-quality tests. Traditionally, politics have trumped these arguments. President Bush proposed the creation of voluntary national standards in elementary and secondary education in the early 1990s, and the Clinton Administration sought voluntary national tests in the mid-1990s. But partisan politics and strong philosophical opposition from both the Left and the Right combined to sink the proposals on Capitol Hill. Liberals argued that the tests would be unfair to students in impoverished communities, while conservatives argued that national standards and testing would amount to a federalization of public schooling. But No Child Left Behind transformed the policy landscape. It established standards, tests, and the holding of local educators accountable for results as a cornerstone of school reform. And its federal mandate for standards and testing nationwide dealt a strong psychological blow to the tradition of local educational control, particularly since the law was proposed by a conservative Republican president and approved by a Republican-controlled Congress--traditional opponents of centripetal forces in policy making. …

ON THE ROAD TO CORE STANDARDS

RETURN TO ISSUEPREVNewsNEXTON THE ROAD TO CORE STANDARDSA drive is under way in the U.S. to develop common education standards in math and English; SCIENCE COULD BE NEXTCELIA HENRY ARNAUDView Author Information C&EN WASHINGTONCite this: Chem. Eng. News 2009, 87, 34, 37–38Publication Date (Print):August 24, 2009Publication History Published online14 November 2010Published inissue 24 August 2009https://doi.org/10.1021/cen-v087n034.p037Copyright © 2009 AMERICAN CHEMICAL SOCIETYArticle Views12Altmetric-Citations2LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (509 KB) SUBJECTS:Students Get e-Alerts

Think inside the Clock

More schools than ever are not meeting Adequate Yearly Progress, and budget cuts are going to make resources for reforms even more scarce. School districts cannot afford to continue a reform agenda unless they can align practices with policies--and vice versa. That alignment begins with how schools use time. Based on 10 years of experience as a school administrator in the early years of Kentucky's reforms and on eight years providing technical assistance to districts and state education departments in eight states, I've learned where and why policies involving time don't fit practice. Moreover, my experience shows that a deliberate strategy of aligning the two can provide supports for teachers, such as professional development time in the school day, even as budgets are reduced. COMMON TIME PROBLEMS The quantity of requirements dumped on the traditional use of time in schools has created a dramatically unrealistic and unwieldy environment for teaching and learning. These are some of the problems encountered by most districts: The math doesn't work. Often, there simply is not enough time available. Schools and districts are held accountable for policies that require more time than is available. Policy requirements are huge, while time is short. When the dust settles, there are many more requirements than can be implemented, leaving mandates mathematically impossible for school leaders. Take, for example, the requirement that all students be proficient in math. Look at the number of standards schools are expected to teach within the time allowed. Then do the math. Here's one example. If a school has 45-minute class periods for 180 days a year, teachers have a maximum of 135 hours of teaching time per course. The actual time for teaching is shorter, and many districts I've worked with estimate that no more than 80% of that time is usable. Early dismissals, assemblies, testing, and other interruptions eat into instructional time. Using this estimate, schools are left with 108 hours of class time. If each course were divided into six-hour instructional days, the teacher would have 18 days of total class time per course. This means three to four weeks to teach algebra to entering 9th graders who may be way behind in math. Or, expressed another way, a student who is required to study four years of math in order to graduate will actually have three to four months to learn all of the math standards. Enough time to meet the volume of expectations, especially for struggling students? I think not. Policies involving time develop in tidy silos, but in practice they become more like a stewpot. Huge numbers of policies involve time. In fact, most policies involve time--some overt, others not. If you look closely, you'll find that policies generally require someone to do something that takes time--school time, staff time, student time, district time. Viewed in isolation, each policy can appear quite reasonable, yet when they interact with one another at the site level, a very different reality emerges. Let's look at three distinct policies that existed in one district--teacher work load, course requirements, and class size caps. The contract required no more than 6 1/2 hours in the student day, with at least 45 minutes for daily prep and an additional 45 minutes for lunch. Students are required to take eight courses per year. When these two policies were combined, the schools ended up with one schedule choice--a block schedule. In a block schedule, teachers teach only 75% of the time, and class sizes tend to go up. Yet the union contract also specified a maximum class size of 25, a number that would have required an impossible increase in the budget formula. Thus, district personnel had to decide which policy to fail to implement or to change because the time requirements became impossible when all of the policies were combined. Policies are aligned with two competing goals. …

