In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sph...

The paper offers insights into extensive reading issue in connection with a person-centered approach. major objective of the study was to ascertain significance not only for improvement language skills learning English but also development learner’s worldview through and discussing authentic texts used as an education resource. Empirical data were graded readers well workbooks manuals support m...

Nation (2006) has calculated that second language (L2) learners require much more vocabulary than previously thought to be functional with language (e.g., 8,000–9,000 word families to read independently). This level is far beyond the highest graded reader, and would be difficult to explicitly teach. One way for learners to be exposed to midfrequency vocabulary is to read authentic materials. Th...

Since the establishment of the Islamic Republic of Iran, there have been three packages used in the state-controlled schools of the country, namely, Graded, Right Path to English, and Prospect/Vision series. These textbooks all include prefaces to indicate the general philosophy of language teaching and education, and how the agents (learners and teachers) have to play roles in the system. This...

Formulaic language and sequence as the core characteristic of real-life language and native-like fluency, has been a subject of inquiry in recent decades. The aim of the present study is to investigate the effects of two extensive reading text types, i.e., adaptive and authentic, on Iranian EFL learners’ development of lexical bundles. To this aim, 20 intermediate EFL learners were chosen to pa...