Analyzing the word-problem performance and strategies of students experiencing mathematics difficulty

The purpose of this study was to examine the word-problem performance and strategies utilized by 3rd-grade students experiencing mathematics difficulty (MD). We assessed the efficacy of a word-problem intervention and compared the word-problem performance of students with MD who received intervention (n = 51) to students with MD who received general education classroom word-problem instruction (n = 60). Intervention occurred for 16 weeks, 3 times per week, 30 min per session and focused on helping students understand the schemas of word problems. Results demonstrated that students with MD who received the word-problem intervention outperformed students with MD who received general education classroom word-problem instruction. We also analyzed the word-problem strategies of 30 randomly-selected students from the study to understand how students set up and solve word problems. Students who received intervention demonstrated more sophisticated word-problem strategies than students who only received general education classroom word-problem instruction. Findings suggest students with MD benefit from use of meta-cognitive strategies and explicit schema instruction to solve word problems.     

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.     

Predetermined accommodations with a standardized testing protocol: Examining two accommodation supports for developing fraction thinking in students with mathematical difficulties

This study examined the effects of two pre-determined accommodations that were provided in a standardized testing. The two accommodations were meant to help students with difficulties in mathematics (SDMs) engage in unit thinking, reasoning, and coordination and consequently improve their ability to process fraction tasks. 23 middle school SDMs took the following tests and were asked to explain their solutions: a baseline fraction test without any accommodation; an annotated test with bolded information and additional simplified explanations; and a warming- up test that involved whole-number multiplicative reasoning tasks followed by the baseline test. Results show that while SDMs were able to construct and coordinate fraction units to solve fraction problems when appropriate accommodations were provided, standardized assessment with a predetermined “one-size-fits -all” accommodation could not meet the specific needs of all students with mathematics learning difficulties.     

Mathematics in the home: Homework practices and mother-child interactions doing mathematics

Parents are a largely untapped resource for improving the mathematics performance of American children, which lags behind the performance of children from other nations. The purpose of the research reported here was to assess homework practices in the home, and to examine interactions between mothers and their 5th grade children as they worked challenging mathematics problems (pre-algebra equivalence problems). Results indicated that children spent on average 23 min per day on mathematics homework, with an average of 8 min of help from parents. Videotapes of mother-child interactions indicated that mothers varied considerably in the quality of the mathematics content that they conveyed while teaching, and in the quality of their scaffolding of the material for the child. As expected, mothers who themselves had more mathematics preparation performed better in conveying mathematical content and in scaffolding. Mothers with more mathematics self-confidence also performed better. The results suggest that children face inequities in the parental resources available to them for math learning; these inequities might be remedied by school-family partnership programs.     

A study of the difficulties experienced with mathematics by engineering students in higher education

This paper describes a study undertaken to investigate the problem of the lack of mathematical expertise demonstrated by polytechnic engineering students. The study is based on a multiple‐choice diagnostic mathematics test, designed for the purpose, which was taken by incoming engineering students over a period of five years. The test aims to identify particular areas of difficulty. These difficulties are analysed and suggestions are made regarding their cause and alleviation. It has been confirmed that there is cause for concern at the overall mathematical ability of the students and it has been possible to identify certain areas of mathematics which appear to be difficult to a large proportion of students. It has also been possible to identify some of the common errors made by students in certain topic areas. Some suggestions have been made regarding the implications for teaching.     

Integer number sense and notation: A case study of a student with a mathematics learning disability

Although approximately 6% of students have a mathematics learning disability (MLD) also known as dyscalculia, little is known about how MLD impacts students beyond basic arithmetic. In this study we focused on one mathematical topic foundational to algebra – integer operations – and conducted a videotaped design experiment with one student with MLD. Through 14 teaching episodes we explored the ways in which standard mathematical tools (e.g., symbols, representations) were inaccessible and evaluated the design of alternative tools. Our detailed retrospective analysis revealed that the student had an unconventional understanding of integer quantities and symbolic notation, which resulted in issues of accessibility and persistent difficulties. Deliberate attempts to address inaccessibility revealed nuances in the student’s understanding, and suggests that both number sense and notational issues needed to be addressed in tandem. Implications for instruction are discussed.     

