In the context of a professional learning research project we investigated the nature of support offered to classroom teachers and school mathematics leaders to facilitate teachers' implementation of sequences of challenging tasks. End of year questionnaire data were collected from 70 Foundation to Year 2 teachers and ten numeracy leaders who…

This paper discusses the design modifications of a sequence of specified learning goals for teaching early number, which characterise an instructional resource developed in a design research collaboration with teachers in Mexican preschools. Highlighted are the types of research involvement that appear to be necessary in designing resources for…

The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their participation in a professional learning project. Findings suggest that teachers': view prompts as important…

This paper outlines the rationale for, and some elements of, a particular approach to teaching and learning mathematics in the early years. The researchers worked with two school systems to offer both centrally delivered and school-based teacher professional learning, which included the application of illustrative teaching resources. The project…

This study reports on an early career Year 2 teacher's reflections of enacting specifically structured resource materials and her practice change when participating in a mathematics professional learning project. A qualitative case study was designed to examine the reflections of a teacher's pre-service and in-service teaching experiences. Data…

In this paper a didactic proposal is presented which consists of a methodology aimed at secondary level mathematics teachers, the aim of this proposal is to provide the teacher with a tool to design teaching sequences in order to take them to the classroom; These designs have the particularity of incorporating digital technology for the…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

This paper reports on a study that explored the use of cognitively challenging tasks with low-attaining mathematics students and in particular, their teachers' attempts at scaffolding. A major finding was that responding appropriately to scaffolding opportunities was challenging for the teachers. In this paper two main factors are discussed which…

Adaptive learning techniques have typically scheduled practice using learners' accuracy and item presentation history. We describe an adaptive learning system (Adaptive Response Time Based Sequencing--ARTS) that uses both accuracy and response time (RT) as direct inputs into sequencing. Response times are used to assess learning strength and to…

Research suggests that basic writers are willing to edit but reluctant to revise their writing. In other words, they make surface-level changes to grammar, spelling, and punctuation but tend not to re-conceive content, structure, style, and cohesion. This paper argues that we need more instructional strategies that will help students understand…

We are researching actions that teachers can take to improve mathematics learning for all students. Structural elements of the lessons being trialled include making aspects of pedagogy explicit to seek to overcome differences in familiarity with schooling processes, and sequencing tasks with the potential to engage students. This article reports…

Freewriting can be more than merely a prewriting heuristic that provides preparation for more advanced kinds of writing. A class at Jefferson Davis State Junior College (Alabama) attempts to promote the lack of pressure as well as the freedom and spontaneity that freewriting allows to a traditional composition course. In this class, freewritings…

Increasing numbers of teachers seem to recognize that sequencing assignments is an effective way to teach writing. A sequence of 20 writing assignments was developed by four composition instructors at the United States Air Force Academy in Colorado. The first eight exercises asked cadets to look at and think about their physical surroundings at…

So that the non-English speaking students could grasp the simple rudiments of English composition with any degree of accuracy, the Oscar Rose Junior College developed a two-semester program involving a sequential, syntactical, linguistic, multimedia approach to composition. The four media utilized are talk-tapes, visual-aid cards…

A study of the effect of an "incremental" version of a generative rhetoric approach to writing instruction was conducted to determine whether such an approach would increase students' syntactic complexity. Ninety-eight college students were randomly assigned to one of five experimental or five control sections of a freshman composition…