Stepping stones : teacher lesson plans : year K

"ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals." -- Publisher website

Time limitations in NAPLAN numeracy tests

The article discusses evidence that time prevented many students from showing what they could do in the 2010 Year 7 and 9 NAPLAN numeracy tests. In addition to analysing the available data, the article discusses some NAPLAN numeracy questions that contribute to this problem. It is suggested that schools should investigate whether time limitation is a problem for their own students. The article discusses the implications of these findings for teachers preparing students for NAPLAN tests and for the developers of the tests.

Jabberwocky : the complexities of mathematical English

Mathematical English is a unique language based on ordinary English, with the addition of highly stylised formal symbol systems. Some words have a redefined status. Mathematical English has its own lexicon, syntax, semantics and literature. It is more difficult to understand than ordinary English. Ability in basic interpersonal communication does not necessarily result in proficiency in the use of mathematical English. The complex nature of mathematical English may impact upon the ability of students to succeed in mathematical and numeracy assessment. This article presents a review of the literature about the complexities of mathematical English. It includes examples of more than fifty language features that have been shown to add to the challenge of interpreting mathematical texts. Awareness of the complexities of mathematical English is an essential skill needed by mathematics teachers when teaching and when designing assessment tasks.

Mid-Career professionals in STEM transiting to school teaching : barriers at the border

In many countries there is a shortage of quality teachers in areas of science, technology, engineering and mathematics (STEM). Additional to the low levels of recruitment is an extraordinary high attrition rate with some 50% of beginning teachers leaving the profession within five years. One solution implemented in several countries has been to encourage mid-career professionals in the area of STEM to become school teachers. These professionals are said to bring to teaching enthusiasm, knowledge and a passion for their subject which will impact engagement and learning by students. However, these career-changers have constructed professional identities and are accustomed to working within a culture of collaboration and inquiry. In contrast, school cultures are quite different and often teaching is a lonely solitary affair with little opportunity for collegial relationships aimed at knowledge building in the context of teaching. Crossing from a culture of STEM to a culture of schools and teaching can be challenging. This study was conducted with 13 teachers who were followed for three years. However, this paper reports on the experiences of one teacher with an engineering background crossing the boundaries from practising STEM to Teaching STEM.

The power of percent

Which statistic would you use if you were writing the newspaper headline for the following media release: "Tassie’s death rate of deaths arising from transport-related injuries was 13 per 100,000 people, or 50% higher than the national average”? (Martain, 2007). The rate “13 per 100,000” sounds very small whereas “50% higher” sounds quite large. Most people are aware of the tendency to choose between reporting data as actual numbers or using percents in order to gain attention. Looking at examples like this one can help students develop a critical quantitative literacy viewpoint when dealing with “authentic contexts” (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2013a, p. 37, 67). The importance of the distinction between reporting information in raw numbers or percents is not explicitly mentioned in the Australian Curriculum: Mathematics (ACARA, 2013b, p. 42). Although the document specifically mentions making “connections between equivalent fractions, decimals and percentages” [ACMNA131] in Year 6, there is no mention of the fundamental relationship between percent and the raw numbers represented in a part-whole fashion. Such understanding, however, is fundamental to the problem solving that is the focus of the curriculum in Years 6 to 9. The purpose of this article is to raise awareness of the opportunities to distinguish between the use of raw numbers and percents when comparisons are being made in contexts other than the media. It begins with the authors’ experiences in the classroom, which motivated a search in the literature, followed by a suggestion for a follow-up activity.

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.

Enhancing the teaching and learning of mathematical visual images

The literacy demands of mathematics are very different to those in other subjects (Gough, 2007; O'Halloran, 2005; Quinnell, 2011; Rubenstein, 2007) and much has been written on the challenges that literacy in mathematics poses to learners (Abedi and Lord, 2001; Lowrie and Diezmann, 2007, 2009; Rubenstein, 2007). In particular, a diverse selection of visuals typifies the field of mathematics (Carter, Hipwell and Quinnell, 2012), placing unique literacy demands on learners. Such visuals include varied tables, graphs, diagrams and other representations, all of which are used to communicate information.

