Analysis of Students' Error In Solving Probability Problem: A Case Study In Guangxi

This research analyzes the types and reasons of students'  mistakes in solving probability and the analysis statistics problems by qualitative research method. The subjects were 20 senior High school students from a senior high school in Guangxi, China. The data were collected through the student diagnostic test. The students' answers were analyzed by using O'Connel's  analysis. The results show that the proportion of misunderstood problems is 48.18% at the largest proportion, and the proportion of computational errors is next, accounting for 36.36%. The proportion of procedural errors is the least, accounting for 15.45%. As we all know, there are many reasons for the above mistakes., so teachers can find some solutions to overcome these mistakes

The Impact of STEM PBL Teacher Professional Development on Student Mathematics Achievement in High Schools

This dissertation consists of three articles that explore the effect of professional development (PD) on teachers‘ understanding and implementation of Science, Technology, Engineering, and Mathematics (STEM) project based learning (PBL), and the effect of STEM PBL on students‘ mathematics achievement. Teachers in three high schools participated in the research activities. They attended sustained PDs provided by one STEM center based in a Southwestern university, and were required to implement STEM PBLs once every six-weeks for three years (2008 through 2010). The first article employed a mixed-method case study to explore the relation between the quality of the teachers‘ in-class STEM PBL implementations, understanding of the PBL in STEM education, and attendance in the STEM PBL activities. Quantitative findings indicate that attendance in the PD activities was significantly correlated with the quality of the in-class PBL implementation in 2010, yet not in 2011. Moreover, qualitative findings show that the teachers viewed the STEM PBL pedagogy as a means to promote student interest in mathematics, cultivate the interdisciplinary research culture in K-12 classrooms, and help improve students‘ content understanding. The second article investigated the effect of STEM PBL, especially on Hispanic and at-risk students‘ mathematics achievement. The participants were 528 students in the three STEM PBL high schools and 2,688 students in non-STEM PBL schools in the same region. Latent growth modeling was used to analyze the repeated measures across years. STEM PBL instruction positively influenced Hispanic students‘ achievement in mathematics, but not at-risk students. The third study investigated whether participating in STEM PBL activities affected students who had varied performance levels, and to what extent students‘ individual factors influenced their mathematics achievement. The participants were 836 high school students in the three schools. The findings from the hierarchical linear modeling showed that low performing students showed statistically significantly higher growth rates on mathematics scores than high and middle performing students, over the three years. In addition, student‘s ethnicity and economic status were good predictors of academic achievement. This dissertation is the first to reveal the effect of STEM PBL on student academic achievement relating to inservice teacher PD by employing the sophisticated research methodology

Exploring teachers’ use of visualisation tools when teaching Grade 9 problem-solving in mathematics. a case of Umlazi District Dinaledi schools in South Africa.

Masters Degree. University of KwaZulu-Natal, Durban.This study focused on exploring Grade 9 mathematics teachers’ use of visualisation tools when teaching problem-solving in their classrooms. This issue has been a challenge in South Africa, particularly in matric and grade 9 mathematics Annual National Assessment. The use of visualisation when teaching problem-solving in the mathematics classroom has been viewed as critical to learner’s performance, in response to the abstract nature of mathematics. However, problem-solving and the importance of the use of visualisation is emphasised in the Curriculum Assessment Policy Statement for the Senior Phase. Moreover, it is also included in every topic of the learners’ Grade 9 mathematics workbook for everyday classroom activities. Therefore, this study aimed to answer the questions of what visualisation tools teachers use and how they use these when teaching problem-solving. Lastly, why do they use them during their lesson in their classroom? Polya’s 4-step problem-solving and Activity theory was used as a theoretical framework for this study. A qualitative case study of two Dinaledi Comprehensive Technical High School in Umlazi District was conducted to explore the use of visual tools by five grade 9 mathematics teachers during their teaching of problem solving. Teacher’s questionnaire, classroom observations, and semi-structured interviews for teachers were used to generate data. The findings revealed that mathematics teachers do teach problem solving in their Grade 9 classrooms as stated by the policy document. However, the use of visualisation tools in the mathematics classroom seems to be infrequent. Therefore, the teachers highlighted the lack of resources and understanding of what problem-solving is, as a challenge to their use of visualisation tools. However, the study suggested that the department of Kwa-Zulu Natal education should provide in-service training for Grade 9 teachers on the effective use of visualisation tools when teaching problem-solving. It was also suggested that schools should provide resources that can enhance problem solving, and mathematically related resources for their mathematics lessons. It was further suggested t schools to have a mathematics classroom, which will provide a mathematics atmosphere with relevant mathematics resources for effective and efficient teaching and learning of mathematics

