From designing to implementing mathematical tasks: investigating the changes in the nature of the T-shirt task

From looking at research literature it is possible to see that research on design, implementation and analysis of mathematical tasks is an actual theme: there is a special issue of the Journal of Mathematics Teacher Education (2007) with Anne Watson, John Mason and Orit Zaslavsky as editors (Watson and Mason, 2007), a book published by Clarke, Grevholm and Millman (2009) concerning “Tasks in primary mathematics teacher education” and under ICME 11 in Mexico (2008) the title of one of the Topic Study Groups was “Research and development in task design and analysis”. In addition several substantial research projects conducted in the United States focus on this issue. For example the QUASAR project (Quantitative Understanding: Amplifying Student Achievement and Reasoning), involving a group of researchers (Stein, Smith, Henningsen & Silver, 2000), aimed at improving mathematics instruction for students by emphasising thinking, reasoning, problem solving and the communication of mathematical ideas. One of the central aspects of their research was to focus on the use of instructional tasks in project classroom and they proposed the elaboration of “the mathematical tasks framework” where the kinds of thinking needed to solve tasks were referred to as “cognitive demands”. They reported on observations concerning the change of cognitive demands during a lesson where “a task that starts out challenging … might not induce the high-level thinking and reasoning that was intended as the students actually go about working on it” (Stein et al., 2009, p.xviii). This aspect is also address by Artigue (1994) arguing that it might be tempting to implement too quickly development products arising from research into products for teaching. She characterises the processes related to the transmission of products from didactic engineering in terms of distortions and she emphasises the distinction between the activities of conducting research and of engaging in teaching. My aim, in this article, is to follow Artigue’s argumentation and to investigate, trace and characterise the distortions of a specific mathematical task (the T-shirt task) from its design by a group of didacticians at University of Adger (UiA) to its implementation by two different teachers. This research is situated in a larger research project conducted at (UiA), the Teaching Better Mathematics project (TBM)

Diving into Assessment & Data with 1:1 Technology as Media Specialists

How do we prove the worth of Information Literacy classes? Where is the data? Learn to use a variety of formative assessments with 1:1 technology in the school library media center. We will explain our use of Socrative, Schoology, Google Apps, and more. Then we will detail a nationally-normed summative tool, TRAILS. Add your voice to help create Minnesota’s TRAILS Benchmarks, while providing individualized feedback to your students and administration. Links for presentation: Today’s Meet: https://todaysmeet.com/ITL Slideshow presentation: http://goo.gl/NqLVfB Biblionasium: https://www.biblionasium.com Schoology: https://www.schoology.com/ Book Trailer Tips: http://www.booktrailersforreaders.com/How+to+make+a+book+trailer TRAILS: http://www.trails-9.org/ TRAILS Wiki: http://goo.gl/KxWmt

Developing Algebraic Thinking in a Community of Inquiry : Collaboration between Three Teachers and a Didactician

In this thesis I report from a study of the development of algebraic thinking of three teachers, from lower secondary school, and a didactician from a university in Norway (myself). The thesis offers an account of the relationship between the participants’ development of algebraic thinking and the processes related to the creation and development of a community of inquiry. In addition, the thesis presents elements of the relationship between the teachers’ development of algebraic thinking and their thinking in relation to their teaching practice. My theoretical framework was elaborated according to the criteria of relevance and coherence. In order to conceptualise the participants’ development of algebraic thinking within the community of inquiry, I started from Wenger’s theory of community of practice and expanded it in order to include both the dimension of inquiry and Karpov’s ideas of cognitive and metacognitive mediation. Methodologically, I understand my study as a case study, within a developmental research paradigm, addressing the development of algebraic thinking within a community of inquiry consisting of three teachers and a didactician. The collaboration between the teachers and the didactician was organised through regular mathematical workshops, and interviews with each teacher both before and after classroom observations. During the workshops, the participants engaged with some mathematical tasks which were offered by the didactician. The results of this study indicate that the participants’ development of algebraic thinking is deeply interwoven with the processes related to the creation and development of the community of inquiry. It seems that the participants’ confidence in the community was developing gradually while the confidence in the subject-matter was related to the nature of the mathematical tasks with which the participants engaged. In addition, the study shows how the teachers engaged in a process of both looking critically into their own teaching practice as a consequence of their collaborative engagement within the community of inquiry, and of envisaging possible implications for their future teaching practice. Furthermore, I offer insights into my own development both as a didactician and as a researcher and how these relate to research outcomes. Overall, the thesis contributes to a better understanding of issues related to collaboration between in-service teachers and a didactician from a university, while focusing on the development of algebraic thinking. Implications are also suggested concerning the way algebra could be addressed in schools

