After acquiring sufficient vocabulary in a foreign language, learners start understanding parts of conversations in that language. Speaking, in contrast, is a harder task. Forming grammatical sentences requires choosing the right tenses and following syntax rules. Every beginner EFL speaker makes grammar errors – and the type of grammar errors can reveal hints about their native language. For instance, Russian speakers tend to omit the determiner “the” because Russian doesn’t use such modifying words. One linguistic phenomenon that is actually easier in English than in many other languages is grammatical gender. English doesn’t assign gender to inanimate nouns such as “table” or “cup.” A few years ago, the differences in grammatical gender between languages helped reveal societal gender bias in automatic translation: translation systems that were shown gender-neutral statements in Turkish about doctors and nurses assumed that the doctor was male while the nurse was female.

At what time does the afternoon start, at 1 p.m. or 3 p.m.? Language understanding requires the ability to correctly match statements to their real-world meaning. This mapping process is a function of the context, which includes various factors such as location and time as well as the speaker’s and listeners’ backgrounds. For example, an utterance like, “It is hot today,” would mean different things were it expressed in Death Valley versus Alaska. Based on our background and experiences, people have different interpretations for time expressions, color descriptions, geographic expressions, qualities, relative expressions, and more. This ability to map language to real-world meaning is also required from the language technology tools we use. For example, translating a recipe that contains instructions to “preheat the oven to 180 degrees” requires a translation system to understand the implicit scale (e.g. Celsius versus Fahrenheit) based on the source language and the user’s location. To date, no automatic translation systems can do this, and there is little “grounding” in any widely used language technology tool.

In order to be effective mathematics educators, teachers need more than content knowledge: they need to be able to make mathematics comprehensible and accessible to their students. Teaching Key Concepts in the Australian Mathematics Curriculum Years 7 to 10 ensures that pre-service and practising teachers in Australia have the tools and resources required to teach lower secondary mathematics.

By simplifying the underlying concepts of mathematics, this book equips teachers to design and deliver mathematics lessons at the lower secondary level. The text provides a variety of practical activities and teaching ideas that translate the latest version of the Australian Curriculum into classroom practice. It covers the challenges of middle year mathematics, including the current decline in student numeracy, as well as complex theories which teachers can struggle to explain clearly. Topics include number, algebra, measurement, space, statistics and probability. Whether educators have recently studied more complicated mathematics or are teaching out of field, they are supported to recall ideas and concepts that they may have forgotten – or that may not have been made explicit in their own education.

Authored by experienced classroom educators and academics, this book is a vital resource for pre-service and practising Years 7 to 10 mathematics teachers, regardless of their backgrounds and experiences.

In order to be effective mathematics educators, teachers need more than content knowledge: they need to be able to make mathematics comprehensible and accessible to their students. Teaching Key Concepts in the Australian Mathematics Curriculum Years 7 to 10 ensures that pre-service and practising teachers in Australia have the tools and resources required to teach lower secondary mathematics.

By simplifying the underlying concepts of mathematics, this book equips teachers to design and deliver mathematics lessons at the lower secondary level. The text provides a variety of practical activities and teaching ideas that translate the latest version of the Australian Curriculum into classroom practice. It covers the challenges of middle year mathematics, including the current decline in student numeracy, as well as complex theories which teachers can struggle to explain clearly. Topics include number, algebra, measurement, space, statistics and probability. Whether educators have recently studied more complicated mathematics or are teaching out of field, they are supported to recall ideas and concepts that they may have forgotten – or that may not have been made explicit in their own education.

Authored by experienced classroom educators and academics, this book is a vital resource for pre-service and practising Years 7 to 10 mathematics teachers, regardless of their backgrounds and experiences.

Non-compositional phrases such as “by and large” are phrases whose meaning cannot be unlocked by simply translating the combination of words they constitute. In particular, figurative expressions – such as idioms, similes and metaphors – are ubiquitous in English. Among other reasons, figurative expressions are acquired late in the language learning journey because they often capture cultural conventions and social norms associated with the people speaking the language. Figurative expressions are especially prevalent in creative writing, acting as the spice that adds flavor to the writing. Artificial intelligence (AI) writing assistants such as ChatGPT are now capable of editing raw drafts into well-written pieces, to the advantage of native and non-native speakers alike. These AI tools, which have gained their writing skills from exposure to vast amounts of online text, are extremely adept at generating text similar to the texts they have been exposed to. Unfortunately, they have demonstrated shortcomings in creative writing that requires deviating from the norm.

In order to be effective mathematics educators, teachers need more than content knowledge: they need to be able to make mathematics comprehensible and accessible to their students. Teaching Key Concepts in the Australian Mathematics Curriculum Years 7 to 10 ensures that pre-service and practising teachers in Australia have the tools and resources required to teach lower secondary mathematics.

By simplifying the underlying concepts of mathematics, this book equips teachers to design and deliver mathematics lessons at the lower secondary level. The text provides a variety of practical activities and teaching ideas that translate the latest version of the Australian Curriculum into classroom practice. It covers the challenges of middle year mathematics, including the current decline in student numeracy, as well as complex theories which teachers can struggle to explain clearly. Topics include number, algebra, measurement, space, statistics and probability. Whether educators have recently studied more complicated mathematics or are teaching out of field, they are supported to recall ideas and concepts that they may have forgotten – or that may not have been made explicit in their own education.

Authored by experienced classroom educators and academics, this book is a vital resource for pre-service and practising Years 7 to 10 mathematics teachers, regardless of their backgrounds and experiences.