National Mathematics Standards Research Articles

Preparing Secondary Mathematics Preservice Teachers for Rural Schools in Colombia

AbstractThis article describes a qualitative research case study that aimed to explore the complexity levels and types of mathematical thinking and national mathematics standards that a group of preservice teachers (PSTs) used to write mathematics word problems for secondary school students. The context was a teacher preparation course at a public university located in a rural region in Colombia, South America. The collected data included PSTs’ community reports, audio recordings of small-group discussions, and mathematics word problems. The data analysis process encompassed inductively created codebooks, several rounds of coding, and the inter-rater technique. The findings of the study demonstrated that most word problems written by the PSTs aligned with a few national mathematics standards and different potential levels of mathematical thinking. However, there was a disconnect between these levels of mathematical complexity and the types of funds of knowledge identified. The article ends by sharing implications for mathematics teacher education and suggestions for future research.

Writing in Mathematics: A Synthesis of Evaluations, Interventions, and Surveys

The national mathematics standards in the United States focus a large amount of emphasis on the function communication plays as a component of mathematical thinking. This is because communication is essential to mathematical reasoning. Writing is one of the many ways people communicate; other means include talking and texting. We did a synthesis in order to analyze the empirical research that has been done on the subject of mathematics in order to get a better knowledge of how students write about mathematics. This was done to better understand how students approach the subject. We discovered 29 studies that included a mathematics-writing evaluation, intervention, or survey for children in the first through twelfth grades. This research was conducted in a variety of different countries. These studies were carried out in a diverse selection of nations worldwide. They were involved in the inquiry in some capacity. Between the years 1991 and 2015, the results of the full study project were initially published for the first time in textual format in academic journals. Although most of the math problems required the students to provide written explanations, less than half of the evaluations used a rubric to rate the solutions provided by the students. Even though the vast majority of the issues required written explanations, they were nonetheless completed. More than half of the therapies mentioned the practice of publishing mathematical material in mathematics journals. This was mentioned in just over half of the treatments. Even fewer clinical studies provided quantitative data on the medicines being explored and their level of success. There are not many intervention studies that directly teach children how to write mathematical expressions, but those that do exist are few. The survey results showed that the vast majority of professors claimed that they only occasionally use mathematical writing in their lectures, even though most students claimed that they enjoy writing about mathematics. However, the overall quality of the studies varies, indicating the need for further empirical research; the findings of a number of studies indicate the potential that mathematical writing serves more than one purpose.

Sleep in New Zealand children aged 7-9: associations with ethnicity, socioeconomic status, and achievement in reading and mathematics.

The aims were (1) to investigate differences by ethnicity and socioeconomic status (SES) in objective measures of sleep in children aged 7-9 years and (2) determine whether measures of sleep predict child achievement in reading or mathematics after controlling for ethnicity and SES. Four groups of parent-child dyads were recruited: Māori, low-SES schools (n = 18); Māori, high-SES schools (n = 17); New Zealand European, low-SES schools (n = 18); New Zealand European, high-SES schools (n = 17). Child sleep was measured by actigraphy. Parents and teachers reported child daytime sleepiness and behavior, and children completed a self-report of anxiety symptoms. Teachers also reported on child achievement in reading and mathematics. Children from low-SES schools went to bed later on school nights (F[1,68] = 12.150, P = .001) and woke later (F[1,68] = 15.978, P < .001) than children from high-SES schools but had similar sleep duration. There were no differences related to ethnicity. Children from low-SES schools were almost 3 times more likely to be below national standards for mathematics. Children not meeting academic standards in mathematics had a later sleep start time, lower sleep period efficiency, and a decreased total sleep time. However, when SES and sleep period efficiency were modeled together neither were found to significantly influence achievement in mathematics. In this study, SES influenced sleep timing but not the quality and quantity of sleep in 7- to 9-year-old children, and a significant independent effect of sleep efficiency on learning could not be demonstrated.

