Teaching fractions to adult learners enrolled in a civil construction course : knowledge, action and materials action in tandem

This paper investigates the teaching and learning of fractions to Indigenous adult learners in a Civil Construction Certificate Course. More specifically it explores why the use of materials is critical to building knowledge and understanding. This focus is important for two reasons. First, it allows for considerations of a trainer’s approach for teaching fractions and, second it provides insights into how adult learners can be supported with representing their practical experiences of fractions to make generalisation thus building on their knowledge and learning experiences. The paper draws on teaching episodes from an Australian Research Council funded Linkage project that investigates how mathematics is taught and learned in Certificate Courses, here, Certificate 11 in Civil Construction. Action research and decolonising methods (Smith, 1999) were used to conduct the research. Video excerpts which feature one trainer and three students are analysed and described. Findings from the data indicate that adult learners need to be supported with materials to assist with building their capacity to know and apply understandings of fractions in a range of contexts, besides construction. Without materials and where fractions are taught via pen and paper tasks, students are less likely to retain and apply fraction ideas to their Certificate Course. Further they are less likely to understand decimals because of limited understanding of fractions.

Curricula integration : identifying and locating engineering education across the Australian curriculum

Science, technology, engineering and mathematics (STEM) has become an educational package emerging throughout the world (e.g. UK, China, US & Australia). Although science, technology and mathematics are taught in schools and engineering education occurs in universities, there appear to be few if any explicit engineering education programs in primary and junior secondary schools. A stronger inclusion of engineering education at these levels could assist students to make informed decisions about career opportunities in STEM-related fields. This paper suggests how engineering education can be integrated with other key learning areas such as English, mathematics, science, history and geography within the new Australian Curriculum.

ORIGO Stepping Stones Grade K Student Journal

A mathematics curriculum for the Common Core Curriculum at the Kindergarten level for the USA

The knowledge base of subject-matter experts in teaching : A case study of a professional scientist as a beginning teacher

One method of addressing the shortage of science and mathematics teachers is to train scientists and other science-related professionals to become teachers. Advocates argue that as discipline experts these career changers can relate the subject matter knowledge to various contexts and applications in teaching. In this paper, through interviews and classroom observations with a former scientist and her students, we examine how one career changer used her expertise in microbiology to teach microscopy. These data provided the basis for a description of the teacher’s instruction which was then analysed for components of domain knowledge for teaching. Consistent with the literature, the findings revealed that this career changer needed to develop her pedagogical knowledge. However, an interesting finding was that the teacher’s subject matter as a science teacher differed substantively from her knowledge as a scientist. This finding challenges the assumption that subject matter is readily transferable across professions and provides insight into how to better prepare and support career changers to transition from scientist to science teacher.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Making meaning in mathematics problem solving using the Reciprocal Teaching approach

This paper examines the application of the Reciprocal Teaching instructional approach to Mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving Mathematical word problems.