High-stakes math tests: How No Child Left Behind leaves newcomer English language learners behind

The No Child Left Behind Act establishes federal education policy for the United States, with a heavy focus on accountability through high-stakes testing. Provisions specific to English language learners (ELLs) include the mandate for their inclusion in state math tests, even for newcomer students enrolled for less than one year. Most ELLs take their state math tests in English with few, if any, accommodations. This study provides an analysis of this policy through the case of fifth grade newcomer Cambodian students in a Texas middle school. A linguistic analysis reveals that the language demands of the state math test far exceeds the language demand of the math work the students were able to do in school (with assistance). A content analysis of the fourth grade math textbooks used in Cambodia and the Texas school district reveals the American textbook had a much higher degree of alignment with Texas math standards, and far exceeded the Cambodian textbook in terms of depth and breadth of mathematical concepts and math problems for students to practice newly learned concepts. We argue that these analyses provide strong evidence that the Cambodian newcomer students were not afforded an opportunity to learn grade-level content before the test, and that the language demands of the test are beyond reasonable for newcomer students. We conclude with a discussion of implications for needed changes to U.S. federal policy which account for the linguistic demands posed by math tests, and which provide students opportunities to learn expected math content before taking high-stakes tests.

Creationism and Evolution: It's the American Way

The recent ruling in the Kitzmiller v. Dover court case that intelligent design is a form of religion and cannot be taught alongside evolution in science classes in US public schools garnered worldwide attention. But why is the antievolution movement so powerful in the United States?

An Ammunition Dump?

WHEN EDUCATORS open their Fibber McGee's closets of past reforms, a pile of silver bullets will spill out onto the floor. For at least the past 20 years, the sense of public confidence in public education has been fed by an arsenal of such quick, often creative, but largely unsubstantiated remedies for turning schools and kids around. And the pile became much larger this fall. The highest-caliber bullet of all--the No Child Left Behind (NCLB) Act--landed on top of the pile. But it was not the only presumed salvation of the public schools to lose some of its luster recently. Collecting data about these failed silver bullets can often tell us more than we've known before. The first National Assessment of Educational Progress (NAEP) report on reading and math scores that fairly reflects changes under NCLB showed essentially that, so far, this silver bullet is pretty much of a dud. Reading scores were flat, and math scores were up only a bit. Despite statements by the Bush Administration that sought to put a happy face on the findings, the NAEP data showed that progress had been better before NCLB became law than it has been since it was enacted. The data also indicate something that few pundits seem willing to acknowledge. Since the passage of NCLB, about four years ago, changes in the demographics of the student population have accelerated, and schools all over the country are feeling the impact of more English-language learners than ever before. It is to the schools' credit that NAEP reading scores--in the early grades, at least --did not go down. Moreover, the very slight improvement in math scores could be attributed partially to the fact that math test items in the early grades, and even to some extent on the eighth-grade tests, do not require advanced reading skills. (Another possible explanatory factor is that the efforts of the National Council of Teachers of Mathematics have given us some semblance of national math standards and that these standards have been in various stages of implementation for more than 15 years.) The NAEP data also underscore the accident-of-birth unfairness built into state accountability systems. The erratic performance of students on state measures of achievement, compared to their performance on NAEP, demonstrates that students in some states are being held accountable for much higher levels of performance than students in other states. And no state has made much progress, as revealed in the NAEP scores. Some 20 states claim to have made progress on their own eighth-grade reading assessments between 2003 and 2005, but only three showed any progress at even the basic level on NAEP. And, according to the Thomas B. Fordham Foundation, only eight of 25 states that did announce progress on their own fourth-grade reading tests had more than one-third as much progress at the basic level on NAEP. As might be expected, proponents and opponents of charter schools took the very same data and came up with different analyses. The National Alliance for Public Charter Schools found them to be making more progress than other schools; the American Federation of Teachers found them to be making less, even after accounting for student-level racial/economic variables. Another silver bullet to land atop the pile of spent ones is the grandiose array of promises made by Edison Schools, Inc. In the immortal tradition of Edward R. Murrow's series You Are There, I was there when Tennessee entrepreneur Chris Whittle announced that he would launch a network of at least 100 new schools that would rival public schools in terms of technology and student achievement. …

