Examining Psychometric Properties and Level Classification of the van Hiele Geometry Test Using CTT and CDM Frameworks

The van Hiele theory and van Hiele Geometry Test have been extensively used in mathematics assessments across countries. The purpose of this study is to use classical test theory (CTT) and cognitive diagnostic modeling (CDM) frameworks to examine psychometric properties of the van Hiele Geometry Test and to compare how various classification criteria assign van Hiele levels to students. The findings support the hierarchical property of the van Hiele theory and levels. Using conventional and combined criteria to determine mastery of a level, the percentages of students classified into an overall level were relatively high. Although some items had aberrant difficulties and low item discrimination, varied selection of the criteria across levels improved item discrimination power, especially for those items with low item discrimination index (IDI) estimates. Based on the findings, we identify items on the van Hiele Geometry Test that might be revised and we suggest changes to classification criteria to increase the number of students who can be assigned an overall level of geometry thinking according to the theory. As a result, practitioners and researchers may be better positioned to use the van Hiele Geometry Test for classroom assessment.     

Preservice Primary Teachers' Geometric Thinking: Is Pre-Tertiary Mathematics Education Building Sufficiently Strong Foundations?

Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level preservice teachers' geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that develop preservice teachers' geometric knowledge to support the task of teaching. This study examines the geometric thinking levels of entry-level Irish preservice primary teachers (N = 381). Participants' geometric thinking levels were determined through a multiple-choice geometry test (van Hiele Geometry Test) prior to commencing a Geometry course within their ITE program. The findings reveal limited geometric thinking among half of the cohort and question the extent to which pre-tertiary experiences develop appropriate foundations to facilitate a smooth transition into ITE mathematics programs. The study also examines the nature of misconceptions among those with limited geometric thinking and presents suggestions to enhance the geometric understandings of preservice teachers.     

Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes

Teaching geometry at the elementary level is challenging. This study examines the impact of van Hiele theory-based instructional activities embedded into an elementary mathematics methods course on preservice teachers’ geometry knowledge for teaching. Pre- and post-assessment data from 111 elementary preservice teachers revealed that van Hiele theory-based instruction can be effective in improving three strands of participants’ geometry knowledge for teaching: geometry content knowledge, knowledge of students’ van Hiele levels, and knowledge of geometry instructional activities. As a result, this paper offers implications for teacher educators and policy makers to better prepare elementary preservice teachers with geometry knowledge for teaching.     

Sex-related differences in the acquisition of the van hiele levels and motivation in learning geometry

The purpose of this study was to examine the acquisition of the van Hiele levels and motivation of sixth-grade students engaged in instruction using van Hiele theory-based mathematics curricula. There were 150 sixth-grade students, 66 boys and 84 girls, involved in the study. The researcher employed a multiple-choice geometry test to find out students’ reasoning stages and a questionnaire to detect students’ motivation in regards to the instruction. These instruments were administered to the students before and after a five-week period of instruction. The paired-samples t-test, the independent-samples t-test, and ANCOVA with α = .05 were used to analyze the quantitative data. The study demonstrated that there was no statistically significant difference as in motivation between boys and girls, and that no significant difference was detected in the acquisition of the levels between boys and girls. In other words, gender was not a factor in learning geometry.     

Development of Arithmetical Thinking: Evaluation of Subject Matter Knowledge of Pre-Service Teachers in Order to Design the Appropriate Course

One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.     

A comparative study on the effectiveness of the computer assisted method and the interactionist approach to teaching geometry shapes to young children

The purpose of this study is to compare and evaluate the effectiveness of computer assisted teaching of geometry shapes and an interactionist approach to teaching geometry in kindergarten versus other more traditional teaching methods. Our research compares the improvement of the children’s geometrical competence using two teaching approaches. The first one employs our ICT oriented learning method specifically targeting Realistic Mathematics Education (RME) and the van Hiele model for geometry shapes. The second method is based on the interactionist approach of teaching children in kindergarten. The sample consisted of 139 Greek kindergarten children from Crete. We conducted interventions based on the above two methods, in two experimental groups. The first experimental group consisted of 50 children who were taught geometry shapes according to the principles of Realistic Mathematics Education with the use of appropriate educational software. The second experimental group consisted of 45 children who were taught about geometry shapes with an interactionist approach without the use of computers. The control group consisted of 44 children and was taught about geometry shapes following the ways teachers chose to put the basic pedagogical principles of Curriculum for kindergarten into practice without the use of ICT. Children in all groups were pre-tested and post-tested for their geometry performance. The results showed that the teaching approaches of our interventions, the one with the additional use of ICT and the interactionist one, contribute significantly more to the development of kindergarten children’s geometry competence as compared to other traditional methods.     

