THE IMPACT OF THE NATIONAL NUMERACY STRATEGY IN YEAR 4 (II): TEACHING

The Nuffield Year 4 project set out to examine selected aspects of the impact of the National Numeracy Strategy (NNS) in primary schools by using comparable data on Year 4 pupil attainment and teaching collected in 1997/98 and 2001/02, two years before and two years after the introduction of the Numeracy Strategy. In this second paper we address the following questions:

• How and to what extent has numeracy teaching in Year 4 changed?

• Why have these changes occurred?

• How can we improve future implementation of reforms?

• How can we inform continuing professional development?

     

THE IMPACT OF THE NATIONAL NUMERACY STRATEGY IN YEAR 4 (I): ATTAINMENTAND LEARNING

The Nuffield Year 4 project set out to examine selected aspects of the impact of the National Numeracy Strategy (NNS) in primary schools by using comparable data collected from 35 schools in 1997/98 and 2001/02 as part of the Leverhulme Numeracy Research Programme. In this first paper we report on changes in attainment using a specially designed test of numeracy administered in October and June. While numeracy attainment rose during the period of the introduction of the NNS, the effect was small and it varied in relation to different aspects of the curriculum. The results of low attainers fell on average, as did results in over a third of schools. The amount of progress made over Year 4 was similar in 2001/02 and in 1997/98. Reasons for these changes are explored.     

Secondary Options and Post‐secondary Expectations: Standards‐based Mathematics Programs and Student Achievement on College Mathematics Placement Exams

Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core‐Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate, however, much less is known about how prepared these students are for post‐secondary education. Therefore this study involving students within one tracked school district used multiple linear regression to examine the role of differential experience within two secondary Standards‐based mathematics programs, gender, and prior mathematics achievement on college algebra and calculus readiness placement test scores. Results show that there are no significant differences between students who had completed three and four years of the CPMP curriculum. UCSMP students with four or five years of experience significantly outperformed CPMP students on both assessments. Prior achievement was a significant predictor of student achievement on both examinations. Male students outperformed female students on the algebra placement exam. Students who had studied from both CPMP and UCSMP significantly outperformed students who had studied from CPMP for four years on the calculus readiness examination.     

Attitude toward mathematics among the students at Nazarbayev University Foundation Year Programme

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender, specialization and final high school score in mathematics are collected. The number of valid returned questionnaires is 108. There are 55 males, 53 females, 73 Mathematical-Physics (MP), 22 Biology-Chemistry (BC) and 13 International Relations-Economics (IRE) students. Generally, they have a positive attitude toward mathematics, with the score mean and standard deviation are 3.999 and 0.531 out of five, respectively. We confirm a hypothesis on a positive correlation between previous high achievement in mathematics and favorable attitude toward it. The correlation value is r = 0.300, its effect size is medium and it is extremely significant (p-value = 0.0008 < 0.001). There is no significant difference between male and female students in terms of their attitude toward mathematics (t = 0.6804, p-value = 002489 > 0.05). There is a very significant difference between students who specialize in IRE and MP in terms of their attitude toward mathematics (F(2, 105) = 5.6848, p-value = 0.0045 < 0.01).     

Numeracy task design: a case of changing mathematics teaching practice

Over the last 15 years, numeracy has become more and more prominent in curriculum initiatives around the world. Yet, the notion of numeracy is still not well defined, and as such, often not well understood by the teachers who are charged with the responsibility of helping our students to develop their numeracy skills. In this article I explore the work of a team of mathematics teachers brought together for the purpose of developing a set of numeracy tasks for use within district wide numeracy assessments. Results indicate that these teachers’ experience designing these tasks, and pilot testing them in their own classrooms, propelled them to make massive changes in their own mathematics teaching practice. Through a lens of Rapid and Profound Change (Journal of Mathematics Teacher Education 13:411–423, 2010) the mechanism and catalyst behind these changes are revealed.     

Socio-economic status and mathematics achievement in China: a review

Mathematics education is a cultural-specific social activity. China, as a developing country with a long history and a unique culture, has the largest number of teachers and students in the world. Hence, it is of significance to explore the issue of the impact of socio-economic status (SES) on mathematics education within the Chinese context. However, investigations aiming to address this issue are relatively rare. This study was designed to examine the relationship between Chinese students’ SES and their mathematics achievements. Results reveal that Chinese students’ SES exerts significant influence on their mathematics achievements, and several important constituents of SES, such as parents’ education and family income, stand out among others. In this paper, the cultural causes of the influence are discussed, together with a general introduction to the social and educational context. These could partly explain the empirical results, along with factors such as the values of education in traditional Chinese culture and the current important status of mathematics in modern society as well as Chinese school curriculum materials’ effect on students’ mathematics achievements. The economic and social situation in China, especially the imbalanced distribution of educational resources between and within the urban and rural areas, could magnify the role of SES in mathematics achievements. Finally, the future direction of measuring and interpreting the SES’s influence on mathematics achievement in the Chinese context is also discussed.     

