Growth in mathematical understanding: How can we characterise it and how can we represent it?

There has been a variety of approaches to the study of mathematical understanding, and some of these are reviewed before outlining the background to the model we are proposing for the growth of such understanding. The model is explained in detail and illustrated with reference to the concept of fractions. Key features of the model include don't need boundaries, folding back, and the complementarities of acting and expressing that occur at each level of understanding. The theory is illustrated by examples of pupils' work from a variety of topics and stages. Finally one of the practical applications of the theory, mapping, is explained in some detail.     

how long,how often,how soon 与 how far

how long主要用来提问动作延续了多长时间，答语通常用“for＋一段时间”、“since＋时间点”或since引导的时间状语从句。问句和答语中的谓语动词通常为延续性动词。例如：     

Discussing Environmental Education Research: how do we speak with each other?

On the Internet, newsgroups exist to promote the rapid exchange of views, critical comment, and information between interested parties. Newsgroups are accessible to everyone with access to the Internet, across the world. We propose a new newsgroup in the specific field of environmental education research to carry items likely to be of interest to those who read this journal.     

how long、how often 与 how soon

一、how long为"多长时间"之意,用来对某一动作或状语时间持续长短的提问,常用于过去、现在完成或将来时态,要用延续性动词.     

how long,how often, how soon

how long,how often与how soon引起的疑问句在译成汉语时均有“多久”之意。那么,它们之间究竟有哪些不同呢? 1.how long表示一段的时间,意为“(行为或状态持续了)多久”。修饰谓语,强调动作或状态延续的时间,多提问陈述句中for或since引     

Sustainable schools programmes: what influence on schools and how do we know?

This paper focuses on our experience of researching the influence of ResourceSmart Schools, a sustainable schools programme in Victoria, Australia. Drawing on ideas from programme theory and realist synthesis, we illustrate and reflect upon our approach to conceptualising, investigating and generating evidence about the programme’s impacts and influence in participating schools. This distinction is deliberate: it helps distinguish between efforts to understand the impacts that a programme has within schools (programme impact), and efforts to understand what it is about a programme that is influential in bringing about those impacts (programme influence). Drawing on evidence from our work in this project and the wider literature, we argue for a more nuanced discussion and more sophisticated investigations into the complexities of programme influence, rather than impacts only. Our conclusions suggest key areas of development for our own work, the provision of environmental and sustainability education, and their evaluation and research more broadly.     

how long,how often和how soon用法辨析

how long,how often和how soon都有“多久”的含意,但实际上它们的意义和用法有较大的差别。how long用来询问谓语动词所表示的动作延续的时间长度有“多久”。它常与延续性动词的现在完成时连用,但有时也与延续性动词的一般将来时(或动词前有情态动词)、一般过去时或过去完成时连用。例如:1.—How long have you known her?—For about four years.2.—How long will it take you to finish the work?—Ten days.3.How long can you stay here?4.How long did your mother teach in the school?5.He asked me how long I had lived in …     

怎样学习应用how long,how often,how soon

通常how long,how often,how soon这三个词组都是表示对时间提问的词组,也都含有"多久"的意思.许多初中低年级学生,在应用的时候混淆不清,经常出现错误.我们应该怎样去区分它们之间的差别呢?     

你会用how long,how often,how soon吗

how long,how often,how soon三者均可译为"多久",但有区别。你知道它们的区别吗?一、how long how long有以下两个主要意思: 1.表示多长时间,主要用来对一段时间(如three days,four weeks等)提问。如:     

A ramble through the cell: how can we clear such a complicated trail?

The arrangement of course information in a logical sequence for molecular life science (MLS) courses remains a matter of some controversy, even within a single subdiscipline such as biochemistry. This is due to the explosion of knowledge, the latest bioinformatic revelations, and the observation that new discoveries sometimes reveal specific connections between previously disparate topics. However, the general outlines of biomedical information are in place, at least the knowledge that should be conveyed to undergraduates taking cell and molecular biology and biochemistry. Despite the increasing amount and complexity of the information to be presented, integration and unification are possible because the molecular reactions and interactions that underlie all life processes are coming into view: they are common to all cellular structural rearrangements, nucleic acid functions, and biochemical reactions, whether of plant or animal origin. Also, it is no longer possible to draw clear boundaries between cell biology, biochemistry, and molecular biology that would not violate the fundamental unity of our understanding. Therefore, an arrangement of content is proposed for a two-semester course that aims to present a unified portrait of upper-division undergraduate MLS.     

怎样学习应用how long,how offen,how soon

通常how long,how often,how soon这三个词组都是表示对时间提问的词组,也都含有"多久"的意思。许多初中低年级学生,在应用的时候混淆不清,经常出现错误。我们应该怎样去区分它们之间的差别呢?     

how many与how much练析

how many与how much均有“多少”之意,都用在特殊疑问句的开头,但二者有明显区别：     

“how much与how many”知多少

how much的意思是"多少钱"。我们用它来询问价格。如果所询问的东西是不可数名词或可数名词的单数时,后面的谓语动词用is;所询问的东西是可数名词复数或不止一种东西时,后面的谓语动词用are。如:     

We can,we know how. But do we want to? Teaching attitudes towards ICT based on the level of technology integration in schools

Teachers’ attitudes towards technology are crucial to foster its use in schools and to improve its educational affordances and this is still a topic for research. This article relates the attitudes school teachers have towards information and communication technologies (ICT) with the different levels of technology integration in schools. A multiple case-study research methodology was applied, and in which the school was the unit of sampling used. Thirty-five schools from eight Spanish regions were selected, and 1222 questionnaires were collected, representing 78.9% of the sample. Three combined variables were utilised to classify schools in four different levels of technology integration. Results suggest level 4 school teachers exhibit better attitudes towards ICT, which results in creating a positive circle which improves the learning process. This becomes relevant for teacher education and professional development, as effective ICT integration in the classroom can perform as a catalyst for educational innovation.