Exploring Relations between Teachers’ Beliefs, Instructional Practices, and Students’ Beliefs in Statistics

We examined the epistemic climate of statistics classrooms across two different classrooms by measuring teachers’ espoused beliefs about teaching statistics and observing their teaching practices. We then explored whether students’ beliefs became more aligned with the epistemic climate of the classroom over time. Post-secondary students’ beliefs were measured at the beginning and end of the semester. To measure the epistemic climate, teachers completed self-reports of their beliefs about teaching and learning, and participated in two semi-structured interviews at the beginning and end of the semester. Moreover, several classroom observations were conducted over the course of the semester. Analyses of the data revealed that for one group of students in one class, their beliefs were well aligned with the classroom climate and remained stable over time whereas for the other group of students, their beliefs shifted over time to align with the classroom climate

Becoming original: effects of strategy instruction

Visual arts education focuses on creating original visual art products. A means to improve originality is enhancement of divergent thinking, indicated by fluency, flexibility and originality of ideas. In regular arts lessons, divergent thinking is mostly promoted through brainstorming. In a previous study, we found positive effects of an explicit instruction of metacognition on fluency and flexibility in terms of the generation of ideas, but not on the originality of ideas. Therefore, we redesigned the instruction with a focus on building up knowledge about creative generation strategies by adding more complex types of association, and adding generation through combination and abstraction. In the present study, we examined the effects of this intervention by comparing it with regular brainstorming instruction. In a pretest-posttest control group design, secondary school students in the comparison condition received the brainstorm lesson and students in the experimental condition received the newly developed instruction lesson. To validate the effects, we replicated this study with a second cohort. The results showed that in both cohorts the strategy instruction of 50 min had positive effects on students' fluency, flexibility and originality. This study implies that instructional support in building up knowledge about creative generation strategies may improve students' creative processes in visual arts education

Stacked Garbling for Disjunctive Zero-Knowledge Proofs

Zero-knowledge (ZK) proofs receive wide attention, especially with respect to non-interactivity, small proof size, and fast verification. We instead focus on fast total proof time, in particular for large Boolean circuits. Under this metric, Garbled Circuit (GC)-based ZK, originally proposed by Jawurek et al. ([JKO], CCS 2013), remains state-of-the-art due to the low-constant linear scaling of garbling. We improve GC-ZK for proof statements with conditional clauses. Our communication is proportional to the longest clause rather than to the entire proof statement. This is most useful when the number of branches $m$ is large, resulting in up to $m\times$ communication improvement over JKO. In our proof-of-concept illustrative application, the prover demonstrates knowledge of a bug in a codebase consisting of any number of snippets of C code. Our computation cost is linear in the size of the codebase and communication is constant in the number of snippets. That is, we require only enough communication for the single largest snippet! Our conceptual contribution is stacked garbling for ZK, a privacy-free circuit garbling scheme that, when used with the JKO GC-ZK protocol, constructs efficient ZK proofs. Given a Boolean circuit $C$ and computational security parameter $\kappa$, our garbling is $L\kappa$ bits long, where $L$ is the length of the longest execution path in $C$. All prior concretely efficient garbling schemes produce garblings of size $|C|\kappa$. The computational cost of our scheme is not increased over prior state-of-the-art. We implemented our technique and demonstrate significantly improved performance. For functions with branching factor $m$, we improve communication by $m\times$ compared to JKO. Compared with recent systems (STARK, Libra, KKW, Ligero, Aurora, Bulletproofs), our scheme offers better proof times for large circuits: $35-1000\times$ or more, depending on circuit size and on the compared scheme. For our illustrative application, we consider four C code snippets. Each snippet has 30-50 LOC; one snippet allows an invalid memory dereference. The entire proof takes 0.15 seconds and communicates 1.5 MB

‘Even though it might take me a while, in the end, I understand it’: a longitudinal case study of interactions between a conceptual change strategy and student motivation, interest and confidence

Although there have been many investigations of the social, motivational, and emotional aspects of conceptual change, there have been few studies investigating the intersection of these factors with cognitive aspects in the regular classroom. Using a conceptual change approach, this case study reports experiences of a student of low to average prior attainment who achieved high levels of conceptual gains in five science topics over a two-year period. Her experience in the cognitive, social and affective domains was probed through analysis of interviews, student artefacts, video recordings of classroom learning, pre/post-tests and questionnaire results. For this student, peripheral or incidental persuasion of belonging to a supportive small group initially led to greater engagement with the construction of understanding through production of multiple student-generated representations, resulting in improved self-confidence and high levels of conceptual change. Evidence of transfer from performance to mastery approach goals, adoption of positive activating emotions and increased interest in science were observed. This study highlights that adoption of a multidimensional conceptual change approach with judicious organisation of small groups to support construction of verbal, pictorial and written representations of understanding may bring about changes in motivational stance, self-confidence and emotions to maximise conceptual change