Exploring the discourses of preservice mathematics teachers when solving geometry problems=Kuhlolwa ingxoxo yothisha bezibalo abangakasebenzi ngesikhathi bexazulula izinkinga zegeometry.

Abstract

Research on teaching and learning that aim to improve preservice mathematics teachers’ (PMTs) knowledge of geometry is increasing globally. The current study explored PMTs’ discourses when solving geometry problems. The amalgamation of the commognitive theory and the Van Hiele levels of geometrical thinking theory was used as the theoretical basis for this study. The study uses the difference between ritualistic and explorative discourse as explicated by Sfard (2008) in commognition together with the four Van Hiele levels of geometrical thinking to view and analyse the data. It goes deeper into the theory of commognition to use not only objectification of mathematical discourse but also the four elements of mathematical discourse to reach its conclusion. The current study aimed to answer the main question: How does preservice mathematics teachers’ thinking as evident in their mathematical discourse during Euclidean geometry problem solving relate to their teaching practices in Euclidean geometry? This will be done through answering four subsidiary questions. A qualitative research approach was used to generate rich and descriptive data to answer the posed research questions. Furthermore, the qualitative approach allowed for the collection of data representing participants’ geometry problem solving experiences which was the core of the current study. I purposively and conveniently sampled 6 participants in this study where they completed a task-based and face-to-face interviews. Consent was obtained from these participants prior their participation in the study. Data generated from the two instruments was thematically analysed. Findings from this study revealed that most PMTs use ritualistic discourse when communicating about their geometry problem solving actions. These findings are a consequence of them performing routines for social acceptance instead of generating endorsed narratives. Furthermore, it was observed that others used ritualistic discourse because they rely on scaffolding from others to perform their routines instead of developing their own routines. Despite the dominance of ritualistic discourse participation in the current study, there were instances where PMTs seemed to be using explorative discourse but get stuck somehow and return to ritualistic discourse. The Van Hiele theory revealed that most PMTs still operate within the lower levels of geometrical thinking. The main findings and contribution of this study is that for PMTs to advance their geometrical thinking from level 0 to level 3, they need to transform their discourse participation from ritualistic to explorative.

IQOQA Ucwaningo mayelana nokufundisa kanye nokufunda oluhlose ukuthuthukisa inkonzo yokulekelela othisha bezibalo ngolwazi lwe-geometry luyakhula umhlaba wonke. Okufundwayo kuhlola ukusetshenziswa kolimi ngesikhathi kuxazululwa izinkinga zegeometry. Ukuqoqela ndawonye kwethiyori ye-commognitive kanye neVan Hiele yamazinga e-geometrical yenjulalwazi yokucabanga yasetshenziswa njengesisekelo sobunjulalwazi sesifundo. Uhlelokwenza locwaningo ngekhwalithethivu lwasetshenziswa ukuchamusela ulwazi oluchazayo nolunonile ukuphendula imibuzo yocwaningo eyaphonswa.

Uma sihlabela phambili, uhlelokwenza ngekhwalithethivu lwavumela ukuqoqwa kolwazi olumele abazibandakanya mayelana nabasebekwazi ukusombulula izinkinga ze-geometry okwakungumgogodla wesifundo. Ngisampule abayisithupha (6) ababamba iqhaza ngenhloso nangokufaneleyo kulesi sifundo njengoba benza umsebenzi kanye nohlelongxoxo ubuso nobuso. Ukuvuma kwababambe iqhaza kwatholakala ngaphambi kokuba basetshenziswe esifundweni. Ulwazi olusengwe emathuluzini amabili lwacutshungulwa ngokobungqikithi. Imiphumela iveza ukuthi iningi lothisha abamukela inkonzo yokusizwa ngokwezibalo basebenzisa inkambiso ethile ngokwezingxoxo uma kukhulunywa ngezinyathelo zokuxazululwa kwezinkinga ze-geometry.

Lemiphumela iyizimpendulo zabo zokwenza izinto ezizodwa ukuze bamukeleke ngokwenhlalo esikhundleni sokuphehla izinkulumo ezivunyiwe. Uma sihlabela phambili, kwabhekwa ukuthi abanye basebenzisa inkambiso ngokwengxoxo ngoba bathembele ekufukulweni ngabanye ukwenza inhlalakhona yabo esikhundleni sokukhulisa eyabo inhlalakhona. Ngaphandle nje kokugxila kwenkambiso yengxoxo yababamba iqhaza kulesi sifundo, izibonelo lapho othisha abenkonzo yokusizwa ngokwezibalo kubukeka besebenzisa ingxoxo kusinga kodwa bese beyakhingxeka kwezinye izindawo bese bebuyela enkambisweni ngxoxo. Injulalwazi yeVan Hiele iveza ukuthi iningi lalabothisha abasizwa ngezibalo nanamhlanje badidizela emazingeni aphansi ngokomcabango wegeometry. Okutholakele okunqala kanye nomnikelo walesi sifundo ukuthi labo thisha abasizwe ngokwezibalo uma befuna ukuqhubekela phambili ngokomcabango we-geometry kusukela ezingni leqanda (0) kuya kwelesithathu (3), kuzodingeka bayiguqule ingxoxo yabo yokuzibandakanya kusukela enkambisweni kuya enhlolweni.