Stop the Insanity!

Who says always has to be drudgery? Sarah Butzin, the founder of the Institute for School Innovation, proposes learning as a way to give children time to play and develop, even as they pursue high standards. WHAT HAS happened to common sense in this era of No Child Left Behind? What makes anyone believe that talking louder makes a deaf man hear? Albert Einstein reputedly defined insanity as doing the same thing over and over and expecting different results. Yet that is what I see happening in elementary schools today. In response to high-stakes testing and higher standards for even the most challenging students, schools have responded by talking louder. They haven't changed the way they teach. Instead, they push more papers in front of the kids, keep them off the playground, and take away music and art. Here in Florida, they make kids repeat third grade if they can't keep up (an estimated 43,000 failed in 2003) and send them to summer reading camps to cram in a little more knowledge. Everything we know about human nature and child development should tell us to pause. Children need time to play and time to develop at a natural pace. Every parent knows that not all infants learn to walk by age 1 and talk by age 2. Neither do all first-graders learn to read at the stroke of midnight on their sixth birthday. Young children need security and encouragement, not pressure and humiliation if they can't keep up. Yet at the same time, there is a legitimate need for rigorous academic standards, high expectations, and reliable assessments to gauge each child's progress so that he or she is not left behind. The stakes are indeed high. Children of the 21st century absolutely need much higher literacy and mathematical skills than their grandparents. The world has been transformed through technology and global competition. So how do you lay a foundation for solid academic skills without killing childhood? One thing is certain. One teacher working solo with a classroom of 20 to 30 children cannot do it in one year -- actually 180 school days. And when you subtract all the non-instructional school time, including getting to know the children and playing catch-up from the previous grade, that 180 days really translates to about 100 days. In essence, one teacher has a little over three months to teach to high standards in reading, writing, math, science, and social studies. What's the solution? Add more days to the school year? Reduce class size? Buy more computers and newer textbooks? Pay for after-school tutors and summer reading camps? Nope, those ideas have all been tried, and they don't work. Plus, they are very expensive remedies. There is another option, which I call learning. It takes a team approach to instruction and gives teachers the time and techniques to meet higher standards without stifling young children's natural desire to play and explore. Children can work at their own pace in diversified classrooms, using a variety of modes that best meet their individual styles. They can be challenged without being coerced. And there are benefits for teachers as well. They become less isolated and stop taking the blame for the failure of the system. It's not their fault. Teachers are being asked to do the impossible -- meet higher standards using the old grade school system in which one teacher is expected to do it all and pass the kids along through first grade, second grade, third grade, and so on. By the time children reach fifth grade, it's not surprising that large numbers of them have fallen by the wayside, especially if they lack a support system at home. For the past 15 years, I've been working on developing a triangulated system that incorporates best practices from the past along with newer innovations such as computers and the Internet. It's really a system of retro-techno teaching. …

