3.1+Principles+of+Teaching+and+Learning

Principles and Standards – Learning

Central to the argument in “Learning” is the need for understanding . NCTM (20-1) mathematics education has been lacking in developing student understanding since the 1930s—which provokes further interest in both the difference in learning mathematics before the 1930s and what has changed since then. This section discusses that true proficiency in mathematics requires being able to apply knowledge with flexibility and being able to take an idea and apply it to different settings; proficiency is not reached without a combination of conceptual, factual and procedural knowledge(.20-2) When students learn for understanding, they are also set up to learn new information because they can apply what they know to what they are learning which is argued to lead to better retention (20-4). “Learning” also suggests that conceptual understanding is especially important because as things change, students can use what they know to solve new problems. Teaching for understanding is also important because it creates self-learners which allow the benefits of ownership over students own learning: confidence, eagerness, flexibility, and learners who reflect on their own learning--- all of which are cited qualities of good learners (20-4). Lastly, a main role of mathematics teachers is to ensure that students are given assignments which promote understanding which include: problem solving, reasoning, and argumentation (21-1).--- Katie

The Teaching Principle

A very vital aspect of a student learning mathematics is the teaching that takes place. The teacher needs to have a deep understanding of the mathematics being taught, and be able to think quickly on their feet for it is almost a guarantee that students will ask questions in which the answer isn’t exactly a simple one. The authors state (17-1) that a mathematics teacher needs to have several different kinds of mathematics knowledge. They need to know the best way in which students learn, have a thorough understanding of the concepts being taught but also the big main ideas that are supposed to be absorbed by the students. There are often common misunderstandings  about certain topics that the teachers need to be aware of, to try to avoid the confusion. One very important piece of knowledge that a teacher has to have, though, would be what the student already knows so that they can build their curriculum off of the prior information. Some teachers forget that, and they assume that everybody starts out at the same level with the same understandings, which is not true. Being able to cater to students who have different abilities i n mathematics is a difficult but necessary task in order to be effective. Also, being positive and motivating the students is very important to help them succeed, according to the authors. Teachers need to create a conductive environment t hat pushes their students to have serious intellectual thoughts. Part of creating that environment includes worthwhile mathematical tasks that actually mean something to the students, that intrigues them and sparks their interest in the subject. Another thing that is necessary in order to have a successful classroom is that the teacher needs to be able to listen, observe, and assess the students so they can gage the effectiveness of their lessons and make changes as needed. All of these things combined together is what makes a teacher a good one. -Shanna Thorn