Geometry in engineering education

In this paper, a few examples are given of the importance of mathematical geometric education for engineers. The newly established information civilization, utilizing new information media, requires an abbreviated form of delivering enormous amounts of information at incredible speed. We use and relay models and involve them in our communication in almost all branches of science, culture, education, or social life. Models are strictly based on some graphical information. They are independent and almost perfectly understood at all levels of human literacy. Different scientific branches invented different models with respect to different needs and applied techniques, while the basic original idea of creating an'image' remained. Engineering education today is a complex knowledge base composed of several separate parts of different scientific and professional technical branches of the complex human knowledge, where geometry plays its definite important role. It is the basic platform to get involved with the creation of models in the form of images. Geometry can offer an unprecedented basis for logical reasoning supported by practical applications. Good three-dimensional visualization, spatial capabilities and geometric understanding are invaluable components of creative work in all kinds of human activities. An information society using communication techniques concentrates nowadays on creating models of an object in the form of computer images. Creative processes of modelling objects in scenes are related basically to the synthetic geometric reasoning and depend on the skills and geometric knowledge of the users. We must take this fact into consideration when speaking about teaching geometry to engineers.

Geometry is not just a simple science, nor the way to knowledge. It is an intellectual arrangement. From the arrangement, all European culture originated.     

Desargues定理及其应用

Desargues定理是高等几何的重要定理,它同时也是从一维射影几何进入二维射影几何的一座重要桥梁;高等几何的许多定理都以它为依据,推出一系列射影几何命题.它也是平面(二维)射影几何的重要基础之一.Desargues定理蕴含丰富的数学思想方法,对具体问题的处理方法具有独特性,灵活性,同时对解决中学几何中的有关命题提供了一种新的模式及有关背景知识.     

Using LOGO with Infant School Children

Abstract The recent introduction of micro‐computers into schools is opening up many new avenues for developmental psychologists interested in studying how children learn. Of particular interest at present are approaches in which children program computers themselves, using languages such as LOGO and PROLOG. This paper describes a study in which a simplified version of LOGO was introduced to a group of six‐year‐olds in a severely deprived area of Edinburgh. The children used a special touch‐sensitive keyboard (Concept Keyboard) to control the movements of a floor‐crawling robot called a Turtle. The sessions with the Turtle were marked by high levels of concentration, collaborative problem‐solving and the use of mathematical language. Pre‐ and post‐tests on the British Ability Scales revealed statistically significant gains on the sub‐scales concerned with number and shape: these gains, however, were found only in the boys.     

普通中学男女生立体几何学习差异的研究

以荷兰学者VanHiele关于几何学习必须经过三个阶段的理论为基础,调查了普通中学男女生学习立体几何的情况．结果表明：在VanHiele理论的第一阶段,男女生之间不存在明显的差异,但在第二、第三阶段则存在较为明显的差异．并对产生差异的原因进行了分析．     

The Relation Between Preschoolers’ Vocabulary Development and Their Ability to Predict and Recognize Words

By age 2, children are developing foundational language processing skills, such as quickly recognizing words and predicting words before they occur. How do these skills relate to children’s structural knowledge of vocabulary? Multiple aspects of language processing were simultaneously measured in a sample of 2-to-5-year-olds (N = 215): While older children were more fluent at recognizing words, at predicting words in a graded fashion, and at revising incorrect predictions, only revision was associated with concurrent vocabulary knowledge once age was accounted for. However, an exploratory longitudinal follow-up (N = 55) then found that word recognition and prediction skills were associated with rate of subsequent vocabulary development, but revision skills were not. We argue that prediction skills may facilitate language learning through enhancing processing speed.     

The Instructional and Emotional Quality of Parent–Child Book Reading and Early Head Start Children's Learning Outcomes

Research Findings: The objective of this study was to understand how two dimensions of parent–child book-reading quality—instructional and emotional—interact and relate to learning in a sample of low-income infants and toddlers. Participants included 81 parents and their children from Early Head Start programs in the rural Midwest. Correlation and multiple regression analyses were used to test the hypothesis that parental book-reading qualities interact and relate to children's concurrent cognitive and language scores. Exploratory analyses examined if patterns of relationships varied for families who had different home languages (i.e., English, Spanish). Results included that book-reading qualities and home language interacted to predict child scores. Practice or Policy: Findings suggest a need to further explore potentially complex patterns of relationships among parental book-reading behaviors and child learning for diverse families. Understanding these patterns could inform the development of culturally-sensitive intervention approaches designed to support high-quality shared book reading.     

对高师"初等几何研究"进行课程整合的可行性研究

在高校扩招的形势下,结合基础教育改革的背景和高师"初等几何研究"的现状,对高师"初等几何研究"课程整合提出了指导思想和方案.其中,强调"高初结合",突出公理化方法和几何变换的思想.     

Dual language development of Latino children: Effect of instructional program type and the home and school language environment

Latino dual language children typically enter school with a wide range of proficiencies in Spanish and English, many with low proficiency in both languages, yet do make gains in one or both languages during their first school years. Dual language development is associated with how language is used at home and school, as well as the type of instructional program children receive at school. The present study investigates how changes in both Spanish and English proficiencies of Latino, second-generation immigrant children (n = 163) from kindergarten to second grade relate to instructional program type as well as language use at home and school. A series of MANCOVAs demonstrated significant dual language gains in children who were in bilingual classrooms and schools where Spanish was used among the teachers, students, and staff. Furthermore, only in classrooms where both Spanish and English were used did children reach age-appropriate levels of academic proficiency in both languages. Home language use was also significantly associated with dual language gains as was maternal Spanish vocabulary knowledge before controlling for maternal education. Educational implications and potential benefits associated with bilingualism are discussed.     

