Mathematics engagement in an Australian lower secondary school

The importance of actively engaging in mathematics discourse in order to learn mathematics is well recognized. In this paper, I use Basil Bernstein’s concepts of pedagogic discourse to document and analyse academic learning time of students in Years 8 and 9 at a suburban lower secondary school: in particular, for what proportion of class time students reported being academically engaged, their explanations for this engagement and how they felt about the discourse. It was found that many students had disengaged from mathematical endeavour as a result of the failure of the instructional discourse either to engage students or to serve the purpose of developing discipline-specific content knowledge. The reasons for this relate to the overemphasis on mundane mathematics resulting in some students lacking the cognitive tools to engage with the concepts and having neither the intrinsic nor instrumental motivation to persist with secondary school esoteric mathematics. The implications for mathematics curriculum development are discussed.     

浅议中职学校的数学教学

文章从职业学校数学教学的特殊性出发，分析了职业学校学生的学习特点，及目前数学教材的现状。提出了关于加强职业学校数学教学的个人看法和做法。     

Relationships of some socio-personal factors to mathematics achievement of secondary school and university students in Bophuthatswana

Poor matriculation mathematics results in Bophuthatswana led us to make exploratory efforts to identify possible non-pedagogical factors responsible for such results. Two small scale studies were carried out to examine relationships of socio-personal variables to mathematics achievement. Study 1 looked into the impact of socioeconomic background, school alienation, sex, self-concept and attitude toward mathematics on mathematics performances of secondary school pupils, while study 2 was aimed at examining relationships of dogmatism and mathematics anxiety to mathematics achievement of first-year university students. The data of these two studies invite the attention of mathematics educators to the importance of attitude toward mathematics, mathematics anxiety, and dogmatism in mathematics achievement of Bophuthatswana secondary school and university students.     

A capstone mathematics course for prospective secondary mathematics teachers

This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered pedagogical and assessment strategies. Examples show how students teach the class, complemented by excerpts from student journals containing students?? perceptions of their learning. Preliminary research indicates the effectiveness of this course for preparing future mathematics teachers.     

Teaching students with Down syndrome in regular classrooms in Ghana: views of secondary school mathematics teachers

ABSTRACT

The recent development of making secondary school education free in Ghana has raised concerns about the level of preparedness of teachers to teach students with diverse needs in one classroom. Significantly, mathematics is one of the core areas that the Ghanaian government has prioritised, and it has institutionalised mechanisms to encourage participation by many students. Accordingly, this qualitative study aimed to document the level of preparedness of mathematics teachers to support the teaching of students with Down syndrome in secondary school classrooms. Twenty-seven mathematics teachers from 14 schools, made up of 18 males and nine females, took part in the study. We found that participants were in favour of implementation of inclusive education. However, regarding the prospect of teaching students with Down syndrome, most of the participants thought that the regular secondary school classroom is not a suitable environment for these students to access education, especially due to a number of challenges. The need for the government to support schools with appropriate teaching materials and facilities is discussed extensively.     

与专业结合的中职数学课程设计

中等职业学校的学生大多数学基础较差,程度差异大.普遍对公修课尤其是数学课感到厌倦.把教学课授课内容与其专业相结合不仅能增加学生学习数学的兴趣,更能促进其专业素质的整体提高.     

讨论式教学法在中职数学教学中的应用

从培养学生兴趣,提高学生自主学习能力,设计完整的教学方案,学生讨论交流等方面对讨论教学法在中职数学教学中的应用作了探讨.     

Effects of response options on the mathematics performance of secondary students with emotional or behavioral disorders

ABSTRACT

This study examined the effects of three response options (traditional responding, response cards, and response systems) on the mathematics performance, participation, and time on-task of secondary students with emotional or behavioral disorders (EBD). A three-way crossover design was utilized to evaluate the efficacy of response options in secondary mathematics classrooms. Thirty-three students with EBD attending an urban high school and their teachers served as participants. Results indicated that the use of response cards (white boards) or response systems (ActivResponders) significantly increased students’ mathematics performance, participation, and time on-task when compared to traditional responding. Further, the use of response cards resulted in significant increases in performance and response accuracy over the increases found when using response systems. Social validity data indicated that students and teachers felt they benefited from the use of response cards and systems. Limitations, discussions, and implications for practice and future research are presented.     