Additive representations of integers

In this paper we shall mainly study additive representations of integers prime to the first m primes as a sum of some integers having a peculiar property. The conjectures of Goldbach and twin primes are also observed in connection with these representations of integers. Received: 20 October 1997     

How students structure their investigations and learn mathematics: insights from a long-term study

This paper reports on the mathematical thinking of participants of a long-term study, now in its 17th year, who did mathematics together through their public school and early university years. In particular, it describes how fundamental ideas and images of a cohort group of students are elaborated and presented in symbolic expressions of generalized mathematical ideas while exploring problems in grades 10 and 11. From high school and university interview data, we learn from participants how they viewed their mathematical activity in structuring their investigations and justifying their solutions.     

“数学模型”课程教学模式的探讨

本文介绍了开设“数学模型”课程在工科院校数学教学改革中的重要性．并讨论如何组织“数学模型”课程的教学．     

Preservice Teachers' Beliefs and Attitude About Teaching and Learning Mathematics Through Music: An Intervention Study

This article presents exploratory research investigating the integration of music and a mathematics lesson as an intervention to promote preservice teachers' attitude and confidence and to extend their beliefs toward teaching mathematics integrated with music. Thirty students were randomly selected from 64 preservice teachers in a southern university. A 90‐minute mathematics lesson integrated with a music composition activity was taught by the first author. Pre‐ and postquestionnaires were provided to evaluate the change in preservice teachers' attitude and beliefs toward mathematics. The results demonstrated that the mathematics lesson integrated with music had a positive effect on preservice teachers' attitude and beliefs toward mathematics teaching and learning.     

From the margin to the center: A framework for rehumanizing mathematics education for students with dis/abilities

Mathematics education for students with dis/abilities has a legacy of exclusion; its scholarship has been dominated by ableist perspective: a focus on rote mathematics facts, procedural instruction, and a narrow range of mathematics content. Grounded in critical pedagogy and critical disabilities studies, we argue for a shift in the focus away from the student as the site of defect and intervention to recognize the complex embodiment of dis/ability as a process produced within historical, political, social, and material contexts. The theoretical assumptions and guiding principles for a framework of culturally responsive and relational understanding of dis/ability will be shared together with a case of such an approach in classroom practice. The paper advances efforts to support all learners in robust mathematics learning communities and to situate research from perspectives that acknowledge the situated, interactional nature of ability, identity, and achievement.     

The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities

The study explored the impact of Please Go Bring Me-COnceptual Model-based Problem Solving (PGBM-COMPS) computer tutoring system on multiplicative reasoning and problem solving of students with learning disabilities. The PGBM-COMPS program focused on enhancing the multiplicative reasoning and problem solving through nurturing fundamental mathematical ideas and moving students above and beyond the concrete level of operation. This is achieved by taking advantages of the constructivist approach from mathematics education and explicit conceptual model-based problem solving approach from special education. Participants were three elementary students with learning disabilities (LD). A mixed method design was employed to investigate the effect of the PGBM-COMPS program on enhancing students’ multiplicative reasoning and problem solving. It was found that the PGBM-COMPS program significantly improved participating students’ problem solving performance not only on researcher developed criterion tests but also on a norm-referenced standardized test. Qualitative and quantities data from this study indicate that, in addition to nurturing fundamental concept of composite units, it is necessary to help students to understand underlying problem structures and move toward mathematical model-based problem representation and solving for generalized problem solving skills.     

林业院校数学教学中存在的问题与思考

分析了现行林业院校数学教学中存在的主要问题 ,认为合理地设置数学课程和学时数是保证教学质量的前提 ,开设数学实验课和建立数学实践教学基地是培养学生应用数学能力的主要手段 .加强师资队伍建设、开展教研活动和学术交流及采用多媒体辅助教学能促进教学水平的提高 .     