No Child Left Behind: The Case of Roosevelt High School

Mr. Ambrosio describes how the punitive effects of NCLB are harming a that was providing an impressive array of services to support its low-income, ethnically diverse student body. LET ME tell you the story of one and how the No Child Left Behind (NCLB) Act has been affecting its teachers and the educational opportunities and outcomes of its students. Roosevelt High School, located in North Portland, Oregon, has the most ethnically diverse student population in what is the largest district in the Pacific Northwest. It serves about 850 students from 33 countries who speak 26 languages. Roosevelt High is situated in a low-income area of a state that has the highest unemployment and second highest hunger rate in the nation. Students often miss meals, work after to help support themselves or their families, and move several times during the year because of evictions, job loss, or domestic violence. Historically, North Portland has been a dumping ground for Portland's industrial waste. It was once the site of cattle yards and slaughterhouses that poured refuse into the Columbia Slough, a waterway running through the St. John's neighborhood. In the morning, the air around the is often fouled by fumes emitted from a nearby waste treatment plant and from pulp mills. Many students suffer from asthma and other respiratory conditions.1 Since 2001, when Congress reauthorized the Elementary and Secondary Education Act in the form of NCLB, state policies of mandatory standardized testing have been codified, complete with enforcement mechanisms, at the national level. For states that wish to receive federal funds under NCLB, the law requires annual testing in reading and math in grades 3 through 8 and at least once in grades 10 through 12. Tests in science - required at least once in each of the grade spans from 3 through 5, 6 through 9, and 10 through 12 - will begin in 2007-08. The Oregon Department of Education already issues annual school report cards for every in the state. And these reports list a school's performance on mandatory standardized tests in reading, writing, and math, which are administered to students in grades 3, 5, 8, and 10 and allow students who meet the standard to earn a Certificate of Initial Mastery in grade 10. The Baseline: 2001-02 In 2001-02, Roosevelt was rated unacceptable in student performance, based on the results of the state testing and on a student behavior measure, which is a combination of attendance and dropout rates.2 In accordance with NCLB, Roosevelt was designated a low-performing and labeled as needing improvement. Under the law's testing and sanctions time line, Roosevelt was given two years to make Adequate Yearly Progress (AYP) - a yearly goal calculated as the ever-increasing percentage of students in all major subgroups (racial and ethnic minorities, English-language learners, low-income students, and special education students) who must score proficient in reading and math if the is to reach 100% proficiency by 2014. Those that fail to meet AYP for two years are subject to an escalating series of punitive sanctions. But schools that failed to meet these targets for two or more years under the previous federal law are subject to penalties under the new law beginning in 2003-04. Because Roosevelt falls into this category, it has been subjected to a series of corrective actions at an accelerated pace - a year before they are required by NCLB.3 As of the spring of 2004, 40% of Roosevelt's students must meet or exceed state standards in reading, and 39% must do so in math. In the spring of 2003, 28% of Roosevelt's students met the reading standard, while 32% reached the math target. The district's Portland Schools Improvement Plan, however, raises the bar much higher. Roosevelt must get 68% of all students to meet the reading standards and 60% to meet the math standards in two years. …

Can We Reach Definitive Conclusions in Mathematics Education Research?

