Learning to pose cognitively demanding tasks through letter writing

Abstract

We have used letter writing as a means for preservice teachers (PSTs) to develop ability to design effective tasks, in terms of eliciting high levels of cognitive activity from students. Studies on student-dependent task analyses, by assessing the levels of cognitive demand indicated in students' responses, have demonstrated significant growth among PSTs over the course of letter-writing exchanges. We examine growth with a qualitative analysis of two PSTs who became effective at designing tasks that elicited high levels of cognitive activity. In particular, we examine how those PSTs accounted for tasks that did not elicit the kinds of activity they expected and how they adjusted their tasks to elicit higher levels of activity. We found disparity between the two PSTs' apparently successful approaches: one that fit the larger goals of the project and one that fit only the descriptions specified in the project rubric. The study affirms the potential value of letterwriting projects while introducing a concern that has implications for all professional development projects.

An Examination of Pre-service Mathematics Teachers’ Perceptions of Mathematics Learning Activities

“…Uluslararası platformda da etkinliklerin tasarlanması ve uygulanması ile ilgili, öğretmenlerin ve öğretmen adaylarının etkinlik konusunda farkındalık ve beceri kazanmalarını sağlamaya yönelik (Arbaugh & Brown, 2005;Horoks & Robert, 2007;Norton & Kastberg, 2012;Yeo, 2007) ve etkinliğe "task" kavramı üzerinden yaklaşarak etkinliğe Swan, 2007Swan, , 2008Yeo, 2007) yönelik olarak çalışmalar gerçekleştirilmiştir. Bu çalışmalar incelendiğinde, araştırmacıların uzlaştığı ortak bir etkinlik tanım olmadığı, genellikle çalıştıkları konu ekseninde bir etkinliğin sahip olması gereken özelliklerden yola çıkarak etkinliği tanımladıkları görülmektedir.…”

Mathematics teachers’ knowledge for teaching problem solving

“…Moyer , Moyer, Sowder, & Threadgill-Sowder, 1984 Students often experience difficulties in understanding the text of a word problem rather than its solution Lewis & Mayer, 1987 Students' ability to solve word problems is affected by the method of presentation and the presentation of accurate pictures aids student achievement with word problems while the presentation of inaccurate pictures hinders their solutions Webb & Sherrill, 1974 Recent studies that helped teachers to enhance their knowledge of meaningful problems also suggest different types of problems that are important for teachers to know for teaching PS. For example, studies have engaged teachers in posing and evaluating problems (Crespo & Sinclair, 2008;Lee, 2012); posing cognitively demanding tasks (Norton & Kastberg, 2012); multiple-solution tasks (Guberman & Leikin, 2013); tasks with potential to occasion/promote mathematical creativity in problem solving (Levenson, 2013); demanding problems that generally allowed for a variety of problem-solving strategies (Szydlik, Szydlik, & Benson, 2003); rich mathematical tasks (Slavit & Nelson, 2010); metamathematical awareness of the interest and difficulty of any given problem (Leiken, 2003); and understanding levels of cognitive demand of problems (Arbaugh & Brown, 2004 2010provides examples of open-ended problems for teachers' learning that will support their MPSKT.…”

Vitsmunaleg áskorun í stærðfræðikennslu á unglingastigi

“…Kennarar virðast þó hafa tilhneigingu til að draga úr áskorun, en með aukinni fagþekkingu gengur þeim betur að viðhalda áskorun eða jafnvel auka á hana (Wilhelm, 2014). Bent hefur verið á gagnsemi þess að kennarar hljóti sérstaka þjálfun í að viðhalda kröfum sem stuðla að greinandi hugsun nemenda (Norton og Kastberg, 2012).…”

“…Niðurstöður benda því til þess að vandasamt sé fyrir kennara að viðhalda kröfum um rökhugsun og þeirri áskorun sem felst í viðfangsefnum. Það er í samraemi við fyrri niðurstöður rannsókna sem sýna að kennara skorti faglegan stuðning til að geta viðhaldið kröfum (Norton og Kastberg, 2012;Tekkumru-Kisa o.fl., 2020;Wilhelm, 2014).…”