Impact of curriculum reform: Evidence of change in classroom practice in the United States

The purpose of the study reported in this article is to examine the impact of curriculum on instruction. Over a three-year period, we observed 579 algebra-related lessons in grades 6-8. Approximately half the lessons were taught in schools that had adopted a Standards-based mathematics curriculum called the Connected Mathematics Program (CMP), and the remainder of the lessons were taught in schools that used more traditional curricula (non-CMP). We found many significant differences between the CMP and non-CMP lessons. The CMP lessons, emphasized the conceptual aspects of instruction to a greater extent than the non-CMP lessons and the non-CMP lessons emphasized the procedural aspects of instruction to a greater extent than the CMP lessons. About twice as many CMP lessons as non-CMP lessons were structured to use group work as a method of instruction. During lessons, non-CMP students worked individually on homework about three times as often as CMP students. When it came to text usage, CMP teachers were more likely than non-CMP teachers to work problems from the text and to follow lessons as laid out in the text. However, non-CMP students and teachers were more likely than CMP students and teachers to review examples or find formulas in the text. Surprisingly, only small proportions of the CMP lessons utilized calculators (16%) or manipulatives (11%).     

An Evaluation of the Connected Mathematics Project

Abstract

A formative, internal evaluation was conducted on the Connected Mathematics Project (CMP), a middle school reform mathematics curriculum used in Lafayette Parish, Louisiana, by the author (lead teacher of said project). Approximately 3,500 students in this public school system were enrolled in this program, and the district school board planned to expand the program to include all 12 public middle schools. An analysis of the Iowa Test of Basic Skills and the Louisiana Education Assessment Program mathematics data indicate that the program is working: The CMP schools significantly outperformed the non-CMP schools on both standardized tests. Questionnaires distributed to the teachers and to a sample of the students indicated that both groups believe the program is helping students become better problem solvers.     

Capitalizing on advances in mathematics and k-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations

This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students’ beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the instructional design theory of Realistic Mathematics Education and the social negotiation of meaning. The main results of the comparison study found no significant difference between project students and comparison students on an assessment of routine skills and a significant difference in favor of project students on an assessment of conceptual understanding. Given these encouraging results, the theoretical underpinnings of the innovative approach may be useful more broadly for undergraduate mathematics education reform.     

High Schools That Work and college preparedness: Measuring the model's impact on mathematics and science pipeline progression

The High Schools That Work school improvement initiative is the nation's largest comprehensive school reform model with over a thousand schools adopting its framework. The initiative's premise is that all students can meet the demands of a college preparatory curriculum if provided the right supports. Analyzing over a decade of data on student course taking and performance, we employ a rigorous comparative interrupted time series strategy to assess the extent to which HSTW meets its goal by increasing students’ successful progression through the mathematics and science pipelines. Each pipeline consists of three college preparatory courses: algebra 1, geometry, and algebra 2 in mathematics and biology plus two physical science courses in science. The results show no effect on pipeline progression for the average student and some evidence of increased gaps in course taking between more advantaged and disadvantaged students.     

Impact of curriculum reform: Evidence of change in classroom practice in mainland China

The study examined the impact of curriculum reform on teaching practice in primary mathematics in mainland China. The participants included 58 fifth grade mathematics teachers from 20 schools. Thirty-two of the classrooms had utilized a reform curriculum for 5 years prior to conducting the study, and the remaining 26 had been using the conventional curriculum. Each of the 58 teachers was videotaped for 3 of his/her classes during a 3-day period and the videotaped class sessions provided the data source for the study. The focus of the study was on the instructional tasks that were implemented in the classrooms and on the teacher and student interaction. Results indicated that a greater proportion of high cognitive level tasks were implemented in the reform classrooms when compared to those in the non-reform classrooms. Numerical symbolic representation as well as single-solution strategies were dominant in the instructional tasks for both groups. However, in the reform classes a higher proportion of instructional tasks were used that involved visual illustrations and hands-on manipulation and multiple-solution strategies. An analysis of classroom discourse showed that most of the teacher questions were related to memorizing exercises and explanations of answers. However, the teachers from the reform classrooms were more likely to ask students to describe the procedure that led to an answer and to inquire further into students’ responses. The results indicated positive changes in classroom practice resulting from implementation of the new curriculum.     

