Kesalahan Calon Guru Matematika dalam Menggunakan Ukuran Pemusatan: Pengabaian Variansi

The measure of the center is an essential topic in statistics. Pre-service mathematics teachers must have the ability to select and use measures of center. The inability to use and select appropriate center measures indicates a low understanding of center measures. Meanwhile, research on the ability to use and select the center's appropriate measures is very limited. This study explores the sources of error for pre-service mathematics teachers in using and selecting the appropriate measures of center. This study involved 177 pre-service mathematics teachers. This research is a qualitative study using the interpretive paradigm. Data were collected using a test containing two problems and clinical interviews. Data were analyzed qualitatively using grouping participant responses based on ways of thinking and ways of understanding to use and select center measures. The results showed that pre-service mathematics teachers could not select an appropriate measure of centers because they were too focused on measures of centers while ignoring the variance. In order to be able to select an appropriate measure of centers because variance must be considered simultaneously. The implication of this study results is the need for a learning approach that introduces concurrent measures of centers with data variance.

Redefining Sociophonetic Competence: Mapping COG Differences in Phrase-Final Fricative Epithesis in L1 and L2 Speakers of French

This article presents a study of measures of center of gravity (COG) in phrase-final fricative epithesis (PFFE) produced by L1 and L2 speakers of Continental French (CF). Participants completed a reading task targeting 98 tokens of /i,y,u/ in phrase-final position. COG measures were taken at the 25%, 50% and 75% marks, normalized and submitted to a mixed linear regression. Results revealed that L2 speakers showed higher COG values than L1 speakers in low PFFE-to-vowel ratios at the 25%, 50%, and 75% marks. COG measures were then categorized into six profile types on the basis of their frequencies at each timepoint: flat–low, flat–high, rising, falling, rising–falling, and falling–rising. Counts of COG profile were then submitted to multinomial logistic regression. Results revealed that although L1 speakers produced predominantly flat–low profile types at lower percent devoicings, L2 speakers preferred multiple strategies involving higher levels of articulatory energy (rising, falling, rise–fall). These results suggest that while L1 speakers realize PFFE differently with respect to phonological context, L2 speakers rely on its most common allophone, strong frication, in most contexts. As such, the findings of this study argue for an additional phonetic dimension in the construct of L2 sociophonetic competence.

Stop the Silence! How to Create a Strategically Social Classroom

By orchestrating social interactions, students learn from one another about data and measures of center.

Secondary mathematics teachers' informal inferential reasoning : the role of knowledge structures for measures of center, spread and shape

This study examined middle and secondary mathematics teachers' knowledge structures, informal inferential reasoning (IIR), and pedagogical content knowledge (PCK) for statistics. Using task-based clinical interviews (Goldin, 1997) and cross-case analysis (Creswell, 2013), a stratified purposeful sample (Patton, 2002) of nine teachers responded to the Goals and Outcomes Associated with Learning Statistics (GOALS-2) instrument (Sabbag and Zieffler, 2015), released items from the Levels of Conceptual Understanding in Statistics (LOCUS) assessment (Jacobbe, 2016) and supplemental questions to assess PCK (Watson et al., 2008). Responses were used to construct maps of teachers' knowledge structures for measures of center, spread, and shape (Groth and Bergner, 2013) and knowledge structures were analyzed for common characteristics. Teachers' IIR was coded for the appropriateness of responses (Means and Voss, 1996) and key components of IIR (Makar and Rubin, 2009) were identified. To distinguish teachers' PCK level, descriptions of four hierarchical levels were used (Callingham and Watson, 2011) and knowledge structures were classified as desirable-connected, undesirable-connected, and undesirable-disconnected. Although teachers largely engaged in the inference and data components of IIR, they rarely referenced the uncertainty component. In general, teachers with more connected knowledge structures and fewer undesirable knowledge elements exhibited more acceptable forms of IIR and higher PCK levels. Within IIR contexts, teachers struggled to exhibit acceptable forms of IIR and demonstrated the lowest levels of PCK, but within non-IIR contexts, they exhibited acceptable reasoning more often as well as higher PCK levels. Implications for teacher education are discussed and recommendations for future research are offered.

Bridging Informal and Formal Reasoning

This fourth-grade task focuses on measures of center to build on students' intuitive thinking.

How Many Jelly Beans are in the Jar?

Students' mathematical intuition about estimation can serve as an entry point for tasks exploring measures of center.

Journey to Centers in the Core

Students travel through a series of lessons as they analyze data and unpack the meaning of measures of center.