Inclusion and standards achievement: the presence of pupils identified as having special needs as a moderating effect on the national mathematics standards achievements of their classmates

ABSTRACT This article investigates the relationship between the achievement level of students in classes and the presence of students identified as having special needs in inclusive settings. In particular, it examines whether the presence of students with special educational needs in inclusive classrooms has an effect on the national mathematics standards achievement of their fellow students. In order to do so, the national standard scores of approximately 75,000 fourth graders in mathematics were used as dependent variable in multi-level regression modelling. As independent variables at class level the number of students with special needs and at the individual level socio-economic, cultural and ethnic background variables were used together with gender and age. Results show only a very small effect of the presence of students with special needs on the national mathematics standard scores of their classmates. The effect can be either positive or negative depending on further class conditions.

Computation Error Analysis: Students With Mathematics Difficulty Compared To Typically Achieving Students

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 third-grade students on a measure of mathematics computation. Results indicated that using the wrong operation was the most common identifiable error for all students. Students with MD had similar accuracy rates for item categories (e.g., addition items) compared to typically achieving students, but students with MD consistently had more variability in incorrect item responses. This study has implications for efficacious computation instruction for students in the elementary grades.

Does Early Algebraic Reasoning Differ as a Function of Students' Difficulty with Calculations versus Word Problems?

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty.

Children’s views about geometry tasks in Māori-medium schools: Meeting Ngā Whanaketanga Rumaki Māori pāngarau (National Standards in mathematics)

Children’s views about geometry tasks in Māori-medium schools: Meeting Ngā Whanaketanga Rumaki Māori pāngarau (National Standards in mathematics)

Assessing the mathematical thinking of young children in New Zealand: the initial school years

This paper provides an overview of assessment policy and practice in mathematics for early years classrooms in New Zealand between 1993 and the present day. It describes the introduction of school entry assessment for children starting school at age five. A numeracy initiative, the Numeracy Development Projects (NDP), for students in Years 1–10 was developed a decade ago out of a pilot project with Count Me In Too. Most recently, a consultation process was undertaken as part of introducing national standards in mathematics for students in Years 1–8. The paper also presents some data from assessments by teachers as part of the NDP initiative, showing the complex relationships between number knowledge and strategy for students in Years 1–4. The paper concludes by asking that individual diagnostic interviews to enable the provision of quality teaching continue to be supported as part of the introduction of national standards.

The Impact of an Ongoing Professional Development Program on Prekindergarten Teachers' Mathematics Practices

Mathematics is a natural part of daily life for young children as they explore and investigate the world around them. To build on these experiences, and to begin establishing a mathematical foundation, early childhood educators must not only be knowledgeable about mathematical concepts, they must also be aware of the most developmentally appropriate ways in which to teach these concepts to young children. After participation in an ongoing professional development program, specifically targeting teachers of prekindergarten children in public school, Preschool Programs for Children with Disabilities (PPCD), Head Start, and child care settings, teachers reported positive changes in math practices. Specifically, teachers reported a stronger alignment to national mathematics standards and increased awareness pertaining to developmentally appropriate mathematics practices as they apply to early childhood classrooms. Teachers reported a shift towards more hands-on activities and a shift away from the use of worksheets in their prekindergarten classrooms. Implications from this study suggest that ongoing professional development that is designed to meet the specific needs of early childhood educators can have a positive impact on reported mathematics content knowledge and instructional practices.

