Creating Profiles of Geometry Teachers’ Pedagogical Content Knowledge

Manizade, Agida G.; Martinović, Dragana

doi:10.1007/978-3-319-77476-3_8

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…We agree with Swafford, Jones, and Thornton (1997, p. 481) who conclude their study by emphasizing that Van Hiele levels have low reliability for adults who have been away from learning for years and whose performance is sensitive to knowledge recall, which is exactly the case for our students. To overcome these criticisms, Manizade and Martinovic (2018) combine Van Hiele's levels and PCK and SMK (Spezialized Mathematical Knowledge), which leads them to propose student profiles based on their PCK and their understanding of geometry. In the same vein, in a study with content closer ours, Chinnappan, White, and Trenholm (2018, p. 145) consider construction problems and conclude with these suggestions that we share: Our analysis suggests future research needs to consider (a) the particular characteristics of the discipline of geometry and (b) the developmental knowledge trajectories of teachers of geometry in order to better understand how teachers ' SMK influences and [is] influenced by PCK.…”

Section: A Study Of How Pre-service Teachers Practice Geometric Workmentioning

confidence: 99%

On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces

Kuzniak

Nechache

2021

Educ Stud Math

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In this paper, we identify various forms of geometric work carried out by student teachers who were asked to perform a geometric task for the estimation of a land area. The theory of Mathematical Working Spaces is used to analyze and characterize the work produced. This study provides evidence that students developed forms of geometric work that are compliant with at least two distinct geometric paradigms, one characterized by the utilization of measuring and drawing tools, and the other by a property-based discourse on proof. Significantly, a sizable number of students also developed work forms that do not correspond to any geometrical paradigm. A broader purpose of this paper is to highlight three criteria born by the theory and shown to be useful for the description and evaluation of geometric work: compliance, completeness, and correctness.

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Section: A Study Of How Pre-service Teachers Practice Geometric Workmentioning

confidence: 99%

On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces

Kuzniak

Nechache

2021

Educ Stud Math

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“…According to this model, the van Hiele test is used to identify geometric thinking in individuals. Some researchers (Manizade, 2006;Lenhart, 2010) have indicated that although different versions of the van Hiele test are used for reliable evaluation of teachers' knowledge of geometry (Usiskin & Senk, 1990;Wilson, 1990), this test does not evaluate their pedagogical knowledge. Therefore, in the processes of developing the geometric thinking of teachers and analysing this development, the "Geometric Habits of Mind -GHoM" was used in this research, which is quite a new theoretical framework when compared to the approaches mentioned above.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…Prema ovom modelu, van Hieleov test koristi se za otkrivanje geometrijskoga razmišljanja kod pojedinaca. Neki istraživači (Manizade, 2006;Lenhart, 2010) ističu da, iako se različite verzije van Hieleova testa koriste za pouzdanu procjenu učiteljskoga znanja geometrije (Usiskin i Senk, 1990;Wilson, 1990), ovaj test ne procjenjuje njihovo pedagoško znanje. Stoga je u procesu razvoja geometrijskoga razmišljanja učitelja i analize ovog razvoja, u ovoj studiji korištene su geometrijske mentalne navike -GHoM (Geometric Habits of Mind), koje predstavljaju potpuno novi teorijski okvir u usporedbi s gore navedenim pristupima.…”

Section: Teorijski Okvirunclassified

A Lesson Study to Develop Teachers' Geometric Habits of Mind / Studija predavanja u svrhu razvoja geometrijskih mentalnih navika nastavnika