Developing Algebraic Thinking in a Community of Inquiry : Collaboration between Three Teachers and a Didactician

In this thesis I report from a study of the development of algebraic thinking of three teachers, from lower secondary school, and a didactician from a university in Norway (myself). The thesis offers an account of the relationship between the participants’ development of algebraic thinking and the processes related to the creation and development of a community of inquiry. In addition, the thesis presents elements of the relationship between the teachers’ development of algebraic thinking and their thinking in relation to their teaching practice. My theoretical framework was elaborated according to the criteria of relevance and coherence. In order to conceptualise the participants’ development of algebraic thinking within the community of inquiry, I started from Wenger’s theory of community of practice and expanded it in order to include both the dimension of inquiry and Karpov’s ideas of cognitive and metacognitive mediation. Methodologically, I understand my study as a case study, within a developmental research paradigm, addressing the development of algebraic thinking within a community of inquiry consisting of three teachers and a didactician. The collaboration between the teachers and the didactician was organised through regular mathematical workshops, and interviews with each teacher both before and after classroom observations. During the workshops, the participants engaged with some mathematical tasks which were offered by the didactician. The results of this study indicate that the participants’ development of algebraic thinking is deeply interwoven with the processes related to the creation and development of the community of inquiry. It seems that the participants’ confidence in the community was developing gradually while the confidence in the subject-matter was related to the nature of the mathematical tasks with which the participants engaged. In addition, the study shows how the teachers engaged in a process of both looking critically into their own teaching practice as a consequence of their collaborative engagement within the community of inquiry, and of envisaging possible implications for their future teaching practice. Furthermore, I offer insights into my own development both as a didactician and as a researcher and how these relate to research outcomes. Overall, the thesis contributes to a better understanding of issues related to collaboration between in-service teachers and a didactician from a university, while focusing on the development of algebraic thinking. Implications are also suggested concerning the way algebra could be addressed in schools

Mediated action in teachers’ discussions about mathematics tasks

This paper presents analyses of teachers’ discussions within mathematics teaching developmental research projects, taking mediation as the central construct. The relations in the so-called ‘didactic triangle’ form the basic framework for the analysis of two episodes in which upper secondary school teachers discuss and prepare tasks for classroom use. The analysis leads to the suggestion that the focus on tasks places an emphasis on the task as object and its resolution as goal; mathematics has the role of a mediating artefact. Subject content in the didactic triangle is thus displaced by the task and learning mathematics may be relegated to a subordinate position

Dual positive and negative regulation of GPCR signaling by GTP hydrolysis

G protein-coupled receptors (GPCRs) regulate a variety of intracellular pathways through their ability to promote the binding of GTP to heterotrimeric G proteins. Regulator of G protein signaling (RGS) proteins increase the intrinsic GTPase activity of G-subunits and are widely regarded as negative regulators of G protein signaling. Using yeast we demonstrate that GTP hydrolysis is not only required for desensitization, but is essential for achieving a high maximal (saturated level) response. Thus RGS-mediated GTP hydrolysis acts as both a negative (low stimulation) and positive (high stimulation) regulator of signaling. To account for this we generated a new kinetic model of the G protein cycle where GGTP enters an inactive GTP-bound state following effector activation. Furthermore, in vivo and in silico experimentation demonstrates that maximum signaling output first increases and then decreases with RGS concentration. This unimodal, non-monotone dependence on RGS concentration is novel. Analysis of the kinetic model has revealed a dynamic network motif that shows precisely how inclusion of the inactive GTP-bound state for the G produces this unimodal relationship

