Designing problems introducing the concept of numerical integration in an inquiry-based setting

Research literature argues for the benefits of inquiry-based approaches to provide opportunities for in-depth understanding of mathematics. This paper studies the design of mathematical problems for the purpose of introducing the concept of numerical integration in an inquiry-based setting. We present a series of six developmental stages (represent, refocus, area, accumulate, approximate, and refine) indicating a natural trajectory for students to follow when inquiring on the concept of numerical integration before any formal introduction to the topic. Further, we present a sequence of three problems illustrating how the developmental stages can be applied in problem design

Bringing Nordic mathematics education into the future : a review of the papers presented at the NORMA20 conference

The NORMA conferences held triennially gather academics from the Nordic area and beyond. The conferences offer a window into the key topics and outcomes of Nordic mathematics education research. This paper presents an analysis of the 73 regular papers presented at the NORMA20 conference held in Oslo in June 2021 and published in the conference pre- and proceedings. The analysis yields research questions, methods, and key findings for the educational levels spanning kindergarten through to higher education. The majority of the papers present research from primary school-level and pre- and in-service teacher education. Across the educational levels, teaching methods and classroom discourse emerged as the most frequent topics, dominated by empirical studies that applied qualitative methods.publishedVersio

Exploring the Interplay between Conceptualizing and Realizing Inquiry—The Case of One Mathematics Teacher’s Trajectory

Inquiry, an approach that departs from traditional mathematics teaching, empowers students through active participation and increased accountability in exploration, argumentation, evaluation, and communication of mathematical ideas. There is broad research consensus on the benefits of inquiry-based approaches to teaching and learning mathematics, including their potential to support equitable mathematics classrooms. While research has separately explored teachers’ conceptions of inquiry and their efforts to enact the practice, little is known about the interplay between mathematics teachers’ conceptions and enactment, and how it could be harnessed in professional development. In this study, we follow Alex, an experienced upper secondary mathematics teacher unfamiliar with inquiry, as he participates in a one-semester professional development course that draws on inquiry in multiple ways. His trajectory towards learning to teach through inquiry is revealed through patterns and shifts in his reflections and classroom actions. Our findings reveal significant developments in Alex’s conception of inquiry and in how he realizes it in his classroom, identifying three paths that illuminate his inquiry trajectory: the teacher’s role in inquiry interactions, a growing idea of inquiry, and orchestrating whole-class situations. In the interplay between enacting and reflecting, he moves from distributing authority separately between himself and ‘the students’ (as one unit) to fostering shared authority, a key aspect of empowerment, between himself and his students (as multiple voices) in both groupwork and whole-class episodes

Hight throughput UHPC-MSMS method for the analysis of phosphatidylethanol (PEth) 16:0/18:1, a specific biomarker for alcohol consumption, in whole blood

Phosphatidylethanol (PEth) is an alcohol biomarker formed in the presence of ethanol in the body. Both due to its specificity and because it has a detection window of up to several weeks after alcohol intake, its application potential is broader than for other ethanol biomarkers. The aim of this study was to develop and validate a robust method for PEth in whole blood with fast and efficient sample extraction and a short analytical runtime, suitable for high throughput routine purposes. A validated ultra-performance liquid chromatography tandem mass spectrometry (UPLC®-MSMS) method for quantification of PEth 16:0/18:1 in the range 0.05–4.00 μM (R2 ≥ 0.999) is presented. PEth 16:0/18:1 and the internal standard (IS) PEth-d5 (0.55 μM), were extracted from whole blood (150 μL) by simple protein precipitation with 2-propanol (450 μL). Chromatography was achieved using a BEH-phenyl (2.1 × 30 mm, 1.7 μm) column and a gradient elution combining ammonium formate (5 mM, pH 10.1) and acetonitrile at a flow rate of 0.5 mL/min. Runtime was 2.3 min. The mass spectrometer was monitored in negative mode with multiple reaction monitoring (MRM). The m/z 701.7 > 255.2 and 701.7 > 281.3 transitions were monitored for PEth 16:0/18:1 and the m/z 706.7 > 255.3 for PEth-d5. Limit of quantification was 0.03 μM (coefficient of variation, CV = 6.7%, accuracy = 99.3%). Within-assay and between-assay imprecision were 0.4–3.3% (CV ≤ 7.1%). Recoveries were 95–102% (CV ≤ 4.9%). Matrix effects after IS correction ranged from 107% to 112%. PEth 16:0/18:1 in patient samples were stable for several days at 30°C. Repeated freezing (−80°C) and thawing did not affect the concentration. After thawing and analysis patient samples were stable at 4–8°C for at least 4 weeks. Results from a proficiency test program, showing |Z| values ≤1.2, confirm the validity of the method. Analysis of the first 3,169 samples sent to our laboratory for routine use has demonstrated its properties as a robust method suitable for high throughput purposes