“应用数学基础”课程改革的思考

本探讨了“应用数学基础”课程改革的必要性，从教师队伍建设、教学内容改革、教学手段与教学方法改革、课程教材建设和教学实战等五个方面提出了我们的想法。     

A multidimensional approach to training mathematics students at a university: improving the efficiency through the unity of social,psychological and pedagogical aspects

The article deals with social, psychological and pedagogical aspects of teaching mathematics students at universities. The sociological portrait and the factors influencing a career choice of a mathematician have been investigated through the survey results of 198 first-year students of applied mathematics major at 27 state universities (Russia). Then, psychological characteristics of mathematics students have been examined based on scientific publications. The obtained results have allowed us to reveal pedagogical conditions and specific ways of training mathematics students in the process of their education at university. The article also contains the analysis of approaches to the development of mathematics education both in Russia and in other countries. The results may be useful for teaching students whose training requires in-depth knowledge of mathematics.     

Experienced engineers becoming mathematics teachers: preliminary perceptions of mathematics teaching

Engineers who choose to change careers and become mathematics teachers are a specific group as far as their mathematics learning in the context of engineering and their previous work experience are concerned. Regarding mathematics, they mainly engaged in applied mathematics associated with engineering, which is a highly practical field. This research explores experienced engineers’ perceptions of mathematics teaching-related topics, before starting their studies in a pre-service mathematics teacher preparation programme. This research explores their perceptions of mathematics as a discipline, mathematics teaching and mathematical understanding. The qualitative research involves three mechanical engineers, two industrial management engineers, and an electrical engineer. Semi-structured interviews were conducted before the beginning of the programme, and analysed qualitatively. The participants view engineering as an applied and changing discipline while perceiving mathematics as closed, rigorous, accurate, systematic, theoretical and as a tool for engineering. They mostly address general features of mathematics teaching while expressing a more multifaceted view of mathematical understanding. Due to the specific characteristics of the participants, this study may contribute to planning mathematics teacher preparation programmes for engineers.     

On the distribution of irreducible algebraic integers

We study large values of the remainder term in the asymptotic formula for the number of irreducible integers in an algebraic number field K. In the case when the class number h of K is larger than 1, under certain technical condition on multiplicities of non-trivial zeros of Hecke L-functions, we detect oscillations larger than what one could expect on the basis of the classical Littlewood’s omega estimate for the remainder term in the prime number formula. In some cases the main result is unconditional. It is proved that this is always the case when h = 2. Author’s address: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland The author was supported in part by KBN Grant # N N201 1482 33.     

The Virginia mathematics specialist initiative: Collaborative effort among all components of the VA mathematics community

The Virginia Mathematics Specialist Initiative (VMSI) is an ongoing collaborative effort among all components of the mathematics and mathematics education community of Virginia spanning more than two and a half decades. This paper describes the use of extensive collaborations to reach shared beliefs about teaching and learning mathematics with the goal of improving student learning; accomplished by preparing and supporting school-based mathematics specialists to coach K-8 teachers. A foundation built on shared beliefs enabled community members to reach consensus on this goal and continues to fuel the accomplishments of the VMSI. Several accomplishments are discussed including identification of the role of K-8 mathematics specialists, the attainment of a Virginia licensure add-on endorsement; and development of a model for a Virginia Mathematics Specialist Preparation Program (VMSPP). Also discussed are the annotated syllabi for core mathematics content and leadership courses in the VMSPP and tools to sustain and extend the VMSI.     

试论应用数学的特征

本文将纯粹数学与应用数学进行比较,概括出应用数学固有的特征.     

The effectiveness of support for students with non-traditional mathematics backgrounds

This article describes an initiative introduced at LoughboroughUniversity by SIGMA, a Centre for Excellence in Teaching andLearning (CETL), to support physics students who were mathematicallyless well-prepared than their counterparts. The article outlineshow students were identified as being less well-prepared. Thesestudents were taught in a separate group, using different materialsand a different teaching style, but the same assessment methodswere used for both groups. An evaluation of the success of thisinitiative is made by comparing the results of the less well-preparedstudents receiving support in 2005–06 with those of theless well-prepared students (taught in the mainstream group)in 2004–05. A key outcome of this comparison is an increasein the pass rate from 48% to 67%.