The reform mathematics curricula present students with problems that cannot be solved using routine methods. Ms. Latterell and Mr. Copes wonder about the best ways to teach students to solve such problems -- a research question that leads them into a classroom where a teacher is refereeing an animated discussion about algebra. WE ARE hearing a lot of noise these days about wars being waged over the content and pedagogy of new math curricula. These disagreements echo similar discussions in other fields: between whole language and phonics in reading, between prophetic versus priestly in the social sciences, between positivists and antipositivists in general. Can we ever decide which of these approaches is better? One way in which the so-called reform curricula in mathematics differ from the more traditional curricula is in their approach to teaching problem solving. Many who have taken mathematics courses remember solving lots of problems. is 3 + 2? Solve the equation 3x + 17 = 2 for x. The National Council of Teachers of Mathematics (NCTM), however, defines problem solving as engaging in a task for which the solution path is not routine.1 Problems in symbol manipulation can be solved by routine methods, and so would not constitute problem solving in the NCTM sense. Those notorious word problems, problems with practical applications, or puzzles more nearly match the NCTM criterion. There are no routine methods by which a student (or a computer) could solve these problems. Certainly, the traditional curricula do not eschew problem solving in the NCTM sense. Indeed, almost all curricula claim to be satisfying the new math standards as they are spelled out in Principles and Standards for School Mathematics. But the differences in how to teach problem solving are very real. What are those differences, and how should problem solving be taught? Let us begin to address these questions by considering one seventh-grade teacher's first-person description of an attempt to teach problem solving. Classroom Episode One I wrote the problem on a transparency as students were coming into the room, and I put it on the overhead projector as they got into their base groups and signed in. The problem was: Represent as an equation the claim that there are six times as many students as teachers in this school. Use S for the number of students and T for the number of teachers. I said, Please work on this for a few minutes in your groups. As I circulated, I found that all but one group had written 6S = T. Then I overheard Chris saying, Wait a minute -- if S was 100, then T would be 600, and that's not right. The group began to argue heatedly. I gave Chris a thumbs-up sign to keep the argument going and sent representatives from other groups to eavesdrop on the discussion. Soon the entire class was in turmoil. Different Approaches to Teaching Problem Solving Is using a problem that provokes controversy like this a good way to teach problem solving? Before we consider that question, let us look at the differences between reform-oriented and traditional approaches to teaching problem solving in mathematics. The restrictions of space demand that we oversimplify. Traditional mathematics curricula are based on the walk before you run philosophy. Until you know how to add 3 + 2, there is no way you can solve a problem such as You have 3 apples and are given 2 more; how many do you have? In these curricula, students learn the and then see how to apply them. That is, students must learn mathematics skills before they learn problem solving. Reform curricula, in contrast, are based on the idea that students retain basic mathematics best while trying to use them to solve engaging problems. Students who are set to work on interesting problems they do not know how to solve can be quite receptive to learning and problem-solving techniques on a need-to-know basis. …

Raising Middle School Math Standards without Raising Anxiety

(2003). Raising Middle School Math Standards without Raising Anxiety. Middle School Journal: Vol. 34, No. 4, pp. 27-35.

Community Resources and Determinants of the Future Health of Manitobans

Life history studies in health show that some of the key determinants of health inequalities lie in biological and social experiences at the earliest times of life. The objectives of this research were to describe the regional distribution of childhood determinants of adult health, such as school achievement, and the environments which contribute to their development. Using Manitoba data from the National Population Health Survey, the National Longitudinal Survey on Children and Youth, the Department of Education, Training and Youth, the Department of Family Services and Housing, the Library Association website and the Agriculture and Food website, the regional distribution of Grade 3 standards test scores and neighbourhood resources such as child care services, libraries, sports participation and food costs were determined for 12 Regional Health Authorities and 12 Winnipeg Community Areas, ranked by a measure of population healthiness, the premature mortality rate. Findings were also reported by income level and larger geographic regions. Children living in neighbourhoods with less healthy populations were more likely to have poorer school performance, as indicated by Grade 3 math standards test scores. They were-also more likely to change schools, less likely to participate in sports, and had decreased access to affordable food and licenced day care. They had similar access to library books as children living in more healthy neighbourhoods, although book lending rates were not measured. We documented regional variation in the availability of resources to support healthy childhood development.

Using Peg- and Keyword Mnemonics and Computer-Assisted Instruction to Enhance Basic Multiplication Performance in Elementary Students with Learning and Cognitive Disabilities

This paper describes the effectiveness of Memory Math, a multimedia software program developed to teach students with learning and cognitive disabilities to effectively use a peg- and keyword mnemonic strategy to learn basic multiplication facts. According to the math Standards (National Council of Teachers of Mathematics, 2000), accuracy with basic facts is a critical element in the development of new skills and achievement in higher levels of math. One avenue for improving accuracy on basic skills is computer-assisted instruction (CAI). CAI offers an alternative to the teacher-intensive coaching often required to facilitate self-directed performance on basic skills. This paper demonstrates that CAI provides an effective mechanism for teaching students a mnemonic memory strategy to increase their independent performance and accuracy on tasks of basic multiplication.