Unraveling the culture of the mathematics classroom: A video-based study in sixth grade

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying these mathematical textbooks impact the current teaching of mathematics. Two problem-solving lessons were videotaped in 10 sixth-grade classrooms and a coding scheme was developed to analyze these lessons with regard to three aspects of the classroom culture that are assumed to enhance students’ mathematical beliefs and problem-solving competencies: (1) the classroom norms that are established, (2) the instructional techniques and classroom organization forms, and (3) the set of tasks students are confronted with. Two instruments were administered to measure students’ beliefs about learning mathematical word problem solving, and to assess their problem-solving processes and skills. The results indicate that some reform-based aspects seemed to be easier to implement (e.g., a strong focus on heuristic skills, embedding tasks in a realistic context) than others (e.g., the use of group work, an explicit negotiation of appropriate social norms).     

Attitudes of high-school students taught using traditional and reform mathematics curricula in middle school: a retrospective analysis

This paper presents findings from a larger research project that provides insight into the attitudes of high-school students who were taught using different types of mathematics curricula when they were in middle school. A total of 44 12th-grade students from 10 high schools in the same urban school district were interviewed. Eighteen (41%) of them had been taught using a reform curriculum in middle school and 26 (59%) had been taught using a more traditional curriculum. Using Di Martino and Zan’s three-dimensional model for attitude, we found that the high-school seniors who had been taught using the reform curriculum in middle school harbored attitudes toward mathematics that differed significantly from the attitudes of those who had been taught using a traditional curriculum in middle school. Our analysis of the student interviews culled seven themes that provide fine-grained information about the students’ attitudes toward mathematics. Significantly greater percentages of reform students than traditional students had a relational Vision of mathematics as opposed to an instrumental Vision; however, there was no significant difference between the proportions of reform and traditional students who had a positive Emotional Disposition toward mathematics or a positive Perceived Competence in mathematics.     

Question Posing, Inquiry, and Modeling Skills of Chemistry Students in the Case-Based Computerized Laboratory Environment

A new learning unit in chemistry, Case-based Computerized Laboratories (CCL) and Computerized Molecular Modeling (CMM) was developed at the Technion. The CCL and CMM curriculum integrates computerized desktop experiments and molecular modeling with an emphasis on scientific inquiry and case studies. Our research aimed at investigating the effect of the CCL and CMM learning environment on students’ higher-order thinking skills of question posing, inquiry, and modeling. The experimental group included 614 honors 12th grade chemistry students from high schools in Israel who studied according to this learning unit. The comparison group consisted of 155 12th grade chemistry honors students who studied other chemistry programs. Pre- and post-tests questionnaires were used to assess students’ higher-order thinking skills. Students’ responses were analyzed using content analysis rubrics and their statistical analysis. Our findings indicated that the scores of the experimental group students improved significantly in question posing, inquiry and modeling skills from the pre-test to the post-test. The net gain scores of the experimental group students were significantly higher than those of their comparison peers in all three examined skills. In modeling skills, experimental group students significantly improved their achievements in making the transfer from 3D models to structural formulae, but only about half of them were able to transfer from formulae to 3D models. By presenting a case-based chemistry assessment tool and content analysis of students’ responses in this paper, we enable teachers and educators to analyze their students’ higher-order thinking skills both qualitatively and quantitatively.     

UNIVERSITY STUDENTS’ VIEWS OF THE ROLE OF MATHEMATICS IN THEIR FUTURE

We report on an international study about mathematics students’ ideas of how they will use mathematics in their future study and careers. This builds on our previous research into students’ conceptions of mathematics. In this paper, we use data from two groups of students studying mathematics: those who participated in an in-depth interview and those who completed an open-ended questionnaire. We found that their responses could be grouped into four categories: don’t know; procedural skills; conceptual skills; and professional skills. Although some students held clear ideas about the role of mathematics, many were not able to articulate how it would be used in their future. This has implications for their approach to learning and our approach to teaching.     

The Enactment and Perception of Mathematics Pedagogical Values in an Elementary Classroom: Buddhism,Confucianism, and Curriculum Reform

The purpose of this case study was to investigate the values demonstrated by an elementary school teacher in her mathematics teaching and what values her students perceived. This research adopted the valuing theory (Raths, Harmin & Simon, 1987) and used classroom observations and interviews to document the teacher’s mathematics pedagogical values and a questionnaire, interviews, and instructional artifacts to document the students’ perceptions of these values. The results of this research identified two educational values and three mathematics pedagogical values that were influenced by the teacher’s personal beliefs about Buddhism, Confucianism, and curriculum. Her goals for education were to reinstate the students’ original enlightenment and the students’ respect for ethics and experts when dealing with people and life; and her values about mathematics learning were that it depends on individual efforts and personal understanding, her central purposes for teaching were to make students understand the mathematics content and to cultivate their problem-solving methods, and her purposes for evaluation were to understand students’ learning and to encourage students to correct their errors. The students’ awareness of these goals and values did not parallel the teacher’s personal priorities. The implications of teachers’ pedagogical values on teacher professional development and curriculum reform are discussed.     

