Putting socio-cultural theories to work in supporting mathematics teachers' professional development

We discuss the contributions of socio-cultural theories to research and design of interventions directed at the professional development of mathematics teachers. We explain how these theories have been put to work in the field. We also bring to attention specific issues arising in the field for which development and adaptation of socio-cultural theory might be a useful resource

Building learning opportunities in classrooms of disadvantage: rethinking the learning trajectories

Researching learning trajectories in classrooms of disadvantage introduces specific challenges as well as opportunities. Situating our work within design research, we illustrate the power of theoretical approaches in which close attention is paid to both learners' conceptual developments and the means capable of supporting such developments for all learners. We illustrate how considerations of teachers' learning can and should inform the formulation of (students') learning trajectories, if these are to become viable outside of research studies

Reciprocal relations of relative size in the instructional context of fractions as measures

The presented study is part of a bigger design and research enterprise in the teaching of fractions as measures. We analyze extracts of a teaching session with a single fifth grade student, in which he flexibly compared the relative sizes of the lengths of three drinking straws, skillfully using unitary, proper, and improper fractions. We identify aspects of his prior instructional experiences that supported the emergence of his relatively sophisticated ways of reasoning. Findings suggest that supporting students' reasoning about reciprocal relations of relative size can be a viable goal in an instructional agenda on fractions as measures

Resources for teaching: supporting a Mexican teacher’s learning

We analyze the role played by a teaching resource in effectively supporting a professional development collaboration with Irene, a Mexican public-school teacher. The resource is an instructional sequence on fractions that was developed through a series of design experiments in Mexican classrooms. As a result of this collaboration, Irene modified significantly her instructional practices. We discuss how the instructional sequence contributed to Irene’s renewed view of a mathematics classroom by providing her with guidance that was explicit, specific, and achievable

Unit fractions in the context of proportionality: supporting students' reasoning about the inverse order relationship

We analyze a classroom design experiment, conducted in a fourth grade classroom, that served to explore an instructional path in which the introduction of unit fractions and supporting proportional reasoning coincide. Central to this path is the use of means of support in which the objects that unit fractions quantify are not characterized as equal-sized parts of a whole, but as entities that are always separate from a reference unit. We argue that such a path is crucial for helping students develop deep quantitative understandings of fractions, where fraction quantities are, from the very start, linked to the reciprocal and multiplicative relations that their use implies. We focus on the first part of the design experiment in which we helped the students make sense of a concept that is important for initial fraction learning and proportional reasoning, the inverse order relationship among unit fractions

Analysis of operational parameters in acid and base production using an electrodialysis with bipolar membranes pilot plant

In agreement with the Water Framework Directive, Circular Economy and European Union (EU) Green Deal packages, the EU-funded WATER-MINING project aims to validate next-generation water resource solutions at the pre-commercial demonstration scale in order to provide water management and recovery of valuable materials from alternative sources. In the framework of the WATER-MINING project, desalination brines from the Lampedusa (Italy) seawater reverse osmosis (SWRO) plant will be used to produce freshwater and recover valuable salts by integrating different technologies. In particular, electrodialysis with bipolar membranes (EDBM) will be used to produce chemicals (NaOH and HCl). A novel EDBM pilot plant (6.4 m2, FuMa-Tech) has been installed and operated. The performance of EDBM for single pass under different flowrates (2-8 L·min-1) for acid, base and saline channels, and two current densities (200 and 400 A·m-2), has been analyzed in terms of specific energy consumption (SEC) and current efficiency (CE). Results showed that by increasing the flowrates, generation of HCl and NaOH slightly increased. For example, AOH- shifted from 0.76 to 0.79 mol·min-1 when the flowrate increased from 2 to 7.5 L·min-1 at 200 A·m-2. Moreover, SEC decreased (1.18-1.05 kWh·kg-1) while CE increased (87.0-93.4%), achieving minimum (1.02 kWh·kg-1) and maximum (99.4%) values, respectively, at 6 L·min-1.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement 869474 (WATER-MINING