Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Co-constructing decimal number knowledge

This mathematics education research provides significant insights for the teaching of decimals to children. It is well known that decimals is one of the most difficult topics to learn and teach. Annette’s research is unique in that it focuses not only on the cognitive, but also on the affective and conative aspects of learning and teaching of decimals. The study is innovative as it includes the students as co-constructors and co-researchers. The findings open new ways of thinking for educators about how students cognitively process decimal knowledge, as well as how students might develop a sense of self as a learner, teacher and researcher in mathematics.

David L. Rosenhan (1929–2012)

Presents an obituary for David L. Rosenhan (1929–2012). A distinguished psychologist and professor emeritus at Stanford University, Rosenhan died February 6, 2012, at the age of 82, after a long illness. Born in Jersey City, New Jersey, on November 22, 1929, he received a bachelor’s degree in mathematics (1951) from Yeshiva College and a master’s degree in economics (1953) and a doctorate in psychology (1958) from Columbia University. A professor of law and of psychology at Stanford University from 1971 until his retirement in 1998, Rosenhan was a pioneer in applying psychological methods to the practice of law, including the examination of expert witnesses, jury selection, and jury deliberation. A former president of the American Psychology–Law Society and of the American Board of Forensic Psychology, Rosenhan was a fellow of the American Association for the Advancement of Science, of the American Psychological Association, and of the American Psychological Society. Before joining the Stanford Law School faculty, he was a member of the faculties of Swarthmore College, Princeton University, Haverford College, and the University of Pennsylvania. He also served as a research psychologist at the Educational Testing Service. As generations of Stanford students can attest, David Rosenhan was a spellbinding lecturer who managed to convey the sense that he was speaking to each individual, no matter how large the group. To his graduate students, he was consistently encouraging and optimistic, always ready to share a joke or story, and gently encouraging of their creativity and progressive independence as researchers. The lessons he cared most about offering, in the classroom as in his research, were about human dignity and the need to confront abuse of power and human frailties.

A sequential Monte Carlo framework for adaptive Bayesian model discrimination designs using mutual information

In this paper we present a unified sequential Monte Carlo (SMC) framework for performing sequential experimental design for discriminating between a set of models. The model discrimination utility that we advocate is fully Bayesian and based upon the mutual information. SMC provides a convenient way to estimate the mutual information. Our experience suggests that the approach works well on either a set of discrete or continuous models and outperforms other model discrimination approaches.

Co-thought gestures : supporting students to successfully navigate map tasks

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged 10–12 years) over a 3-year period as they solved map tasks that required spatial reasoning. The map tasks were representative of those typically found in mathematics classrooms for this age group and required route finding and coordinate knowledge. The results indicated that co-thought gestures were used to navigate the problem space and monitor movements within the spatial challenges of the respective map tasks. Gesturing was most influential when students encountered unfamiliar tasks or when they found the tasks spatially demanding. From a teaching and learning perspective, explicit co-thought gesturing highlights cognitive challenges students are experiencing since students tended to not use gesturing in tasks where the spatial demands were low.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

New constructions of anonymous membership broadcasting schemes

An anonymous membership broadcast scheme is a method in which a sender broadcasts the secret identity of one out of a set of n receivers, in such a way that only the right receiver knows that he is the intended receiver, while the others can not determine any information about this identity (except that they know that they are not the intended ones). In a w-anonymous membership broadcast scheme no coalition of up to w receivers, not containing the selected receiver, is able to determine any information about the identity of the selected receiver. We present two new constructions of w-anonymous membership broadcast schemes. The first construction is based on error-correcting codes and we show that there exist schemes that allow a flexible choice of w while keeping the complexities for broadcast communication, user storage and required randomness polynomial in log n,. The second construction is based on the concept of collision-free arrays, which is introduced in this paper. The construction results in more flexible schemes, allowing trade-offs between different complexities.

Mathematical Models of Tumor-Immune System Dynamics

"This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction between the immune system and a growing tumor. The multidimensional nature of these complex interactions requires a cross-disciplinary approach to capture more realistic dynamics of the essential biology. The papers presented in this volume explore these issues and the results will be of interest to graduate students and researchers in a variety of fields within mathematical and biological sciences."--Publisher website

The aerospace engineering challenge

Integrating Science, Technology, and Engineering in Mathematics authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms. This article describes an activity that introduced fourth-grade students to the work of aerospace engineers and to the science, technology, and mathematics principles associated with flight.

Literacy report 2008 [2008 futureSACE School to Work Innovation Program]

This project was designed to support high school teachers in participating schools to work with students whose literacy proficiency in key elements of the literacy component of the Year 9 LaN tests were in the low bands. -- p. 5.

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.

Personas of students accessing a peer-facilitated support for learning program

STIMulate is a support for learning program at the Queensland University of Technology in Brisbane, Australia. The program provides assistance in mathematics, science and information technology for undergraduate students. This paper develops personas - archetypal users - that represent the attitudes and motivations of students that utilise STIMulate (in particular, the IT stream). Seven different personas were developed based on interviews gathered from Peer Learning Facilitators (PLF) who are experienced students that have excelled in relevant subject areas. The personas were then validated by a PLF focus group. Developing the personas enabled us to better understand the characteristics and needs of the students using the STIMulate program, enabling a more critical analysis of the quality of the service provided.

Motivation and behavioural patterns of students accessing a peer-facilitated support for learning program

This paper describes the development and use of personas, a Human Computer Interaction (HCI) research methodology, within the STIMulate peer learning program, in order to better understand student behaviour patterns and motivations. STIMulate is a support for learning program at the Queensland University of Technology (QUT) in Brisbane, Australia. The program provides assistance in mathematics, science and information technology (IT) for course work students. A STIMulate space is provided for students to study and obtain one-on-one assistance from Peer Learning Facilitators (PLFs), who are experienced students that have excelled in relevant subject areas. This paper describes personas – archetypal users - that represent the motivations and behavioural patterns of students that utilise STIMulate (particularly the IT stream). The personas were developed based on interviews with PLFs, and subsequently validated by a PLF focus group. Seven different personas were developed. The personas enable us to better understand the characteristics of the students utilising the STIMulate program. The research provides a clearer picture of visiting student motivations and behavioural patterns. This has helped us identify gaps in the services provided, and be more aware of our assumptions about students. The personas have been deployed in PLF training programs, to help PLFs provide a better service to the students. The research findings suggest further study on the resonances between some students and PLFs, which we would like to better elicit.

ANZIAM 2015

The 51st ANZIAM Conference was held on 1–5 February 2015 in the Outrigger Hotel, Surfers Paradise, Australia. A total of 229 people registered for the conference, with nine plenary presentations, 78 student presentations and 107 non-student presentations. Highlights of the conference included the plenary talks, presentations by the 2014 Michell and ANZIAM Medalists, the Women in Mathematics Lunch and the Conference Dinner and Awards Ceremony. The main conference was followed by a one-day workshop entitled ‘Discrete mathematical models in the life sciences’, held at Queensland University of Technology, Brisbane, on February 6, 2015.

Introducing the multi-faceted teaching experiment

A mathematics classroom is comprised of many mathematicians with varying understanding of mathematics knowledge, including the teacher, students and sometimes researchers. To align with this conceptualisation of knowledge and understanding, the multi-faceted teaching experiment will be introduced as an approach to study all classroom participants’ interactions with the shared knowledge of mathematics. Drawing on the experiences of a large curriculum project, it is claimed that, unlike a multi-tiered teaching experiment, the multi-faceted teaching experiment provides a research framework that allows for the study of mathematicians’ building of knowledge in a classroom without privileging the experience of any one participant.