Interview with David Greenwood, lead author of Essential Mathematics for the Australian Curriculum Second Edition

Big things have happened in 2015 at Cambridge University Press!


One of these big things is the second edition release of Essential Mathematics for the Australian Curriculum, our popular Years 7-10 mathematics series. Cambridge recently spoke with lead author David Greenwood about these new editions.

Cambridge University Press: What general revisions have the authors made for the second edition of Essential Mathematics for the Australian Curriculum?
David Greenwood: The authors have carefully considered a number of state interpretations of the Australian Curriculum and altered and added some content. Other refinements have been made to confirm mathematical rigour and remove ambiguity. Accessibility of questions to students of varying ability levels continues to be a focus.

CUP: What other new features have been introduced?
DG: Progress quizzes have been added at about the halfway point of each chapter to help assess progress up to that point. These are linked to the relevant section so it is clear what is being tested in each question. These quizzes are formative assessment tools and could be used individually by students or set as a class task.

Problem-solving receives a further boost with a Working with Unfamiliar Problems poster providing a reference guide for systematically tackling problem-solving questions. It is designed to be applied to a new, dedicated set of ‘unfamiliar problems’ at the start of the book, as well as the problems and challenges at the end of every chapter, and the Problem-solving and Reasoning questions in every exercise.

CUP: What has been retained for the second edition?
DG: The overall chapter and section structure has been retained. These structures allow teachers to realistically cover the Australian Curriculum in a given year and also provide varying pathways in mathematics for all students. The unique proficiency strand exercise structure is retained and is enhanced through the use of videos and other interactive components. Each exercise continues to offer enrichment problems to assist in the provision for able students. Calculator icons have been retained to help students and teachers decide when technology may be effective in their solutions to problems.

CUP: HOTmaths is now fully integrated with each Essential Mathematics interactive textbook. How does this benefit students?
DG: Students can now find all their resources including the text questions in one place without the need for extra logins. They can link to text problems, videos, walkthrough examples, widgets and other resources at anytime. They can also do the online tests set by their teachers in the same area or take part in the competitive Scorcher activity.

CUP: How does HOTmaths streamline teaching, assessment and reporting?
DG: Teachers can set tasks for their students and have the built-in learning management system record all the data and receive automatically generated reports. They could use the videos as part of their lesson plan and produce assessment task using the test-maker facility. In front of the classroom they may wish to explore interactive walkthroughs and widgets. They can print tests and HOTsheets to add to the activities and assessment for the topic.

CUP: The interactive textbooks feature many video worked examples. Why were these videos created and how do you envisage them being used?
DG: Videos of worked examples can be a very effective resource for students and teachers. They can be set for homework in a flipped classroom model or assist students when difficulties are experienced with related questions. Videos can also be used to catch up lesson content if classes have been missed. Teachers may also wish to ask students to watch videos in class if differentiated learning methods are being employed.

Professionally constructed, these videos include many visual and aural elements which aim to help build understanding. The videos can be paused and replayed at any time.

CUP: Changes have been made in the second edition that focus on differentiation in the classroom. Can you explain this in greater detail?
DG: At a course level, we differentiate by clearly labelling sections which are essentially Revision or Extension from a curriculum perspective. The following labels are used:

Consolidating: These sections cover essential elements of a topic which should be mastered before tackling new curriculum content for that year level. Note that these sections are structured in the same way as other core and extension sections so that all students can find opportunity and challenge from the graded problems within the exercise. Schools may wish, however, to condense or skip these sections for highly able students or classes.

Extending: These sections go beyond the core Australian Curriculum for that year level but add logical extensions to each topic which open pathways to higher levels of mathematics in the senior years. Like other sections in the text, a level of differentiation is also offered inside each of these extension sections providing flexibility for teachers with students of varying ability levels.

At a class by class level we have embedded the three differentiated pathways into each exercise. These pathways (Foundation, Standard and Advanced) form three different learning schemes for students operating at different levels. Teachers or students can choose which pathway is the most suitable.

Further differentiation is offered through a range of text and interactive resources including: problems and challenges, investigations, problem-solving focus questions, interactive walkthroughs and widgets, HOTsheets, etc.

CUP: Why have the exercises been structured as they are?
DG: All exercises have been structured to provide all students with the opportunity to work within all four Proficiency Strands of the Australian Curriculum: (Understanding, Fluency, Problem-solving and Reasoning). While working with the embedded pathways, student of all ability levels can access problems from the different Proficiency Strands. A level of grading not only exists from beginning to end in each exercise but also within each Proficiency Strand section.

CUP: What do the three columns in the working programs mean? How do the working programs assist with differentiation?
DG: The three columns allow students of all ability to work through an exercise with exposure to problems which fit all Proficiency Strands. Weaker students focus more on Understanding and Fluency but still try some appropriate Problem-solving and Reasoning problems, while more advanced students have a lighter load of Understanding and Fluency problems and a more challenging pathway through Problem-solving, Reasoning and Enrichment. Standard level students are provided a balanced selection of problems. Teachers and students can negotiate changes to the pathway selection as they see fit.

CUP: How might teachers use the working programs in the classroom?
DG: In a mixed-ability classroom, teachers could choose the most appropriate pathway for their student based on previous performance data or by using the pre-test. In a streamed setting, teachers may wish to set a particular program for the entire class and make minor adjustments if required.

Via the interactive site, students can select their designated pathways and only those questions will be visible. This provides a well-balanced selection of problems without the distraction of all the other questions or parts in the section.

To find out more about Essential Mathematics for the Australian Curriculum Second Edition head to our website

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