I believe it is important for educators to not provide students with the answers but instead guide them on the right path to success. Many readings from this course have encouraged this particular way of teaching; Lessons from the TIMSS Videotape Study, Strategies For Advancing Children’s Mathematical Thinking, as well as Chapter four in the text Elementary and Middle School Mathematics Teaching Developmentally.
During my personal math education, teachers would traditionally provide step-by-step instructions while students were expected to memorize formulas and complete textbook questions as quickly as possible. The article speaking about the TIMSS videotape study explains that countries like Japan have a much better success rate due to the fact that students are treated like mathematicians. The study explained how students normally have difficulties when they are being asked to learn too much at one time. In Japan, students are only given a few questions at a time to encourage “ hands on, real world mathematics, cooperative learning, and a focus on thinking” (Geist). I believe that it is important students have the chance to experience as well as experiment with math problems in as many ways as possible rather than being told what to do, step by step. When hands on experiences do not happen, students do not truly understand concepts. Van de Walle explains, “If the student forgets a step, or if there is a variation in the problem, the student becomes lost and must wait for the teacher to place him “back on track” (Van de Walle). Today’s students need be able to adapt to their surroundings and solve problems much easier than in the past. It is important to reflect on these cross-cultural differences and change the school system for the better, rather than being asked to teach more topics in less depth than teachers in Japan. To become a mathematician it is important that teachers include the following. Students must be encouraged to prove for themselves that their solutions are correct, complex problems are encouraged, and students must be able to receive satisfaction from the process (Geist). The teacher needs to emphasize unsuccessful attempts as a way of learning rather than focusing on the negative. These attempts are crucial stepping-stones to the solutions (Geist). During my future teaching practice, I will ensure that all students are able to learn what is being taught in their own unique way. It is important to understand that all students have different learning needs and there is no such thing as “one size fits all”. Fraivillig explains how important it is for teachers to encourage students to consider alternate methods when figuring out answers rather than sticking to one path. “Humans are naturally adept at learning from examples” (Fraivillig). Alternative methods are also encouraged because students will have a better understanding of a certain concept if they are able to solve it in more ways than one. Fraivillig discusses the model of Advanced Children’s Thinking, also known as ACT. There are three distinct aspects of this model. The first one includes the teacher challenging students to describe and analyze their solution methods. These explanations should be focused as most of the lesson content. Errors and efforts should be transformed into teachable moments while collaboration is valued during problem solving (Fraivillig).. The second stage is the capacity to support students’ conceptual understanding (Fraivillig). It is important for the teacher to remind students of background knowledge that connects with similar problem situations. The teacher needs to be aware of the different zones of proximal development and teach in a way to support these needs, while encouraging students to ask for support when needed (Fraivillig). The next and final step is when students’ mathematical thinking is extended (Fraivillig). A list of different solution methods should be posted on the board to promote reflection while individuals are encouraged to try the alternative methods. It is so important to engage students with the idea of a “challenge”. If students know that the teacher has maintained high standards and expectations for the class, students will think more highly of themselves and succeed further (Fraivillig). Chapter four explains that the learning through inquiry should be based on three steps. The first section occurs before the lesson, as the teacher activates students’ prior knowledge as well as establishing clear expectations while ensuring the task is understood (Van de Walle). It is important for students to connect with past schemas to ensure the math concept is understood. Teachers need to remember that students’ past experiences are what will encourage and interest them when solving problems. The second section happens during the lesson, as the teacher is encouraged to step back and allow the students’ minds to become curious, however, it is important to provide appropriate guidance along the way and provide worthwhile extensions (Van de Walle). As a teacher, it is important to step back and allow students to learn on their own terms. It is important to find the solution that fits best for them rather than being told what to do. This allows students to become more independent, rather than relying on step by step instructions. The third step occurs “after”, which is when active listening is key as well as promoting a mathematical community of learners (Van de Walle). I believe it is important that students are challenged while justifying their answers to make sense of them rather than being told how to solve questions without fully understanding “why”(Van de Walle). My math experience did not relate to this certain inquiry method at all. The teacher would teach concepts step by step and then head back to his desk where he did not want to be bothered as the students completed many questions out of the textbook. I remember one experience where I did not understand how my teacher had gotten the answer, so when I got home my Father taught me an alternative method, which I understood and completed my homework with. I was marked wrong due to the fact it was not the way that the teacher had taught. I will never forget this and I truly believe as long as a student receives the correct answer, all method should be encouraged. It is known now how collaboration between peers is very important in learning. Sharing of ideas allows students to understand a higher order of thinking and able to see that there are many different ways to solve a problem. Inquiry is key when learning in all subjects and I cannot wait until I can implement it into my own classroom. Teaching students with different needs has to be acknowledged rather than being pushed to the side like it has in the past. Work Cited Fraivillig, Judith. Strategies For Advancing Children’s Mathematical Thinking. Retrieved from https://mycourselink.lakeheadu.ca/d2l/le/content/371 59/viewContent/371672/View Geist, E. A. (2000). Lessons from the TIMSS Videotape Study. Teaching Children Mathematics, 7(3), 180. Retrieved from http://ezproxy.lakeheadu.ca/login?url=http://go.galegroup.com.ezproxy.lakehea du.ca/ps/i.do?p=AONE&sw=w&u=ocul_lakehead&v=2.1&it=r&id=GALE%7CA67379030&asid=4f9013b5af8a0bc3163f96112bb95c1c Van de Walle, John., Karp, Karen., Bay-Williams, Jennifer., McGarvey, Lynn., Folk., Sandra. (2015). Elementary and Middle School Mathematics Teaching Developmentally. Toronto: Pearson.
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