Influence of instruction in mathematics for low performing students on strategy use

Effects of two subtraction instruction types for low achieving children were compared. The first was based on constructivist ideas. The second was more or less traditional but did include interaction opportunities comparable to those in constructivist classrooms. Sixteen students (eight in each condition) with an average age of 10.5 years were trained during 34 lessons. Results showed no performance differences between the two groups on the subtraction problems instructed. There was a performance advantage for the traditional group on transfer problems without regrouping. The constructivist group used more different strategies but was not able to use this bigger repertory in a flexible way; instead, they used their strategies rather randomly. These findings pose questions on the usefulness of constructivist teaching in mathematics for low performers.     

建构主义：一种富有成效的数学教学实践范式

建构主义是一种新的认知理论，这种理论正逐渐成为国际数学教育改革中的一种主流理论。建构主义的基本观点为人们提供了反思数学教学的别样视角，同时也为数学教学提供了一种富有成效的应用框架。     

Towards a more inclusive approach to intervention research: the case of research in learning disabilities

Intervention research in special education tends to rely on comparisons of mean differences to determine instructional strategies that ‘work’ for students with disabilities. This reliance on mean differences obscures individual variation that is always present in educational research. This paper examines the degree to which individual variation is acknowledged in reports of intervention research published in four leading learning disabilities journals over a five-year period. It was found that, although there was considerable variance present in intervention studies published in these journals, this variability was often unacknowledged. This paper concludes with suggestions for how researchers might acknowledge variance in their research.     

Teaching early numeracy to students with autism using a school staff delivery model

Mathematics is one of the core school subjects in the UK and an emphasis is placed on developing pupils’ mathematical competencies throughout all key stages. Despite that, the attainment of students with disabilities in mathematics remains low. The current study explored ways in which the Teaching Early Numeracy to children with Developmental Disabilities (TEN-DD) programme could be implemented by teaching staff in a special school in the UK to improve the numeracy skills of students with autism. Adaptations to the delivery of the programme were made during the study as a result of continued collaboration with the participating school. The findings suggest that it may be feasible to implement the TEN-DD programme using a school staff delivery model and it may help learners improve their early numeracy skills. Practical aspects of TEN-DD’s implementation highlighted the need to incorporate more systematic adaptations for minimally verbal students, as well as for learners who might need additional training with prerequisite skills.     

A comparison of US and Korean students' mathematics skills using a cognitive diagnostic testing method: linkage to instruction

The purposes of the present study were (a) to compare US and Korean 8th graders' mastery of knowledge and skills in the mathematics test of the Trends in International Mathematics and Science Study (TIMSS) 2003 using a cognitive diagnostic testing method and (b) to find links between teachers' instruction and students' mastery of mathematics knowledge and skills. The participants included 740 US and 439 Korean 8th graders who took the Booklet 3 mathematics test. The results showed substantial differences between the US and Korean students' performance in problem restructuring and reasoning, measurement, and geometry. The most helpful instructional strategy for both Korean and US students was encouraging students' independent problem solving. Reviewing, re-teaching, and clarifying content were especially effective for the US students. Implications for teaching and learning are discussed.     

A reaction to “mathematics education: A vision of its evolutio” by Ricardo Cantoral and Rosa M. Farfán

The present article compares Cantoral and Farfan's socio-epistemological approach to mathematics education research (MER) with approaches of other current constructivist schools (such as emergent and sociocultural constructivism), in which interactionist and realistic approaches blend together. The theoretical problems of all these perspectives seem to center on the role that cultural tools are to play in future discourse of the different approaches to MER and identifying a set of problems with common ground in order to make comparisons possible. This revised version was published online in July 2006 with corrections to the Cover Date.     

高等数学"目标导向+阅读自学指导"教学模式的设计

针对高职高专《高等数学》教材及学生特点,采用“目标导向 阅读自学指导”教学模式可取得良好的教学效果。该模式以建构主义、主体性学习及人本主义为理论基础,具体设计时要抓好教学目标、教学方法、教学评价等环节的设计。     