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The new Australian Curriculum and national standardised testing have placed the teaching of numeracy across the curriculum at the forefront of what Australian schools must do. However, it has been left to schools to determine how they do this. Although there is a growing body of literature giving examples of pedagogies that embed numeracy in various learning areas, there are few studies of cross-curricular numeracy from the management perspective. This paper responds to the research question: How do selected Queensland secondary schools interpret and apply the Australian Curriculum requirement to embed numeracy throughout the curriculum? A multiple case study design was used to investigate the actions of the senior managers and mathematics teachers in three large secondary schools located in outer Brisbane. The numeracy practices in the three schools were interpreted from asocial constructivist perspective. The study found that in each school key managers had differing constructions of numeracy that led to confusion in administrative practices, policy development and leadership. The lack of coordinated cross-curricular action in numeracy in all three schools points to the difficulty that arises when teachers do not share the cross-curricular vision of numeracy present in the Australian Curriculum. The managers identified teachers’ commitment, understanding, or skills in relation to numeracy as significant barriers to the successful implementation of numeracy in their school. Adoption of the Australian Curriculum expectation of embedding numeracy across the curriculum will require school managers to explicitly commit to initiatives that require persistence,time and, most importantly, money.

Challenges in embedding numeracy throughout the curriculum in three Queensland secondary schools

The Australian Curriculum identified seven General Capabilities, including numeracy, to be embedded in all learning areas. However, it has been left to individual schools to manage this. Whilst there is a growing body of literature about pedagogies that embed numeracy in various learning areas, there are few studies from the management perspective. A social constructivist perspective and a multiple case study approach were used to explore the actions of school managers and mathematics teachers in three Queensland secondary schools, in order to investigate how they meet the Australian Curriculum requirement to embed numeracy throughout the curriculum. The study found a lack of coordinated cross-curricular approaches to numeracy in any of the schools studied. It illustrates the difficulties that arise when teachers do not share the Australian Curriculum cross-curricular vision of numeracy. Schools and curriculum authorities have not acknowledged the challenges for teachers in implementing cross-curricular numeracy, which include: limited understanding of numeracy; a lack of commitment; and inadequate skills. Successful embedding of numeracy in all learning areas requires: the commitment and support of school leaders, a review of school curriculum documents and pedagogical practices, professional development of teachers, and adequate funding to support these activities.

Expectation and variation with a virtual die

By the time students reach the middle years they have experienced many chance activities based on dice. Common among these are rolling one die to explore the relationship of frequency and theoretical probability, and rolling two dice and summing the outcomes to consider their probabilities. Although dice may be considered overused by some, the advantage they offer is a familiar context within which to explore much more complex concepts. If the basic chance mechanism of the device is understood, it is possible to enter quickly into an arena of more complex concepts. This is what happened with a two hour activity engaged in by four classes of Grade 6 students in the same school. The activity targeted the concepts of variation and expectation. The teachers held extended discussions with their classes on variation and expectation at the beginning of the activity, with students contributing examples of the two concepts from their own experience. These notions are quite sophisticated for Grade 6, but the underlying concepts describe phenomena that students encounter every day. For example, time varies continuously; sporting results vary from game to game; the maximum temperature varies from day to day. However, there is an expectation about tomorrow’s maximum temperature based on the expert advice from the weather bureau. There may also be an expectation about a sporting result based on the participants’ previous results. It is this juxtaposition that makes life interesting. Variation hence describes the differences we see in phenomena around us. In a scenario displaying variation, expectation describes the effort to characterise or summarise the variation and perhaps make a prediction about the message arising from the scenario. The explicit purpose of the activity described here was to use the familiar scenario of rolling a die to expose these two concepts. Because the students had previously experienced rolling physical dice they knew instinctively about the variation that occurs across many rolls and about the theoretical expectation that each side should “come up” one-sixth of the time. They had observed the instances of the concepts in action, but had not consolidated the underlying terminology to describe it. As the two concepts are so fundamental to understanding statistics, we felt it would be useful to begin building in the familiar environment of rolling a die. Because hand-held dice limit the explorations students can undertake, the classes used the soft-ware TinkerPlots (Konold & Miller, 2011) to simulate rolling a die multiple times.

Tekstiilityötä ja matematiikkaa yhdistävän oppimateriaalin käyttökelpoisuus perusopetuksen yläluokilla