To what extent are students expected to participate in specialised mathematical discourse? Change over time in school mathematics in England

ABSTRACT

From a discursive perspective, differences in the language in which mathematics questions are posed change the nature of the mathematics with which students are expected to engage. The project The Evolution of the Discourse of School Mathematics (EDSM) analysed the discourse of mathematics examination papers set in the UK between 1980 and 2011. In this article we address the issue of how students over this period have been expected to engage with the specialised discourse of school mathematics. We explain our analytic methods and present some outcomes of the analysis. We identify changes in engagement with algebraic manipulation, proving, relating mathematics to non-mathematical contexts and making connections between specialised mathematical objects. These changes are discussed in the light of public and policy domain debates about ‘standards’ of examinations.     

The Mathematics Writer's Checklist: The Development of a Preliminary Assessment Tool for Writing in Mathematics

The use of writing as a pedagogical tool to help students learn mathematics is receiving increased attention at the college level ( Meier & Rishel, 1998 ), and the Principles and Standards for School Mathematics (NCTM, 2000) built a strong case for including writing in school mathematics, suggesting that writing enhances students' mathematical thinking. Yet, classroom experience indicates that not all students are able to write well about mathematics. This study examines the writing of a two groups of students in a college‐level calculus class in order to identify criteria that discriminate “;successful” vs. “;unsuccessful” writers in mathematics. Results indicate that “;successful” writers are more likely than “;unsuccessful” writers to use appropriate mathematical language, build a context for their writing, use a variety of examples for elaboration, include multiple modes of representation (algebraic, graphical, numeric) for their ideas, use appropriate mathematical notation, and address all topics specified in the assignment. These six criteria result in The Mathematics Writer's Checklist, and methods for its use as an instructional and assessment tool in the mathematics classroom are discussed.     

Development and Analysis of a Mathematics Aptitude Test for Gifted Elementary School Students

This paper describes the development and preliminary analysis of a mathematical test targeted for high mathematical ability elementary school students, the Stanford Education Program for Gifted Youth (EPGY) Mathematical Aptitude Test (SEMAT). A version was administered to 248 students, 9–11 years old, in EPGY. The SEMAT was developed because no other satisfactory test was designed or normed for this population. Most standardized tests assess mathematics proficiency for the general population so that gifted students' scores cluster in the few top percentiles. The SEMAT discriminated among this extreme upper end. Item response theory determined proficiency estimates, which were then used as scores to predict various outcomes in EPGY. The SEMAT proved to be a strong predictor of acceleration in EPGY.     

Students' Perceptions of Single‐Gender Science and Mathematics Classroom Experiences

While participating in single‐ and mixed‐gender science and mathematics classes, ninth‐grade urban high school students' (n= 118) academic self‐concept, self‐efficacy, and school climate perceptions were examined. Their perceptions were measured quantitatively from the Fennema‐Sherman Mathematics (modified for Science) Attitude and the Patterns of Adaptive Learning scales. Five factors arose from each instrument: confidence/efficacy, utility, instruction, climate, and anxiety/performance avoidance. Comparative factor analysis of the science‐modified Fennema‐Sherman Scale showed similar constructs within the mathematics scale. Our findings are congruent with reports concerning single‐gender classrooms that find few significant differences in students' attitudes toward science and mathematics, or classroom climate, with regard to single‐gender classes. Lastly, our results supported three structural equation models for the hypothesized factors from each instrument.     

Developing the roots of modelling conceptions: ‘mathematical modelling is the life of the world’

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a Modelling conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity, actions and conceptions of both modelling and mathematics that these beginners to modelling displayed. Understanding the conceptions of mathematics that students might hold or be developing and how these can be influenced in early schooling are essential ingredients in any plans for introducing modelling seriously into primary school classrooms. The majority of the students (22/25) were identified as displaying a developing conception of modelling as a way of problem handling. The three other students displayed the developmental roots of a way of understanding the world conception of modelling. These three students also displayed a Modelling conception of mathematics with one showing indications of developing towards a Life conception of mathematics.     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

Investigating changes in high-stakes mathematics examinations: a discursive approach

ABSTRACT

This article focuses on the theoretical-methodological question of how to identify reform-induced changes in school mathematics. The issue arose in our project The Evolution of the Discourse of School Mathematics (EDSM), in which we studied transformations in high-stakes examinations taken by students in England at the end of compulsory schooling. We have adopted a conceptualisation that draws on social semiotics and on a communicational approach, according to which school mathematics can be thought of as a discourse. Methods of comparing examinations of different years developed on the basis of this definition enable identification of subtle disparities that are nevertheless significant enough to make an important difference in students’ vision of mathematics, in their performance and, eventually, in their ability to cope with problems that can benefit from the use of mathematics. In this article, we present these methods and argue that they have wider application for comparative studies of school mathematics.     