The effect of distributed practice on students’ conceptual understanding of statistics

In this study the effect of the reduced distribution of study activities on students’ conceptual understanding of statistics is investigated in a quasi-experiment. Conceptual understanding depends on coherent and error free knowledge structures. Students need time to construct such knowledge structures. A curriculum reform at our university resulted in statistics courses which were considerably shortened in time, thereby limiting students’ possibility to distribute study activities. Independent samples of students from before and after the reform were compared. To gauge conceptual understanding of statistics, students answered open ended questions in which they were asked to explain and relate important statistical concepts. It was shown that the reduction of distributed practice had a negative effect on students’ understanding. The finding that condensed courses make it more difficult for students to reach proper understanding of the subject matter is of interest for anyone who is engaged in reforming curricula or designing courses.     

THE LENGTH MEASUREMENT IN THE TURKISH MATHEMATICS CURRICULUM: ITS POTENTIAL TO CONTRIBUTE TO STUDENTS’ LEARNING

“Knowing and doing measurement” is a fundamental competency in real life since measuring attributes of objects in appropriate units and using measuring tools assist students to quantify and understand the world. For this reason, the study of measurement has a special place in every mathematics curriculum. Among the domains of measurement, length measurement is extremely important for students to understand basic ideas about measurement and to construct bases for more advance topics as area and volume measurement. However, research on students’ understanding of length measurement reveals serious difficulties varying from incorrect alignment with a ruler to confusion of perimeter with area. One of the reasons for students’ struggles in measurement is considered as weaknesses in the intended (written) curriculum. In this respect, this study was designed to investigate the content of length measurement in the Turkish mathematics curriculum (1st–fifth grade) in terms of its potential to support students’ understanding. For this purpose, the Turkish Mathematics Curriculum Guide was carefully analyzed by considering main components of the curriculum (e.g. learning objectives). In spite of some weaknesses, the length measurement content in the curriculum seems to provide meaningful opportunities for students to develop the concepts and skills involved in length measurement.     

Year 12 students’ attainment of scientific investigation skills

One of the main goals of science education is the development of scientific investigation skills (Bryce & Robertson, 1985; Woolnough & Allsop, 1985). This paper describes a practical test instrument developed to assess students’ attainment of skills associated with problem analysis and planning experiments, collecting information, organizing and interpreting information, and concluding. During administration of the test, students verbalized their thoughts as they worked on the task and their performance was videotaped for analysis. Preliminary results reveal important areas of student weakness and lead to recommendations for curriculum reform. Specializations: Science teacher education, development of problem-solving expertise, concept development and conceptual change, assessment of laboratory work. Specializations: Chemistry education, concept development and conceptual change, role of laboratory work.     

试论新课改下小学数学教学的创新

随着新课程改革的不断深入,小学数学教师也应转变传统的教学观念,创新数学教学方法,以达到新课程改革对小学阶段数学教学目标的新要求。小学阶段的数学教学能为学生未来更好地学习数学知识打好理论基础,在这一段时间内培养学生的良好学习习惯能使学生的学习达到事半功倍的效果。因此抓住这一关键期对学生进行教育,对帮助学生形成数学思维、提高学生运用数学知识解决实际问题的能力有重要作用。基于此,本文将研究在新课改背景下小学数学教学方法的几种创新形式。     

Curriculum reform in Irish secondary schools – a focus on algebra

Algebra has long been identified as an area of difficulty in the teaching and learning of mathematics. Evidence of this difficulty can be found in Irish secondary-level classrooms. Chief Examiner Reports have consistently identified algebra as an area of student weakness in State examinations. In light of poor student performance, and as part of a nationwide reform of secondary mathematics curricula, a functions-based approach to teaching algebra has been adopted in Irish schools. It was introduced in September 2011 in place of the transformational (rule and procedure)-based approach which was previously used. Through comparing the diagnostic test scores of incoming students in an Irish university in the years before and after the reform, this study finds that the reformed approach has coincided with a decline in students’ technical algebraic skills. However, interviews with practising mathematics teachers reveal that this decline is not a direct result of the functions-based approach, but rather of a mixture of approaches being implemented in classrooms. Such divergence of approaches can be linked to the common mismatch between the intended curriculum prescribed by policy-makers and the implemented curriculum that is actually carried out by teachers in their classrooms.     