In this study the researcher wanted to show the observed connection of mathematics and textile work. To carry this out the researcher designed a textbook by herself for the upper secondary school in Tietoteollisuuden Naiset TiNA project at Helsinki University of Technology (URL:http://tina.tkk.fi/). The assignments were designed as additional teaching material to enhance and reinforce female students confidence in mathematics and in the management of their textile work. The research strategy applied action research, out of which two cycles two have been carried out. The first cycle consists of establishing the textbook and in the second cycle its usability is investigated. The third cycle is not included in this report. In the second cycle of the action research the data was collected from 15 teachers, five textile teachers, four mathematics teachers and six teachers of both subjects. They all got familiar with the textbook assignments and answered a questionnaire on the basis of their own teaching experience. The questionnaire was established by applying the theories of usability and teaching material assessment study. The data consisted of qualitative and quantitative information, which was analysed by content analysis with computer assisted table program to either qualitative or statistical description. According to the research results, the textbook assignments seamed to be applied better to mathematics lessons than textile work. The assignments pointed out, however, the clear interconnectedness of textile work and mathematics. Most of the assignments could be applied as such or as applications in the upper secondary school textile work and mathematics lessons. The textbook assignments were also applicable in different stages of the teaching process, e.g. as introduction, repetition or to support individual work or as group projects. In principle the textbook assignments were in well placed and designed in the correct level of difficulty. Negative findings concerned some too difficult assignments, lack of pupil motivation and unfamiliar form of task for the teacher. More clarity for some assignments was wished for and there was especially expressed a need for easy tasks and assignments in geometry. Assignments leading to the independent thinking of the pupil were additionally asked for. Two important improvements concerning the textbook attainability would be to get the assignments in html format over the Internet and to add a handicraft reference book.

Student understandings of numeracy problems: Semantic alignment and analogical reasoning

Despite compulsory mathematics throughout primary and junior secondary schooling, many schools across Australia continue in their struggle to achieve satisfactory numeracy levels. Numeracy is not a distinct subject in school curriculum, and in fact appears as a general capability in the Australian Curriculum, wherein all teachers across all curriculum areas are responsible for numeracy. This general capability approach confuses what numeracy should look like, especially when compared to the structure of numeracy as defined on standardised national tests. In seeking to define numeracy, schools tend to look at past NAPLAN papers, and in doing so, we do not find examples drawn from the various aspects of school curriculum. What we find are more traditional forms of mathematical worded problems.

Além da Linha Vermelha: um estudo sobre a formação de professores em Física, Química e Matemática na interface das políticas públicas e do mundo do trabalho

Esta pesquisa realiza um estudo sobre a formação de professores em Física, Química e Matemática na dimensão das políticas públicas educacionais e das novas ordenações do mundo produtivo. O eixo metodológico investe na abordagem qualitativa, elegendo como campo empírico o Instituto de Educação, Ciência e Tecnologia do Rio de Janeiro (IFRJ), mais especificamente, o campus Nilópolis, localizado na região da Baixada Fluminense (recorte geopolítico), no Estado do Rio de Janeiro. A técnica de pesquisa baseou-se na realização de entrevistas com licenciandos cujo perfil compreende àquele que tenha realizado atividades de estágio docente. Esta escolha justifica-se por ser este o perfil de estudante mais próximo do término do curso e que, principalmente, através desta experiência, apresenta concepções, ainda que iniciais, da realidade da educação básica. Este estudo investiu na história dos sujeitos participantes através de seus respectivos relatos, onde foi possível categorizá-los em importantes aspectos que se interconectam: 1) na análise das políticas públicas para a educação superior a partir da ênfase na investigação de como estas se efetivam em uma territorialidade e no contexto de uma nova institucionalidade; 2) na reflexão sobre o impacto das transformações do mundo do trabalho na subjetividade dos licenciandos, engendrando a possível atividade docente no cenário de crise de identidades profissionais; e 3) no exame da realidade das escolas da educação básica, espaço onde a formação se destina. Este caminho permitiu refletir sobre o lugar do magistério nas escolhas de formação e nas perspectivas profissionais.

Uma proposta para introdução de noções de Cálculo no ensino médio

A presente dissertação tem o objetivo de propor a reinclusão de elementos de Cálculo no ensino médio, pois no passado o Cálculo fazia parte do currículo e foi abolido após uma reforma no ensino da matemática. O trabalho apresenta os resultados de um levantamento estatístico sobre os índices de reprovação na disciplina Cálculo Diferencial e Integral I nos períodos mais recentes da Universidade do Estado do Rio de Janeiro (UERJ) e, também, uma pesquisa quantitativa com quarenta professores de matemática com o objetivo de analisar a viabilidade do projeto e os problemas a serem enfrentados. Por fim, a dissertação conta com uma série de atividades comentadas sobre o tema de limites, que é o foco do trabalho. Tais atividades podem ser incluídas já no 1 ano do ensino médio, paralelamente ao conteúdo de funções, e visam proporcionar aos estudantes o contato com elementos de Cálculo em uma linguagem acessível, e orientar o professor nesta tarefa

Miniprojetos interculturais na aula de matemática : quatro estudos de caso

Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2014