EvoCraft: A New Challenge for Open-Endedness

This paper introduces EvoCraft, a framework for Minecraft designed to study open-ended algorithms. We introduce an API that provides an open-source Python interface for communicating with Minecraft to place and track blocks. In contrast to previous work in Minecraft that focused on learning to play the game, the grand challenge we pose here is to automatically search for increasingly complex artifacts in an open-ended fashion. Compared to other environments used to study open-endedness, Minecraft allows the construction of almost any kind of structure, including actuated machines with circuits and mechanical components. We present initial baseline results in evolving simple Minecraft creations through both interactive and automated evolution. While evolution succeeds when tasked to grow a structure towards a specific target, it is unable to find a solution when rewarded for creating a simple machine that moves. Thus, EvoCraft offers a challenging new environment for automated search methods (such as evolution) to find complex artifacts that we hope will spur the development of more open-ended algorithms. A Python implementation of the EvoCraft framework is available at: https://github.com/real-itu/Evocraft-py

Biological insights from a simulation model of the critical FtsZ accumulation required for prokaryotic cell division

A simulation model of prokaryotic Z-ring assembly, based on the observed behavior of FtsZ in vitro as well as on in vivo parameters, is used to integrate critical processes in cell division. According to the model, the cell’s ability to divide depends on a “contraction parameter” (χ) that links the force of contraction to the dynamics of FtsZ. This parameter accurately predicts the outcome of division. Evaluating the GTP binding strength, the FtsZ polymerization rate, and the intrinsic GTP hydrolysis/dissociation activity, we find that inhibition of GTP–FtsZ binding is an inefficient antibacterial target. Furthermore, simulations indicate that the temperature sensitivity of the ftsZ84 mutation arises from the conversion of FtsZ to a dual-specificity NTPase. Finally, the sensitivity to temperature of the rate of ATP hydrolysis, over the critical temperature range, leads us to conclude that the ftsZ84 mutation affects the turnover rate of the Z-ring much less strongly than previously reported

A critical evaluation of systematic reviews assessing the effect of chronic physical activity on academic achievement, cognition and the brain in children and adolescents: A systematic review

Background. International and national committees have started to evaluate the evidence for the effects of physical activity on neurocognitive health in childhood and adolescence to inform policy. Despite an increasing body of evidence, such reports have shown mixed conclusions. We aimed to critically evaluate and synthesise the evidence for the effects of chronic physical activity on academic achievement, cognitive performance and the brain in children and adolescents in order to guide future research and inform policy. Methods. MedLine, Embase, PsycINFO, Cochrane Library, Web of Science, and ERIC electronic databases were searched from inception to February 6th, 2019. Articles were considered eligible for inclusion if they were systematic reviews with or without meta-analysis, published in peer-reviewed (English) journals. Reviews had to be on school-aged children and/or adolescents that reported on the effects of chronic physical activity or exercise interventions, with cognitive markers, academic achievement or brain markers as outcomes. Reviews were selected independently by two authors and data were extracted using a pre-designed data extraction template. The quality of reviews was assessed using AMSTAR-2 criteria. Results. Of 908 retrieved, non-duplicated articles, 19 systematic reviews met inclusion criteria. One high-quality review reported inconsistent evidence for physical activity-related effects on cognitive- and academic performance in obese or overweight children and adolescents. Eighteen (critically) low-quality reviews presented mixed favourable and null effects, with meta-analyses showing small effect sizes (0.1–0.3) and high heterogeneity. Low-quality reviews suggested physical activity-related brain changes, but lacked an interpretation of these findings. Systematic reviews varied widely in their evidence synthesis, rarely took intervention characteristics (e.g. dose), intervention fidelity or study quality into account and suspected publication bias. Reviews consistently reported that there is a lack of high-quality studies, of studies that include brain imaging outcomes, and of studies that include adolescents or are conducted in South American and African countries. Conclusions. Inconsistent evidence exists for chronic physical activity-related effects on cognitive-, academic-, and brain outcomes. The field needs to refocus its efforts towards improving study quality, transparency of reporting and dissemination, and is urged to differentiate between intervention characteristics for its findings to have a meaningful impact on policy

Mediated action in teachers’ discussions about mathematics tasks

Published version of an article in the journal: ZDM. Also available from the publisher at: http://dx.doi.org/10.1007/s11858-012-0423-0This paper presents analyses of teachers’ discussions within mathematics teaching developmental research projects, taking mediation as the central construct. The relations in the so-called ‘didactic triangle’ form the basic framework for the analysis of two episodes in which upper secondary school teachers discuss and prepare tasks for classroom use. The analysis leads to the suggestion that the focus on tasks places an emphasis on the task as object and its resolution as goal; mathematics has the role of a mediating artefact. Subject content in the didactic triangle is thus displaced by the task and learning mathematics may be relegated to a subordinate position