Text comprehension strategy instruction with poor readers

The goal of this study was to investigate the effects of teachingtext comprehension strategies to children with decoding andreading comprehension problems and with a poor or normallistening ability. Two experiments are reported. Four textcomprehension strategies, viz., question generation, summarizing,clarification, and predicting were taught through directinstruction and reciprocal teaching. In both experiments, effectswere measured according to a pretest – posttest – retentiontest – control group design. Dependent variables wereexperimenter-developed strategic reading and listening tests, andstandardized reading and listening comprehension tests. In thefirst experiment the subjects were 9 to 11-year-old poor readersfrom special schools for children with learning disabilities. Inthis experiment, the intervention program's texts and strategyinstructions were presented in listening settings only. Thesubjects in the second experiment were 10-year-old children fromregular elementary schools and 9 to 11-year-old children fromspecial schools. They were also poor readers but their decodingperformance was not as poor as in the subjects in experiment 1.In experiment 2, the intervention program involved textpresentations in alternating reading and listening lessons.Although in general, normal listeners performed better on allcomprehension tests than poor listeners, there were nodifferential program effects for the two listening levels. Cleareffects of both programs were found on strategic reading andlistening tests administered directly after the interventions. Inthe first experiment, maintenance test performance showedprolonged program benefits, whereas in the second experimentthese maintenance effects were blurred by unexpected gains of thecontrol groups of students, especially from regular schools.Finally, apart from some local successes, neither of the twoexperiments offered stable evidence of transfer of comprehensionstrategy training to standardized general listening and readingcomprehension tests.     

特殊教育数学教学改革的一次成功尝试

我国特殊教育的数学教学现状,很难适应我国经济社会又好又快发展,也与建设社会主义和谐社会的目标背道而驰.由MM数学教育方式演变而来的TEC数学教学方式不仅适用于一般学生的数学教育,同样也适用于特殊教育中的数学教育.     

专业化的课堂教学评价工具RTOP评介

诞生于上个世纪末,以"基于标准"和"探究取向"为核心的经过严格开发程序的课堂教学评价工具RTOP,已经在美国有了大面积的评价实践,取得了很好的成效。十多年来,它在美国的中小学科学与数学教育改革进程中发挥了不可替代的作用。RTOP具有权威、可靠、易于操作的特点,既可用于大规模的教育科研、教育督导,也可以用于师范生的教学实训以及一线教师的在岗培训。     

Web-based science instruction for deaf students: What research says to the teacher

Web-based science education often involvesactivities that may enhance deaf students'learning. Research efforts to date indicategreat potential for web-based instruction,while simultaneously revealing precautionswhich need to be considered when developingmaterials for use with students who are deaf.Educators of deaf students need to beparticularly aware of such factors as readingability, motivation engagement of the students,and the need for visual reinforcement of thescience content.In this paper, three empirical research studiesrelated to earth science, chemistry, andphysical science are summarized. The results ofthese studies, as well as those from relatedempirical research, support the view that theremay be a beneficial synergistic learning effectobtained by the careful interspersing of textand American Sign Language explanations withanimation and other graphic organizers, and byencouraging the deaf learner to interact withthe materials through such techniques as theuse of adjunct questions.     

Learner Resistance to English-medium instruction practices: a qualitative case study

The internationalization of higher education has resulted in the growth of English-medium instruction (EMI) practices and research. The existing EMI research has documented learners’ favorable attitudes toward EMI but not necessarily its practices. Learners’ dissatisfaction has not been viewed as a form of resistance. Through the notion of learner resistance that underscores agency in defiance, this study examined the occurrences of learner resistance and the reasons for it by investigating Chinese learners’ experiences in an undergraduate business English-taught program in Taiwan. Multiple sources of data, including interviews, stories, and class observations, were gathered for analysis. The findings showed that most Chinese learners resisted an unhelpful curriculum, pedagogy, and context. Their resistance may be related not simply to academic disciplines but more importantly to a Confucian Heritage Culture of learning. Such findings highlight learner agency in resisting actions and call for further investigation into potential learner resistance in EMI practices.     

Improving seventh grade students’ learning of ratio and proportion: The role of schema-based instruction

The present study evaluated the effectiveness of an instructional intervention (schema-based instruction, SBI) that was designed to meet the diverse needs of middle school students by addressing the research literatures from both special education and mathematics education. Specifically, SBI emphasizes the role of the mathematical structure of problems and also provides students with a heuristic to aid and self-monitor problem solving. Further, SBI addresses well-articulated problem solving strategies and supports flexible use of the strategies based on the problem situation. One hundred forty eight seventh-grade students and their teachers participated in a 10-day intervention on learning to solve ratio and proportion word problems, with classrooms randomly assigned to SBI or a control condition. Results suggested that students in SBI treatment classes outperformed students in control classes on a problem solving measure, both at posttest and on a delayed posttest administered 4 months later. However, the two groups’ performance was comparable on a state standardized mathematics achievement test.     

