We investigated whether Early Algebra lessons that explicitly aimed to elicit mathematical discussions (Shift-Problem Lessons) invoke more and qualitatively better mathematical discussions and raise students’ mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group) was conducted in 6 seventh-grade classes (N =160). An analysis of the interaction processes of five student groups showed that more mathematical discussions occurred in the Shift-Problem condition. The quality of the mathematical discussions in the Shift-Problem condition was better compared to that in the Conventional Textbook condition, but there is still more room for improvement. A qualitative illustration of two typical mathematical discussions in the Shift-Problem condition are provided. Although students’ mathematical levels were raised a fair amount in both conditions, no differences between conditions were found. We concluded that Shift-Problem Lessons are powerful for eliciting mathematical discussions in seventh-grade Shift-Problem Early Algebra Lessons.
The purpose of the design-based research reported here is to show – as a proof of principle – how the idea of scaffolding can be used to support primary teachers in a professional development programme (PDP) to design and enact language-oriented science lessons. The PDP consisted of six sessions of 2.5 h each in which twelve primary school teachers took part over a period of six months. It centralised the language support that pupils need to reason during science lessons. In line with the idea of scaffolding, the structure of the PDP targeted teachers' gradual independence in designing lessons. The first research question is how scaffolding was enacted during the PDP. The analysis of video recordings, field notes, researcher and teacher logs, and teacher design assignments focused on the enactment of three scaffolding characteristics: diagnosis, responsiveness and handover to independence. The second research question concerns what teachers learned from the participation in the PDP that followed a scaffolding approach. The data analysis illustrates that these teachers had learned much in terms of designing and enacting language-oriented science lessons. In terms of diagnosis and responsiveness, our PDP approach was successful, but we problematise the ideal of scaffolding approaches focused on handover to independence.
We studied 12 smart city projects in Amsterdam, and –among other things- analysed their upscaling potential and dynamics. Here are some of our findings:First, upscaling comes in various forms: rollout, expansion and replication. In roll-out, a technology or solution that was successfully tested and developed in the pilot project is commercialised/brought to the market (market roll-out), widely applied in an organisation (organisational roll-out), or rolled out across the city (city roll-out). Possibilities for rollout largely emerge from living-lab projects (such as Climate street and WeGo), where companies can test beta versions of new products/solutions. Expansion is the second type of upscaling. Here, the smart city pilot project is expanded by a) adding partners, b) extending the geographical area covered by the solution, or c) adding functionality. This type of upscaling applies to platform projects, for example smart cards for tourists, where the value of the solution grows with the number of participating organisations. Replication is the third and most problematic type of upscaling. Here, the solution that was developed in the pilot project is replicated elsewhere (another organisation, another part of the city, or another city). Replication can be done by the original pilot partnership but also by others, and the replication can be exact or by proxy. We found that the replication potential of projects is often limited because the project’s success is highly context-sensitive. Replication can also be complex because new contexts might often require the establishment of new partnerships. Possibilities for replication exist, though, at the level of working methods, specific technologies or tools, but variations among contexts should be taken into consideration. Second, upscaling should be considered from the start of the pilot project and not solely at the end. Ask the following questions: What kind of upscaling is envisioned? What parts of the project will have potential for upscaling, and what partners do we need to scale up the project as desired? Third, the scale-up stage is quite different from the pilot stage: it requires different people, competencies, organisational setups and funding mechanisms. Thus, pilot project must be well connected to the parent organisations, else it becomes a “sandbox” that will stay a sandbox. Finally, “scaling” is not a holy grail. There is nothing wrong when pilot projects fail, as long as the lessons are lessons learned for new projects, and shared with others. Cities should do more to facilitate learning between their smart city projects, to learn and innovate faster.
