Plane Geometry - Bruce E. Shapiro

SECTION 2. NCTM 7and connected subject. They must know where commen misunderstandingsarise, and be able to present important concepts like “a fraction ispart of the whole” with different or multiple representations of each ideaor concept. Effective teaching also requires a challenging and supportiveclassroom environment. Well chosen tasks can encourage students’ curiosity.Teachers must decide which aspect of a task to highlight, what questionsto ask, and how to support students without doing the thinking forthem. Finally, effective teaching requires continually seeking improvement.You will learn much by observing your students, listening carefully to theirquestions, ideas, and explanations, and analyzing what your students aredoing and how your actions affect your students’ learning.Learning. Students must learn mathematics with understanding, activelybuilding new knowledge from experience and prior knowledge. Factualknowledge, procedural proficiency, and conceptual understanding are thethree components to this. Memorization of facts without understandingleaves students unable to apply these facts or procedures to knew domains,while conceptual understanding together with factual and proceduralknowledge makes subsequent learning easier. Autonomous learningthen becomes possible, and students can eventually take control of theirown learning.Assessment. Assessment shouldsupport the learning of importantmathematics and furnish useful informationto both teachers and students.In the modern age of standardizedtests and numerical metricsfor corporate quality and productionthis seems to have been forgotten.Good assessment practicesprovide information to both thestudent and the teacher. Scoringguides or rubrics can help teachersunderstand students’ proficiencies.And poor student performance is just as often an indication that the teacheris not providing sufficient grounding in the content being assessed. Finally,since students have different learning methods different types of assessmentsmay be necessary to make an effective decision regarding student success.Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.