Schema-based instruction: Effects of experienced and novice teacher implementers on seventh grade students' proportional problem solving

This study examined the effects of a research-based intervention, schema-based instruction (SBI), implemented by experienced- (taught SBI in previous study; Jitendra et al., 2015) and novice-teacher implementers (taught SBI for the first time with professional development) on the mathematics outcomes of seventh-grade students. SBI is a multicomponent intervention that emphasizes the mathematical structure of problems through the use of schematic diagrams and incorporates problem solving and metacognitive strategy instruction. Results indicated that both experienced- and novice-teacher implementers delivered SBI with similar levels of fidelity; there was no SBI experience effect on the immediate and 10-week retention tests of proportional problem-solving, on a general measure of problem solving, or on the end of the year state mathematics achievement test. These results provide evidence that the effectiveness of SBI generalizes over time to different cohorts of teachers and that the impact of SBI on student mathematics outcomes is maintained over time without additional PD.     

Using inquiry-based instruction to encourage teachers' historical thinking at historic sites

This study explores the use of inquiry-based instruction for constructing historical understanding in historic site-based teacher professional development programs. In an historic site-based professional development workshop, fifteen teachers of grades 5 through 12 engaged in guided inquiry with documents drawn from said historic site. Participants showed significantly increased curiosity about the site and use of problem-solving strategies in interactions with the site and staff, but no improvement in other elements related to historical thinking at historic sites. Improvements correlated to neither length of teaching experience nor testing group characteristics, indicating broad applicability for improving historic site-based professional development programs.     

Using Internet delivered video cases,to support pre-service teachers' understanding of effective early literacy instruction: An exploratory study

This preliminary study explores the effects ofusing CTELL (Case Technologies EnhancingLiteracy Learning) cases on preserviceteachers' learning. Students participated inone of three instructional treatments:traditional, traditional plus video, andtraditional plus CTELL cases. A pre-postconcept web, describing students' understandingof effective reading instruction, served as themajor outcome measure. This was supplementedwith a unidimensional confidence measure,journal entries, and student interviews. Nosignificant differences were found for any ofthe three treatment conditions on the conceptmapping task or the confidence measure.However, the journal entries and interview datahighlight important issues, challenges andbenefits, with respect to the use of multimediacases. Implications for teacher education areexplored.     

Race and class silences in teacher education: resisting strategy-based approaches to literacy methods instruction

This article draws on qualitative and practitioner research methodologies to unpack one critical incident from an undergraduate literacy methods course in which possessing complex understandings of endemic poverty proved central to assessing student achievement. In particular, we use an example of a comprehension lesson based on the children’s book Leah’s Pony as a key example through which to consider the dangers inherent in teaching pre-service teachers to adopt strategies that seem universal and innocuous, like answering comprehension questions or filling in worksheets, outside of broader critiques of social class, racism, poverty and student positioning in schools.     

Quantitative Literacy Across the Curriculum: Integrating Skills From English Composition,Mathematics, and the Substantive Disciplines

Quantitative literacy is an important proficiency that pertains to “word problems” from science, history, and other fields. Unfortunately, teaching how to solve such problems often is relegated to math courses alone. This article examines how quantitative literacy also involves concepts and skills from English composition and the substantive disciplines. The author outlines a systematic approach to writing the answers to word problems—a fundamental skill that applies to ongoing education, everyday life, and the workplace.     

Thinking styles: teaching and learning styles in graduate education students

This study investigated the relationship between two intellectual styles approaches: Sternberg’s thinking styles of teachers and Felder and Silverman’s learning styles. Ninety‐five graduate students majoring in special education, reading, educational leadership and curriculum, and elementary education completed the Thinking Styles in Teaching Inventory (TSTI) and the Index of Learning Styles Questionnaire (ILS). Several thinking styles from Sternberg’s theory of self‐government were highly to moderately correlated with Felder’s learning styles. The TSTI did not differentiate between master’s and doctoral students, but the ILS did so. Participants differed in their thinking styles in teaching and in their learning styles, based on their educational major.     

Critical perspectives on testing teaching: reframing teacher education for English medium instruction

The investigation reported here provides a basis for considering the role of corrective and transformative critiques in producing knowledge through testing teaching for reframing teacher education in response to, and as an expression of, the globalisation of English. This knowledge-producing approach to critique begins with a literature review of prior testing models of content and language integrated learning through English medium instruction (EMI) programmes. Delphi procedures were employed with a panel of 30 experts from three focus groups, namely teachers, testing experts, and teacher evaluation administrators. A comparison of relative importance of the indicators generated through this study via the analytic hierarchy process yielded practical implications for reframing the internationalisation of education using EMI. The analysis of interviews with teachers was used to critically rework or otherwise correct the testing model. Through adopting the practice of critique as a knowledge-producing venture, this study offers a model of EMI testing that can contribute to improvements in the organisation of professional learning and change, as well as certification procedures.