Using virtual microscopy to scaffold learning of pathology: a naturalistic experiment on the role of visual and conceptual cues

New representational technologies, such as virtual microscopy, create new affordances for medical education. In the article, a study on the following two issues is reported: (a) How does collaborative use of virtual microscopy shape students’ engagement with and learning from virtual slides of tissue specimen? (b) How do visual and conceptual cues scaffold students’ reasoning? Fifteen pairs of medical students participated in two sessions in which the students used a virtual microscope as a diagnostic tool in the context of learning pathology. The slides provided the students with varying levels of visual and conceptual cueing. The sessions were videotaped, and the students’ reasoning while using the microscope was analysed. The students’ written answers were analysed in terms of the findings they made and the diagnoses suggested. At a general level, the results show that students engage actively in this kind of virtually-mediated environment. The visual and/or conceptual cues improve students’ performance, and guide the students’ perception and reasoning in a manner that is productive from the point of view of learning to make clinically relevant observations. Scaffolding students’ reasoning process through cues furthermore assists the students in avoiding the most obvious pitfalls such as overlooking critical areas of a specimen. Overall, visual and conceptual cues improve students’ reasoning in perceptual and cognitive terms, while still allowing space for the making of “relevant mistakes” that may further the students’ diagnostic skills.     

Educational effects of the Tools of the Mind curriculum: A randomized trial

The effectiveness of the Tools of the Mind (Tools) curriculum in improving the education of 3- and 4-year-old children was evaluated by means of a randomized trial. The Tools curriculum, based on the work of Vygotsky, focuses on the development of self-regulation at the same time as teaching literacy and mathematics skills in a way that is socially mediated by peers and teachers and with a focus on play. The control group experienced an established district-created model described as a “balanced literacy curriculum with themes.” Teachers and students were randomly assigned to either treatment or control classrooms. Children (88 Tools and 122 control) were compared on social behavior, language, and literacy growth. The Tools curriculum was found to improve classroom quality and children's executive function as indicated by lower scores on a problem behavior scale. There were indications that Tools also improved children's language development, but these effects were smaller and did not reach conventional levels of statistical significance in multi-level models or after adjustments for multiple comparisons. Our findings indicate that a developmentally appropriate curriculum with a strong emphasis on play can enhance learning and development so as to improve both the social and academic success of young children. Moreover, it is suggested that to the extent child care commonly increases behavior problems this outcome may be reversed through the use of more appropriate curricula that actually enhance self-regulation.     

Urban High School Students’ Critical Science Agency: Conceptual Understandings and Environmental Actions Around Climate Change

This study investigates how the enactment of a climate change curriculum supports students’ development of critical science agency, which includes students developing deep understandings of science concepts and the ability to take action at the individual and community levels. We examined the impact of a four to six week urban ecology curriculum on students from three different urban high schools in the USA. Data collection included pre and posttest written assessments from all students (n = 75) and pre and post interviews from focal students (n = 22) to examine how students’ conceptual understandings, beliefs and environmental actions changed. Our analyses showed that at the beginning of the curriculum, the majority of students believed that climate change was occurring; yet, they had limited conceptual understandings about climate change and were engaged in limited environmental actions. By the end of the curriculum, students had a significant increase in their understanding of climate change and the majority of students reported they were now engaged in actions to limit their personal impact on climate change. These findings suggest that believing a scientific theory (e.g. climate change) is not sufficient for critical science agency; rather, conceptual understandings and understandings of personal actions impact students’ choices. We recommend that future climate change curriculum focus on supporting students’ development of critical science agency by addressing common student misconceptions and by focusing on how students’ actions can have significant impacts on the environment.     

论清代广东书院的课程理念与教学模式

古代的"课程"是指学生根据考课目标而自我安排的学习规程。清代广东书院存在着两种课程模式,一种为应付科举而设置,一种为崇尚经史古学而设置。这一差异导致了"无课程"与"有课程"之书院的分野,展现了两类书院不同的教学风格,进而导致不同的教学效果:"无课程"书院注重围绕科举内容进行考课,这导致书院生徒不能潜心做学问,而有追求科名等沽名钓誉之行为;"有课程"之书院注重经史教学,强调学问的经世致用,进而保障生徒的自主学习,体现出对传统教育本真的回归,这是晚清书院改革的精髓所在。     

Unpacking the inequality among Turkish schools: Findings from PISA 2006

The study investigates the effects of certain school characteristics on students’ mathematics performances in Turkey in the PISA 2006 while controlling for family background and demographic characteristics. Three models of Hierarchical Linear Modeling (HLM) are constructed. The results reveal that 55% of the variance is attributable to between-schools and the remaining 45% to individual student characteristics. About two-thirds of the 55% is explained by selectivity in admissions, time to study mathematics and students’ SES, gender and the geographical region. The findings are interpreted to explain why Turkish schools differed greatly in average student performance in PISA 2006 by using the conceptual efforts on school quality factors and family background characteristics.