A DGS gesture dictionary for modelling on mobile devices

Interactive or Dynamic Geometry System (DGS) is a tool that help to teach and learn geometry using a computer-based interactive environment. Traditionally, the interaction with DGS is based on keyboard and mouse events where the functionalities are accessed using a menu of icons. Nevertheless, recent findings suggest that such a traditional model of interaction has a steep learning curve and is inadequate to develop DGS for devices with multi-touch screens. Thus, we propose a new interaction model for DGS based on a gesture dictionary which enables the construction and manipulation of geometric objects without the need of accessing a menu of icons. The dictionary is divided into three types: (i) kernel gestures: which are the basis for defining gestures; (ii) navigation gestures: related to the manipulation and editing of geometric objects; and (iii) basic gestures of construction: to construct geometric objects. To validate our interaction model, a DGS for mobile device, GeoTouch, has been developed using the proposed dictionary. Usability tests were performed comparing GeoTouch with three other DGS for mobile devices. The results indicate that the GeoTouch interface has fewer usability problems than the other three DGS software and it is easier to learn and interact with.     

A comparison of preservice and in-service earth and space science teachers' general mental abilities,content knowledge,and problem-solving skills

The purpose of this study was to compare in-service and preservice earth and space science teachers on their general mental abilities, their content knowledge or declarative knowledge of earth and space sciences, the Gagnean levels of their content knowledge or declarative knowledge, and the procedural knowledge used in solving earth and space science problems. This study used a contrast-group design to compare in-service (n = 30) and preservice (n = 30) earth and space science teachers. The in-service earth science teachers (a) bring more declarative knowledge to the problem-solving situation, (b) use fewer steps while problem solving, (c) generate more subroutines and alternate hypotheses, and (d) possess different structural knowledge than do preservice earth science teachers. Findings from this study support Norman's theory of learning that experts (in-service teachers) function at the tuning mode of learning, whereas novices (preservice teachers) function in an accreting or structuring mode. In-service earth science teachers exhibited smoothness, automaticity, and decreased mental effort not exhibited by preservice earth and space science teachers.     

Talking Shape: Parental Language With Electronic Versus Traditional Shape Sorters

As the traditional toys of the past are quickly being replaced with electronically “enhanced” toys, it is important to understand how these changes impact parent–child interactions, especially in light of the evidence that the richness and variety of these interactions have long‐term effects on diverse areas of cognition (Hart & Risley, 1995). Here, we compared the quantity and quality of the language children hear during play with either a traditional (nonelectronic) or an electronic shape sorter designed to teach children about geometric shapes. Spatial toys and spatial language, in particular, were explored since recent work has established that parents' use of spatial language links to children's short‐ and long‐term performance on spatial tasks (Pruden, Levine, & Huttenlocher, 2011), and that spatial skills are relevant to success in learning mathematics and science (Newcombe, 2010). Traditional toys prompted more parental spatial language and more varied overall language than did electronic toys.     

Relationships Among Teachers’ Use of Mental State Verbs and Children’s Vocabulary Growth

Research Findings: Mental state verbs (MSV), a component of literate and academic language, may facilitate vocabulary growth, as they relate to metacognitive and metalinguistic awareness as well as decontextualized talk, all of which have been associated with vocabulary growth. In this study, we examined teacher MSV use in group content instruction and book reading in Head Start classrooms (N = 49) to determine the prevalence of teachers’ use of MSV. We sought to determine whether there was an association between teachers’ MSV use and children’s (N = 402) receptive and expressive vocabulary scores across 1 year of preschool. Results from hierarchical linear modeling revealed that teachers’ use of MSV in group content instruction was positively associated with children’s end-of-year receptive, but not expressive, vocabulary scores. No significant relations emerged for book reading. Positive associations between MSV in which the child was the referent of the verb and children’s receptive vocabulary were found, which indicates a potential scaffolding effect. Practice or Policy: Results indicate that teachers should consider including MSV in their content-rich instruction and provide support by placing the child as the referent of the verb. Additional instructional implications are addressed.     

LISTEN TO THE SILENCE: THE LEFT-BEHIND PHENOMENON AS SEEN THROUGH CLASSROOM VIDEOS AND TEACHERS’ REFLECTIONS

This study uses classroom videotapes to examine the phenomenon of students who are left behind during whole-class teaching. Zooming in via these videos enabled us to analyze these classroom situations by means of a compact, multi-perspective set of theories – van Hiele theory, conceptualization, and visual perception. The analysis provided a picture of the classroom interaction in which the sound of silence of those students who might not share understanding during the class discourse is ignored. Based on a sample of Taiwanese junior high school geometry classes, the study demonstrated how investigating situations of silence uncovered the possibility of teachers’ unawareness of student difficulties or their unsuccessful efforts to cope with them. Teachers’ post-lesson interviews and questionnaires shed additional light on the perspective of left-behind students. Implications of this method for pre- and in-service teachers’ programs are briefly discussed, and some recommendations for change are proposed. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.