Classroom learning environment and motivation towards mathematics among secondary school students in Uganda

This article reports a study of secondary students’ perceptions of mathematics classroom learning environment and their associations with their motivation towards mathematics. A sample of 81 students (19 male and 62 female) in two schools were used. Student perceptions of the classroom environment were assessed using a modified What Is Happening In this Class? (WIHIC) questionnaire. Associations between student perceptions of the learning environment and motivation towards mathematics were examined using simple correlation and multiple regression analyses. The results of the t tests for independent samples indicated a statistically significant difference in student perceptions between different school types. Student perceptions on some of the modified WIHIC scales were statistically significantly associated with student motivation. The results suggest that teachers wishing to improve student motivation towards mathematics, in general, should emphasise the learning environment dimensions that are assessed by the WIHIC. The findings have implications for teachers of mathematics and head teachers, particularly those in secondary schools.     

A case study of integration and destreaming: Teachers and students in an Ontario secondary school respond

The direction that secondary school reform should take has become a contested question in the province of Ontario, Canada, during the 1990s. This case study of one secondary school examines some of the issues surrounding the transition years. Two policies, destreaming and integration, mandatedbythe OntarioMinistryof Education in 1993, and fully implemented by 1995, are examined by means of interview and survey. Administrators, teachers and students commented on the transition from elementary to secondary school. We discuss questions related to destreaming (especially how teachers contend with mixed-ability classes) and integration (with a particular focus on mathematics, science and technology).     

微课教学技术支持下的中职数学教学反思

数学是中职教育阶段一门非常重要的基础学科,由于长期以来人们对中职教育存在错误的认识,中职院校的生源普遍基础很差,因此,在数学知识的学习方面很多学生都感到压力很大。文章通过对中职数学教学中存在问题的反思,提出利用微课技术这种新的教学方式改善中职数学教育的方法,以此来提高中职数学教学的质量。     

Declining trends in student performance in lower secondary education

Student performance is related to motivation to learn. As motivation generally declines during lower secondary education, one might expect performance to decline as well during this period. Though, until now, it has been unclear whether this pattern exists. In the present study, we examined student performance during the early years of secondary education from a developmental perspective. Participants were 1544 Dutch secondary school students across three grades (grades 7 to 9). To investigate student performance trends, we analysed report card grades by using hierarchical linear modelling with two levels (level 1, time point; level 2, student). Potential moderators to be examined were (1) gender, (2) school type and (3) initial level. A linear decline in report card grades from grade 7 to 9 was found for boys and girls, in all school types, and regardless of initial level. Two variables moderated the steepness of the decline: school type and initial level. Gender and school type had a main effect on performance level. The same pattern was observed for the subset of ‘core subjects’—Dutch, English and mathematics. Motivational and cognitive factors that may explain the performance decline are discussed.     

Research mathematicians as teacher educators: focusing on mathematics for secondary mathematics teachers

We believe that professional mathematicians who teach undergraduate mathematics courses to prospective teachers play an important role in the education of secondary school mathematics teachers. Thus, we explored the views of research mathematicians on the mathematics that should be taught to prospective mathematics teachers, on how the courses they teach can serve teachers in their work with school students, and on the changes they would implement if their courses were designed specifically for prospective teachers. We constructed profiles of the four mathematicians based on their responses to a clinical interview. We employed the construct of mathematics teacher-educators’ triad in the reflective analysis of our findings and extended the construct based on the results of this study. In conclusion, we commented on potential ways to draw stronger connections between university mathematics and the mathematics taught in schools.     

Long‐term effects of primary schools on mathematics achievement of students at age 17

In the field of educational effectiveness research, school effects are generally studied in the short term (i.e. during the same phase of schooling). The aim of this study is to investigate long‐term primary school effects on students’ achievement in mathematics at the end of secondary education. We also investigate which primary school characteristics are of importance in the long term. Data from the longitudinal SiBO project, in which a cohort of 6,000 Flemish pupils were intensively followed from kindergarten to grade 7, was used. At the age of 17, the same cohort participated in follow‐up data collection. Cross‐classified multilevel models showed small continuing effects of primary school on the mathematics achievement of students (i.e. over and above what had been reached at the end of primary education). No long‐term effect was found of the proportion of high‐risk students at primary school. Students coming from a primary school with a higher effectiveness obtained higher mathematics results at age 17, but when the mathematics achievement of students at the end of primary school was taken into account, this effect disappeared. We also observed that students coming from Catholic primary schools performed better in mathematics at age 17 compared with students coming from public schools. The implications of the findings are discussed.     