Ünal

Köse

2019

Croatian Journal of Education

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The general purpose of this study is to investigate the development of geometricthinking of elementary school mathematics teachers. To achieve this, the model ofresearch is defined as a lesson study. The implementation process of the study wascarried out with five mathematics teachers from different schools. Firstly, a fiveweekseminar process was carried out with teachers. As part of this process, thelesson study was explained with the theoretical framework of Geometric Habits ofMind and its practices were implemented. Then a lesson study was performed whichtook about three months. Data was collected by using multiple data collection toolsand data analysis was carried out by using a video analysis model developed byPowell, Francisco, and Maher (2003). As a result of this study, geometric thinking ofteachers has improved through the lesson study. During the process from the first lessonstudy to the seventh lesson study, we observed the improvement in the mathematicallanguage used by teachers, their explanations, student questions in class, together withactivities and problems produced by teachers based on the geometric habits of mindfor the relevant concepts. In the instructional processes, we also observed the teachersconsidering and assessing these components and planning for and implementing themin the geometry lessons. After the lesson studies, teachers also considered the geometrichabits in their own school settings and reflected on the instructional process throughprepared activities and problems which were then identified.Keywords: geometric habits of mind; geometric thinking; lesson study; teacherprofessional development ---SažetakGlavni cilj ove studije je proučavanje razvoja geometrijskoga razmišljanja učiteljamatematike u osnovnim školama. Kako bi se to postiglo, model istraživanja definiranje kao studija predavanja. Proces provedbe studije proveden je uz sudjelovanjepet nastavnika matematike iz različitih škola. Prvo je s nastavnicima održanopet tjedana seminara. Kao dio ovoga procesa, studija predavanja objašnjena jeteorijskim okvirom geometrijskih mentalnih navika te je isti primijenjen u praksi.Zatim je izvedena studija predavanja koja je trajala oko tri mjeseca. Prikupljanjepodataka provedeno je pomoću nekoliko alata za prikupljanje podataka, a analizapodataka izvedena je pomoću modela videoanalize koju su razvili Powell, Franciscoi Maher (2003). Kao rezultat ovoga istraživanja, geometrijsko razmišljanjenastavnika poboljšalo se tijekom studije predavanja. U procesu od prve do sedmestudije predavanja, primijetili smo poboljšanje matematičkoga jezika kojim sekoriste nastavnici, njihova objašnjenja, pitanja učenika u učionici, kao i aktivnostii zadatke koje su nastavnici stvorili na temelju geometrijskih mentalnih navikaza relevantne pojmove. U procesima učenja, promatrali smo i nastavnike kakorazmatraju i vrednuju ove komponente te ih uključuju u planiranje i provedbusvojih satova geometrije. Nakon studija predavanja, nastavnici su takođerrazmatrali geometrijske navike u vlastitim školskim okruženjima i razmišljali oprocesu učenja putem pripremljenih aktivnosti i problema koji su se tad definirali.Ključne riječi: geometrijske mentalne navike; geometrijsko razmišljanje;profesionalno usavršavanje nastavnika; studija predavanja

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“…Moreover, coders focused on developing aspects versus solely the presence of MKT. Finally, to triangulate qualitative results, a short‐answer PCK measure for middle level geometry (Manizade, ) and MKT multiple choice geometry measures were administered (Hill, Schilling, & Ball, ) (see Figure ).…”

Section: Introductionmentioning

confidence: 99%

Prompting Teacher Geometric Reasoning through Coaching in a Dynamic Geometry Software Context

Knapp

Barrett

Moore

2016

School Sci & Mathematics

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This study investigated the ways in which four middle grades teachers developed mathematical knowledge for teaching (MKT) geometry as they implemented dynamic geometry software in their classrooms with the assistance of a coach. Teachers developed various components of MKT by observing coaches teach, by dynamic discourse with students, which is discourse with respect to dynamic geometry software images, and by discussions with coaches. The dynamic geometry software environment proved productive as coaches guided teachers’ growth in explanations, examples, and definitions. The environment also helped teachers discover unnoticed abilities among their low achievers. Moreover, teachers developed confidence to teach with more expert uses of dynamic geometry software.

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Creating Profiles of Geometry Teachers’ Pedagogical Content Knowledge

Cited by 6 publications

References 17 publications

On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces

On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces

A Lesson Study to Develop Teachers' Geometric Habits of Mind / Studija predavanja u svrhu razvoja geometrijskih mentalnih navika nastavnika

Prompting Teacher Geometric Reasoning through Coaching in a Dynamic Geometry Software Context

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