Predicting performance in a first engineering calculus course: implications for interventions

At the University of Louisville, a large, urban institution in the south-east United States, undergraduate engineering students take their mathematics courses from the school of engineering. In the fall of their freshman year, engineering students take Engineering Analysis I, a calculus-based engineering analysis course. After the first two weeks of the semester, many students end up leaving Engineering Analysis I and moving to a mathematics intervention course. In an effort to retain more students in Engineering Analysis I, the department collaborated with university academic support services to create a summer intervention programme. Students were targeted for the summer programme based on their score on an algebra readiness exam (ARE). In a previous study, the ARE scores were found to be a significant predictor of retention and performance in Engineering Analysis I. This study continues that work, analysing data from students who entered the engineering school in the fall of 2012. The predictive validity of the ARE was verified, and a hierarchical linear regression model was created using math American College Testing (ACT) scores, ARE scores, summer intervention participation, and several metacognitive and motivational factors as measured by subscales of the Motivated Strategies for Learning Questionnaire. In the regression model, ARE score explained an additional 5.1% of the variation in exam performance in Engineering Analysis I beyond math ACT score. Students took the ARE before and after the summer interventions and scores were significantly higher following the intervention. However, intervention participants nonetheless had lower exam scores in Engineering Analysis I. The following factors related to motivation and learning strategies were found to significantly predict exam scores in Engineering Analysis I: time and study environment management, internal goal orientation, and test anxiety. The adjusted R² for the full model was 0.42, meaning that the model could explain 42% of the variation in Engineering Analysis I exam scores.     

Mathematics for All: Perspectives and Promising Practices

The Core-Plus Mathematics Project (CPMP, 1995) is one of four comprehensive curriculum development projects that, in 1992, were awarded 5-year grants by the National Science Foundation to design, evaluate, and disseminate innovative high school curricula that interpret and implement the recommendations of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics ( NCTM, 1989 ) and Professional Standards for Teaching Mathematics ( NCTM, 1991 ). This article describes CPMP perspectives on a new curriculum organization for high school mathematics, identifies implications of these perspectives for promoting access and equity for all students, and reports some of the supporting oral data from an ongoing formative evaluation of the curriculum.     

Reading mathematics for understanding—From novice to expert

As students progress through the college mathematics curriculum, enter graduate school and eventually become practicing mathematicians, reading mathematics textbooks and journal articles appears to become easier and leads to increased proficiency and understanding. This study was designed to begin to understand how mathematically more advanced readers read for understanding in mathematical exposition as it appears in textbooks compared to first-year undergraduate students. Three faculty members and three graduate students participated in this study and read from a first-year graduate textbook in an area of mathematics unfamiliar to each of them. The observed reading strategies of these more mathematically advanced readers are compared to observed reading strategies of first-year undergraduate students from an earlier study. The reading methods of the faculty level mathematicians were all quite similar and were markedly different from those that have been identified for undergraduate students, as well as from those used by the graduate students in this study. A Mathematics Reading Framework is proposed based on this study and previous research documenting the strategies that first-year undergraduate students use for reading exposition in their mathematics textbooks.     

Facing the change and meeting the challenge: mathematics curriculum of Tongwen Guan in China in the second half of the nineteenth century

It is commonly recognized that the second wave of transmission of Western science and mathematics into China took place in the second half of the nineteenth century, thereby starting a process of modernization which has become synonymous with ??westernization?? of the country. In this context mathematics education in China also went through a process of modernization. During this period of great change reformers faced serious challenge and went through a ??mental struggle??. This paper discusses this challenge and mental struggle by taking a close look at the controversy over the establishment of Tianwen Suanxue Guan (School of Astronomy and Mathematics) in Tongwen Guan (School of Combined Learning), one of the schools of Western learning at the time. The attempt to integrate Western mathematics with Chinese traditional mathematics is also discussed through the study of some questions sampled from examinations and students?? homework assignments of this school.