Origami Instruction in the Middle School Mathematics Classroom: Its Impact on Spatial Visualization and Geometry Knowledge of Students

Within the study of geometry in the middle school curriculum is the natural development of students’ spatial visualization, the ability to visualize two- and three-dimensional objects. The national mathematics standards call specifically for the development of such skills through hands-on experiences. A commonly accepted method is through the instruction of Origami, the art of paper folding. This study focused on Origami’s impact as a teaching tool in the middle school mathematics classroom. The effects of Origami instruction on a group of seventh grade mathematics students’ (n = 56) spatial visualization skills and level of geometry understanding were investigated using a pre-test/post-test quasiexperimental design. A 2 (group) × 2 (gender) factorial method was used on gathered data via three separate spatial tests (Card Rotation, Paper Folding, and Surface Development Tests) and a subset of released National Assessment of Educational Progress questions. After controlling for initial differences, an analysis of covariance revealed a significant interaction effect between group and gender for one of three spatial visualization tests. For geometry knowledge, no significant differences were found. Results imply that Origami lessons blended within mathematics instruction are as beneficial as traditional instruction in building an understanding of geometric terms and concepts, though the approach affects the spatial ability of males and females differently.

Gender differences in the mathematics achievements of German primary school students: results from a German large-scale study

In Germany, national standards for mathematics for the end of primary school were established in 2004. In the present study, data were collected to evaluate these standards, and were used to compare the mathematical skills of girls and boys. Many studies have shown that gender differences are strongest at the highest levels of education. The findings from primary school are less consistent. Thus, in our study we analyzed achievement differences in a sample of approximately 10,000 third and fourth graders, representative of the German elementary school population. Gender-specific competencies were compared in the different content domains, both for the general mathematical competence, and for the cognitive levels of the tasks. Overall, boys outperformed girls, but substantial variation was found between the content domains and general mathematical achievement. Differences were higher in grade three than in grade four. The proportion of boys in the classroom did not appear to affect the individual level of performance. Analysis of the items on which boys or girls clearly outperformed each other reproduced a pattern of specific item characteristics predicting gender bias consistent with those reported in previous studies in other countries.

Test Scores and Economic Growth

SOMEWHERE around 2000, I observed that, while people argued vehemently that good schools led to improved national economies, there wasn't much in the way of evidence for that contention. And there was certainly one glaring counterexample: Japan. Kids in Japan continued to ace tests, just as they had during Japan's boom years in the 1980s, but the country had been mired in recession or stagnation for a decade. (People now think that 2006 may have been the year that Japan finally started an expansion that will last for more than a quarter or two.) Out of curiosity, I correlated the ranking of countries on the Third International Mathematics and Science Study (TIMSS) with the rankings for global competitiveness issued by the World Economic Forum. The resulting number for about 35 countries was quite small and became negative if I removed the bottom five nations, which were quite low on both rankings. Richard Rothstein and Rebecca Jacobsen's article in the December Kappan observed that the goals for American education have seldom been cast in economic terms. Instead, right from the founding of the nation, they have more often been stated in terms of moral and civic outcomes. The dominance of an economic reference point is new. An aberration, Rothstein and Jacobsen called it. Moreover, the focus on the economy is new elsewhere as well. A Belgian critique of the Programme for International Student Assessment (for details on this critique, see the June 2005 Research column) implied that ranking education systems according to test scores was, well, dumb: Hit parades have been flourishing here for some years: the best schools, the world's best universities, the top-performing research centers, etc. Some 30 years ago this sort of ranking would have produced a smile as we were of the view that the broad and long-term effects of education cannot be reduced to a few trivial indicators and that every education system could be validly understood only by taking account of its history, its aims, and the complexity of its structures. Now, in too many places, people seem to think that a good education means only more math and science so students can compete for good jobs in the global economy. Yet there remains very little evidence of the impact of math and science achievement on the economic growth of nations. This makes the powerful rhetoric calling for ever more math and science somewhat hard to understand. On the day that I began to write this column, for instance, a program called Preparing U.S. Students for the Global Economy took place in Washington, D.C. It featured Sen. Christopher Dodd (D-Conn.), Rep. Vernon Ehlers (R-Mich.), and various pundits from think tanks. A Dodd-Ehlers bill calling for the National Assessment Governing Board to establish national standards in mathematics and science has been introduced in Congress. From a different perspective, in the November 2006 issue of the American Journal of Education, Francisco Ramirez and John Meyer of Stanford University, Xiaowei Luo of the University of Illinois, and Evan Schofer of the University of Minnesota observe the disjuncture between strong rhetoric and weak impact: The dramatic portrait of achievement and development presupposes a world of enormous variation with respect to curriculum, teaching, and achievement. But cross-national investigations actually show considerably less variation with respect to curriculum, teaching, and achievement than expected in policy discourse.... So, from a research perspective, one should not expect robust achievement effects on economic growth. Or, as I have more crassly put it on occasion, education is critical, but among the developed nations differences in test scores are trivial. Ramirez and his colleagues go on to look for data that bear on the relationship between achievement and development. Their principal variables were changes in Gross Domestic Product (GDP) in 38 countries over two 20-year periods, 1970-90 and 1980-2000, and various international test comparisons up to the initial TIMSS in 1995. …