Effects of the application of graphing calculator on students’ probability achievement

A Graphing Calculator (GC) is one of the most portable and affordable technology in mathematics education. It quickens the mechanical procedure in solving mathematical problems and creates a highly interactive learning environment, which makes learning a seemingly difficult subject, easy. Since research on the use of GCs for the teaching and learning of probability in institutions of higher learning appears to be limited, a study was conducted to examine the effects of the use of GCs on students' performance in probability. The study involved 65 pre-university students in a private institution of higher learning in Malaysia. Hypothesis testing showed that there is a significant difference in the mean score of the post achievement test between the experimental and control groups. Students in the experimental group displayed higher achievement than their peers in the control group in the Probability Achievement Test (PAT). Findings also showed that the use of GCs benefits students of all levels, that is, high, average and low mathematics achievers. Qualitative data provides a more lucid picture of how GCs aid in improving understanding and performance. Recommendations made will provide researchers, policy-makers and educators an alternative means of enhancing the quality of probability education. (C) 2011 Elsevier Ltd. All rights reserved

Designing for Statistical Reasoning and Thinking in a Technology-Enhanced Learning Environment

Difficulties in learning and understanding statistics in college education have led to a reform movement in statistics education in the early 1990s. Although much work has been done, there is more work that needs to be done in statistics education. The progress depends on how well the educators bring interesting real-life data into the classroom. The goal was to understand how course design based on First Principles of Instruction could facilitate tertiary-level students\u27 conceptual understanding when learning introductory statistics in a technology-enhanced learning environment. An embedded single descriptive case design was employed to investigate how integrating technology and real data into a tertiary level statistics course would affect students\u27 statistical literacy, reasoning, and thinking. Data including online assignment postings, online discussions, online peer evaluations, a comprehensive assessment, and open-ended interviews were analyzed to understand how the implementation of First Principles of Instruction affected a student\u27s conceptual understanding in a tertiary level introductory statistics course. In addition, the teaching and learning quality (TALQ) survey was administered to evaluate the teaching and learning quality of the designed instruction from the student\u27s perspective. Results from both quantitative and qualitative data analyses indicate that the course designed following Merrill\u27s First Principles of Instruction contributes to a positive overall effectiveness of promoting students\u27 conceptual understanding in terms of literacy, reasoning, and thinking statistically. However, students\u27 statistical literacy, specifically, the understanding of statistical terminology did not develop to a satisfactory level as expected

A tecnologia no desenvolvimento do currículo de Matemática no Ensino Básico - o contributo da Teoria da Mediação Semiótica

Este estudo refere-se a uma experiência de ensino que se realizou no âmbito de um projeto de desenvolvimento curricular, em algumas unidades de ensino, nos 7.º e 8.º anos de escolaridade. Recorreu-se a tarefas diversificadas de índole exploratória, que envolveram o uso da calculadora gráfica, artefacto que não é prevista a sua utilização no ensino básico, cujo objetivo foi criar uma dinâmica curricular inovadora. A Teoria da Atividade, a Génese Instrumental e a Teoria da Mediação Semiótica, foram as linhas teóricas que compõem os quadros teóricos deste estudo e suportaram a análise dos dados. Procurou-se compreender como é que o aluno, envolvido no seu sistema de atividade, na resolução de tarefas com o artefacto mediador, calculadora gráfica, promoveu signos de artefacto através do desenvolvimento de esquemas de uso e de ação instrumentada. E posteriormente, na discussão coletiva, com a orquestração da professora, se operacionalizou a passagem desses signos de artefacto para signos matemáticos. Metodologicamente, adotou-se um paradigma qualitativo, de natureza interpretativa e descritiva, fundamentado num processo de Design Research, recorrendo a uma experiência de ensino, na modalidade, estudo de caso. Os métodos para recolher os dados basearam-se em gravações áudio de algumas aulas, relatórios escritos dos alunos e imagens das representações gráficas dos ecrãs da calculadora gráfica, decorrentes da realização das tarefas, observação participante e diário de bordo da professora-investigadora. A análise dos dados incidiu nos trabalhos de dois pares de alunos, que constituíram o grupo, estudo de caso, em quatro tarefas do 7.º ano de escolaridade. Concluiu-se que no ambiente social da sala de aula, o artefacto calculadora gráfica, funcionou como um instrumento de mediação semiótica. Os alunos evidenciaram o desenvolvimento de esquemas de ação instrumentada e de uso. Os primeiros esquemas, fundamentados na função de arrastamento e de visualização, articularam-se com os segundos, e conjuntamente, com a orquestração da professora, deu-se o desenvolvimento do potencial semiótico do artefacto, resultando a construção do conhecimento matemático