Exploring the effects of project-based learning in secondary mathematics education

This mixed-method, longitudinal study investigated the benefits of project-based learning (PBL) on secondary-mathematics students' academic skill development and motivated strategies for learning (i.e., cognitive, social, and motivational). The focus of this study was academic skill development (algebra- and geometry-assessment scores) and other factors related to secondary mathematics learning, with comparable traditional high schoolers serving as the control group. In addition, the relationship between PBL and racially/ethnically and economically diverse secondary students was investigated. Results showed that at-risk and minority students benefited greatly from PBL in learning mathematics. The academic performance gap was present, but its width diminished significantly. Compared to their public school counterparts, PBL students were more intrinsically motivated, showed significantly higher critical thinking skills, and appreciated peer learning. Impact of socioeconomic status on the PBL approach needs further investigation.     

Profiling secondary school students in mathematics and German language arts using learning-relevant cognitive and motivational-affective characteristics

This study aims to investigate how learning-relevant cognitive and motivational-affective characteristics, such as pre-knowledge and interest, are intrapersonally connected within students. This person-centered research thereby adds to prior findings by simultaneously analyzing student profiles in the domains of mathematics and German language arts on all school tracks within the German secondary school system. In a subsample of the German National Educational Panel Study involving 10,025 ninth-grade students, a latent profile analysis is conducted to identify student profiles. The results reveal five student profiles in German language arts (strong, struggling [motivation], struggling [cognitive], over,- underestimating) and five student profiles in mathematics (strong, struggling, over,- underestimating, average-uninterested). One of the student profiles, the underestimating student profile, is found most frequently in both domains (Ø32%). Students from higher school tracks, and especially females, are most often allocated to an underestimating profile in both domains. Lastly, the results indicate domain-specific student profiles.     

创新思维在中等职业教育数学中的培养

自我国颁布《中等职业学校教育大纲》以来,各个中等职业学校逐渐重视起职业教育数学工作。中等职业数学既是对初中数学知识的继承,也是为更高层次数学知识的学习打下良好的基础。在数学教育过程中,应该建立＂方法多样,灵活多变,兴趣、能力培养＂的现代教学方法。     

基于中职数学教学内容的教学策略探究

文章分析了中职数学在职业教育中的重要性,部分中职生对数学不感兴趣,动力不足,针对不同的教学内容,结合当今中职生的认知特征,提出了生活实例、动手操作、课堂游戏、源流教学及动画展示几种教学策略,主要目的是激发学生的兴趣,提高数学课堂效果。     

Klassenwiederholen in PISA-I-Plus: Was lernen Sitzenbleiber in Mathematik dazu?

This study analyses the effects which repeating a class has on ninth grade students’ development of mathematical competency. The following research questions were addressed: How many students repeat grades in the different types of schools? How do students who repeat a grade differ from those who do not in their performance and background characteristics? How much extra mathematics do students repeating a grade learn in one school year? What are the differences between various types of school? Can students with poor mathematics grades in particular profit from repeating a grade? The sample is a sub-sample of the PISA-I-Plus study and comprises N = 360 ninth grade students. The total sample of PISA-I-Plus is representative for all ninth/tenth grade students from the different school types in Germany. The data survey was carried out in the ninth grade and then repeated after the students had repeated a year. The results document differences in the amount of grade repeat quotas between types of school. Furthermore, compared to students not repeating, those repeating a grade had lower mathematics (d = 1.02) and german (d = 1.14) grades, a lower level of mathematical literacy (d = 0.51), and lower test results with regard to basic cognitive abilities (d = 0.32). In terms of the development of mathematical literacy, the students repeating a grade could improve by an average of 23 points (d = 0.27) on the PISA mathematics scale. However, the results identify 38 percent of students repeating a grade who do not make any significant improvement in mathematics or even get worse. A differentiation according to school types shows that students repeating a grade in integrated comprehensive secondary schools and in schools with several educational levels in particular do not, on average, show any noteworthy improvement in their mathematical literacy. The analysis of the school grades received in mathematics shows that students whose mathematics grades are unsatisfactory do not benefit more from repeating a grade than students whose mathematics performance has been rated as being “satisfactory” or better. The article concludes with a discussion of the possible consequences of changing the way in which repetitions of grades are dealt with.     

再次呼唤中学数学教学的返朴归真——一次高一新生数学测验调查及启示

数学差生是一个值得注意的问题。数学差生产生的原因与我们数学教育的深层问题有关,即：过分注重“结论”而忽视“过程”;过分注重“程序”而忽视“意义”;以落实知识点为目标的“机械”的、“线性”的训练使目标教学法发生了异化。这些弊端严重影响了中学生数学学习的效果,也是数学差生产生的根本原因之一。为此,应再次呼唤中学数学教学的返朴归真。