Body Data

Perhaps one of the strongest connections between the national standards in mathematics and science education is their shared emphasis in all these areas: students collecting, organizing, and describing data; constructing appropriate charts and graphs to summarize the data; making predictions based on the data; and testing these predictions and conclusions (NCTM 1989, 2000; NRC 1996).

Curriculum coherence: an examination of US mathematics and science content standards from an international perspective

In recent years, US curriculum policy has emphasized standards‐based conceptions of curricula in mathematics and science. This paper explores the data from the Third International Mathematics and Science Study (TIMSS) to argue that the presence of content standards is not sufficient to guarantee curricula that lead to high‐quality instruction and achievement. An examination of the content topics covered in each grade of a group of six of the highest‐achieving TIMSS countries in mathematics and science shows a pattern in which new topics are gradually introduced, are a part of instruction for a few grades, and then often leave the curriculum as separate topics. This contrasts sharply with mapping of topics in the various US national standards in mathematics and science. Topics enter and linger, so that each grade typically devotes instructional attention to many more topics than is typical of the six high‐achieving countries; in addition, each topic stays in the curriculum for more grades than in the high‐achieving countries. An examination of mathematics and science content standards from 21 states and 50 districts in the US shows a pattern more like that of the US national standards than those of the high‐achieving TIMSS countries. While content standards have become integral to US curriculum development and reform, they have yet to reflect the coherence that is typical of countries that achieved significantly better than the US in the TIMSS study.

National Curriculum Mathematics Tests in England at Key Stage 2: Weights and measures?

This paper reports on a series of statistical analyses carried out on some of the National Curriculum tests in mathematics for 11-year-olds in England. In England all 7-, 11- and 14-year-olds are tested in English, mathematics and science (11- and 14-year-olds only). The tests for 11-year-olds are very high stakes, in that the results are published in a school-by-school basis in newspapers etc. The analyses were prompted by the suggestion (from governmental organisations) that the balance of the curriculum content in the mathematics tests should be changed to accommodate better the require ments of the government-initiated National Numeracy Strategy. The analyses were carried out on two datasets, involving nationally representative samples of 11-year-old pupils. The analyses reveal some interesting patterns of change in the overall outcomes when Handling Data questions were statistically replaced by Number items of various kinds and also some interesting changes at the individual level, which could potentially affect the Level outcomes of a significant number of children nationally. However, the final conclusion reached is that, given an appropriately sized and structured pool of items across the curriculum content areas, tests can be constructed which are of an appropriate level of difficulty and discrimination power and which still allow year-on-year calibration of the national standards in mathematics.

Do We Need NEW National Standards in Mathematics And Science?

As long as teachers have the time, information, and leadership to help make decisions about essential learnings; the opportunity to imple ment changes in curriculum materials and teaching strategies; the abil ity to use assessments to improve student learning; and the support of the community to do their best, our students have a chance to be "first in the world in mathematics and science."